Dynamics of single-species population growth: Experimental and statistical analysis

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The logistic model, widely used for describing population growth, assumes that the per-capita rate of growth linearly decreases as the population size increases. Experimental data, however, suggest that often the per-capita rate of growth is not linearly related to population density. The theta model removes such linearity assumption by means of an additional parameter, θ; when θ = 1, the theta model reduces to the logistic model. We advance a method, the “jackknife” statistic, for estimating the rate of population growth (the largest eigenvalue and its variance) in the serial transfer system. Also, we propose a statistical method, PRESS, for quantifying the success of a given model in fitting experimental data. The criterion of success is the ability of a model to predict accurately new observations. One advantage of PRESS is that, contrary to what happens with other statistics such as R 2, it tends to make a model less successful as the number of parameters increases (unless there is a disproportionate decrease in the bias of the new model). We have studied the rate of population growth in 25 genetically different populations of Drosophila melanogaster. The theta model provides a consistently better description of population growth in these populations than the logistic model. Moreover, the results indicate that the rate of growth is affected by the genetic constitution of a population.