Evaluation of survival and cause-specific mortality rates using telemetry data

Methods are presented for estimating survival and cause-specific mortality rates from radiomarked animals. Time is partitioned into intervals during which the daily rates are assumed to be constant. The rates are estimated from the number of transmitter-days, the number of mortalities due to particular causes, and the number of days in the time intervals. Potential biases arising from combining data from several individuals marked at different times within an interval or from combining rates from different intervals are identified. Variances and confidence intervals for the estimators are presented. Hypothesis testing and sample-size considerations are also illustrated. Simulation showed that the influence of errors in date of death was small, but misdiagnosis of fate had serious consequences. A microcomputer program is available for performing the analyses. J. WILDL. MANAGE. 49(3):668-674 Important mortality agents for wildlife species are legal hunting, wounding loss, poaching, predation, weather, accidents, and disease. Most mark-and-recapture techniques allow investigators to, at most, partition mortality into hunting and "other" sources (Anderson 1975). Radiotelemetry techniques should enable the importance of cause-specific mortality factors to be determined because tagged animals can be located soon after death and the agent of mortality ascertained, regardless of the cause of death. In most radiotelemetry studies, however, the importance of a mortality factor is given as the number of deaths caused by the agent expressed as a percent (Dumke and Pils 1973, Trent and Rongstad 1974, Brand et al. 1975, Trainer et al. 1981). If a sample of animals is marked at the start of a period of interest, calculation of survival and cause-specific mortality rates as simple percentages is appropriate (Hessler et al. 1970). But more often, animals are radiomarked at more than one time, even during different periods within a year for which survival rates differ, and this may lead to two serious biases. First, when some animals are marked midway through a period, animals that died early are not available for sampling and this biases the observed survival rate upwards. And second, if daily survival rates are not constant between intervals, intervals within the period that have the largest sample sizes are most influential in determining the estimates. Methods that avoid these biases with regard to survival rates were first adapted by wildlife biologists to estimate nesting success (Mayfield 1961, 1975; Miller and Johnson 1978; Johnson 1979; Bart and Robson 1982) and have been This content downloaded from 157.55. 39.35 on Tue, 30 Aug 2016 05:07:11 UTC All use subject to http://about.jstor. org/terms J. Wildl. Manage. 49(3):1985 SURVIVAL-MORTALITY RATES * Heisey and Fuller 669 Table 1. Definition of variables used in models to determine survival rates and cause-specific mortality rates from telemetry data. i = Interval number (i = 1, 2, . , I) j = Cause of mortality (j = 1, 2, . , J) xi = Total number of transmitter-days during interval i yi = Total number of mortalities occurring during interval i yij = Total number of mortalities occurring during interval i due to cause j Li = Total number of days in interval i si = Daily survival rate during interval i Si = Survival rate for entire interval i S* = Survival rate for all I intervals mij = Daily mortality rate in interval i due to source j Mij = Interval mortality rate for entire interval i due to source j Mj* = Mortality rate for all I intervals due to source j applied to survival rates in wildlife radiotelemetry studies (Gilmer et al. 1974, Trent and Rongstad 1974, Brand et al. 1975, Trainer et al. 1981). Agent-specific mortality rates in telemetry studies have been evaluated only as simple percentages that are subject to the aforementioned biases. In this paper, we generalize the basic approach of Mayfield (1961, 1975) and Trent and Rongstad (1974) to determine unbiased estimates of cause-specific mortality rates. Standard statistical methodology for competing risk analysis is used (Chiang 1968, Kalbfleisch and Prentice 1980). Radiotelemetry applications are emphasized, although the techniques are applicable to any situation where the subjects can be relocated at will and the cause of death identified. A microcomputer program called MICROMORT is available which performs most of the described calculations for moderate size problems. Versions are available for the IBM PC. A diskette containing the program and documentation can be requested from T. K. Fuller. We are grateful to J. R. Cary, D. H. Johnson, and G. C. White for their constructive comments and encouragement. E. K. Fritzell, J. M. Hoenig, D. W. Kuehn, and R. E. Lake also made helpful suggestions. Reprint requests should be made to Todd K. Fuller.