Dr Alexandru Hening from tufts University will deliver two seminars on stochastic population dynamics. Seminar 1: TITLE. Harvesting of populations in stochastic environments ABSTRACT. We consider the harvesting of a population in a stochastic environment whose dynamics in the absence of harvesting is described by a one dimensional diffusion. Using ergodic optimal control, we find the optimal harvesting strategy which maximizes the asymptotic yield of harvested individuals. When the yield function is the identity, we show that the optimal strategy has a bang-bang property: there exists a threshold x*>0 such that whenever the population is under the threshold the harvesting rate must be zero, whereas when the population is above the threshold the harvesting rate must be at the upper limit. We provide upper and lower bounds on the maximal asymptotic yield, and explore via numerical simulations how the harvesting threshold and the maximal asymptotic yield change with the growth rate, maximal harvesting rate, or the competition rate. We also show that, if the yield function is ð¶2 and strictly concave, then the optimal harvesting strategy is continuous, whereas when the yield function is convex the optimal strategy is of bang-bang type. This shows that one cannot always expect bang-bang type optimal controls. SEMINar 2: TITLE. The competitive exclusion principle in stochastic environments ABSTRACT. The competitive exclusion principle states that a number of species competing for a smaller number of resources cannot coexist. Even though this is a fundamental principle in ecology, it has been observed empirically that in some settings it will fail. One example is Hutchinson’s ` paradox of the plankton’. This is an instance where a large number of phytoplankton species coexist while competing for a very limited number of resources. Both experimental and theoretical studies have shown that in some instances (deterministic) temporal fluctuations of the environment can facilitate coexistence for competing species. Hutchinson conjectured that one can get coexistence because nonequilibrium conditions would make it possible for different species to be favored by the environment at different times. In this talk I will look at how environmental noise interacts with competitive exclusion. I will show that, contrary to Hutchinson’s explanation, one can switch between two environments in which the same species is favored and still get coexistence.