Part II: Continued
[Return to Sections I-IV]
Models for Inventory, Monitoring,
and Management
of Threatened and Endangered Plant Species

PART II TABLE OF CONTENTS

ON THIS PAGE
Section V: Descriptions of Models
5.1: Habitat-Based Models
5.1.1: Species Habitat Matrices (SHM)
5.1.2: Habitat suitability index and habitat capability models
5.1.3: Pattern recognition (PATREC, Bayesian) models
5.1.4: Habitat preference models
5.1.5: Hierarchy models
5.1.6: Community structure models
5.1.7: Statistical models
5.1.7.1: Models for a single dependent variable
5.1.7.2: Models for several dependent variables
5.1.8: Indicator-species models
5.1.9: Guild life-form models
5.1.10: Landscape-scale ecological models
5.1.11: Stand growth models
5.1.12: Succession models
5.1.13:Community and ecosystem simulation models
5.2: Population-Based Models
5.3: Decision-Support Processes
5.3.1: Habitat evaluation procedures, fish and wildlife habitat relationships program, and integrated inventory and Classification System
5.3.2: Adaptive models
5.3.3: Decision-support models
5.3.4: Expert system models
Section VI: Summary, Conclusion, and Future Directions
6.1: Habitat Characterization Models for Plants
6.2: Conclusions
Table 1: Summary of Model Characteristics
References Cited: Part I; Part II
Previous Page
Part II: Sections I-IV

Section V: Descriptions of Models

The varied approaches used in modeling have resulted in considerable overlap among the details of model types for example, between indicator species models and the various models that use indicator concepts, or the use of multivariate statistical techniques to develop HSI models (e.g., Brennan et al. 1986). We have divided these models into two categories: 1) models applicable for survey, inventory, and monitoring of species and habitat, 2) management "decision-support" models generally used for habitat and species management.

5.1 Habitat-based Models

5.1.1 Species Habitat Matrices (SHM)

Definition
Species-habitat matrix models are tables listing environmental variables and vegetation types associated with wildlife species. There are many variations on this approach. For example, relative density values observed in certain habitat can be indexed (e.g., H = high, M = medium, and L = low density). Similarly, the season of use or abundance classes (e.g., abundant, common, rare) can be indicated (Cooperrider 1986). Species-habitat matrices are one of the simplest forms of multi-species model. The information presented in species-habitat matrix models is often provided by computer-based systems such as RUNWILD (Patton 1978).

Historical Uses
Historically, species-habitat matrices have been used to summarize data which has been previously collected, not to characterize and monitor plant and animal species. However, species-habitat matrices have been widely used by the USFS and the USFWS to summarize habitat relationships of a variety of animals from amphibians and birds to large game animals (Thomas 1979, Verner and Boss 1980). These models have also been used in environmental impact statements (EIS) to characterize how wildlife can be affected by various land-use management practices (Cooperrider, 1986).

Hoover and Willis (1984), and Verner and Boss (1980) provide several examples of applications of this model. For the greater sandhill crane, information such as ecosystems used, rearing requirements, feeding requirements, cover requirements, season of use and minimum habitat area are summarized in simple matrix form expressing the relative importance of each to the persistence of the species.

Thomas (1979), in developing a guild life-form model, created special-use matrices which were helpful in identifying species of special concern (i.e., threatened, endangered, or rare). The matrices were based on a versatility index which rated the sensitivity of each species to habitat changes. The versatility score for a wildlife species is derived by determining the total number of plant communities and the total number of successional stages to which the species show primary orientation for feeding and reproduction. Such versatility indices may help to identify those species that are more rigid in their habitat requirements, and thus most likely to be affected by forest management decisions.

Species-habitat matrices have been used by the FWHRP of the USFS to develop species-habitat matrices in Colorado (Hoover and Willis 1984), California (Verner and Boss 1980, and New England (DeGraff and Chadwick 1987).

Limitations
The most significant limitation of the SHM approach is that it is not useful to predict which species will be affected given a certain management activity, or how species will be affected (Cooperrider 1986, Laymon 1990). Another deficiency is that these models do not quantify population response, and therefore cannot be used to evaluate population density factors or changes in population trends (Morrison et al. 1992).

Strengths
A strength of this method is that it provides a first approximation as to what habitat elements may be important to a species. However, any such relationships which appear to exist according to the matrix model should be rigorously tested and validated to ensure that any apparent correlation is important in defining a species' habitat.

Validation of a wildlife-habitat relationships model by Raphael and Marcot (1986) showed that species-habitat matrices and other multiple species models of this sort are probably best used to predict species richness and abundance values over broad areas, not at the scale of the individual stand.

Applications for Plant TES
It seems feasible to apply the habitat matrix method to plant species. Multi-species indices could be established in much the same manner as they are for animal species. The suitability of a particular habitat would be based on professional evaluation of scientists working with the species of concern, review of literature, and the opinions of others having field experience with the species. Although this method is admittedly subjective (Verner and Boss 1980) it provides a first best approximation of what land managers should consider when making management decisions. Furthermore, use of this approach may raise questions which can be addressed in future, more detailed research efforts.

If designating species of concern which include TES (Verner and Boss 1980), managers should be aware of any known special habitat requirements of these species. Matrix approaches provide a qualitative basis on which decisions and evaluation of potential impacts of habitat alteration on plant TES can be based.

5.1.2 Habitat Suitability Index Models and Habitat Capability Models

Definition
A habitat suitability index (HSI) is a numerical value that represents the capacity of a given habitat to support a selected fish or wildlife species (USFWS 1981). HSI models can be constructed from basic habitat data, expert opinion, literature survey, or by modifying existing habitat models. An HSI model may proceed from graphical, word, or mathematical information. Its essential feature is that it produces an index value. Criteria for data collection or conversion of existing data, model development, and reporting for HSI are provided in USFWS (1981). The procedures were developed for use in the USFWS Habitat Evaluation Procedures (HEP) (USFWS 1980b), and are used to calculate the habitat unit (HU) for HEP (see Section 5.2). Construction of a simple HSI model could proceed as follows: important habitat variables are identified, either from qualitative (assumed) or quantitative (sampled) information. The range of variation in each habitat variable is assigned suitability index (SI) values on a scale of 0 to 1 for a particular species. Often the relationship between the variable and suitability is assumed to be linear. The habitat suitability index value can then be calculated as some combination of the SI values.

The HSI has a minimum value of 0.0, representing unsuitable habitat, and a maximum value of 1.0 which represents optimum habitat. Functions that have been used to derive HSI values include the geometric mean. Others are discussed in Van Horne and Wiens (1991). Nonlinear approaches to calculate SI values have also been used (e.g., Brennan et al. 1986, Van Horne and Wiens 1991).Habitat Capability models (HC) are also procedures for calculating an index value that represent the overall suitability of a habitat for a species. HSI and HC are very similar in concept. However, used with the FWHR methodology (Nelson and Salwasser 1982) developed by USFS, HC models predict carrying capacity ("capability") as described below in our discussion of general models for assessment and inventory. HC procedures, which were based on HSI, are detailed in Hurley et al. (1982). Wisdom et al. (1986) offer examples of HC models.

Historical Uses
Rosenthal (1985) lists 114 habitat suitability index models published in the FWS/OBS and Biological Reports series through June 1985. A total of 156 HSIs had been published by USFWS when the series ended in 1989 (personal communication, NBS Library, Fort Collins, Colorado). HSI models have been constructed for endangered animal species, including the black-footed ferret (Houston et al. 1986), bald eagle (Peterson 1986), and spotted owl (Laymon et al. 1985).

Limitations
HSI models have been subject to close scrutiny and criticism since the late 1980's (Van Horne 1986, Van Horne and Wiens 1991). Because of their similarity, what follows applies to HC models as well. A frequent lack of predictivity in this type of model results from several problem sources: 1) the common assumption of linearity in relationships between wildlife density and individual habitat parameters (Meents et al. 1983, O'Connor 1986); 2) the use of simple index values as predictive tools (Green 1979, Van Horne and Wiens 1991); 3) the assumption of invariable habitat use by species regardless of life stage or season (Patterson 1976); 4) the assumption that a species' observed density is adequate as an indicator of habitat quality (Van Horne 1983); 5) questions of whether measured habitat variables are in fact meaningful to the species in question (Van Horne and Wiens 1991); and 6) lack of attention to scale and details of pattern in developing the models (Dick Lawrence, personal communication). Additional problems with combining single-species models into general models for several species using similar habitats are addressed by Van Horne and Wiens (1991). Little specific consensus exists on how model predictivity can be improved, except that both more extensive and more intensive studies may be necessary to provide data for useful predictive habitat modeling by these methods (Van Horne 1986).

Concerns regarding model accuracy partly account for the decline in published HSI models since 1989, since the predictivity of many is unknown because they have not been field tested or validated. In response to both peer and internal doubts, USFWS has shifted its emphasis from development of new models to evaluation and testing of existing models (Jim Terrell, Supervisory Fish and Wildlife Biologist, National Biological Service (NBS), personal communication). Use of HSI -type models continues in environmental assessments (e.g., USFS 1994).

Strengths
HSI and HC models represent attempts to predict the distribution and abundance of species at large geographic scales for natural resource management. Their applications are often at large scales in the context of general habitat assessment.

Applications for Plant TES
Because of the many difficulties associated with the HSI-type models, their application to TES management should be approached cautiously. Problems with the use of HSI/HC models, as previously listed, may be overcome in some cases, especially for use with plant species. For instance, data collected on species density and various habitat variables can be used to formulate more accurate relationship descriptions other than that of linearity; data transformation may also be used to obtain linearity when plant-abiotic relationships are non-linear. Index values, such as HSI, are often the reduction of complex relationships among organisms and their environment into a simplistic expression; but, ecology, by definition, is the "study of the relationship of organisms to their environment". Often, first order approximations, using simple ratios, are useful for development of an understanding such relationships. The presence of a species in a given habitat may not provide deductions of a full set of important habitat variables, but neither can such variables be deduced as being antagonistic to the species presence. Use of these models for prediction, as with others, should be field tested prior to management use.

5.1.3 Pattern Recognition (PATREC) (Bayesian) Models

Definition
Pattern recognition (PATREC) models provide a form of risk analysis of the effects of habitat quality on population parameters.

Historical Uses
Typically a PATREC approach begins with a set of habitat attributes that is assigned conditional probabilities based on field observations. For example, Smith et al. (1991) constructed a PATREC model for Rocky Mountain bighorn sheep (Ovis canadensis canadensis). They assigned conditional probabilities for both high and low population densities for several habitat attributes for separate ram and ewe ranges in spring and summer, and for both sexes together in fall and winter. Model evaluation units (MEU's) for potential habitat were calculated using submodels of conditional probabilities for habitat attributes combined with prior probabilities estimated to reflect local abundance of such habitats, using Bayes' theorem (see Williams et al. 1978). Other examples of PATREC applications can be found Williams et al. (1978) and Holl (1982).

Limitations
The determination of prior probabilities for the natural occurrence of habitat is problematic and may represent an educated guess. The calculated value of the posterior probability of high density population support in the habitat can therefore be affected by poor estimates of these values (Morrison et al. 1992).

PATREC models rely heavily on the use of density as an indicator of habitat quality. Problems with this assumption have been discussed by Van Horne (1983). See our section on models for TES plants for a discussion of the relationship of this problem to plants.

Strengths
PATREC techniques can provide limited prediction of population distribution or abundance, using habitat relationships, for management guidance.

Applications for Plant TES
Like other habitat modeling approaches, PATREC techniques could provide some indication of habitat potential to support plant TES research, and therefore are potentially useful for delineation of TES-habitat relationships, or identification of potential TES habitat. We have noted elsewhere in this report that difficulties associated with the use of density as an indicator of habitat quality may be less restrictive for rare plants. As always, field verification of model predictions is necessary.

