DISPERSAL DATA AND THE SPREAD OF INVADING ORGANISMS

Models that describe the spread of invading organisms often assume tha t the dispersal distances of propagules are normally distributed. In c ontrast, measured dispersal curves are typically leptokurtic, not norm al. In this paper, we consider a class of models, integrodifference eq uations, 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 th e redistribution kernel and, in particular, to the tail of the distrib ution; (2) fat-tailed kernels can generate accelerating invasions rath er than constant-speed travelling waves; (3) normal redistribution ker nels (and by inference, many reaction-diffusion models) may grossly un derestimate 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 depe nds, 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 introdu ce a critical range; the population must surpass this spatial threshol d in order to invade successfully. Fat-tailed kernels and Allee effect s provide alternative explanations for the accelerating rates of sprea d observed for many invasions.