NDLI: A Wright–Fisher model with indirect selection

Content Provider	Springer Nature Link
Author	Zitt, Pierre André Goudenège, Ludovic
Copyright Year	2015
Abstract	We study a generalization of the Wright–Fisher model in which some individuals adopt a behavior that is harmful to others without any direct advantage for themselves. This model is motivated by studies of spiteful behavior in nature, including several species of parasitoid hymenoptera in which sperm-depleted males continue to mate despite not being fertile. We first study a single reproductive season, then use it as a building block for a generalized Wright–Fisher model. In the large population limit, for male-skewed sex ratios, we rigorously derive the convergence of the renormalized process to a diffusion with a frequency-dependent selection and genetic drift. This allows a quantitative comparison of the indirect selective advantage with the direct one classically considered in the Wright–Fisher model. From the mathematical point of view, each season is modeled by a mix between samplings with and without replacement, and analyzed by a sort of “reverse numerical analysis”, viewing a key recurrence relation as a discretization scheme for a PDE. The diffusion approximation is then obtained by classical methods.
Ending Page	1450
Page Count	40
Starting Page	1411
File Format	PDF
ISSN	03036812
e-ISSN	14321416
Journal	Journal of Mathematical Biology
Issue Number	6-7
Volume Number	71
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-03-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Diffusion approximation Wright–Fisher model Reverse numerical analysis Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) Mathematical and Computational Biology Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) Applications of Mathematics Problems related to evolution
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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