5.1.4 Habitat Preference Models

Definition
The goal of this approach is to determine the kind of habitat a population depends on for survival and to describe the abundance, sizes, and quality of the environmental variables necessary to ensure persistence of both the habitat and the dependent species (Ruggiero et al. 1988).

Historical Uses
Recently, the two major areas of research in habitat preference modeling have worked to define the concept of ecological dependency and expand our understanding of habitat preference. Rosenzweig (1987) reviewed how selection for certain habitat variables contributes to variations in overall biodiversity. Porter and Church (1987) provide a critical review of habitat preference modeling and discuss the effects that natural environmental patterns have on different methods of analyzing habitat preference. Ruggiero et al. (1988) critically reviewed recent attempts to evaluate habitat dependence and the modeling of habitat preference.

Limitations
"Habitat needs" are generally described as those components of a habitat upon which a species depends for survival. However, there are often problems distinguishing what a species prefers from what a species requires for survival. Habitat preference analysis has been conducted with limited success in the Pacific Northwest to determine the habitat-dependency relationships of the northern spotted owl (Taylor 1990). The amounts, sizes, and arrangements of landscape features necessary to ensure persistence of both the environment and the species of concern must be described in addition to basic characteristics (Ruggiero et al. 1988). Consequently, due to the complexities involved, neither a standard definition of dependency nor a viable operational approach for measuring it has yet been developed.

Porter and Church (1987) point out three major weaknesses of these habitat preference models. First, in many environments, a priori decisions in defining habitats and study area boundaries can result in spurious inferences. Second, some habitat preference models do not allow for examination of the habitat characteristics that may be most important, such as interspersion and juxtaposition of vegetation. In addition, they concluded that the spatial pattern of a habitat (random, aggregated) could have a significant influence on the location of study site boundaries. If study sites are incorrectly imposed on the landscape, then false inferences may result.

Strengths
Ruggiero et al. (1988) suggest that in the absence of empirical data demonstrating dependency of a species for a specific habitat type, inferences about habitat use can be made by observing patterns of habitat preference.

Habitat preference analysis also has potential for delineating different habitats and their respective uses for wildlife species. However, the limitations pointed out by Porter and Church (1987) and Ruggiero et al. (1988) must be considered if one is to avoid incomplete or spurious conclusions regarding the ways in which different habitats are used by plants and animals.

Applications for Plant TES
Habitat preference studies have largely grown out of the ESA, which requires the maintenance of viable populations of listed species. Defining the concept of habitat dependency and preference, as well as values corresponding to minimum viable population sizes and their relationship to habitat, have proved to be complex. Currently, descriptions of the amounts, sizes, and arrangements of landscape features necessary to ensure persistence of both the environment and the species of concern have yet to be fully developed into a recommended set of procedures for plant TES habitat preference modeling. Observations on plant distribution and habitat characteristics should be used to provide information for future research, so that important habitat variables for species can be scientifically validated.

5.1.5 Hierarchy Models

Definition
A hierarchy model can be considered as a higher level theory that interprets and processes the summaries or results of many simultaneous variables (competition, predation, habitat preference, abiotic limiting factors etc.). Hierarchy modeling views habitat as a structure in which abiotic and biotic factors can be sorted into various levels and compartments of hierarchical organization (Allen et al. 1984, Kolasa 1989, Morrison et al. 1992). In this way, these models allow both structural and functional components of ecosystems to be characterized by a variety of hierarchies.

Historical Uses
Recently, the major focus of hierarchy modeling has been on the development of conceptual frameworks and mathematical models; e.g., fractals, which are helpful for identifying and categorizing phenomena occurring at different spatial and temporal scales (Kolasa 1989).
For example, Morse (1985) examined the relationships between leaf structure, spatial scale, and the abundance of leaf animals. Other authors have used hierarchy modeling to explain other aspects of community-level phenomena, such as the correlation between species ranges and abundance, (Kolasa and Strayer 1988) and differences in species abundances related to differing climatic conditions and resource levels (Morrison et al. 1992).

Kolasa and Strayer (1988) used hierarchy modeling to investigate patterns of species abundances. They proposed that each unit of habitat be conceived of as a number of subunits which are organized in a hierarchical fashion. These subunits could then be correlated to patterns of species abundance.

Although conceptual models have proved to be useful as a means for the sorting and classification of microhabitats and levels of structure in habitat analysis, Kolasa (1989) pushed the concept of hierarchy modeling further, exploring the direct applications of this concept to the analysis of patterns in community ecology. To simplify what can be an enormous amount of information about community interactions, Kolasa proposed to analyze the community-level patterns. He suggested that such simplification would help in the formulation of testable hypotheses about underlying environmental structures and functions responsible for these patterns.

Kolasa's (1989) research appears promising. His model validation attempts led him to conclude that the model was compatible with commonly observed as well as irregular patterns of species abundance, high local abundance of some species, as well as differentiation of extinction probabilities. Other research efforts in this area also may allow further development of our understanding of hierarchical organization in different ecological systems.

Limitations
Kolasa cautions that a hierarchy model may best serve as a framework or "skeleton" to which specific mechanisms are applied. In his own model, a number of assumptions were made, including: 1) the ecological efficiency of all species, and 2) negligible metabolic and trophic differences. Such assumptions may be ecologically inaccurate. This does not mean, however, that this model cannot still make predictions to be incorporated into a conceptual framework. For managerial and applied purposes however, such models would lack credibility unless specifically validated in the field.

Strengths
Hierarchy modeling in general sorts species, habitat characteristics, and abiotic factors etc., into a summary of simultaneous processes. Such a framework may be of twofold benefit to resource managers. First, sorting species and habitats into various levels and microhabitats may have heuristic value all its own. Even if not directly applicable to a management plan, such a model may provide additional information on the ecology of the species in question. Second, hierarchical concepts may provide a basic framework that, while not complete in itself, may at least may provide a context for the exploration of more complex phenomena. The primary advantage of a hierarchical model is its use to categorize and represent different spatial scales and facets of biological function (Morrison et al. 1992). If the model is designed correctly, according to Kolasa (1989), then no matter what detailed interactions force species into using different microhabitats and fragments, the model should still work because patterns of organization are inherent in the community structure.

Hierarchical models are useful for organizing and interrelating functional ecosystem properties. Higher levels of organization are particularly problematic, and ecologists have recently obtained the computational power necessary to analyze such physically large systems. For these reasons, hierarchical modeling may be an important tool for linking small and large scale concerns into an ecologically valid framework.

Applications for Plant TES
The main limitation of hierarchy models for application to plant TES is that they are generally constructed as conceptual models. Hierarchy models may be useful for classifying and integrating information concerning the general ecology of specific TES which may then aid in the characterization of their habitat. However, the use of hierarchy models for predictive and managerial applications needs to be validated by field research.

5.1.6 Community Structure Models

Definition
Community structure models are used to depict wildlife species distributions, abundance, and diversity based on the structure of their environment. Similar to guild models, community structure models are multi-species models which can be used to classify areas of high species richness within certain geographic areas. This approach can be useful in attempting to conserve biological diversity both for purposes of habitat classification and as a planning device.

Historical Uses
Historically, community structure models have related species distributions to the environment and specific geographic locations. Recently, geographic information systems (GIS) have been utilized to define habitats according to features of the environment at the landscape level. GIS are able to manipulate, reference, and catalogue data on species distributions as they relate to geographic locations. Resource managers can thus use these systems to present, categorize, and sort information in a way that is easy to analyze (Scott et al. 1987). For example, researchers in Hawaii recently used information gathered from GIS on range, population density, and vegetation types to classify and visualize potential conservation areas for endangered forest birds (Scott et al. 1987); for mammal and avian species, vegetation data obtained from GIS were used to identify areas of preferred habitat by overlaying various map layers. Remote sensing data from aircraft and satellites are steadily improving our ability to map vegetation over large areas and understand its relation to vegetation types, patterns, and temporal dynamics.

Other types of community structure models have been developed to evaluate community-level and landscape interactions. Swift et al. (1984), for example, studied the relationship between the density of breeding birds and vegetation structure in deciduous forested wetlands in Massachusetts; their results indicated that vegetation structure had a significant effect on the densities of breeding birds found. For example, it was observed that as the number of small shrubs increased, both breeding bird densities and species richness increased as well.

Our knowledge of the factors that act on communities is limited at best. It is known that the physical environment (soils, climate, topography), biological interactions (competition, predation, spatial distribution), and evolutionary history (chance extinctions, climate change, dispersal) all play roles in determining community structure within a given habitat. Combining these kinds of information within the framework of a spatial model may allow land managers to integrate information on the physical structure of the environment with knowledge of various abiotic and biotic control factors which affect species distributions and abundance values.

Limitations
Erdelen (1984), in a comparison of objective and quantitative indices of bird communities and the vegetation structure of their habitats, found that different research methodologies produced different results. For example, Erdelen discovered that significant correlations of his model depended solely on the inclusion or exclusion of three low-vegetation plots which differed in character from the rest of the study plots. The problems recognized by Erdelen (1984) can be mitigated by the careful placement of study plots; rather than placing study plots along a gradient from grassland to forest, as Erdelen did, better results are expected from more homogeneous plots, such as those studied by Swift et al. (1984). In this effort (Swift et al. 1984), a strong correlation between total breeding bird density and three habitat variables was found.

Another limitation of community structure models was found by Raphael and Barret (1983) as they attempted to characterize the diversity of wildlife in late successional forests; individual species exhibited a wide range of variation, while the measures of community structure as a whole remained fairly constant. Thus, like guild life-form models, community structure models would appear to be inadequate for the characterization of individual species and their habitat.

Another important limitation of community structure models is that wildlife or habitat managers may not adequately characterize all aspects of their habitat management goals in terms of community species diversity. Often measures of species diversity are not sensitive enough to detect changes in a unique species of concern, so impacts of different management schemes may not be easily detectable using this kind of model.

Strengths
Community structure models may be useful in attempts to conserve overall biodiversity. For example, Scott et al. (1987) concentrated on mapping geographic areas of high species richness as target areas for future conservation projects. In this way, community structure models may be very useful for planning purposes and for characterizing habitat of high biodiversity that merits conservation. Thus the strengths of this model type can be found in its applications to large-scale habitat classification, and for long-range planning and conservation efforts.

The integration of vegetation data into a model of community structure can serve a threefold purpose, according to Scott et al. (1987): 1) species ranges can be refined according to habitat preference, 2) vegetation types and their distribution can provide supplemental information for the analysis of natural diversity, and 3) unique or rare habitat types likely to harbor especially significant concentrations of plant and animal species can be identified.

Application to Plant TES
This type of model may have limited utility for animal and plant TES. For example, habitat areas that contain diverse and abundant communities which may have potential for containing TES could be identified and targeted for future conservation or protection. However, such models would probably not work well if attempting to characterize or monitor the habitats of individual TES, as this approach provides little description of the environmental factors unique to each individual species. Thus, one potential difficulty, which is common to most habitat-based models, would be isolation of the habitat elements that make up preferred or necessary habitat for a TES. In addition, a large amount of initial effort may be required to adequately sample a habitat to determine which characteristics are important to a particular species, and this may not be a cost-effective approach if used exclusively to characterize habitat for TES.

5.1.7 Statistical Models

5.1.7.1 Models for a single dependent variate

A. Correlation Models

Definition
In correlation analyses, no control is exercised over the values that variables can take on; rather, we only observe the numerical value of the variables of interest. Any set of variables can co-vary whether the set consists of plant or habitat characteristics, or a combination of each. Correlation analyses permits the study of relationships that exist among such variables. In this type of model, only the linear relationship is estimated and one cannot make casual interpretations with respect to the relationship that may exist among the variables (Kachigan 1986). Autocorrelation and canonical correlation methods are presented in the sections on spatial statistics and multivariate procedures, respectively.

