Are diffusion models too simple? a comparison with telegraph models of invasion

Area of Science:

• Ecology
• Mathematical Biology
• Zoology

Background:

• Diffusion models for animal movement often assume infinite velocity and random motion, which may not reflect reality.
• Telegraph models offer an alternative, incorporating finite velocity and directional persistence in movement.

Purpose of the Study:

• To compare the predictions of diffusion and telegraph models for animal dispersal and range expansion.
• To investigate the impact of movement assumptions on ecological modeling outcomes.

Main Methods:

• Comparison of diffusion and telegraph models in two scenarios: dispersal of non-reproducing organisms and range expansion of reproducing organisms (reaction-diffusion/telegraph models).
• Estimation of model parameters using published data for six diverse species/pathogens: cabbage butterfly, gypsy moth, European starling, collared turtledove, Black Death, and rabies.

Main Results:

• Both models produced similar dispersal patterns for non-reproducing organisms.
• For reproducing organisms, diffusion and telegraph models predicted substantially different range expansion rates across most parameter values.
• The greatest disparity was observed in organisms with high population growth and low movement rates.

Conclusions:

• The choice between diffusion and telegraph models is critical for accurately predicting range expansion rates in reproducing populations.
• Despite theoretical differences, the studied real-world cases (insects, birds, pathogens) all fell within a parameter range where both models yield similar predictions for range expansion.
• This suggests that for certain organisms and conditions, the simplifying assumptions of diffusion models may be adequate for range expansion predictions.