What Models Are Useful in Describing the Growth of a Population?
The world population first reached one billion people in the year 1800. Current projections suggest that the world's seven billionth person will be born in October or November of 2011. The models used to predict the birth of baby #7,000,000,000 originated with the work of Thomas Malthus back in 1798. Malthus observed that, when constraints were ignored, human populations increased according to a fixed proportion that is unaffected by population size. Different models account for various constraints and considerations depending on the population you are interested in describing.
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Geometric/Exponential Model
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Commonly associated with Thomas Malthus, the geometric or exponential model operates on the assumption that population growth is population-independent. The simple form of the model is that the next year's population equals the product of the growth rate times the current population. Growth rate is defined as the difference between births and deaths over a set time on a per-individual rate. The geometric model operates on the same principle; however, it models the growth of a population that increases only during select times.
Logistic Model
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The exponential model can only describe a population if certain assumptions are true of the population. For populations that may grow or shrink from migrations, difference in growth rates between generations, individual fertility rates or encounter finite resources, growth models must include more complex considerations. The logistic model accounts for limits imposed on population sizes due to resources. The model is similar to the exponential model, but includes a term called the negative feedback term to correct the growth. According to this model, populations have a maximum limit called the carrying capacity. Populations will shrink if they grow beyond the carrying capacity to achieve equilibrium.
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Deterministic Model
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Deterministic models provide a single value as their result. This category of model proves easier to calculate; however, its accuracy relies on a large number of assumptions about population conditions and environmental factors. Analysts can evaluate deterministic models by finding the deviation between predicted and actual population size.
Stochastic Model
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Accounting for unpredictable variations and fluctuations, the stochastic model shows the probability that the population growth will fall within a certain range. For convenience, stochastic models provide the mean result as their prediction. Standard deviation from the mean assists analysts in determining the probability ranges for various potential population ranges.
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References
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