讲座题目: How Phenological Variation Affects Species Spreading Speeds

讲座人: Bingtuan Li， professor, Department of Mathematics，University of Louisville

讲座时间: 2018年7月2日，星期一，下午4:00-5:00

讲座地点: 数学与统计学院理科楼408

Abstract:

We discuss a phenologically explicit reaction-diffusion model to analyze the spatial spread of a univoltine insect species. Our model assumes four explicit life stages: adult, larval, and pupa, with a fourth, implicit, egg stage modeled as a time delay between oviposition and emergence as a larva. As such, our model is broadly applicable to holometabolous insects.  To account for phenology (seasonal biological timing), we introduce time dependent phenological functions describing adult emergence, oviposition and larval conversion, respectively.   This very general formulation allows us to accommodate a wide variety of alternative insect phenologies and lifestyles. We provide the moment generating function for the general linearized system in terms of phenological functions and model parameters. We prove that the spreading speed of the linearized system is the same as that for non-linear system.   We find explicit solutions for the spreading speed of the insect population for the limiting cases where 1) emergence and oviposition are impulsive (i.e. take place over an extremely narrow time window), larval conversion occurs at a constant rate, and larvae are immobile,  and 2) emergence, oviposition, and larval conversion are impulsive. To consider other biological scenarios, including cases with emergence and oviposition windows of finite width as well as mobile larvae, we use numerical simulations.  Our results provide a framework for understanding how phenology can interact with spatial spread to facilitate (or hinder) species expansion.  This is an important area of research within the context of global change, which brings both new invasive species and range shifts for native species, all the while causing perturbations to species phenology that may impact the abilities of native and invasive populations to spread.

讲座人简介：

Li Bingtuan教授、博士生导师，现任“Discrete and Continuous Dynamical Systems” 编委。长期从事微分方程、生物数学模型的研究工作。1998 年于 Arizona State University 获应用数学博士学位。1999 年至 2001 年分别在 University of Minnesota、University of Utah 从事博士后研究工作。2001 年至今在 University of Louisville 数学系工作。已在“SIAM J. Appl. Math.” “J. Differential Equations” “J. Math.Biol.” “Nonlinearity” “Math. Biosci. Eng.”“Bull. Math. Biol.”“Math.Biosci.” 等 SCI 期刊上发表论文 50 余篇。