Estimating spatial and temporal components of variation in count data using negative binomial mixed models

Transactions of the American Fisheries Society
By: , and 

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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.

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Additional publication details

Publication type Article
Publication Subtype Journal Article
Title Estimating spatial and temporal components of variation in count data using negative binomial mixed models
Series title Transactions of the American Fisheries Society
DOI 10.1080/00028487.2012.728163
Volume 142
Issue 1
Year Published 2013
Language English
Publisher Taylor & Francis
Contributing office(s) Coop Res Unit Leetown
Description 12 p.
First page 171
Last page 183
Country United States
State Iowa, Maine, Michigan, Ohio, Wisconsin
Online Only (Y/N) N
Additional Online Files (Y/N) N