Generalized Procedures for Testing Hypotheses about Survival or Recovery Rates

Abstract

Comparisons of survival or recovery rates from different time periods or geographic regions may be difficult to accomplish using the Z-tests suggested by Brownie et al. (1985). We propose a general Chisquare statistic that addresses an unambiguous null hypothesis of homogeneity among several survival or recovery rates. With this statistic, specific hypotheses of differences in rates can be simultaneously tested using contrasts. If necessary, a posteriori multiple comparisons can also be conducted that incorporate an adjustment for Type I error. J. WILDL. MANAGE. 53(1):137-142 Recent advances in analytical techniques (Seber 1965, Brownie et al. 1985) have enabled biologists to estimate survival and recovery rates and the standard errors of these estimates for animal populations. As band-recovery (or markrecapture) data accumulate for many populations, increasing interest has focused on temporal and geographic variation in survival and recovery rates. We briefly review methods of testing hypotheses about homogeneity in these rates, and describe a Chi-square test that can be of general use in their analyses. This statistical method supplements a full banding analysis, and can be of value when the hypotheses of interest cannot be tested using the models available, when survival or recovery rate estimates (and associat d variances and covariances) are already av ilable from previous analyses, or when the band recovery analysis procedures are unavailable or inconvenient to use. We discuss applications to multiple comparisons of survival rates derived from band-recovery models (Brownie et al. 1985). However, the methods are applicable to any rate estimates that have associated variances and covariances. We thank R. E. Trost for suggesting that we prepare this manuscript. J. D. Nichols, G. W. Pendleton, E. A. Rexstad, R. L. Kasul, and R. E. Trost critically reviewed the manuscript. METHODS OF COMPARING SURVIVAL RATE ESTIMATES Several methods have been proposed as statistical tests for homogeneity of survival or recovery rates. These methods can be divided into those using original data, and those using rate estimates derived from data, with associated I Present address: U.S. Fish and Wildlife Service, Patuxent Wildlife Research Center, Laurel, MD 20708. This content downloaded from 207.46.13.101 on Sat, 08 Oct 2016 05:29:35 UTC All use subject to http://about.jstor.org/terms 138 SURVIVAL RATE COMPARISONS * Sauer and Williams J. Wildl. Manage. 53(1):1989 variances and covariances. Methods using banding and recovery data have been described by Brownie et al. (1985), who developed a series of band recovery models that incorporate different assumptions about timeand age-specificity of survival and recovery rates. These models have been generalized to include a greater variety of patterns of variation in recovery and survival rates by White (1983) and Conroy and Williams (1984). As part of the model selection procedure, these authors provided likelihood-ratio tests to determine which model best fits the data. However, their procedures were limited in the nature of the hypotheses that are testable. Once the proper band-recovery model from Brownie et al. (1985) is selected, it often is useful to examine differences in survival rates for subsets of the time periods used in the original data. For example, Rogers et al. (1979) assessed the effect of hunting regulations on mallard (Anas platyrhynchos) populations by identifying years in which regulations were liberal or restrictive. Using survival rate estimates from Brownie et al. (1985), Rogers et al. (1979) tested for differences between mean survival rates in the 2 sets of years. In some instances it is practical to test such hypotheses by incorporating them directly in the band recovery procedures (White 1983, Conroy and Williams 1984). However, if the original data are not available, if the data fail to meet the requirements of the procedures (due to small sample sizes that require the merging of many cells), or if the hypotheses themselves are nonstandard (e.g., comparisons are desired for survival rates across several populations), then another approach is necessary. The use of analysis of variance (ANOVA) (Anderson 1975) is an inefficient alternative, because the variances of the survival or recovery rates are ignored. An alternative method circumventing these problems would be of great value. Brownie et al. (1985:180-182) suggested a Z-statistic as a general method of comparing groups of survival rates. As Brownie et al. (1985) point out, this is actually a test of the null hypothesis that some contrast of the survival rates (s) is equal to zero, or: Ho: cs, + c2s, + ... + CNSN = 0, (1) where each c is a constant with the constraint