Math Biology Seminar: Michael Irvine

   
The measurement of dynamic persistence of a population has been a long standing problem in Ecology. For spatial processes, fractal measurements such as the Korcak exponent or the boundary dimension have often been proposed as indicators of the persistence of the underlying dynamics. Recently it has been shown that the value of the Korcak exponent does not necessarily correlate with persistence. I shall explore under what conditions there does exist a strong relationship between persistence and fractal measures. I show that theoretically a Korcak-persistence relationship is expected under fairly generic conditions. I will then introduce a model of spatial vegetative growth with non-local competition and use numerical simulation to elucidate this relationship and find that environmental factors strongly affect both return rate and fractal measures. The theory and model are then supported by a long-term study of Seagrass in the Scilly Isles,UK.