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We develop a new discrete-time model, called the boundary-layer model, to describe the dynamics of single species that have a capacity for fast growth at very low population densities. The model explicitly separates the dynamics of the population at very low densities (within the "boundary layer") and at high densities. The boundary-layer model provides a better fit than other models such as the logistic or the theta model to data from experimental populations of Drosophila willistoni and D. pseudoobscura.

Boundary-layer model for the population dynamics of single species