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Thou Shalt not Diversify: Why ‘Two Of Every Sort’?

Part of: Distribution theory - Probability Stochastic processes Mathematical biology in general

Published online by Cambridge University Press:  14 July 2016

Rustam Ibragimov
Rustam Ibragimov*
Affiliation:
Harvard University
*
∗ Postal address: Department of Economics, Harvard University, Littauer Center, 1875 Cambridge Street, Cambridge, MA 02138, USA. Email address: [email protected]
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Abstract

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This paper presents a study of the intertemporal propagation of distributional properties of phenotypes in general polygenic multisex inheritance models with sex- and time-dependent heritabilities. It further analyzes the implications of these models under heavy-tailedness of traits' initial distributions. Our results suggest the optimality of a flexible asexual/binary mating system. Switching between asexual and binary inheritance mechanisms allows the population effectively to achieve a fast suppression of negative traits and a fast dispersion of positive traits, regardless of the distributional properties of the phenotypes in the initial period.

Keywords

Multisex inheritance modelmultifactorial inheritancephenotypic traitheritabilitytime series

MSC classification

Primary: 60E05: Distributions 60G07: General theory of processes 92B05: General biology and biomathematics 92D15: Problems related to evolution
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 1 , March 2007 , pp. 58 - 70
Copyright
Copyright © Applied Probability Trust 2007 

References

An, M. Y. (1998). Logconcavity versus logconvexity: a complete characterization. J. Econom. Theory 80, 350–369.CrossRefGoogle Scholar
Birnbaum, Z. W. (1948). On random variables with comparable peakedness. Ann. Math. Statist. 19, 76–81.Google Scholar
Czárán, T. L. and Hoekstra, R. F. (2004). Evolution of sexual asymmetry. BMC Evolutionary Biol. 4, 1471–2148.CrossRefGoogle ScholarPubMed
Hurst, L. D. (1995). Selfish genetic elements and their role in evolution: the evolution of sex and some of what that entails. Phil. Trans. R. Soc. London Ser. B 349, 321–332.Google Scholar
Ibragimov, R. (2005). New majorization theory in economics and martingale convergence results in econometrics. , Yale University.Google Scholar
Ibragimov, R. (2007). Efficiency of linear estimators under heavy-tailedness. Convolutions of α-symmetric distributions. Econometric Theory 23, 501–517.Google Scholar
Iwasa, Y. and Sasaki, A. (1987). Evolution of the number of sexes. Evolution 41, 49–65.Google Scholar
Karlin, S. (1984). Mathematical models, problems, and controversies of evolutionary theory. Bull. Amer. Math. Soc. (New Series) 10, 221–274.CrossRefGoogle Scholar
Karlin, S. (1992). Stochastic comparisons between means and medians for i.i.d. random variables. In The Art of Statistical Science, ed. Mardia, K. V., John Wiley, Chichester, pp. 261–274.Google Scholar
Karlin, S. and Lessard, S. (1986). Theoretical Studies on Sex Ratio Evolution. Princeton University Press.Google Scholar
Marshall, A. W. and Olkin, I. (1979). Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.Google Scholar
Nanney, D. L. (1980). Experimental Ciliatology: An Introduction to Genetic and Development Analysis in Ciliates. John Wiley, New York.Google Scholar
Proschan, F. (1965). Peakedness of distributions of convex combinations. Ann. Math. Statist. 36, 1703–1706.Google Scholar
Zolotarev, V. M. (1986). One-Dimensional Stable Distributions. American Mathematical Society, Providence, RI.Google Scholar