Estimating Spatial and Temporal Components of Variation for Fisheries Count Data Using Negative Binomial Mixed Models

Abstract

Partitioning total variability into its component temporal and spatial sources is a powerful way to better understand time series and elucidate trends. The data available for such analyses of fish and other populations are usually nonnegative integer counts of the number of organisms, often dominated by many low values with few observations of relatively high abundance. These characteristics are not well approximated by the Gaussian distribution. We present a detailed description of a negative binomial mixed-model framework that can be used to model count data and quantify temporal and spatial variability. We applied these models to data from four fishery-independent surveys of Walleyes Sander vitreus across the Great Lakes basin. Specifically, we fitted models to gill-net catches from Wisconsin waters of Lake Superior; Oneida Lake, New York; Saginaw Bay in Lake Huron, Michigan; and Ohio waters of Lake Erie. These long-term monitoring surveys varied in overall sampling intensity, the total catch of Walleyes, and the proportion of zero catches. Parameter estimation included the negative binomial scaling parameter, and we quantified the random effects as the variations among gill-net sampling sites, the variations among sampled years, and site × year interactions. This framework (i.e., the application of a mixed model appropriate for count data in a variance-partitioning context) represents a flexible approach that has implications for monitoring programs (e.g., trend detection) and for examining the potential of individual variance components to serve as response metrics to large-scale anthropogenic perturbations or ecological changes.

Received February 28, 2012; accepted August 19, 2012

ACKNOWLEDGMENTS

We thank the U.S. Fish and Wildlife Service Great Lakes Restoration Act for funding this work and the Michigan Department of Natural Resources for additional support. We acknowledge Mike Seider, Dave Fielder, Lars Rudstam, and Chris Vandergoot for providing the Walleye gill-net data used here. We thank Nigel Lester for contributing to this work. We also thank Josh Schmidt and Joe Witt for helpful suggestions. This paper is contribution number 2013-01 of the Quantitative Fisheries Center at Michigan State University. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.