An Introduction to Structured Population Dynamics
Interest in the temporal fluctuations of biological populations can be traced to the dawn of civilization. How can mathematics be used to gain an understanding of population dynamics? This monograph introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models. This theory bridges the gap between the characteristics of individual organisms in a population and the dynamics of the total population as a whole. In this monograph, many applications that illustrate both the theory and a wide variety of biological issues are given, along with an interdisciplinary case study that illustrates the connection of models with the data and the experimental documentation of model predictions. The author also discusses the use of discrete and continuous models and presents a general modeling theory for structured population dynamics.
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a)da ac(t adult age-structured models age-structured population Allee effect Assume assumption asymptotic dynamics attractor autonomous bifurcation diagram bifurcation point biological Biosci characteristic value chemostat class distribution Consider continuum Ct critical value cycle death rate defined denote discrete eigenvector equilibrium pairs example exists extinction equilibrium fertility formula function global growth implies individuals inherent net reproductive interactions J. M. Cushing Jacobian juveniles Lemma Leslie matrix limiting equation linear locally asymptotically log-residuals Math Mathematical matrix equation matrix model McKendrick model nonlinear nonnegative ordinary differential equation parameter estimates parasitoid partial differential equation population densities population dynamics population level population models positive equilibrium projection matrix reproductive number resource result Ricker model Rºº saddle-node bifurcation satisfies scalar ſº solution pairs species stable 2-cycle stochastic strictly dominant structured population t e IIO Theorem unstable vector vital rates weighted total population