Correlation analysis has been used to estimate the relationship between any two variables or simultaneously among more than two variables. The former case is simple correlation analysis while the latter is multiple correlation analysis, which includes partial correlation methods.
Historical Uses
The commonly used measure of the amount of correlation that exists between variables taken two at a time is the product moment correlation coefficient, r, as developed by Karl Pearson (Freedman et al. 1978). This measure, when used alone, can be misleading as to the relationship among variables.

When more than two variables are analyzed for correlation, one variable is first considered to be a weighted combination, or a response variable, of the remaining set of variables. This is similar to regression models, but differs in that the correlation model provides an estimation of the degree of relationship that exists between the weighted variable and the remaining set of variables; the coefficient is the multiple correlation measure, R. This value is used to measure the amount of variation of the weighted variable that is explained by the set of variables.

Other coefficients may be more appropriate when data for two variables are not continuous nor linearly related as required by the Pearson coefficient. These coefficients include: the rank correlation coefficient to be used for ordinally scaled variables; the biserial correlation coefficient for use with a normally distributed variate and a dichotomous variable, and the ratio coefficient (called "eta") used to relate two variables which are curvilinearly related (Kachigan 1986).

Strengths
The correlation index provides a quantitative indication of relationships that exist among variables. As Kachigan (1986) states, "It tells us how things are in the world, which is certainly something worth knowing, even though it does not put the world under our control". Correlation analysis also provides predictive information about the value of one variable based on information about another variable. Thus, in spite of limitations based on theoretical concerns, the coefficient has great practical value for use in plant TES work. Correlation coefficients can also be used effectively in accounting for the variation of one variable by measuring a different, but perhaps easier-to-measure variable that is correlated with that variable. This is so because the variables have a common amount of overlap as shown by their covariance.

Limitations
Measures of correlation among variables do not imply that causality exists even when such correlation has been found statistically significant. Neither can the direction of correlation be determined from the sign of the coefficient; that is, positive or negative values associated with the coefficient do not necessarily mean that one has a positive or negative influence on the response of the other (Kachigan 1986); in fact, quite often spurious coefficients arise which are not meaningful. The proper interpretation can only be made when the physical, chemical, or biological relationships are understood.

Applications to Plant TES
Habitat variables of plant TES can be measured and screened for use as predictors of TES presence by using the correlation that exists between sets of habitat variables and presence of the plant TES. In the former case, soil variables such as moisture, nutrient levels, pH, etc. can be analyzed one at a time or in multiples with one or more measured plant variables such as density, seed production, number of reproductive stems, or other measures of TES abundance.

B. Regression Models

Definition
A regression model is used to describe the "nature of the relationship" between two variables (Kachigan 1986). While correlation analysis is used to determine the extent of the linear relationship existing between two variables. The two models are distinct in method of analysis as well as in purpose. While correlation analysis determines whether a variable can be predicted from another, correlated variable, regression determines the accuracy with which that variable can be predicted from another variable. In other words, regression analysis is proposed to "explain" a measurement of a single response variable, Y, in terms measurements of one or more predictor variables. In prediction, one variable is usually referred to as the response variable while the remaining variable or set of variables are the predictor variables.

Historical Uses
There are two reasons for using regression analysis: to simply fit a large data set to an equation that is then used to recover individual values, referred to as data fitting; and/or to describe the relationship that exists between one response and one or more predictor variables. There are three general forms of regression models: 1.) a simple linear model that involves one response variable that is dependent upon one independent variable, 2.) a multiple regression model that includes one response variable that is dependent upon more than one independent variables, and 3.) more than one response variable which are dependent upon one or more independent variables. The latter model is here considered multivariate and is presented under the section on models for several dependent variates. Both the simple regression and the multiple regression models are extensively used by ecologists and numerous references exist for their use.

The correlation coefficient, presented above, is used as an index to measure the closeness of fit of observed data to the estimated line (or plane) of regression (Li 1964). Details of the methods used in regression analysis, such as ordinary least squares, to solve for model coefficients are provided in applied statistical textbooks (e.g., Draper and Smith 1966, Sokal and Rohlf 1981, and Snedecor and Cochran 1980).

Limitations
Regression models are assumed to represent the relationship that exits between a dependent (or response) variable and the independent variables used in the models. A common problem with regression models is that predictor variables may be correlated among themselves; that is, they may have collinearity which often leads to erroneous results in estimates of the model coefficients. The use of transformations does not always eliminate this collinearity, but should be considered. Multicollinearity exists when partial correlation exists among the predictor variables (Bare and Hann 1981). The degree of collinearity or multicollinearity determines the seriousness of problems that may arise in prediction of future responses. However, even a model with high degree of multicollinearity still provides unbiased estimates of the coefficients; although they may be of opposite signs and change with change in new data.

The availability of computer programs today has contributed to the careless use of regression analysis by biologists. All too often, researchers do not make careful study of the relationships existing between animals, plants, and their environment before selecting a model for use in predicting plant responses to environmental characteristics. As a result, the model used may be rejected by statistical tests for use in such prediction. Proper exploratory analysis of data may reveal a more appropriate model in such cases.

Strengths
The strengths of regression models are found in the objectives for using these models: to determine if a relationship exists among a set of variables, to describe and explore that relationship, to estimate the accuracy of prediction by the model, and to determine the relative importance of each variable in the set in predicting the response variable. Regression modeling is well suited for assessing which environmental variables contribute most to species response and which of these variables can be eliminated as unimportant (Kachigan 1986, Freedman et al. 1978, Afifi and Clark 1984, Harris 1975, ter Braak and Looman 1995). Regression models have been successfully used in all these cases to study plant-environmental relationships.

Plant characteristics and associated environmental factors have been studied for decades by use of regression analyses, to predict, for example, occurrences of plant cover values from measures of soil moisture, and plant biomass from soil nutrient levels. Presence-absence of a species has been predicted from measured soil pH values (ter Braak and Looman 1995).

Application to Plant TES
Regression models have been applied to both animal and plant species for decades and have obvious application to the study, description, and prediction of characteristics of plants. The single largest drawback for their use is the lack of data on plant TES and their associated habitat. In particular, prediction of potential habitat of TES requires that variables that are biologically important to the species be selected. Then regression models may be used to predict presence for changes in plant TES populations based on relevant habitat information.

C. Spatial Models

Definition
Pattern in a plant species distribution is defined as a departure from randomness (Greig-Smith 1982). If the distribution is nonrandom, then patterns are formed as the result of one or more plant species occurring in clusters. Turner et al. (1991) present patterns as "patches" and discusses them from the landscape viewpoint.

The basic components of spatial analysis of measurements are the locations of the variable of interest and the data observed at those locations (Cressie 1993). Basically, the models can be classified as models for point, line, or surface patterns (Czaplewski et al. 1994). Cressie (1993), on the other hand, suggests that models be grouped according to the kinds of data to be analyzed: geostatistical, lattice, or point patterns. The two classification approaches are basically the same and neither are not exhaustive of model possibilities for patterned data, but do include the most commonly used models.

Geostatistical models recognizes spatial variability at both large and small scales; i.e., they model both spatial trend and spatial correlation. Lattice models are used when data occur on regularly spaced points in a region of interest and point pattern models are useful when the most important interest is in the location of the data values (Cressie 1993). Kriging for prediction of the variable over space is often part of the procedures used in spatial data analysis.

Historical Uses
Student, in 1907, is credited with early development of data analysis techniques which considered spatial positions of the data; by the 1930s R. A. Fisher is known to have recognized the role of spatial effects on field data (Cressie 1993). Since that time effects of neighbor on nearest neighbor data values have been of interest. More recently, the spatial analysis has included much more sophisticated models for analyzing vegetation and associated environmental data.

Shiyomi and Yamamura (1993) reviewed a class of methods using distance measures among neighbors to analyze patterns classified as random, aggregated, and regular patterns; indices were provided for each of the models used and included a new index based on distances between individual plants on a line transect.

The presence of spatial variability may: 1) increase or decrease the significance of plant response differences to habitat differences; 2) result in unexplained interaction between species responses and environmental variability; or 3) have no effect at all on the measured responses (Box et al. 1978). In 1 and 3, assuming there is no interaction, the commonly used analysis of variance does not detect the influence of spatial variability. A pattern is clearly detectable only when responses are affected by other variables which are measured; location is such a variable (Reich and Arvanitis 1989). Variability in responses can be caused by differences in topography, species composition, elevation, and latitude.

Moran's I (Moran 1948) is one method used to identify the presence of spatial pattern. This statistic has been used by ecologists to test for the presence of spatial autocorrelation in a two-dimensional plane (Cliff and Ord 1973, Jamars et al. 1977, Legendre and Fortin 1989, and Ripley 1981). A variable is said to be spatially autocorrelated when it is possible to predict the value of this variable at some point in space from the known values at other sampling points whose locations are known ( Legendre and Fortin 1989). Czaplewski et al. (1994) used a spatial autocorrelation model to explain the spatial distribution of environmental conditions and slow-growth in natural stands of pine. They concluded that growth rate could be caused by local environmental conditions rather than by other factors such as air pollution. Reich et al. (1995) used a spatial cross-correlation model to study undisturbed, natural shortleaf pine stands and found that basal area growth and other stand characteristics were, in a large part, due to a subset of stands located in a small region; i.e., growth was not due to regional or broad-scale variation as previously thought. Both of these papers provide extensive references on models used for these kinds of problems.

Bonham et al. (1995) also used a spatial cross-correlation statistic to interpret grassland species and associated soil and terrain features on a landscape level. In particular, they found that an infrequently occurring species in the area was spatially associated with certain commonly occurring species, with soil pH and with elevation; this spatial association enabled the interpretation of the species occurrence and related effects of grazing.

References on spatial models and their uses are found in Cliff and Ord (1973), Cliff and Ord (1981), Jamars et al. (1977), Legendre and Fortin (1989), Ripley (1977), Ripley (1981), and Upton and Fingleton (1985). Turner et al. (1991) presents a comprehensive review of spatial statistical models that have been or could be used to analyze spatial data; emphasis is on landscape ecology.

Limitations
There are many spatial models and only a few are being used in a limited way by ecologists because this approach to data analysis is not well understood. Therefore, the ecologist wishing to use these models should know which model to select for the particular purpose of analysis. Turner et al. (1991) may provide assistance. While spatial statistics is an emerging discipline and the literature is abundant describing models used for biological and non-biological data analysis, most ecologists do not have sufficient background in mathematics and statistics to use spatial models.

Strengths
Spatial statistical models can be used effectively to account for the influence of spatial variation of variables over geographical space. These models are important in properly interpreting results of analysis of variance and regression models. Because location coordinates of data are used in these models, measurements of habitat variables can be analyzed in conjunction with species data to study species demographics of the study area. In which case, environmental factors associated with those demographics could be selected and used for monitoring.

Applications for Plant TES
Spatial models can be effectively used to determine spatial characteristics of plant TES. Spatial characteristics of plants are needed to develop more informative models for description of plant TES-environmental relationships on community or landscape levels. For example, spatial models include those which predict the average cluster size and the average number of individual plants within each cluster over a study region. These results would be useful in selection of populations for monitoring, determination of environmental impacts on TES populations, and to predict potential habitat sites.

5.1.7.2 Models for several dependent variates

A. P-Variate Model

Definition
Use of the p-variate model includes explaining or predicting p correlated response variates by means of q predictor variables. The p-variate model provides the general model for regression and has been described by Seal (1968). The single dependent variate regression model described above is a special case of this multivariate model; this is the case with all multivariate models. Therefore, the model has all of the same assumptions as the single regression model and uses the least squares method for solution of the coefficient. The dependent variables may be plant or animal responses (size, weight,etc.) to their environment as indicated by the independent variables. Rather than using the independent variables to predict a single dependent variable, the p-variate model is used to solve the p-variate, simultaneous equations (corresponding to the number of dependent variables used) in one procedure (Seal 1968).

