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1: Population Dynamics

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    Populations grow in size when the birth rate exceeds the death rate. Thomas Malthus, in An Essay on the Principle of Population (1798), used unchecked population growth to famously predict a global famine unless governments regulated family size-an idea later echoed by Mainland China’s one-child policy. The reading of Malthus is said by Charles Darwin in his autobiography to have inspired his discovery of what is now the cornerstone of modern biology: the principle of evolution by natural selection.

    The Malthusian growth model is the granddaddy of all population models, and we begin this chapter with a simple derivation of the famous exponential growth law. Unchecked exponential growth obviously does not occur in nature, and population growth rates may be regulated by limited food or other environmental resources, and by competition among individuals within a species or across species. We will develop models for three types of regulation. The first model is the wellknown logistic equation, a model that will also make an appearance in subsequent chapters. The second model is an extension of the logistic model to species competition. And the third model is the famous Lotka-Volterra predator-prey equations. Because all these mathematical models are nonlinear differential equations, mathematical methods to analyze such equations will be developed.

    This page titled 1: Population Dynamics is shared under a CC BY 3.0 license and was authored, remixed, and/or curated by Jeffrey R. Chasnov via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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