Band Reporting Rate
Otis and White (2002) provide further discussion on the relationship between the probability that a hunter reports a band and the parameter r of the dead recoveries model. In his original development, Seber (1970) did not formulate his model specifically for game birds, and thus not all recoveries were derived from banded animals killed during the hunting season. Therefore, recovery rate as he defined it was affected by natural as well as harvest mortality rate. Brownie et al. (1978) also used the term recovery rate, and defined it (f) as the probability that a bird alive at the beginning of the hunting season is shot, and its band is reported, i.e. f =(1 - S)r. Thus, as White and Burnham (1999) point out, this parameter depends on survival as well as reporting rate (lambda equals the probability that the band from a harvested bird is reported) processes. This parameterization has been adopted for use in the management of game birds, because the vast majority of bands do accrue during the hunting season, and because Brownie's recovery rate is a logical index to harvest rate. However, this model structure does not lend itself to modelling of survival with covariates, as it becomes unclear how to model the survival portion of the f parameter with the same relationship as is used in the S parameter. This is the reason Otis and White (2002) chose to use Seber's model, i.e. r is defined conditionally on the animal dying, and thus is independent of the survival process. It should be clarified, however, that lambda is not equal to r. Comparison of the two models reveals that, when only recoveries from hunters are used in the analysis, lambda/r = 1 + theta/h, where h equals harvest rate and theta equals non-hunting mortality rate. Thus, the relative difference in these parameters depends on the ratio of annual non-hunting versus hunting mortality.