Mathematical models of ecology and evolution : Analysis of size-structured populations and communities in aquatic ecosystems

Abstract

Understanding the dynamics and structure of populations and communities is one of the most important challenges in ecological theory. The thesis consists of theoretical investigations of how these phenomena at high level are in uenced by the ecological and evolutionary processes occurring at low level (i.e. individual level). Individual-level processes are all parameterized with body size. Being one of the important characteristics of individual organisms, body size determines the qualitative and quantitative relationships among individuals, and in uences most, if not all, key life-history processes. By characterizing species and life history with traits, the interrelationship between community-level properties of ecological interest and individual-level performance is explored. Paper I examines the in uences of two dierent mechanisms of energy partitioning among individual life-history processes: net-assimilation mechanism of 􀀀rule and net-reproduction mechanism of size dependence using a simple model comprising a size-structured consumer Daphina and an unstructured resource alge. It is found that in contrast to the former mechanism, the latter tends to destabilize population dynamics but as a trade-o promotes species survival by shortening juvenile delay between birth and the onset of reproduction. Paper II compares the size-spectrum and food-web representations of communities using two traits (body size and habitat location) based unstructured population model of Lotka-Volterra type and shows a robust reconciliation between the two representations. Paper III investigates the eects of growth variability induced by the trait (maximum body size) on the dynamics of marine size spectrum. It shows that the introduction of trait expands the set of parameters for which the equilibrium is stable, and if the community is unstable, the non-linear non-equilibrium dynamics has much smaller, slower, and more regular oscillations than if trait is excluded. Paper IV develops four types of density-dependent interference competition at the individual level in a trait (size at maturation) based size-structured population model, that is, interference in foraging, maintenance, survival, and recruitment. Their impacts on the ecology and evolution of size-structured populations and communities are explored. Ecologically, interference aects population demographic properties either negatively or positively, depending on the balance between interference induced gain and cost. Evolutionarily, the maturation size is either depressed (interference in foraging and maintenance) or elevated (interference in survival and recruitment) in a monomorphic population environment. Moreover, among the four interference mechanisms, survival interference is more likely to produce large communities with complex trophic patterns through gradual evolution and successive speciation