# Achievement

## Model to determine differential diffusion of fish

### Project

IGERT: Spatial Ecology and Evolution: Quantitative Training in Biology, Statistics, and Mathematics

### University

University of Florida

(Gainesville, FL)

### PI

## Research Achievements

### Model to determine differential diffusion of fish

Theoretical models assuming homogeneous movement predict that densities of highly mobile species will decrease inside but increase outside a Marine Protected Area (MPA) relative to less mobile species; the predictions have not been confirmed by field studies. Thus, mathematician Jessica Langebrake, with biology collaborators, developed a model to determine if differential diffusion of fish inside vs. outside a Marine Protected Area (MPA) could explain the contradiction. They examined the steady state and stability of their model under changing adult mobility but consistent relative inequity in the diffusion constant. Their results with heterogeneous diffusion were consistent with previous theoretical results. They therefore developed a model with movement bias at the MPA boundary, which gave radically different density profiles. The movement bias model reconciled empirical data and theoretical results.

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