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Classical Markov Chains: A Unifying Framework for Understanding Avian Reproductive Success
Citation:
ETTERSON, M. A. Classical Markov Chains: A Unifying Framework for Understanding Avian Reproductive Success. Presented at UMD Mathematics Department , Duluth, MN, February 26, 2009.
Impact/Purpose:
Our primary objective in developing these models is to provide a regulatory tool for integrating laboratory testing data on adverse reproductive effects with avian life history information to inform ecological risk assessments.
Description:
Traditional methods for monitoring and analysis of avian nesting success have several important shortcomings, including 1) inability to handle multiple classes of nest failure, and 2) inability to provide estimates of annual reproductive success (because birds can, and typically do, make multiple nest attempts in a year). Both of the above limitations may be relaxed by treating the avian nesting process as a Markov chain. In the first case the transition matrix is assumed unknown and maximum likelihood estimates for the transition probabilities are easily obtained. In the second case the asymptotic behavior of Markov chains may be used to gain remarkable insight from fairly simple hypotheses about the transition probabilities. With the above underpinnings, I will describe and demonstrate time-heterogeneous Markov chain models that we are currently developing at the EPA lab here in Duluth. Our primary objective in developing these models is to provide a regulatory tool for integrating laboratory testing data on adverse reproductive effects with avian life history information to inform ecological risk assessments.