Dispersal Data and the Spread of Invading Organisms

• Published in: Ecology (Durham) Vol. 77; no. 7; pp. 2027 - 2042
• Main Authors: Kot, Mark, Lewis, Mark A., van den Driessche, P.
• Format: Journal Article
• Language: English
• Published: Washington, DC Ecological Society of America 01.10.1996
• Subjects: Animal and plant ecology; Animal populations; Animal, plant and microbial ecology; Animals; Biological and medical sciences; Biological invasions; Concepts; Demecology; Density distributions; Dispersal; Drosophila pseudoobscura; Ecological invasion; Ecological modeling; Ecology; Flowers & plants; Fundamental and applied biological sciences. Psychology; General aspects; Modeling; Phytopathology; Plant diseases; Population biology; Population density; Population ecology; Population growth; Spatial models; Population growth; Insecta; Dispersion; Invasion; Drosophilidae; Invasive species; Spatial distribution; Arthropoda; Drosophila pseudoobscura; Models; Invertebrata; Expansion; Diptera
• ISSN: 0012-9658; 1939-9170
• DOI: 10.2307/2265698

Models that describe the spread of invading organisms often assume that the dispersal distances of propagules are normally distributed. In contrast, measured dispersal curves are typically leptokurtic, not normal. In this paper, we consider a class of models, integrodifference equations, that directly incorporate detailed dispersal data as well as population growth dynamics. We provide explicit formulas for the speed of invasion for compensatory growth and for different choices of the propagule redistribution kernel and apply these formulas to the spread of D. pseudoobscura. We observe that: (1) the speed of invasion of a spreading population is extremely sensitive to the precise shape of the redistribution kernel and, in particular, to the tail of the distribution; (2) fat—tailed kernels can generate accelerating invasions rather than constant—speed travelling waves; (3) normal redistribution kernels (and by inference, many reaction—diffusion models) may grossly underestimate rates of spread of invading populations in comparison with models that incorporate more realistic leptokurtic distributions; and (4) the relative superiority of different redistribution kernels depends, in general, on the precise magnitude of the net reproductive rate. The addition of an Allee effect to an integrodifference equation may decrease the overall rate of spread. An Allee effect may also introduce a critical range; the population must surpass this spatial threshold in order to invade successfully. Fat—tailed kernels and Allee effects provide alternative explanations for the accelerating rates of spread observed for many invasions.