Are Diffusion Models too Simple? A Comparison with Telegraph Models of Invasion

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Abstract
Diffusion models of animal movement are often criticized because they assume animals have infinite velocity and completely random motion. To investigate the impact of these assumptions, I compared a diffusion model with a telegraph model of dispersal The telegraph model assumes organisms have finite velocity and tend to maintain their direction. I compared the models in two settings: (i) as models for dispersal of nonreproducing organisms and (ii) as models for range expansion of organisms that simultaneously disperse and reproduce (so-called reaction-diffusion or reaction-telegraph models). Both models predict very similar dispersal patterns for nonreproducing organisms. In the case of reproducing organisms, however, they predict grossly different rates of range expansion for all but a small range of parameter values. The disparity is greatest for organisms with high population growth and low movement rates. To assess the magnitude of disparity for different organisms, I used published data to estimate model parameters for the cabbage butterfly (Pieris rapae), gypsy moth (Lymantria dispar), European starling (Sturnus vulgaris), collared turtledove (Streptopelia decaocto), Black Death (Yersinia pestis), and for rabies. All six cases fell within the narrow parameter range where the diffusion and telegraph models yield indistinguishable predictions regarding the rate of range expansion.

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