Optimal allocation of sample sizes between regular banding and radio-tagging for estimating annual survival and emigration rates

Many authors have shown that a combined analysis of data from two or more types of recapture survey brings advantages, such as the ability to provide more information about parameters of interest. For example, a combined analysis of annual resighting and monthly radio-telemetry data allows separate estimates of true survival and emigration rates, whereas only apparent survival can be estimated from the resighting data alone. For studies involving more than one type of survey, biologists should consider how to allocate the total budget to the surveys related to the different types of marks so that they will gain optimal information from the surveys. For example, since radio tags and subsequent monitoring are very costly, while leg bands are cheap, the biologists should try to balance costs with information obtained in deciding how many animals should receive radios. Given a total budget and specific costs, it is possible to determine the allocation of sample sizes to different types of marks in order to minimize the variance of parameters of interest, such as annual survival and emigration rates. In this paper, we propose a cost function for a study where all birds receive leg bands and a subset receives radio tags and all new releases occur at the start of the study. Using this cost function, we obtain the allocation of sample sizes to the two survey types that minimizes the standard error of survival rate estimates or, alternatively, the standard error of emigration rates. Given the proposed costs, we show that for high resighting probability, e.g. 0.6, tagging roughly 10-40% of birds with radios will give survival estimates with standard errors within the minimum range. Lower resighting rates will require a higher percentage of radioed birds. In addition, the proposed costs require tagging the maximum possible percentage of radioed birds to minimize the standard error of emigration estimates.