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Mathematical Models in Biology

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TLDR
The theory of linear difference equations applied to population growth and the applications of nonlinear difference equations to population biology are explained.
Abstract
Part I. Discrete Process in Biology: 1. The theory of linear difference equations applied to population growth 2. Nonlinear difference equations 3. Applications of nonlinear difference equations to population biology Part II. Continuous Processes and Ordinary Differential Equations: 4. An introduction to continuous models 5. Phase-plane methods and qualitative solutions 6. Applications of continuous models to population dynamics 7. Models for molecular events 8. Limit cycles, oscillations, and excitable systems Part III. Spatially Distributed Systems and Partial Differential Equation Models: 9. An introduction to partial differential equations and diffusion in biological settings 10. Partial differential equation models in biology 11. Models for development and pattern formation in biological systems Selected answers Author index Subject index.

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Spatial heterogeneity and irreversible vegetation change in semiarid grazing systems

TL;DR: A spatially explicit vegetation model is presented to investigate possible mechanisms explaining irreversible vegetation collapse on coarse spatial scales and indicates that the dynamics of vegetation on coarse scales are determined by the interaction of two spatial feedback processes.
Journal ArticleDOI

Evolutionary consequences of asymmetric dispersal rates.

TL;DR: The model predicts that the population will be most likely to adapt to that habitat if the dispersal rates in both directions are high, highlighting the general message that the effect of gene flow upon local adaptation should depend profoundly on the demographic context of selection.
Journal ArticleDOI

Establishment of a tetraploid cytotype in a diploid population: Effect of relative fitness of the cytotypes

TL;DR: The conditions for the establishment of a tetraploid in a diploids population were investigated by means of a deterministic model, on the assumption that the diploid cytotype produces some 2n gametes.
Journal ArticleDOI

Chaotic dynamics of a discrete prey-predator model with Holling type II

TL;DR: In this paper, a discrete-time prey-predator model with Holling type II was investigated, and the existence and stability of three fixed points were analyzed for this model, the bifurcation diagrams, phase portraits and Lyapunov exponents were obtained for different parameters of the model.
Journal ArticleDOI

Three‐Way Interactions among Mutualistic Mycorrhizal Fungi, Plants, and Plant Enemies: Hypotheses and Synthesis

TL;DR: This work formalizes the alternative outcomes of multispecies interactions among plant enemies, plants, and mycorrhizal fungi, and explores the long‐term dynamics of the plant‐enemy interactions using a general model of interactions between plants and plant enemies.
Trending Questions (1)
Mathematical models in biology?

The paper discusses mathematical models in biology, including linear and nonlinear difference equations, continuous models, and partial differential equation models.