Markov chain Monte Carlo methods for assigning larvae to natal sites using natural geochemical tags.

Geochemical signatures deposited in otoliths are a potentially powerful means of identifying the origin and dispersal history of fish. However, current analytical methods for assigning natal origins of fish in mixed-stock analyses require knowledge of the number of potential sources and their characteristic geochemical signatures. Such baseline data are difficult or impossible to obtain for many species. A new approach to this problem can be found in iterative Markov Chain Monte Carlo (MCMC) algorithms that simultaneously estimate population parameters and assign individuals to groups. MCMC procedures only require an estimate of the number of source populations, and post hoc model selection based on the deviance information criterion can be used to infer the correct number of chemically distinct sources. We describe the basics of the MCMC approach and outline the specific decisions required when implementing the technique with otolith geochemical data. We also illustrate the use of the MCMC approach on simulated data and empirical geochemical signatures in otoliths from young-of-the-year and adult weakfish, Cynoscion regalis, from the U.S. Atlantic coast. While we describe how investigators can use MCMC to complement existing analytical tools for use with otolith geochemical data, the MCMC approach is suitable for any mixed-stock problem with a continuous, multivariate data.