Markov Chain Monte Carlo Methods for Assigning Larvae to Natal Sites Using Natural Geochemical Tags

Abstract

Abstract. 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.

Connectivity as a Management Tool for Coastal Ecosystems in Changing Oceans

“…However, this method necessitates identifying the elemental profiles from all potential sources (Berumen et al, 2010), and moreover, it can be variable in time (seasonally, yearly) (Cook, 2011;Fodrie et al, 2011;Walther & Thorrold, 2009). Even though some statistical methods can be used to increase the precision of assignments (White et al, 2008), some limitations of this method appear for marine organisms because chemical distinctions among origin areas are sometimes too small to enable accurate assignment of individuals (Berumen et al, 2010), and the processes of integration of these trace elements in the hard parts of these organisms is not fully understood Warner et al, 2005). The applicability of these techniques over multiple years has been shown recently and has provided new insights on the variability in connectivity.…”

Spatial pattern of natal signatures in the otoliths of juvenile kelp rockfish along the Californian coast

“…Recruit 'natal signature types' for each year were determined using an MCMC classification algorithm (Munch & Clarke 2008, White et al 2008. Given a particular number of natal signature types, this Bayesian analytical technique simultaneously estimates the parameters corresponding to each type (i.e.…”

“…means and covariances of natal signatures) and assigns individuals in the samples to each type. When coupled with a model selection procedure, this approach can also estimate the number of natal signature types post hoc (White et al 2008). Thus with limited prior information, the technique estimates the number of types and assigns individuals to them.…”

“…Thus with limited prior information, the technique estimates the number of types and assigns individuals to them. This technique generally matches or exceeds alternative approaches such as hierarchical or k-means clustering because it allows greater flexibility in the covariance structure of the data (White et al 2008).…”

“…We implemented the MCMC algorithm in Matlab 7.10 (Mathworks) following the procedures outlined by White et al (2008). Briefly, elemental data were log transformed, and the probability of membership in a cluster was assumed to follow a multivariate normal distribution.…”