# Evolution of Dispersal with Starvation Measure and Coexistence

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## Abstract

Many biological species increase their dispersal rate if starvation starts. To model such a behavior, we need to understand how organisms *measure* starvation and *response* to it. In this paper, we compare three different ways of measuring starvation by applying them to starvation-driven diffusion. The evolutional selection and coexistence of such starvation measures are studied within the context of Lotka–Volterra-type competition model of two species. We will see that, if species have different starvation measures and different motility functions, both the coexistence and selection are possible.

## Keywords

Coexistence Evolutional selection Global asymptotic stability Linear stability Starvation driven diffusion## Notes

### Acknowledgments

This work was started when the second author was working at the Center for Partial Differential Equation in East China Normal University, Shanghai, China. He would like to thank all the hospitality and supports provided by the center during his stay.

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