Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 25, Issue 8, Pages 1589-1616Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202515500426
Keywords
Selection dynamics; evolutionary stable distribution; relative entropy; convergence rates
Categories
Funding
- National Science Foundation [DMS1312636]
- NSF [RNMS (Ki-Net) 1107291, DMS 1312142, RNMS (Ki-Net) 1107444]
- China Scholarship Council
- Tsinghua University
- Iowa State University
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1312142] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1107291, 1312636] Funding Source: National Science Foundation
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This paper is concerned with the discrete dynamics of an integro-differential model that describes the evolution of a population structured with respect to a continuous trait. Various time-asymptotic convergence rates towards the discrete evolutionary stable distribution (ESD) are established. For some special ESD satisfying a strict sign condition, the exponential convergence rates are obtained for both semi-discrete and fully discrete schemes. Towards the general ESD, the algebraic convergence rate that we find is consistent with the known result for the continuous model.
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