Generalized Capture-Recapture and Band-Recovery Analysis Theory

Contents – Index

Generalized Capture-Recapture and Band-Recovery Analysis Theory

Sampling and analysis theory for biological populations has also seen an explosion in the literature in recent years (Fig.  1).  Fig.  1 shows the rapid increase in the amount of literature on theory and application, but also indicates a slowing in the rate of increase. We attribute this to the fact that the questions remaining are increasingly difficult to address.  That is, the easier problems have been solved and only the harder ones remain.  The solution to these more difficult problems requires increased knowledge and sophistication in mathematical statistics and computer science and thus, fewer people can contribute.  In general, additional advances and extensions are possible due to new findings in the science of statistics and increased computer capabilities.
The literature on estimation methods for biological populations can be partitioned into two groups; the first relates to unmarked populations and makes simple (often unrealistic) assumptions and results in estimates with high precision but often very large bias, while the second assumes that a sample of animals are marked and allows more realistic assumptions, considers several candidate models and results in estimates of population parameters with less precision, but often negligible bias.  Unless animals are marked, very strong assumptions must be made, or parameters of interest cannot be identified.  This leads to the frequent requirement that animals are marked, at least with a batch mark; however, unique, individual marks are necessary for most advanced analyses.  The use of marked animal populations is critical in many applications (including risk assessment, Anderson et al. unpubl. ms.), but then one must address the proper simultaneous estimation of survival and recapture probabilities.  The presence of the recapture probabilities (sampling probabilities) makes modeling and estimation difficult for capture data.  
Keystone papers for open population capture-recapture models are Cormack (1964), Jolly (1965) and Seber (1965).  The fundamental papers for band recovery models are Seber (1970), Robson and Youngs (1971), and Brownie et al. (1978).  A very extensive literature provides many important extensions to these early cornerstones. Books by Morgan and North (1980), North (1987), Anonymous (1990), Blondel et al. (1990), Lebreton et al. (1990), Perrins et al. (1991), and Lebreton and North (1993) provide strong evidence of the explosion in the theory and application on capture-recapture and band recovery methods just for avian species!  Other taxonomic groups are discussed in the large book by McCullough and Barrett (1992).
The Pollock et al. (1990) monograph provides a summary of the Jolly-Seber type models and illustrates their application.  Computer programs JOLLY and JOLLYAGE accompany this monograph and allow careful testing and the computation of the maximum likelihood estimates (MLEs).  Burnham et al. (1987) provides a comprehensive theory for manipulative experiments with marked animal populations.  This book provides documentation for program RELEASE, a sophisticated computational algorithm for analysis of capture-recapture experimentation, including an efficient goodness of fit testing routine.  The focus of the book by Burnham et al. (1987) is on fish populations, however, the application is more general (examples are given of applications to pintail ducks, desert tortoise, lazuli buntings, and European starlings).
Lebreton et al. (1992) provides many extensions for open population capture-recapture modeling, including quasi-likelihood theory, modeling survival or recapture probabilities as functions of external covariates, and Akaike-type model selection strategies.  Program SURGE (Pradel 1989) provides unparalleled flexibility in modeling and estimation in Cormack-Jolly-Seber type models.  A prototype, interactive interface, SURGEIN, allows SURGEto be easily used, and to incorporate some quasi-likelihood extensions.
Programs ESTIMATE, BROWNIE and MULT (Brownie et al. 1985) have been useful for the analysis of band recovery data and have seen extensive use.  At present, these algorithms lack the flexibility now available in the routines for analysis of open population capture-recapture models.  In addition, they do not allow the computation of efficient goodness of fit tests, deviance, relative deviance, the value of the log-likelihood function, and other important quantities.
Burnham (1993) provided a unified theory for the joint analysis of capture-recapture and band recovery data. This theory has obvious extensions for the analysis of multiple data sets, but no software exists for this unified analysis theory.  Program SURVIV (White 1983) has seen extensive use in the analysis of both capture-recapture and band recovery data.  However, SURVIV is a very general procedure, and while useful as a research tool to investigate parameter estimation problems of complex models, the program is clumsy to use for parameter estimation with a series of real or routine data sets.