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Department of Mathematical Sciences

# Seminar Archives

## Statistics Seminars: Extinction risk and optimal management of populations: applications of $\lambda$-invariant measures and vectors
"I will present some recent results from two threads of research in mathematical and applied ecology. The first, the calculation of extinction risk, has been of great interest to ecologists for several decades. Many methods to quantify extinction risk exist, each motivated by a different mathematical or pure or applied scientific purpose. A choice must often be made between conciseness and precision in developing these methods. For Markov population processes, the decay parameter $\lambda$ and associated $\lambda$-invariant measure and vector quantify the long-term risk of extinction in a way that is arguably both concise and precise. Surprisingly, their application to this area was only recently recognised in the ecological literature. The second thread that I will discuss concerns the optimal management of populations, in particular managing populations in order to maximise persistence or financial value over time. This maximisation can also be expressed in terms of a more general concept of long-term risk in a modified population process. I will draw on this connection between extinction risk and optimal management to argue that in long-term risk there is an intersection between theoretical and applied interests. This provides a powerful quantitative tool for informing practical decision-making in conservation. (This is joint work with John McNamara and Karin Harding.)"