Additional comments on the assumption of homogenous survival rates in modern bird banding estimation models

We examined the problem of heterogeneous survival and recovery rates in bird banding estimation models. We suggest that positively correlated subgroup survival and recovery probabilities may result from winter banding operations and that this situation will produce positively biased survival rate estimates. The magnitude of the survival estimate bias depends on the proportion of the population in each subgroup. Power of the suggested goodness-of-fit test to reject the inappropriate model for heterogeneous data sets was low for all situations examined and was poorest for positively related subgroup survival and recovery rates. Despite the magnitude of some of the biases reported and the relative inability to detect heterogeneity, we suggest that levels of heterogeneity normally encountered in real data sets will produce relatively small biases of average survival rates. J. WILDL. MANAGE. 46(4):953-962 Pollock and Raveling (1982) recently emphasized the importance of considering the assumptions underlying modern bird banding estimation models (e.g., Seber 1970, Robson and Youngs 1971, Brownie and Robson 1976, Brownie et al. 1978), and devoted special attention to the assumption that all banded individuals of an identifiable demographic group (e.g., an age-sex class) have identical survival and recovery probabilities for any given year. They pointed out that in a large number of instances this assumption is biologically unrealistic, and they approximated the bias of recovery and survival rate estimators that could be expected to result from heterogeneous survival and recovery rates. Here, we present additional results that are relevant to the problem of heterogeneous survival and recovery rates. Pollock and Raveling (1982) presented results on bias for cases in which (1) there is a negative relationship between survival and recovery probabilities of an individual and (2) individual survival probabilities differ but recovery probabilities are similar. They did not consider the situation in which survival and recovery probabilities are positively correlated. We expect this situation to occur frequently when the banding and recovery periods are separated by time spans that are not negligible with respect to mortality. Let pi be the conditional probability that a bird is recovered in the hunting season of year i given that it is alive at the beginning of season i. Let Sbh,i be the probability that a bird alive at the midpoint of the banding period in year i survives until the beginning of the hunting season in year i. Let Shb,i be the analogous probability of surviving the interval between the beginning of the hunting season of year i and the banding period of year i + 1. The annual survival probability between banding periods, Si, is then given by the product, Sbh,iShb,i. If the banding period immediately precedes the hunting season (i.e., preseason banding), then Sbh,i 1.0. If the banding period is not preseason, then Sbh,i < 1.0, with smaller Sbh,i corresponding to longer intervals (and hence more mortality) between the banding period and the hunting season. The recovery probability of J. Wildl. Manage. 46(4):1982 953 This content downloaded from 157.55.39.176 on Sat, 09 Apr 2016 06:16:11 UTC All use subject to http://about.jstor.org/terms 954 HETEROGENEOUS SURVIVAL RATES AND BANDING MODELS* Nichols et al. the Brownie et al. (1978) models can be defined as fi = Sbh,iPi. In the case of preseason banding (Sbh,i ' 1.0), it seems reasonable to expect either no relationship or a negative relationship between subgroup S, and f , depending on whether or not there is a negative relationship between hunting mortality (which should be reflected in pi) and Shb,i and on whether or not this relationship is the basis for subgroup differences. When banding and recovery periods are separated by time spans that are not negligible with respect to mortality (i.e., when Sbh,i < 1.0), then positive, negative, or no relationship between subgroup Si andf, is possible. If the main difference between subgroups involves hunting mortality and Shb,i, then a negative relationship between fi and Si could easily result. If the subgroups differed primarily in Shb,J, but if this difference was not associated with differences in hunting mortality (or pi), then no relationship would be expected between subgroup Si and ft. However, if the principal difference between subgroups occurs in the Sbh,i, then we would expect a positive relationship between Si and fi. In postseason or winter banding operations, we suspect (see Discussion) that subgroup differences in Sbh,i will be common, and sufficiently important to produce such positive relationships between Si and f. Our objectives are to: (1) consider the magnitude and direction of bias resulting from positively correlated subgroup survival and recovery rates; (2) consider the importance of subgroup proportions in the population to the magnitude of bias, and (3) consider the power of standard goodness-of-fit tests to detect heterogeneity in survival and recovery probabilities. We thank R. Wilcox for typing the manuscript and D. R. Anderson, K. P. Burnham, P. H. Geissler, B. R. Noon, K. H. Pollock, and an anonymous referee for providing helpful comments on an earlier draft.