Lewis, M. A.; Kareiva, P. Allee dynamics and the spread of invading organisms. (English) Zbl 0769.92025 Theor. Popul. Biol. 43, No. 2, 141-158 (1993). Summary: We examine how an Allee effect in local population dynamics (reduced reproductive success at low densities) influences the spatio-temporal dynamics of ecological invasions. Our approach is to use a partial differential equation model of dispersal and population growth, and then ask whether we can identify “rates of spread” for an invading organism subject to an Allee effect.Results indicate that an Allee effect may substantially reduce the rate at which the invader moves into a new environment. Analysis of spread in two spatial dimensions entails application of a singular perturbation theory approach. Here the two-dimensional spread velocity is given in terms of the one-dimensional asymptotic spread rate and the curvature of a boundary between invaded and non-invaded regions. Using this result, we show that invasions cannot propagate unless they initially exceed a critical area. This prediction is verified by numerically solving the original model. Numerical solutions are used throughout in demonstrating the nature of the two-dimensional spread. Cited in 178 Documents MSC: 92D40 Ecology 35Q92 PDEs in connection with biology, chemistry and other natural sciences Keywords:reduced reproductive success at low densities; rates of spread; Allee effect; local population dynamics; spatio-temporal dynamics of ecological invasions; dispersal; population growth; singular perturbation theory approach; two-dimensional spread velocity PDFBibTeX XMLCite \textit{M. A. Lewis} and \textit{P. Kareiva}, Theor. Popul. Biol. 43, No. 2, 141--158 (1993; Zbl 0769.92025) Full Text: DOI