Contents - Index

Closed Captures Models with Mis-identification


The closed captures models originally consisted of 6 models.  However, the need to be able to estimate the probability that animals were mis-identified due to poor quality or low quantity of DNA prompted the additon of a mis-identification parameter to the existing 6 models.  The parameter alpha is defined as the probability that an animal was correctly identifed.  Thus, the mis-identification models with alpha fixed to 1 result in the same model as the equivalent model without the alpha parameter.
The 6 basic closed captures models in MARK have a parameter, alpha, is added to the likelihood to estimate the probability of mis-identification.  These models were added to accommodate the the mis-identification of animals that takes place with DNA analyses when the amount and quality of DNA available is low and of poor quality.  The likelihoods were developed by Lukacs and Burnham (2005).  As a result, there are a total of 12 closed captures models in MARK.  The definition of alpha is the probability of a correct classification, so that fixing alpha = 1 makes these 6 additional models equivalent to the first 6 models described in the closed captures help topic.

The effect of mis-identification is to bias the estimates of population size high caused by 2 factors.  First, the number of unique genotypes found [M(t+1) above] is biased high because some of the unique genotypes found are actually errors in that the identified genotype was incorrect.  Second, this increase in the numbers of animals supposedly encountered causes the estimated probability of detection to be smaller than it should be.  The effect of these two factors is to cause the estimate of N to be too high.

As described in the closed captures help topic, both the simple and complex heterogeneity models are available for the mis-identification closed capture models.  However, incorporation of both mis-identificaiton and heterogeneity typically leads to inconclusive results, in that mis-identification is somewhat (almost totally) confounded with heterogeneity.  Intuitively, mis-identification is detected by too many animals only appearing once in the encounter histories.  Thus, a large amount of individual heterogeneity may appear as mis-identification, and vice versa, mis-identification may appear as individual heterogeneity.

None of the mis-identification models include N in the likelihood, so that this parameter appears as f0 in the PIMs.  Rather, the estimates of population size (N) are generated as derived parameters.  To allow model averaging of population estimates from any of the 12 closed captures models, all produce estimates of N as derived parameters, even when N appears as a real parameter.  The Huggins models and the models with N (or more correctly f0) in the likelihood do not produce comparable likelihoods, so model averaging across these different data types does not make sense.  However, model averaging the derived parameter N across models with and without mis-identification is reasonable.

Confidence intervals (95%) for N are computed with a lognormal distribution as
Lower = N/C
Upper = N*C
C = exp(1.96 sqrt(log(1 + CV(N-hat))^2))
This lognormal confidence interval is explained on page 212 of Burnham et al. (1987).