Historical Uses
The p-variate model has not been used extensively by biologists and no references are available for its use in the ecological literature. References are limited to those provided by Seal (1968) who referred to the model as the "p-variate linear model"; i.e., one that has several dependent variables that are interconnected to one another.

Seal provided references to agronomic and biological examples for the application of the model. For instance, the model was used to study crop yields as affected by variety and location (Bartlett 1939). Bartlett (1939) used the model as an analysis of variance model (ANOVA) to estimate the effects of location and other variables on production of cereal crops. The p-variate model was also used early on as a multivariate analysis of variance model (MANOVA) (Rao 1952, Kendall 1957, and Smith et al. 1962). The model was also briefly referred by Harris (1975) as a special case of regression analysis, but he gave no examples for its use. To the time of Seal, only the references above were found for use of p-variate analysis; the lack of incentive among biologists to learn the technique has probably been the cause of the paucity of references (Seal 1968). This lack is still evident today.

Limitations
Limitations of the p-variate model are the same as those for the single dependent variate regression model. There must exist a correlation among the independent variables and the dependent variables. It is assumed that collinearity does not exist among the independent variables, or the predictions of the dependent variables will not be without large errors.

Strengths
The major strength of the p-variate model is that the responses of several dependent variables can be predicted from the same set of independent variables. This model can also be used to select an optimal set of independent variables that will simultaneously predict a set of dependent variables.

Applications to Plant TES
The p-variate model can be used to study relationships that exist among habitat, plants, and the plant TES that occur simultaneously in a given habitat. Results of the analysis would yield a set of habitat variables that predict response of the TES associated plant species to changes in these habitat variables. Additionally, other plant species characteristics can be used as a set of independent variables to predict a set of characteristics of a given plant TES occurring in the community.

B. Principal Components Analysis (PCA)

Definition
The principal component model is used to summarize a set of original variables into new, but uncorrelated variables. These new variables, in turn, hopefully reduce the dimensionality of the data set. That is, it takes fewer of these newer variables to explain the relationships existing among the original variables. These new variables are referred to as "principal components" and are uncorrelated to one another (Afifi and Clark 1984). Graphically, the model rotates the original variable axes to new axes which are orthogonal to one another; this rotation in turn provides variables which are independent of one another in the statistical sense. Each principal component can be interpreted by amount of correlation of the original variables to this new variable; the components are defined in terms of the plant and soil variables and their sites (habitats) of measurements (Barkham and Norris 1970). The reference by Tabachnik and Fidell (1990) is a practical guideline to the use and interpretation of principal component analysis. Practical textbook references include Manly (1994) and Kachigan (1982).

Historical Uses
The principal component method was derived by Pearson in 1931. Hotelling developed Pearson's method and provided the original application in educational testing, showing that there are two major components of entrance tests, verbal and quantitative ability in 1933 (Gauch 1994). Ecologists began to use the model for vegetation-environmental analysis during the early 1950's (Goodall 1954). Goodall referred to the procedure as "factor analysis" which he used to conduct an "ordination" of the data; thus originating the term "ordination". His work largely went unnoticed as a data analysis method until computers became more available to ecologists (Ludwig and Reynolds 1988). In general, the model has been used as an exploratory analysis to develop an understanding of the complexity existing among a multivariate data set made up of intercorrelated variables; in other words, the model is used to find underlying commonality of the data (Seal 1968, Morrison 1976, Afifi and Clark 1984).

James (1971) used PCA to study the microhabitat of forest birds and from her results coined the term "niche gestalt" to describe the vegetational profile associated with selection of breeding territory by particular species. Her work laid the foundation of future approaches used to characterize bird habitats (Morrison et al. 1992). Urban and Smith (1989) presented a short summary of work on microhabitat pattern and structure of forest bird communities and proceeded with use of PCA to define the principal component space and the subsequent statistical characterization of a forest stand. The wide application of the model can be seen in such studies of habitat characteristics of seed-dispersing ants. Their nest chemistry was differentiated using PCA to model plant and soil nutrients and heavy metals (Beattie and Culver 1983).

Plant ecologists have used PCA extensively in studies of plant-environmental relationships. Among numerous uses of the model are studies of tree forms (Newcomer and Myers 1984), the distribution of tree species according to climate (Newnham 1968), the spatial distribution of climate and associated range in plant species and ecosystem site classification (Denton and Barnes 1987), the community structure of managed forests (Swindel et al. 1990), and community analyses (Ludwig and Reynolds 1988, Gauch 1994, Jongman et al. 1995). The most extensive use of the model has been to provide "scores" for an ordination of the species and/or environmental measurements. The reference by Tabachnik and Fidell (1990) provides practical guidelines for use and interpretation of factor analysis.

Strengths
The greatest advantage of using the model is to reduce large data sets to a smaller set consisting of new variables which preserves the original variation structure. The PCA model accomplishes this by concentrating the total variation of measured habitat variables into a smaller number of new variables which are not correlated and thus can be used in regression models to predict suitable habitat for a TES. Underlying environmental variables influencing measured variables and their range in variation can be deduced from the analysis. The model provides an objective method for conducting gradient-ordination analyses on plant-animal-habitat data in order to interpret relationships. The model "...provides a workable strategy to investigate a complex vegetation-soil system" (Barkham and Norris 1970).

Limitations
Interpretation of the "principal components" is not a quantitative process, but rather depends entirely on the knowledge of the ecologist using the method. Further, PCA results depend on variables of importance being selected for measurement. Otherwise, input measures will give false or inadequate information as to importance of variables in which case selection of variables for prediction of habitat suitability will not be valid. The model does not provide for problem-free tests of hypotheses (Gauch 1994).

Applications to Plant TES
This model continues to be used extensively as an "ordination" procedure to study plant communities and can be used to study communities in which TES occur. Ordinations using PCA can provide insight into habitat variables accounting for the range in variation of TES characteristics. In this way PCA models can be used to determine the underlying environmental influences on occurrences of TES if appropriate habitat information is collected. The original data set can be reduced for interpretation and correlation of measured variables can be used to select variables accounting for a given percent of the total measured variability of habitat characteristics.

C. Factor Analysis (FA)

Definition
Factor analysis is similar to principal component analysis and since Goodall's (1954) paper, terminology, even today, is often unclear as to which model is being used. The latter model accounts for as much of the total variance as possible, while the former concentrates on using correlations between variables to determine underlying causes of variable responses (Ludwig and Reynolds 1988, Gauch 1994, Kachigan 1982). The factors resulting from the analysis are used to explain the interrelationships existing among variables (Afifi and Clark 1984). The objective of using the model is to partition the correlation into a reduced data set that contains common factors plus a factor unique to each measured response variable. In other words, factor analysis removes redundancy from a set of correlated variables and groups similar variables. Textbook references include Seal (1968), Green (1978), Anderson (1958), and Kent and Coker (1992).

Historical Uses
Factor analysis was presented by Spearman in 1904 and generalized over a period of years by others into a method "...capable of analyzing correlation matrices into as many common factors behind the variables as may be necessary to account for all the observed correlations" (Cattell 1965a, 1965b). Cattell presents the best review of the method, its uses, and interpretation; this review is often better than textbooks written solely on the model.

Lawley and Maxwell (1963) pointed out "that whereas a principal component analysis is variance-orientated, a factor analysis is covariance-orientated". A comparison between PCA and FA is provided by Ivmey-Cook and Proctor (1967); they emphasized that PCA is concerned primarily with the distribution of the individuals in relation to the axes of greatest variance in the data, while FA is concerned with exploring patterns of relationship among the variables. This model is still confused in some current literature with PCA when referring to ordination methods (Jongman et al. 1995).

Strengths
The factor analysis model is a powerful method to reduce data sets to simpler forms. pplications include the identification of underlying factors that account for responses of a variable set such as plant cover. Small groups can be formed from large numbers of variables; each group is represented by a hypothetical factor. For example, such factors could be soil moisture, plant morphology, nutrient availability, etc.

The model provides for a new set of variables (as does PCA) which are independent and can be used to develop regression equations for prediction of plant-environmental relationships. Such prediction models are constructed without the restriction of collinearity effects. Additionally, the FA model is effectively used to summarize large data sets of plant-environment measures by concentrating the largest portion of variance into one or two factors; then the selection of variables for measurement can be made since there is no need to measure the same information more than once.

Limitations
The largest limitation to use of the model is that of identification of the factors which result from the analysis. This process is largely a qualitative, subjective one rather than a quantitative one (Ludwig and Reynolds 1988, James and McCulloch 1990, Kent and Coker 1992). The method depends on the premise that the data is truly representative of the plant-environment relationships; i.e., that appropriate responses of plants to their environment have been measured. Factor analysis does not create new information, it only re-arranges the old information in a data set.
Factor analysis consists of very complex procedures and the method may not provide the optimal display of plant-environment relations. Because of this feature, FA models are difficult to interpret and require that the ecologist have both statistical and field knowledge to effectively use the model.

Applications to Plant TES
Because of similarities to PCA, the FA models have the same general uses for study of TES plants and their environmental relationships. Results can be used in prediction models to describe the habitat characteristics associated with TES and may do so more effectively than models developed from regression approaches. FA models, like PCA, can be used to describe plant characteristics and habitat relations at landscape levels because plant community data is the most common level of data collections made when FA is used. The analysis provides a method for selection of plant characteristics (variables) most closely associated with "factors" that are often interpreted as being associated with soil and terrain features.

D. Discriminant Analysis (DA)

Definition
The discriminant analysis (DA) model has been used in two primary ways to analyze plant-animal-habitat data. The most widely used model is the "classification" model. Data are placed into groups a priori according to criteria of the ecologist. Groups can be vegetation types, treatment levels, etc. Then the analysis is conducted to develop discriminant functions which are used to assign each observation (individual plant, animal, plot) to the group having the most similar multivariate set of measured characteristics. These data are studied for differences among groups. Environmental interpretations have been made for a wide range of communities (Ludwig and Reynolds 1988).

Historical Uses
The discriminant function was first introduced by R. A. Fisher in 1936 as a statistical technique to classify species of Iris (Hope 1969). Rao (1948) discussed the use of multiple measurements in biological classification while Seal (1968) showed that discriminant functions for two groups could be reduced to one function to classify individual observations of a frog species by measuring crania breadths and lengths.

The model was used by Seagle et al. (1987) to describe habitat variability of the Red-cockaded woodpecker using information on a large set of variables thought to describe the habitat. A subset of the variables were used in DA to analyze differences between two groups of compartments; those having active colonies and those having no colonies. The resulting function represented a habitat quality continuum related to the occurrence of longleaf pine. The discriminant scores were suggested to be useful as a potential management tool. Matthews (1979) used DA to study successional and climax plant assemblages and concluded that it was effective in rejecting the hypothesis commonly put forth that successions tend to converge.

Limitations
Rexstad et al. (1988) used the model, among others, and concluded that multivariate statistical techniques, including DA, should not be used in studies of wildlife habitat. These authors pointed out that discriminant function coefficients are interpreted by either considering the relative size of standardized coefficient, or by determining which variables have the highest correlation with discriminant scores. Because the two approaches do not select the same set of variables, the authors conclude that interpretations may be in conflict and conclusions arbitrary. If the DA model is used to select important variables, one should be aware that the error rate of assigning observations to the correct group or class does not decrease as the number of measured variables increase (Murray 1977). The problem is with the bias associated with searching through large numbers of subsets in quest of an optimal set to define discriminant functions. This problem has raised some doubt as to the usefulness of DA in classifying observations, but Murray gives options for forming optimal subsets of variables.

