Using mixed models to quantify variability in fish populations
Georgia Chapter of the American Fisheries Society
Monitoring programs are widely used to provide essential information for the restoration and management of fish populations. It is generally assumed that these monitoring surveys produce representative data on how fish populations vary over space and time. For example, observed fish-population metrics may vary among repeated samples from a single location, from site to site within a lake, from lake to lake, and among sampling years. We will discuss the use of mixed models to partition variability into multiple spatial and temporal components. Models for estimating variance components have been applied to a wide variety of aquatic indices including water chemistry variables, measurements of species richness, stream habitat characteristics, metrics of fish growth, and catch-per-unit effort data. To date, most variance-components frameworks have been based on linear models that assume normally distributed error structures. However, assuming a normal distribution for observations of abundance is often not ideal because these counts are typically non-negative integers with high variances and low means, not to mention other issues that arise when log-transforming data such as how to treat zero observations during the analysis. We will use data collected by fishery-independent surveys to illustrate the idea of variance partitioning and discuss its relevance for monitoring programs. We will also describe the negative binomial distribution within the mixed-model framework as an alternative to log-transformation (e.g., an alternative assumption about the mean-variance relationship) that can be applied to discrete count data in a variance-partitioning context.