# Entropy Satisfying Schemes for Computing Selection Dynamics in Competitive Interactions

@article{Liu2015EntropySS, title={Entropy Satisfying Schemes for Computing Selection Dynamics in Competitive Interactions}, author={Hailiang Liu and Wenli Cai and Ning Su}, journal={SIAM J. Numerical Analysis}, year={2015}, volume={53}, pages={1393-1417} }

- Published in SIAM J. Numerical Analysis 2015
DOI:10.1137/140965739

In this paper, we present entropy satisfying schemes for solving an integro-differential equation that describes the evolution of a population structured with respect to a continuous trait. In [P.-E. Jabin and G. Raoul, J. Math. Biol., 63 (2011), pp. 493--517] solutions are shown to converge toward the so-called evolutionary stable distribution (ESD) as time becomes large, using the relative entropy. At the discrete level, the ESD is shown to be the solution to a quadratic programming problem… CONTINUE READING

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## Time-asymptotic convergence rates towards the discrete evolutionary stable distribution

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## Selection-Mutation dynamics with spatial dependence

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