# Population Growth

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Submitted By deoliveira
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Pages 7
Population

Growth and Ecological Footprints

The population size (N) of a species at any point in time (t) is determined by its size at (t-1), its per capita birth rate (b), its per capita death rate (d), and immigration and emigration. Each of these values is, in turn, affected by a huge suite of biotic and abiotic conditions. Human populations are governed by these same variables. In this laboratory, you will use models of population growth to understand how population growth is affected by changes in b and d, and why the actual values of b and d are important. You will also explore some dimensions of human impacts on the environment.

A model is a mathematical description of how one thinks a system works. For a population growing at a constant rate, where b and d never change, an appropriate model for population growth is the exponential growth model:

dN/dt = rN

where r = b – d, assuming that immigration and emigration are negligible. This is a density-independent model since neither b nor d change with increasing population size. Conversely, the logistic model is a density-dependent model, where b and d change with changes in the population size:

dN/dt = rN [(K-N)/K]

where K = carrying capacity of the environment.

In this lab you will use a simple Excel spreadsheet model to explore how population size (N) changes as b and d change under the two different growth models, exponential and logistic. The spreadsheets have areas that you cannot change (where the actual equations are stored). But there are also areas where you can enter numbers and see how population growth changes. You will simulate: (1) exponential growth, (2) classical logistic growth (density-dependent growth with N approaching K in a smooth, controlled manner), (3) growth of an unstable population, and (4) growth of a stable, but oscillating, population....

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