Modeling Spatial Covariance Using the Limiting Distribution of Spatio-Temporal Random Walks

ABSTRACT

We present an approach for modeling areal spatial covariance in observed genetic allele data by considering the stationary (limiting) distribution of a spatio-temporal Markov random walk model for gene flow. This stationary distribution corresponds to an intrinsic simultaneous autoregressive (SAR) model for spatial correlation, and provides a principled approach to specifying areal spatial models when a spatio-temporal generating process can be assumed. We apply the approach to a study of spatial genetic variation of trout in a stream network in Connecticut, USA.

KEYWORDS:

• Autoregressive models
• Diffusion
• SAR models
• Spatial autocorrelation

Acknowledgments

The author gratefully acknowledges conversations with John Fricks, whose suggestions were instrumental in the analysis of Section 3.1.