Strengths
The discriminant analysis model has been used effectively in the analysis of plant and animal groupings into classes or types. The method has two primary uses: to classify observations into groups known to exist a priori and to statistically test the existence of different groups. When used for the former purpose, there may be sufficient biological reasons not to be concerned about statistical significance among groups; in which cases no test is made. On the other hand, the purpose is to find the smallest number of existing groups from the statistical viewpoint. Then the technique is used to differentiate among any groups in any classification system and permits the classification of the variability within and between types from analysis of variance models (Matthews 1979). Therefore, the nature of assemblages, such as plant communities, can be interpreted, leading to a better understanding of the assemblage. DA models can be used to verify the existence of plant-assemblage types that were derived by some other method.

Applications for Plant TES
The DA model has potential for the study of plant TES and associated habitat conditions. Plant communities can be tested for differences, and for variables, both plant and environmental, which discriminate among communities. Other groupings based on levels of disturbance can likewise be tested for differences in associated plant species, soil differences, etc. and classification models can be derived for future prediction of habitat suitability. Matthews (1979) used to the model to study successional convergence-divergence of vegetation systems and concluded that divergence is the rule; plant TES and their habitat characteristics, including associated plant species, can be better understood through such analysis of successional systems.

E. Classification Models

Definition
Classification models include the use of statistical procedures such as discriminant analysis (DA) and multivariate analysis of variance models (MANOVA). Non-statistical procedures include Cluster Analysis (CLA), the most widely used analysis; this procedure uses measures of distances (geometric) as the main variables. When clusters are formed by minimum variance methods or K-Means, for example, then the model is based on statistical criteria. For references, see Gauch 1994, Jongman 1995, and Ludwig and Reynolds 1988. Discriminant analysis (DA) as a classification tool has been addressed previously and will not be repeated here. MANOVA models are used for classification in concert with DA models to provide a "step-wise" approach to selection of statistically important variables for use in discriminant function development; MANOVA models are not addressed here. A comparison of methods of ordination and classification of vegetation data is presented by Podani (1989), while Goodall (1963) provides a very clear analysis of the issues concerning classification and ordination.

Cluster Analysis (CLA)

Definition
Cluster analysis models are based on the concept of grouping together observations with similar characteristics in mathematical space (Kent and Coker 1992). This model is used to define groups from individual observations as contrasted to discriminant analysis (DA) wherein groups are known a priori. The method does not usually involve any statistical approaches to form groups. Dependent variables in cluster analysis are generated from a combination of multiple variables in an observation and the dependent variables can be similarity measures (Jongman et al. 1995) or measures of distance between each possible pair of sites, stands, habitats, etc. There are several kinds of data used to form clusters from data sets. Discussions of ecological uses are presented in Kent and Coker (1992) and Ludwig and Reynolds (1988).

Historical Uses
Cluster analysis has developed over the past 25 years into a commonly used method for study of taxonomy of plants, plant communities, and classification of plant and animal habitats. Reviews of the methods used in cluster analysis are presented in Afifi and Clark (1984), Ludwig and Reynolds (1988) and Burton et al. (1991). The use of cluster analysis in taxonomy is attributed to the development by Sneath and Sokal (1973). Others in plant ecology adapted the method to study plant assemblages (Ludwig and Reynolds 1988). Kent and Coker (1992) present details of uses in classifying vegetation and they present at least eight characteristics of methods of numerical classification and provide extensive details for the various models used.

Limitations
The important limitation of using numerical methods such as cluster analysis to classify observations into groups is that different algorithms produce dissimilar classifications when applied to the same data set (Podani 1989, Ludwig and Reynolds 1988). Studies have shown that even a random data set can be classified into groups. These problems indicate that cluster analysis is highly empirical (Afifi and Clark (1984). This indicates that such models can produce spurious classifications of biological data and may not be subject to meaningful interpretations.

Strengths
The models used in cluster analysis can be used to form groups of observations, each of which places measures of plant species characteristics into meaningful units, interpretable as communities, if the ecologist is knowledgeable of the vegetation-environmental relationships existing in the area of study. These newly formed units can be tested for accuracy using discriminant analysis (DA). Additionally, important species can be identified from this latter analysis. Observations on habitat varibles can also be classified by cluster techniques and overlays with the vegetation types can be used for interpretation.

Applications to Plant TES
Cluster techniques can be used to study the relationships of plant TES to other plant species that occur with it. Vegetation types associated with the TES, defined from cluster analysis, can be interpreted as to characteristic species composition or successional stage.

F. Ordination Models

Definition
There are many different ordination procedures and they differ only in how species weights are obtained and how sampling unit (stands, etc.) scores are obtained. The most common methods of obtaining scores are from PCA, FA, DA, COA, and DCA models. The first three are statistical models, while the latter two may not be; instead, the last two models may use scores developed from measures of similarity indices.

Other non-statistical models for ordination include polar ordination and the continuum index; both are from the Wisconsin school. The former model "locates" stands (sampling units) relative to two end-points which are often subjective (Beals 1984). The latter model is the original "quantitative" ordination from Wisconsin ecologists Curtis and Bray and used a single weighted averaging for species "importance" value. For detailed explanations, see Gauch (1982), Jongman et al. (1995), and Ludwig and Reynolds (1988). These two models are not presented here because they are rarely used today. As previously stated, a comparison of ordinations and classifications of vegetation data is presented by Podani (1989), while Goodall (1963) provides a very clear analysis of the issues concerning classification and ordination. Austin (1985) presents a brief, but effective history of continuum and ordination methods.

Correspondence Analysis (COA)

Definition
This model is used to obtain ordination scores of sampling units such as stands and/or species. For stands or sample sites, the dependent variables are scores for a stand or site weighted by species attributes in the sample unit. For example, the attribute of species may be the total abundance of a species across all sites, which is weighted by the sum of abundance over all species (Ludwig and Reynolds 1988 and Jongman et al. 1995). Scores can be calculated with the same weighting formula.

Historical Uses
Kent and Coker (1992) provide a brief historical review of the COA model and its uses. In 1969 Benzecri presented the development of a simple calculation for one axis. Beals (1984) demonstrated that the second axis was an "arch" and was difficult to interpret. The detrended correspondence analysis (DCA) was developed to overcome this problem. The model was used extensively for ordination analysis from 1969 to 1985 and now is largely replaced by DCA. However, Ludwig and Reynolds (1988) suggest that the model is widely used, as is the DCA form of it. The procedure also uses the reciprocal averaging procedure that is used in other ordination methods.

Limitations
The model was shown to produce an "arch" in ordinations using the second axis of an ordination which is difficult to interpret. The curved pattern of sampling units within an ordination results from nonlinear relationships among the species; the nonlinearity is the result of sampling communities over broad environmental gradients.

Strengths
Correspondence analysis is more robust than PCA when data sets are nonlinear (Ludwig and Reynolds 1988). The COA model obtains an ordination of the "corresponding" sample units (stands, sites) and species ordinations simultaneously. Ecologists interested in community analysis can examine the interrelationships between the sample units and species in a single analysis (Ludwig and Reynolds 1988). Studies have shown that COA performs better as an ordination method than PCA when there is only one dominant species with a relatively broad enviromental gradient (Ludwig and Reynolds 1988).

Applications to Plant TES
The COA model may be effectively used to ordinate data obtained from several populations of a plant TES because the plant could be treated as a "dominant" species by data transformation to attain this feature. Then the scores could be used in an ordination in conjunction with say, soil moisture as a habitat variable. The ordination of populations used as sampling units could be interpreted in terms of plant TES requirements and responses across the soil moisture gradient.

Detrended Correspondence Analysis (DCA)

Definition
This model is a modification of COA to correct for at least two problems arising from an ordination analysis using COA: 1.) the ends of the ordination axes are compressed relative to the axes middle and 2.) the second axis frequently shows a quadric (an arch-shaped) relation with the first axis (Jongman et al. 1995, Ludwig and Reynolds 1988). The model was formulated to "detrend" the data to remove the arch. In particular, the process involves dividing the first axis from the COA ordination into a number of segments. The site or sample unit scores for the second axis are adjusted by substracting the within-segment mean on the second axis from the score for each site or sample unit (Gauch 1982, Jackson and Somers 1991). The results produces a mean value of zero for scores on the second axis; the process is repeated several times and results are averaged to obtain axis scores. Additional axes are detrended in the same manner. This procedure results in a DCA eigenvector ordination of the species with no arch and a set of sample unit scores which are weighted species scores.

Historical Uses
Hill developed the technique in 1973 to adjust results of COA ordinations that produce a nonlinear response curve because of the relation between the first and second axes (Gauch 1982). Further work reported by Gauch (1982) found that adjusting sample units (sites, stands) is more robust than adjusting species because of the need to have the within-sample unit standard deviation be unity; then the average species abundance profile has a standard deviation also equal to unity.

Limitations
There has been criticism of the DCA model on the basis that the model uses an arbitrary rescaling procedure and that only one axis is used for the ordination (Wartenberg et al. 1987). It has been suggested that all ordinations should be reported in two or more dimensions, unscaled. Others believe that multidimensional configurations obtained with DCA may be unstable and potentially misleading (Jackson and Somers 1991).

Strengths
Use of the DCA model for ordination of sample sites, stands, and other units has shown that the method produces results that are superior to most other ordination methods (Gauch 1982). The model is useful for analyzing community data for subsequent interpretation because it provides robustness, no distortion, and meaningful axis units of DCA. Niche ordination of birds by foraging position and behavior has been done by Sabo (1980) using DCA. Gauch (1982) states that the method is most appropriate to the Gaussian community model and most successful in applications to community analysis.

Applications for Plant TES
The DCA model may be useful to study plant TES and their environmental relationships, but as with other ordination methods caution must be used in interpretation of results. There would be no advantage to the method unless known relationships were found in the ordination of sample units such as populations or known communities.

5.1.8 Indicator Species Models

Definition
Ecological indicator species are species considered to be indicative of some parameter of populations of other species, of habitat conditions for other species, or of environmental conditions, e.g., presence of contaminants. Regulations pursuant to the NFMA of 1976 (Code of Federal Regulations 1985 36 CFR Chapter II 219.19:64) require the use of "management indicator species," including ecological indicators, in development of all National Forest Plans. Management indicator species also may include a) recovery species, those listed by states or federally as rare, threatened, or endangered; b) featured species, those considered to have economic or social value; and c) sensitive species, considered especially vulnerable to management effects on habitat.

Historical Uses
Mealy and Horn (1981) suggested that forest management for elk (Cervus elaphus) and three hawk species, used as indicators, could provide management for over 400 vertebrate forest species. Powell and Powell (1981) interpreted poor reproductive success in a Florida population of great white heron (Ardea herodias) as indicative of generally poor habitat quality for the estuary in which the population nested.

According to Van Horne and Weins (1991) the validity of the guild indicator approach is dependent on the consideration of two questions: 1) Is the indicator species representative of the larger suite of species of interest? 2) What does change in population density or productivity of the indicator really indicate? If these two questions can be satisfactorily answered, then the indicator approach to management may be useful.

Next, problems also arise if species are assigned to a guild based on literature which may or may not apply to the case at hand. Research conducted by Block et al. (1987) supports the idea that guild structure and indicator species should be based on site specific information.

Limitations
Many habitat-relationships models have been developed on the assumption that the species selected for modeling is indicative of the status of populations of other species or the status of their habitats for other species. In reality, species respond differently to change, utilize resources differently, and behave differently (Morrison et al. 1992). Thus, a species cannot indicate the status of other species or the quality of habitat for other species. The value of indicators in species and habitat management has been questioned by Landres et al. (1988) and Morrison et al. (1992). Use for animal-habitat description and monitoring may continue primarily because of agency mandates (Landres et al. 1988).

Strengths
In spite of the current thought among some academic and agency personnel, the utility of ecological indicator species should be considered. Ecological indicator species may convey accurate information on plant environments useful in TES management.

