Assumptions of Modern Band-Recovery Models, with Emphasis on Heterogeneous Survival Rates

Abstract

The assumptions inherent in modern band-recovery models are reviewed with particular attention to homogeneity of survival and band-recovery rates for all individuals in the population. If this assumption fails, the following implications emerge: (1) the models only enable estimation of average annual survival and band-recovery rates; (2) estimators of these averages probably give underestimates; (3) the degree of underestimation in practical studies is difficult to assess, but may sometimes be important for survival estimates; (4) if sampling is nonrandom and heterogeneity of survival and recovery rates is present in the population, then any estimates could be misleading; and (5) if survival rates are homogeneous but recovery rates are heterogeneous (due perhaps to geographical variation in hunting pressure and reporting rates), then there is no bias in survival estimates. An example where data from neck-collared birds showed heterogeneity in segments of a Canada goose (Branta canadensis) population is discussed. We believe that the practical limitations of bird-banding studies deserve careful review by population biologists and managers. J. WILDL. MANAGE. 46(1):88-98 Band-recovery data have long been used to estimate mortality rates in exploited migratory bird populations. However, it is only in recent years that methods of analysis of banding data have been rigorously considered. By making certain assumptions, Seber (1970, 1971, 1972, 1973) formulated a rigorous statistical model that gave rise to explicit maximum-likelihood estimators of survivaland recovery-rate parameters. Extensions allowing for age dependence of survival and recovery rates were made by Johnson (1974), Brownie and Robson (1976), and Brownie et al. (1978), who, in a comprehensive monograph, detailed a variety of age-dependent models. Development of modern methods clearly identified the weaknesses of some of the older procedures such as the composite dynamic life table. Burnham and Anderson (1979) analyzed 45 substantial data sets from migratory waterfowl band recoveries and demonstrated that the 1 Present address: Department of Statistics, North Carolina State University, Box 5457, Raleigh, NC 27650. composite dynamic life table should no longer be used, as only 2 data sets (4%) fit the model at a = 0.05. Burnham and Anderson (1979) also found that modern methods are not necessarily always adequate for analyzing banding data, as 14 of 45 data sets (30%) did not fit. In this paper we further examine the assumptions of the modern methods. An important assumption of all recovery models is that all banded individuals of an identifiable class (e.g., by species, age, sex) in the sample have the same annual survival and recovery rates (Brownie et al. 1978:6). We consider what happens when this assumption fails, and the importance of random sampling in conjunction with homogeneity of survival and recovery rates. First, we consider a specific model (Model 1: Adults Only Banded) when the homogeneity assumption holds. We shall refer to this as the Homogeneous Population Model. This will be followed by the same model when the homogeneity assumption fails, the Heterogeneous Population Model. We discuss a populaJ. Wildl. Manage. 46(1):1982 88 HETEROGENEOUS SURVIVAL RATES Pollock and Raveling 89 tion of Canada geese for which segments with heterogeneous survival and recovery rates are known to exist from the use of individually identifiable neck-collared birds (Raveling 1978). Finally, we provide a general discussion of all the assumptions underlying modern band-recovery models, with an emphasis on the practical implications of assumption failure. We thank D. R. Anderson, D. W. Anderson, K. P. Bumham, D. S. Gilmer, D. H. Johnson, and R. M. McLandress for helpful comments on an earlier version of the manuscript. HOMOGENEOUS POPULATION MODEL Here we consider the situation where all birds are banded as adults and all birds have the same survival and recovery rates in a particular year (Model 1 of Brownie et al. 1978:15). For simplicity, we will also assume the number of years of recoveries is the same as the number of years of banding. The data matrix for observed recoveries is given in Table 1. Under this model, each row of recoveries follows a multinomial distribution, and the expected recoveries take the form given in Table 2. The maximum-likelihood estimators of the survivaland recovery-rate parameters are given by the following equations: