2011-Winkel, Brian - Parameter Estimates in Differential Equation Models for Population Growth
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Winkel, B. 2011. Parameter Estimates in Differential Equation Models for Population Growth. PRIMUS. 21(2): 101-129.
See https://www.tandfonline.com/doi/abs/10.1080/10511970.2010.534834 .
Article Abstract: We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and multiple species competition models. We discuss student evolved strategies and offer Mathematica code for a gradient search approach. We use historical (1930's) data from microbial studies of the Russian biologist, G.F. Gause, and estimate growth rates, carrying capacities, and “coefficients for the struggle for existence.”
This article contains data from the studies in the 1930’s by G. F. Gause, the Russian biologist, first separate paramecia populations and then competing populations. The emphasis is on parameter estimation for the logistic growth equation y’(t) = r y(t) (K – y(t))/K for a population level of y(t) at time t. Details are given on a number of different approaches to estimate the parameters r and K in the model.
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