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Mathematical Models of Social Evolution: A Guide for the Perplexed$
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Richard McElreath and Robert Boyd

Print publication date: 2007

Print ISBN-13: 9780226558264

Published to Chicago Scholarship Online: February 2013

DOI: 10.7208/chicago/9780226558288.001.0001

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PRINTED FROM CHICAGO SCHOLARSHIP ONLINE (www.chicago.universitypressscholarship.com). (c) Copyright University of Chicago Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in CHSO for personal use.date: 26 October 2021

Sex Allocation

Sex Allocation

(p.261) Chapter 7 Sex Allocation
Mathematical Models of Social Evolution: A Guide for the Perplexed

Richard Mcelreath

Robert Boyd

University of Chicago Press

This chapter explains why a 50:50 sex ratio is so common and why sex ratios sometimes deviate from 50:50. It shows that a sex ratio is really about appreciating the ways that parents invest in sons and daughters. There are deep reasons why, under most circumstances, mothers should invest the same amount in their sons and daughters. There are also interesting exceptions to this rule. This chapter also introduces two new tools, the calculus of reproductive value and matrix methods that extend equilibrium analysis to dynamic systems with two or more state variables. It first describes Fisher's theory of sex allocation and then discusses reproductive value and Fisherian sex ratios, biased sex ratios, and the eigen barrier. It also looks at the Shaw-Mohler theorem, which is used in cases when there are limits that force mothers to trade off the number of sons and daughters, so that one of the two terms is positive and the other negative. This chapter also examines how population structure can lead to a biased sex ratio.

Keywords:   sex allocation, reproductive value, sex ratios, Shaw-Mohler theorem, biased sex ratios, eigen barrier, population structure, matrix methods, parents

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