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Generalized linear models and point count data: statistical considerations for the design and analysis of monitoring studies

The success of avian monitoring programs to effectively guide management decisions requires that studies be efficiently designed and data be properly analyzed. A complicating factor is that point count surveys often generate data with non-normal distributional properties. In this paper we review methods of dealing with deviations from normal assumptions, and we focus on the application of generalized linear models (GLMs). We also discuss problems associated with overdispersion (more variation than expected). In order to evaluate the statistical power of these models to detect differences in bird abundance, it is necessary for biologists to identify the effect size they believe is biologically significant in their system. We illustrate one solution to this challenge by discussing the design of a monitoring program intended to detect changes in bird abundance as a result of Western juniper (Juniperus occidentalis) reduction projects in central Oregon. We estimate biologically significant effect sizes by using GLMs to describe variation in bird abundance relative to natural variation in juniper cover. These analyses suggest that for species typically positively associated with juniper cover, a 60-80 percent decrease in abundance may be expected as a result of juniper reduction projects. With these estimates of expected effect size and preliminary data on bird abundance, we use computer simulations to investigate the power of GLMs. Our simulations demonstrate that when data are not overdispersed and sample sizes are relatively large, the statistical power of GLMs is approximated well by formulas that are currently available in the bird literature for other statistical techniques. When data are overdispersed, as may be the case with most point count data, power is reduced.