Applications for Plant TES
Research conducted by Block et al. (1987) indicated that guild-indicator species were not necessarily effective as representatives of the entire guild. On the other hand, selection of indicator plant species can be based on site specific information and other plant species whose habitats are most similar to those of other members of the plant associations. Then modeling the habitat of plant TES may find success with guild-based models. Small populations of plant TES and possibly unique ecological requirements may, in fact, make them good indicator species within the larger framework of a guild (see Guild Life-Form Models).

5.1.9 Guild Life-Form Models

Definition
A guild is defined as, "a group of species that exploit the same class of environmental resources in a similar way" (Root 1967). In general, guild or life-form models are designed to characterize how a set of species with similar characteristics or attributes will respond to a change in environmental conditions (Severinghaus 1981).

The guild-indicator approach assumes that members of a guild use identical rather than similar resources (Severinghaus 1981). Verner (1983) further refined the scope of guild life-form models when he suggested that guilds should be analyzed and monitored as a single indicator unit, rather than monitoring a single indicator species.

Historical Uses
Historical definition of guilds and their applications have varied greatly and thus, have influenced formal procedures for their use in wildlife evaluation. Short and Burnham (1982) developed procedures for applying guild theory with their "community guild model." First, the model parameters are defined and the habitats used for feeding and breeding are identified. Data from field studies and literature review is then used to classify species as to their predominant habitat use patterns. Analysis of factors that make this guild unique can be used to predict effects different management decisions will have on these life forms in general, and on their patterns of feeding and breeding.

Block et al. (1987) used a guild of ground foraging birds to evaluate the ability of a guild-indicator species to assess habitat suitability for the guild as a whole. However, because different species appeared to use different microhabitats, Block et al. were forced to conclude that it was more efficacious and economical to monitor the population of the guild as a unit, rather than monitoring any single species as an indicator. Thus investigators cannot infer the habitat suitability factors required for other species, based solely on the presence of the guild-indicator species.

Limitations
Verner (1983) indicated that inordinately large species counts were necessary to detect population change using the guild-indicator approach. Verner suggested that if species in a guild are combined and monitored as a single unit, fewer samples are required to detect demographic changes within the guild. Even if species within a guild exhibit similar characteristics and are monitored as a unit, this method may still be questionable if individual species within the guild respond differently to environmental disturbance (Mannan et al. 1984, Block et al. 1987).

The utility of guild models largely depends on which definition of a guild is used and the ways in which the concept is applied (De Graaf et al. 1985, Block et al. 1987, Mannan et al. 1984). For example, Mannan et al. (1984) point out that while closer definition of the target species and geographic area in question improve the utility and predictive value of the model, this simultaneously decreases the scope of guild-based management. In addition, the environmental conditions of the area in question need to be well understood if the model is to work well as a predictive or management tool.

The fundamental limitation of the guild-indicator models is that while individual species responses may vary greatly in response to environmental disturbance, the guild as a whole may exhibit little or no detectable fluctuations (Block et al. 1987, Mannan et al. 1984). Although species in a guild may act almost identically in their exploitation of a particular resource, they may differ greatly in other aspects of their general ecology.

Strengths
The guild concept simplifies assessment of management effects by grouping ecologically similar species from diverse taxa into a single management guild. This simplification may make habitat assessment easier for land managers who are constrained by time and budgets.

Verner (1983) suggests that monitoring guilds as a unit may reduce the amount of data collection required, and still produce ecologically meaningful results. Guilds may thus be useful for modeling species with similar functions. Block et al. (1987) and Cooperrider (1986) also indicate that guild life-form models do have some predictive value and are potentially useful in wildlife management.

Applications for Plant TES
Guild life-form models may also be useful for application to plants, in general. Exclusively, guilds have been used for animals and easily based on how resources are used by individual species (i.e., for nesting, breeding, and hiding etc.). Yet, much information is available on plant environmental associations, which could be formulated into the "guild" concept. But the problem of a plant's response to unfavorable changes in its environment may be much more subtle or occur over a much longer period of time than responses of animals. In addition, it is much more difficult to ascertain how specific plants are utilizing their habitat resources based solely on visual observation. Detailed field research may be needed to find plant nutrient and other resource use variables to establish guilds.

For these reasons it appears that utilizing guild life-form models to characterize plant and TES habitats, may not be a particularly efficient or straightforward method for characterizing and monitoring individual species responses to habitat disturbance or other environmental change.

5.1.10 Landscape-scale Ecological Models

Definition
At the scale of the landscape, habitats exist as patches distributed in space. The degree of isolation of habitat patches from one another and their dynamics of vegetation change and disturbance can affect populations of species. Landscape models of habitat study the effects of habitat fragmentation, isolation, and abiotic factors on populations.

Historical Uses
Concepts of island biogeography (MacArthur and Wilson 1967), including the effects of island size and distance between islands on the extinction rates of enclosed populations, are central to many landscape-scale habitat studies. Metapopulation dynamics (see our section on population models) and patch dynamics (Picket and White 1985) are other related fields.

Natural and anthropogenic disturbance (for example fire, treefall) affects populations by maintaining a patchwork of vegetation community stages across a landscape, amounting to a diversity of habitats. The NFMA of 1976 mandates maintenance of habitat diversity on National Forests in the interest of maintaining plant and animal diversity. Prediction of change in habitat conditions resulting from disturbance is therefore of interest to managers. Further, concepts of a dynamic landscape represent a departure from the traditional paradigms of a stable climax (Clements 1936) and other equilibrium concepts (Pickett et al. 1992) used by agencies for resource management.

Fragmentation of habitat can affect populations by limiting genetic flow among populations, disruption of social behavior, exclusion of wide ranging species and particular microhabitats, and introduction of edge-adapted species (Wilcove 1987). Models may consider the effects on population processes of the spatial arrangement of habitat patches (Fahrig and Paloheimo 1988), the degree of isolation of patches (Fahrig and Merriam 1985), and the size of patches (Lynch and Wigham 1981). Fragmentation and patchiness create situations analogous to the processes that affect populations on islands, whereby the diversity of species in a patch "relaxes" to some predictable point as species go extinct.

Limitations
In general the techniques described here address effects on diversity (the number of species) in patches of habitat, rather on than individual species.

Strengths
Habitat loss and fragmentation are major causes of declines of plant and animal populations. Landscape-scale approaches address the effects of these processes on total diversity of an area.

Applications to Plant TES
Direct approaches to habitat loss and fragmentation have obvious relevance for plant TES. While habitat requirements of TES are often specific, effects of fragmentation and disturbance models may be useful for plant TES habitat description and monitoring at larger scales.

5.1.11 Stand Growth Models

Definition
Models have been developed to predict forest conditions, such as stand growth and harvest yield, for silvicultural applications. These include FORCYTE (Kimmins 1987), DF-SIM (Douglas-fir simulator) (Curtis et al. 1981), SPS (Stand projection system) (Arney 1985), and CLIMACS (Dale and Hemstrom 1984). These computer-based models typically project future forest structure following a particular harvest method, in terms of stem volume, density, diameter, basal area, and tree height. Other models that relate harvest rates to populations have been applied in marine fisheries science (Dennis et al. 1985).

Historical Uses
While these models do not explicitly link wildlife to habitat, they have been used to predict suppression mortality in forest stands. A mortality estimate can in turn be used to predict standing dead (snags) and down dead trees at a future time, which are important to some wildlife species. Neitro et al. (1985) used DF-SIM in this way, and Morrison et al. (1992) report that SPS could be used for the same purpose.

Limitations
Not surprisingly, stand growth models are constrained in the same ways as habitat-relationships models, and have similar problems with unvalidated models, poor performance in extrapolation of model results, and variation in natural systems (Dennis et al. 1985, Morrison et al. 1992).

Strengths
Stand growth models can be used to predict forest stand conditions that may be related to wildlife habitat needs.

Applications to Plant TES
TES plants may be dependent on particular seral stages of forests that might be predicted with stand-growth models.

5.1.12 Succession Models

Definition
Succession models predict change in habitat as succession proceeds through the various seral stages of vegetation. The most prominent is DYNAST (DYNamically Analytic Silviculture Technique) (Boyce 1980, Benson and Laudenslayer 1984), a computer model developed to assess production in forested resource areas under different management regimes within a multiple use scenario. The model combines models for timber, wildlife, and erosion with models of succession, and links these with alternative timber harvest strategies (Benson and Laudenslayer 1984). DYNAST predicts response in wildlife and habitat vegetation to alternative management activities and may use HSI-type models and HSI values. Barrett and Salwasser (1982) discuss construction of habitat models for use with DYNAST.

Historical Uses
DYNAST has been used to predict carrying capacity (habitat capability) of habitat for several animal species (Morrison et al. 1992). For example, Benson and Laudenslayer (1986) developed HSI values from models they developed for band-tailed pigeon, pileated woodpecker, and mule deer. The HSI values ranged from 0 to 1 with the highest value representing the set of successional stages considered to provide the highest quality habitat for each species, and 0 representing the set of successional stages providing lowest quality habitat. These values were used in DYNAST under three different timber-harvest strategies. The simulation thus considered the successional stages that the harvest strategies would produce and their benefits for each species and for timber production. Based on the authors' interpretation of the model's output, the mixed rotation harvest alternative (harvest of half of the acreage of each successional stage at 120 years, and half at 200 years) produced a rating of moderate desirability for pileated woodpecker and timber production, and a rating of moderate to high for band-tailed pigeon and mule deer. Values were obtained similarly for the other two harvest strategies.

Limitations
Because habitat and index values are often used in succession models, these models are subject to the limitations of the habitat models and problems associated with selection of habitat variables. Benson and Laudenslayer (1986) point out that "the wildlife and other resource models used within DYNAST may not relate directly to those variables, so resource [including wildlife] responses may not be realistic" (brackets ours). They point out that the DYNAST model had not been tested for accuracy in any system in the U.S., and that the wildlife models were not validated. Assumptions by users regarding local successional processes are also involved.

Strengths
The DYNAST model presents tradeoffs among alternative management strategies in a format accessible to land managers. While they may not provide accuracy, such approaches at least illustrate that habitat alteration involves compromises among wildlife species and other resources.

Applications to Plant TES
Morrison et al. (1992) characterize succession models as lacking sensitivity to spatial patterns of seral stages, because they are based on land area occupied by vegetation types rather than on development of individual stands (see also Benson and Laudenslayer 1986). Morrison et al. (1992) point out that for wildlife "species requiring scarce or declining habitat", prediction error may be high. Some indication of broad habitat types available for plant TES may be provided by succession models. However, restriction of many plant TES to small or specific habitats will make accurate prediction difficult.

5.1.13 Community and Ecosystem Simulation Models

Definition
Simulation modeling is an approach to the study of complex systems such as communities or ecosystems. Simulation models describe the dynamics of systems by modeling change in the main elements (state variables or compartments) of the system. For example, vegetation, a state variable, is affected by the processes of photosynthesis, grazing, and respiration, among others. The effects of these processes for all state variables can be presented as a system of differential equations (Swartzman and Kaluzny 1987, Peters 1991). Simulation models overlap with model types discussed elsewhere in this report, which may be considered types of simulation modeling, for example, DYNAST models, discussed in the subsection on succession models.

Historical Uses
Simulation models have been applied to systems rather than to the habitat relationships of individual species. Systems modeling was a major component of the IBP; however the models developed were disappointing (Ricklefs 1990). Simulation models have been developed for management applications, primarily from the large-scale perspective of the ecosystem (see Swartzman and Kaluzny 1987 and Morrison et al. 1992 for discussions).

Limitations
Difficulties associated with modeling in general can be considered as magnified when numerous variables with unverifiable relationships mimic the complexity of natural systems (Ricklefs 1990). While this type of modeling is heavily used in theoretical studies of ecosystems, it has not developed to the point of practical use.

Strengths
Simulation models are often mechanistic in that they attempt to describe mathematically the mechanisms controlling processes in systems, in contrast to many of the other model types treated in this report, which bypass mechanism by establishing or assuming relationships between species and habitat.

