Backward Bifurcation in Evolutionary Models of Populations Dynamics with Applications to Life History Adaptions
报告题目：Backward Bifurcation in Evolutionary Models of Populations Dynamics with Applications to Life History Adaptions
报告时间：2019年7月6日，星期六，上午 10:50-11:50
报告地点：数学楼2-3会议室
报告人: Prof. Cushing Jim Michael，University of Arizona
Abstract:
A fundamental bifurcation in population dynamic models occurs when extinction equilibrium loses stability due to a change in a model parameter. This destabilization (which is important in applications because it concerns extinction versus survival) results in the bifurcation of survival (positive) equilibria whose stability depends on the direction of bifurcation. My collaborators and I have generalized this theorem to Darwinian versions of population models. In these models coefficients that represent various vital rates (fertility, survival, resource consumption, metabolism, competitive effectiveness, etc.) are not constant in time, but change according to adaptations driven by natural selection. Forward bifurcation produce stability survival equilibria and backward bifurcations produce unstable survival equilibria. However, backward bifurcations are important because, in general, they produce a multiple attractor scenario (called a strong Allee effect) in which both extinction and survival equilibria are stable. I will briefly discuss two applications which illustrate the key role of such a scenario. One application addresses a historically old question which asks: what basic life history strategy does evolution favor: semelparity (e.g. annual plants) or iteroparity (e.g. perennial plants)? A second application addresses phenomena observed at our field site on Protection Island, USA, where marine birds (glaucous-winged gulls) are being subjected to climate warming and, in response, are engaging in higher rates of egg cannibalism. The question is: can cannibalism be a long term, evolutionarily stable strategy?
报告人简介：
Cushing Jim Michael老师是University of Arizona教授。1964年毕业于科罗拉多大学数学系，获学士学位；1968年毕业于马里兰大学，获博士学位。曾任IBM博士后，德国图宾根大学洪堡研究员。 Cushing Jim Michael教授在国际著名期刊Nature, Proceedings of the National Academy of Sciences，Proceedings of the National Academy of Sciences，Journal of Biological Dynamics，SIAM Journal on Applied Mathematics, SIAM Journal on Applied Dynamical Systems，J. Differential Equations., Bulletin of Mathematical Biology，Mathematical Biology等发表论文170多篇。现任学术期刊Natural Resource Modeling高级顾问，Journal of Difference Equations and Applications (JDEA)主编、Journal of Biological Dynamics共同主编、 任Journal of Dynamics and Games, Theoretical Ecology Series，International Journal of Nonlinear Differential Equations: Theory, Methods and Applications，Mathematical Modelling and Analysis of Complex Systems，Communications on Applied Nonlinear Analysis，Mathematical Modelling of Natural Phenomena，Nonlinear Studies，Letters in Biomathematics等杂志的编委。此外，Cushing Jim Michael教授多次组织和参与有关生物数学方面的国际学术会议，受邀做过250余次的报告，是该领域的具有国际影响力的专家。
