Biodiffusion

Biodiffusion is a concept used in ecology and evolutionary biology to describe the spatial spread of biological entities through diffusion-like processes. It encompasses the movement of individuals, the spread of populations, and the distribution of genes or other biological material across space. In modelling terms, biodiffusion treats dispersal as a continuous process that smooths population density over a habitat, akin to the diffusion of a substance.

A common modelling framework is the reaction-diffusion equation, which combines a diffusion term with a local growth or decay term. A typical form is ∂u/∂t = D ∇^2 u + f(u), where u represents population density, D is the diffusion coefficient, and f(u) captures local reproduction, mortality, and density dependence. In homogeneous spaces, traveling-wave solutions give invasion fronts with characteristic speeds, such as those described by the Fisher-KPP model, where the front speed depends on both dispersal and intrinsic growth rates. More complex models incorporate landscape heterogeneity, anisotropic diffusion, and stochastic effects.

Applications of biodiffusion include predicting the spread of invasive species, assessing habitat connectivity and corridor design for conservation, modeling gene flow and population expansion, and forecasting the spread of pests or diseases. They also underpin assessments of extinction risk under climate change and inform restoration planning by estimating how quickly restored habitats can be colonized.

Limitations and alternatives exist. Real landscapes are discrete and heterogeneous, and organism movement can be directed, seasonal, or long-range, which pure diffusion may not capture well. Alternatives include dispersal kernels, integrodifference equations, and stochastic or agent-based models that incorporate more detailed movement rules such as Lévy flights or behavior-driven dispersal.