Applications to Plant TES
Habitat relationships of TES could obviously be viewed as systems controlled by the processes linking species to their habitats, and therefore could be linked into simulation models. We consider simulation modeling an analytical research tool, though potential applications can be seen in our section on succession models.

5.2 Population-based Models

Definition
Population trend and viability models are not strictly habitat-based models, but proceed from genetic or demographic data. In population trend models, the demographic parameters of the population itself may be used to predict future population status, as in age-, size-, or stage-based population matrix models (Leslie 1945, Lefkovitch 1965). Extinction models generally estimate the time to or probability of population extinction (Burgmann et al. 1988, Menges 1992, Morrison et al. 1992). Metapopulation models consider the effects of dispersal and migration among subpopulations. Minimum viable population models (MVP) (Shaffer 1981, Franklin 1980) consider the availability and proximity of habitat and their effects on populations. An MVP as defined by Shaffer (1981) is " . . . .the smallest population having a 99% chance of remaining extant for one thousand years despite the foreseeable effects of demographic, environmental, and genetic stochasticity, and natural catastrophes."

Historical Uses
Haig et al. (1993) conducted a population viability analysis (PVA, which is a form of extinction modeling) of a small population of red-cockaded woodpecker in South Carolina, with consideration given to genetic and demographic factors. A matrix population model was used for the loggerhead sea turtle (Caretta caretta) by Crouse et al. (1987) and matrix models have been applied to rare plants by Menges (1986).

Limitations
Like any application where there is broad spatial or temporal extrapolation of data, models of population viability and extinction are subject to errors resulting from incomplete or false data, violation of model assumptions, and/or erroneous model construction. Population matrix models are predictive only over the period of time that habitat conditions remain unchanged, because demographic parameters may be affected by environmental change. Conner (1988) argued that the maintenance of populations at minimally viable levels is inadequate for conservation, and that populations should actually be maintained at higher "ecologically functional" levels.

Strengths
Extinction and MVP models quantify the viability of populations, and can therefore highlight the vulnerability of sensitive populations to environmental, habitat, genetic, or demographic change brought about by stochastic or anthropogenic sources. Demographic-based models such as stage-based population matrix models utilize model variables associated with the basic parameters affecting population change (Schemske et al. 1994); therefore, they do not use the intermediate and difficult process of extrapolating habitat information to effects on populations. Demographic studies have been recommended as means of evaluating habitat-based models (Van Horne and Wiens 1991).

Applications to Plant TES
Because population viability is of primary concern in plant TES recovery, population-based modeling has found applications in their study and management. Menges (1990) conducted a PVA of the endangered plant Pedicularis furbishiae (Furbish's lousewort) which demonstrated the important role of metapopulation dynamics in the persistence of the species. Applications of population matrix simulation models to rare plant populations can be found in Fiedler (1987) and Menges (1986). The use of population matrix models for validation (field-checking) of habitat-based models is another promising use of these models in plant TES management.

5.3 Decision-Support Processes

5.3.1 Habitat Evaluation Procedures, Fish and Wildlife Habitat Relationships Program, and Integrated Inventory and Classification System

Definition
USFWS, the U. S. Forest Service (USFS) and the Bureau of Land Management (BLM) have developed protocols for species-habitat assessments that will be discussed in a later section on "approach"-type models. These consist of broad guidelines and models for habitat and species evaluation for land-use planning, and at the agency level, have been the driving force behind development of habitat-based models for wildlife using both single-species and multispecies approaches. These protocols define ways in which the goals of general wildlife species and habitat management are addressed, and are not specific to TES. They are procedural models as well as guidelines for development and use of specific species-habitat relationships models. Models developed under these systems have been applied only to animal TES.

USFWS's Habitat Evaluation Procedures (HEP) is a ". . . planning and evaluation technique that focuses on the habitat requirements of fish and wildlife species" (Schamberger et al. 1982). The BLM has also developed a multispecies approach to habitat assessment under the Integrated Habitat Inventory and Classification System (IHICS) (BLM 1982). The NPS has established general guidelines relating to natural resource inventory and monitoring (NPS 1992), providing a general rationale and a broad methodology for inventory and monitoring of species and habitats on National Parks. The FWHRP of USFS established regional programs whose goal is ". . . to provide a systematic method for evaluating habitats for all fish and wildlife species so that they can be effectively considered in land and resource planning, projects that affect fish and wildlife habitat, and efforts to improve habitats for selected species" (Nelson and Salwasser 1982).

Agency approaches to habitat assessment provide broad guidelines and models for extrapolation of species-habitat information, consider various geographic scales, may or may not specify methodology to be used in habitat assessment, and do not provide detailed guidelines for studies concerning TES species. Their application is generally the assessment of the effects of habitat alteration.

Historical Uses
The U. S. Army Corps of Engineers (USACE) and the U.S. Bureau of Reclamation (USBR) took part in development of HEP. HEP has been used most in water projects involving mitigation of habitat loss (Cooperrider 1986). The system uses HSI models extensively. HEP is based on the habitat unit, which is defined as the product of an index of the quality of a habitat (derived from an HSI model) and habitat area. Thus a range of habitats can be assigned relative values for particular species (Morrison et al. 1992). Morrison et al. (1992) reports that HEP procedures are often used to assess impacts and design mitigation of habitat alterations resulting from proposed federal projects for sensitive animal species.

Species selected for USFWS HEP modeling are often chosen as an indicator species or "evaluation species" (USFWS 1980a), which, under USFWS ecological criteria, may be a sensitive species, a keystone species crucial to a natural community, or an individual species used in a guild model (see our discussion of guild models). Like USFS, USFWS also has socioeconomic criteria for selection of indicators (Landres et al. 1988).

Under FWHRP, habitat is characterized hierarchically, using 1) dominant vegetation, 2) structural attributes of the vegetation, and 3) habitat resources of particular species. This classification of habitat is then characterized in terms of species relationships at three scales of resolution: Level one rates stand-level habitats in quality for each species in question. Levels two and three relate management indicator species to larger areas using variants of HSI models called HC models. Specifically, level two integrates level one habitat variables to subpopulations of indicator species at a larger geographic scale, for example, a watershed or the winter range of a subpopulation of an animal species. Level three aggregates the habitats of a still larger area in order to model and predict habitat capability (carrying capacity) for a population of the species in question.

Limitations
The appropriateness of simple index values for prediction, such as obtained from HSI models, has been questioned by Green (1979) and Van Horne and Wiens (1991). This problem is particularly at issue when the relationships between habitat variables and habitat suitability, on which the model is based, are assumed and/or unvalidated. HEP and FWHRP models often employ the indicator species concept ("evaluation species"), which has been questioned in applications to wildlife-habitat modeling (see our section on indicator species models). Due to the fact that HEP often uses indicator species as predictive variables, these procedures may not be appropriate for use with plant TES which have very specific habitat requirements. These approaches described in this section are intended for large-scale, general species, and habitat management.

Strengths
HEP, FWHRP, and IHICS provide structured guidelines for documenting habitat conditions using habitat-based models; thus providing a level of standardization in habitat assessment. In addition, these procedures also include considerations of scale, an aspect of habitat characterization that is often ignored or not dealt with directly in other methodologies.

Applications to Plant TES
These methods may be useful as general guidelines for survey and monitoring. Due to the unique and tenuous nature of TES however, methods would need to be tailored to site-specific conditions.

5.3.2 Adaptive Management

Definition
Adaptive management refers to a feedback process of using monitoring results to guide management, and the subsequent modification of management direction as indicated by monitoring. Adaptive management is therefore not a habitat characterization model, but provides a useful paradigm for management response to habitat-species monitoring (Holling 1984).

Historical Uses
The iterative development of models as described in Starfield and Bleloch (1986) (discussed in Section 4.2, Model Validation) can be considered as part of this process, where models are checked by some form of validation (which should include monitoring) and are adjusted appropriately, while providing tentative guidance to management. The adaptive management paradigm can be viewed as the definitive context for habitat-relationships modeling if all predictions are regarded as tentative, and subject to verification through monitoring, before management steps are taken.

As an example of adaptive management, Crouse et al. (1987) found that a stage-based population matrix model, based on monitoring of declining populations of loggerhead sea turtle (Caretta caretta) predicted higher population growth rate when survivorship of large juveniles was increased, but a continuing negative rate of growth when fecundity or survivorship at the egg and hatchling stages was increased. The results for the early life stages agreed with empirical data showing that several decades of nest protection had not produced positive population growth rates. This indicated that the crucial life stage for population growth was large juveniles, many of which die in the nets of shrimp trawlers. The study resulted in a recommendation to modify shrimp nets to prevent large juvenile turtle capture (Krebs 1994).

Limitations
An adaptive stance towards habitat perturbation is not necessarily a program of conservation and recovery as is mandated by law, but should be implemented within the context of research and monitoring as a way of using results tentatively.

Strengths
The adaptive paradigm provides a guide for proceeding carefully regarding habitat and species, but without waiting for absolute answers. It highlights the hypothetical and tentative nature of models by recognizing that management must respond and adapt as monitoring field data becomes available.

Applications to Plant TES
Our emphasis throughout this report on verification of model predictions, through on-site monitoring of populations, presumes an adaptive approach to plant TES management. All management actions affecting TES, especially those precipitated by the predictions of models, should be subject to change as their actual effects on populations are revealed by detailed monitoring.

For example, the threatened orchid Spiranthes diluvialis was initially managed by restriction of activities, including cattle grazing, on its riparian habitat in Colorado. Monitoring, however, revealed population declines following the construction of exclosures that had been intended to protect populations. It was ultimately determined that the species was dependent on habitat conditions maintained by grazing. This resulted in a recommendation to continue cattle grazing as part of management for the species (Wayne Leininger, Department of Rangeland Ecosystem Science, Colorado State University, personal communication).

5.3.3 Decision-Support Models

Definition
Decision-support (DS) models provide a framework for weighing and prioritizing resource management decisions, plans, and goals. According to Maguire (1985), decision-support models provide a three-tiered framework for decision analysis: 1) integration of scientific conclusions with considerations of political and social values; 2) evaluation of the effects of uncertainty, subjective information, and values on management decisions; and 3) facilitation of communication between resource managers and public interest groups. DS models are also generally helpful for documenting and organizing information on specific resource management plans and procedures (Morrison et al. 1992).

Historical Uses
Decision-support models first became popular in the 1960s and 1970s. These models included conceptualizations of game theory, goal programming, control theory, and spatial analysis (Morrison et al. 1992, Salwasser and Tappeiner 1981). These concepts have now evolved into more complex models of integrated resource management which incorporate theory, objective data, and subjective judgment into a straightforward and cohesive management evaluation system.

The NFMA of 1976 called for an ecosystem approach to resource management with consideration given to the multiple-uses required of the land and wildlife. Under these guidelines, coordination of political mandates and field application thus left land managers with a complex list of concepts, philosophies, and guidelines, but no standardized and validated procedures. This multiple-use philosophy was at the heart of the resource integration concerns that led to development of DS Models. Thus, the literature of the 1960's introduced concepts such as indicator species, analysis of species-habitat relationships, and the scheduling of practices to accommodate multiple objectives (Salwasser and Tappeiner 1981).

Salwassser and Tappeiner (1981) exemplify these concerns for integrated resource management in their decision support model combining wildlife-habitat relationships with multiple resource forest management objectives. Their model requires, for example, input information on resource goals, habitat characteristics, activity scheduling, and monitoring.

