Evolutionary games on the torus with weak selection
Publication
, Journal Article
Cox, JT; Durrett, R
Published in: Stochastic Processes and their Applications
December 7, 2015
We study evolutionary games on the torus with N points in dimensions d≥3. The matrices have the form Ḡ=1+wG, where 1 is a matrix that consists of all 1’s, and w is small. As in Cox Durrett and Perkins (2011) we rescale time and space and take a limit as N→∞ and w→0. If (i) w≫N−2/d then the limit is a PDE on Rd. If (ii) N−2/d≫w≫N−1, then the limit is an ODE. If (iii) WªN−1 then the effect of selection vanishes in the limit. In regime (ii) if we introduce mutations at rate μ so that μ/w→∞ slowly enough then we arrive at Tarnita's formula that describes how the equilibrium frequencies are shifted due to selection.
Duke Scholars
Published In
Stochastic Processes and their Applications
DOI
ISSN
0304-4149
Publication Date
December 7, 2015
Volume
126
Issue
8
Start / End Page
2388 / 2409
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 4901 Applied mathematics
- 1502 Banking, Finance and Investment
- 0104 Statistics
- 0102 Applied Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Cox, J. T., & Durrett, R. (2015). Evolutionary games on the torus with weak selection. Stochastic Processes and Their Applications, 126(8), 2388–2409. https://doi.org/10.1016/j.spa.2016.02.004
Cox, J. T., and R. Durrett. “Evolutionary games on the torus with weak selection.” Stochastic Processes and Their Applications 126, no. 8 (December 7, 2015): 2388–2409. https://doi.org/10.1016/j.spa.2016.02.004.
Cox JT, Durrett R. Evolutionary games on the torus with weak selection. Stochastic Processes and their Applications. 2015 Dec 7;126(8):2388–409.
Cox, J. T., and R. Durrett. “Evolutionary games on the torus with weak selection.” Stochastic Processes and Their Applications, vol. 126, no. 8, Dec. 2015, pp. 2388–409. Scopus, doi:10.1016/j.spa.2016.02.004.
Cox JT, Durrett R. Evolutionary games on the torus with weak selection. Stochastic Processes and their Applications. 2015 Dec 7;126(8):2388–2409.
Published In
Stochastic Processes and their Applications
DOI
ISSN
0304-4149
Publication Date
December 7, 2015
Volume
126
Issue
8
Start / End Page
2388 / 2409
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 4901 Applied mathematics
- 1502 Banking, Finance and Investment
- 0104 Statistics
- 0102 Applied Mathematics