## Elements of Mathematical EcologyElements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems thoughout the text that aid understanding, and supplementary mathematical and historical material that enrich the main text. |

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asymptotically stable attractor Beverton—Holt bifurcation diagram Biology birth and death birth rate boundary conditions capita carrying capacity chaotic characteristic equation chemostat coefficients coexist competition Consider constant corresponding curve decreases density dependence difference equation diffusion discrete-time dynamics ecology eigenvalues equilibrium point Euler–Lotka equation example exponential extinction Figure Fisher equation fishery fishing functional response growth rate harvest heteroclinic homoclinic Hopf bifurcation increase individuals initial condition integral equation Jacobian Leslie matrix limit cycle linear logistic difference equation Lotka Lotka–Volterra males Mathematical mutualism nonlinear nontrivial equilibrium number of females oscillations parameter parasitoids partial differential equation periodic orbit phase plane Phase portrait pn(t population positive predator predator—prey models prey zero-growth isoclines probability generating function problem real roots Recommended readings reduces reproduction saddle point satisfies simple ſº solve spatial species stable manifold stable node substrate theorem transcritical bifurcation traveling wave unstable zero