Maguire (1985) utilized a model of integrated decision-support to analyze the management of endangered populations. The use of a model provides the basis for assessing tradeoffs and weighing alternative actions, and demonstrates the application of formal methods of decision-making under uncertainty. The two major components of this model include: 1) the development of probabilistic models relating the outcomes of various actions to random ecological events, and 2) an assessment of the value structures underlying preferences for different outcomes given one or more criteria. In this way, Maguire (1985) shows how decision-making under uncertainty can go beyond the subjective or intuitive decisions of select resource managers, and instead can be modeled to integrate ecological theory, objective data, subjective judgments, and financial concerns.

Limitations
One significant limitation of DS models is that the model will be ineffective unless the resource manager and planners involved, through listing of prioritized objective and concerns, provide quality implementation at the field level. Thus, detailed planning is necessary (Maguire 1985).

Another limitation of DS models is that the integration of political, ethical, economic, social and environmental concerns is still an analysis and prioritization. Although these models may provide a framework for evaluating resource plans and goals, they do not provide an inference control structure or "rule network" similar to the organization of expert systems models (see Expert Systems Models).

Strengths
Most people do not make reasonable or consistent judgments when confronted with uncertain events. Random events such as fires or storms can be identified and given appropriate probabilities in a DS model (Maguire 1985). This makes it easier for the decision-maker to evaluate the information and assumptions made concerning a certain action, and decide upon the appropriate management strategy. Parties disputing the case also are provided information they need, if all the information is prioritized and presented in a DS model. Thus, in the contentious world of resource management, where insufficient information and information overload go hand in hand, a model which incorporates uncertainty, subjective information, and objective data into a formalized protocol for decision-making is a potentially useful tool. For this reason, one of the greatest strengths of DS models is that they force attention to the fact that (from a management point of view) information is only important when it alters a decision (Maguire 1985).

Applications to Plant TES
This kind of model may prove to be useful for evaluating the effects of different management decisions on plant TES after a basic system of habitat characterization and monitoring has already been implemented. In addition, decision-support models could serve a useful role in mitigating and clarifying the well-known debate surrounding the management of endangered species.

5.3.4 Expert Systems Models

Definition
An expert system is a computer program that mimics a human expert in order to solve problems in classification, evaluation, monitoring, and prediction. A wildlife-habitat expert system may use, for example, probabilistic methods in computer programming and computation to predict the response of different species to changing environmental conditions. These models can be used as screening tools, to check for environmental problems associated with a proposed activity, as devices for monitoring habitats and activities over time, and for decision-making purposes (Loehle and Osteen 1990, Marcot et al. 1986, Morrison et al. 1992).

Historical Uses
Predicting the response of plant and animal species to changes in habitat conditions is the objective of many land-use and general management schemes. Systems based on indices such as species-matrix models and HSI models, have been used for cataloguing, indexing, and data retrieval of information on various natural systems. Such models are still currently in use by the USDAFS and the USFWS (Marcot et al. 1986). Expert systems, however, may prove to be the next generation in predictive computer modeling, using computers simulating human expertise to integrate information from field studies, scientific literature, and expert opinion.

Expert systems have already been applied to a range of uses, including fire management (Lambert and Wood 1989), remote sensing of vegetation (Estes, Sailer, and Tinney 1986), and environmental impact assessment (Loehle and Osteen 1990). Other applications to the management of big game habitat, road planning, entomology, and a number of other fields have also been documented (Lambert and Wood 1989, Morrison et al. 1992). Lambert and Wood (1989) provide a survey of expert systems currently being developed or that are available for use. Their survey includes a list of expert systems both for agricultural and natural resource management. Examples include: PMAS expert systems - currently in development to assist with the land management of a major Australian Army base; and XCT-1 - currently in use to estimate the degree of cross country trafficability for a variety of Australian Army vehicles.

One of the most rapidly expanding uses of expert systems technology is in the field of geographic information systems (GIS) and remote sensing. GIS systems assemble and analyze diverse data pertaining to select geographic areas, with spatial location of the data serving as the basis for the information system. GIS can manipulate, store, and retrieve numerous layers of data specific to the species or area of concern. Use of expert systems in conjunction with GIS technology will thus enhance the interface between GIS digital databases and the user, helping to extract pertinent information from remotely sensed data, and expediting decision-making and interpretation.

An example is ASPENEX, an expert system/GIS tool that is used to determine the ecological conditions of aspen stands (Morrison et al. 1992). Site conditions such a stand size, soil type and water drainage are classified according to a predetermined set of "if-then" rules. In this way, development of pertinent questions and basic reasoning is facilitated through the use of these built-in rules, allowing the resource manager to analyze more information with greater efficiency and clarity. Then, ASPENEX / GIS expert systems technology identifies mature stands of aspen that are located on well-drained sites close to accessible roads for potential logging purposes (Morrison et al. 1992).
In general, the field of expert systems technology is expanding rapidly. Areas of future development include landscape design, mapping, analysis of terrain features, and general evaluation of habitat conditions.

Limitations
One of the major limitations of these systems is that there can be typically more than one solution to any map design problem or wildlife-habitat management issue. For example, if attempting to design landscapes to maintain viable wildlife populations, a number of different designs or habitat patch patterns may be appropriate (Morrison et al. 1992). Designing a set of specific "if then" rules and built-in standards to solve a problem is difficult. Hundreds of these rules are compiled into what are called "rule networks" and these networks are ultimately dependent upon the knowledge base (Marcot et al. 1986).

Strengths
Expert systems models appear to have enormous potential for wildlife-habitat management in the future. These information systems can be very useful for helping managers present large quantities of information in an efficient and organized manner. The simultaneous integration of a wide range of information including field studies, literature, and expert opinion can greatly increase a manager's expertise in habitat evaluation. Future development of expert systems in conjunction with GIS technology also shows great potential for aiding our understanding of land use patterns, interpretation of data collected from remote sensing, landscape design, and habitat evaluation.

Applications for Plant TES
Expert systems may have application to plant TES. Given the necessary information base concerning the location of plant TES, their biological needs, and general ecology, an expert system appears to be a potential way to help evaluate, monitor and classify the information at hand. Applications to wildlife management are already currently in use (Lambert and Wood 1989, Marcot et al. 1986, Morrison et al. 1992).

However, habitat characterization of plants TES may be limited by current lack of site and species-specific information. Although expert systems are still in a developmental stage in a number of different areas, given a sufficient combination of field data, expert opinion, and literature review, the use of such a system may be very useful in characterizing the habitat of plant TES.

[Return to Table of Contents]

Section VI: Summary, Conclusions, and Future Directions

6.1 Habitat Characterization Models for Plants

Few examples exist of single-species, habitat-based predictive modeling for plant TES. Bowles et al. (1993) used an ordination technique to model potential habitat for a threatened plant (see Section 5.1.2, Statistical Models). A GIS-based model of potential habitat for three species, one a rare plant (Allotropa virgata, candlestick), is being developed at the University of Idaho (Carl Chang, Department of Geography, University of Idaho, personal communication). However, Chang does not expect the model to be suitable for management of the plant species, due to the large scale of the model. Another example of a GIS model of sensitive plant habitat was initiated for impact avoidance by Southern California Edison Company (Myatt 1986). Campbell (1987) estimated the distribution of Douglas fir (Pseudotsuga menziesii) in Oregon using a habitat-based GIS model. In the latter cases, GIS models were designed to characterize habitat for inventory purposes, and they were not designed for plant TES management applications.

Many studies have modeled the distribution of vegetation in relation to environmental gradients (ordination) (Gauch 1982, Austin 1985) while other approaches have classified communities on the basis of species composition. Both approaches are discussed in our sections on ordination and statistical techniques. In general these "phytosociological" approaches work within a vegetation or community concept that addresses groupings of species. While they have been used to develop ecophysiological investigations of individual species in relation to their environments, their primary applications have been to community-level work. They are essentially "multispecies models". Management applications of these techniques have also been at the community level (e.g., the Habitat Type and Community Type classification systems of USFS: see Padgett et al. 1989, Youngblood and Mauk 1985). However, as discussed in our section on statistical models, ordination can explore the composition of the plant community with which a particular species is associated, as well as its range of environmental tolerance.

Despite these complications, several sources suggest to us that habitat-relationships modeling may be well-suited to plants in general and to rare species. First, modeling of the habitat relationships of habitat-specialist species of both plants and animals may tend to be more accurate than for species with general habitat requirements. Rare and declining species, we note, are often habitat specialists (Schemske et al. 1994). An inverse relationship was noted by Flather and King (1992) between habitat specialization and the error rates of a discriminant function analysis-based habitat-relationships model for three wildlife species, one the endangered red-cockaded woodpecker. Wiens and Rotenberry (1981) found that correlations between shrub-steppe bird distribution and habitat variables yielded the clearest patterns among habitat specialist species. Van Horne (1983) has suggested that the "decoupling" of habitat attributes from population parameters should be more pronounced for habitat generalists than for specialists. That is, models may be more predictive where the habitat alternatives of species are highly limited by narrow habitat requirements. Therefore, plant TES may in fact be more efficiently and accurately modeled than other plants and other taxa.

Second, we speculate that difficulties associated with the use of population density as an indicator of habitat quality for animals (Van Horne 1983) may be less restrictive for plants and for rare species of both plants and animals. If stressed, animal populations may irrupt periodically into unsuitable habitat where reproduction is reduced or nonexistent, or where the population is not viable over time for other reasons (Van Horne 1983, Maurer 1986). Measurement of habitat variables in such an area, and correlating them with density of animals for use in a model will be misleading and will lead to poor predictions about habitat quality for species.

The use of population density as an indicator of habitat quality should be less problematic for plant modeling, because plants are sessile. Mature populations of plant species would seem to clearly indicate suitable habitat. Van Horne (1983) has suggested that density may be a better indicator of habitat quality for rare animals than for nonrare animals because rare animals tend to have specialized habitat requirements and limited ranges. The same case may also apply to plants. While both of these points may be somewhat speculative, we believe that field work will support the use of population density of plant TES to indicate suitable habitat for a large number of TES plants.

6.2 Conclusions

The variety of habitat-based and other model types described in this report implies fundamental differences in terms of applications of models. While individual model types may have some clear applications to particular kinds of species (for example, PATREC is well-suited to Bighorn sheep studies because of the ease of collecting animal density data in their open habitat), or may have limitations peculiar to individual model construction, all predictive habitat-relationships models proceed from correlations found or assumed to exist between habitat attributes and the attributes of populations. Therefore, the predictivity of such models may be limited in part by the extent to which these relationships are accurate and hold true when extrapolated to other locations.
As noted in the introduction, the research conducted for an animal TES typically includes significant amounts of attention to areas other than habitat relationships. This implies that species cannot be managed adequately based on habitat relationships alone, however predictive models might be useful.

We suggest that applications of modeling for plant TES fall primarily into the areas of preliminary and field surveys, habitat monitoring, and management, i.e., identification and monitoring of potential habitat for the purpose of indicating potential range, potential introduction sites, and potential areas for protection. For example, various predictive methods (e.g. statistical models, HSI models) were given as examples of potential models to be used to facilitate location of plant TES populations. Predictive or extrapolative models can be used to help identify possible locations of extant populations of plant TES, either for verification by field searches, or, where field searches are not practicable, for tentative identification and protection of habitat. These should be followed by field surveys to verify predictions.

However, in addition to the potential uses outlined above for survey, habitat monitoring, and management, we point out that the long-range value of modeling is exploration of hypotheses: models of TES habitat relationships will continue to add to general knowledge about the nature of rarity and the habitat relationships of rare species.

As mentioned earlier in this report, the applicability of habitat-relationships models to plant TES is largely unknown. Our conclusions are therefore based on information gleaned from the literature of applications to animals, and from established techniques used in plant conservation. We suggest that development and testing of predictive habitat models may represent a productive area for research on the application of these models as an integral part of adaptive management for plant TES and their habitats.

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Back to Part II, Sections I-IV
References Cited in Part II

Part I: Protocol for Inventory and Monitoring
of Threatened and Endangered Species
Sections I-III
Sections IV & V

Glossary of Acronyms

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