J. theor. Biol. (1992) 158, 195-198

Female Infanticide and Human Sex Ratio Evolution MAGNUS NORDBORG

Department of Biological Sciences, Stanford University, Stanford, CA 94305-5020 U.S.A. (Received on 15 July 1991, Accepted on 30 March 1992) The possible effect on the evolution of the human sex ratio of a preference for male children is examined in a genetic model. It is shown that the killing of infant daughters can lead to either a female- or a male-biased sex ratio, the outcome depending on the decision rule used to determine the fate of a child. This reconciles long-standing contradictory results. Throughout history, human societies have tended to value offspring of one sex (usually males) more than the other. Often, such preferences have resulted in higher pre-adult mortality rates for the unwanted sex, through infanticide as well as neglect (Williamson, 1976; Dickemann, 1979; Johansson, 1984; Scrimshaw, 1984). Darwin (1874) noted this and speculated that "There is reason to suspect that in some cases man has by selection indirectly influenced his own sex-producing powers". He believed that the tendency to give birth to more sons than daughters in certain cultures could be due to earlier traditions of female infanticide. Previous attempts to model the effects of infanticide on the human sex ratio have obtained strikingly disparate results. It has been concluded that infanticide of females will not bias the sex ratio (Shaw, 1961), that it will lead to a male-biased sex ratio (Uyenoyama & Bengtsson, 1979), and that it will lead to a female-biased sex ratio (Harada, 1989). I will show how each of these conclusions may be correct, depending on the manner in which the parental preferences are implemented. It is assumed that a single autosomal diallelic locus expressed in one parent can alter the sex ratio (defined as the fraction of males) at conception. This locus may, for example, influence the relative proportions of X and Y sperm or the probability of survival of these sperm within the mother (James, 1987; Chahnazarian, 1988). After conception, the sex ratio is affected by differential mortality of the sexes, before and/or after birth. For instance, male mortality might be higher at the fetal stage, leading to a lower sex ratio at birth, or female infants might be killed, leading to a higher sex ratio among adults. Clearly, such processes may also affect the total number of offspring that survive to reproductive age. Table 1 shows the specifics of the model. The genotype of one parent (say, the mother) at the A locus influences the sex ratio of her offspring. The genetically determined sex ratio (fraction of males) is known as the "primary sex ratio". The original sex ratio within a family can then be altered during the life cycle to produce the "adult sex ratio", i.e. the sex ratio at reproductive age. Some ways of altering the sex ratio will also affect the number of offspring produced. Both the adult sex 195

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ratio (s,~-) and the total offspring number (iv) are thus functions of the primary sex ratio (s;j) and the specific processes studied. Discrete generations and a very large population size are assumed. Given these assumptions, the dynamics of the genotype frequencies are described by a system of recursion equations (see Appendix). The question here is which primary sex ratio (Table 1) is favored by natural selection. We approach this by assuming that only one allele is present initially and ask if a rare new allele may increase in frequency. This type of local analysis is, of course, in general not sufficient for understanding the dynamics of the system. However, for simple sex ratio models like the present one, it gives a very good picture (Eshel & Feldman, 1982). TABLE 1

Definition of variables used in model Genotype

Frequency in males Frequency in females Primary sex ratio Adult sex ratio Offspring number

AtAI

AIA2

A2A2

xt~ Yll st~ s~t tit

xt2 yl2 s~z s~: tt2

xz~ y22 s22 s~2 t22

Conditions for initial increase can be found through local stability analysis of the fixation point. In the present model, allele A2 will invade a population fixed on allele Ai if the following is positive: (s~2-s~l)(l -2s~l)ttt +(tl2--tll)[S~l(1 --S~z) + (1 --S~I)SI2].

(1)

We seek the value s* of st~ for which the corresponding values of sit and ttl are such that (a) if s~ does not equal s*, alleles leading to a sex ratio closer to s* will always invade, and (b) if sit does equal s*, then a new allele leading to a different sex ratio can never invade. A few examples will demonstrate the range of situations covered by the model. First, assume a strong preference for a particular male-biased family sex ratio (8) achieved by infanticide and no usage of birth control. In terms of the model, s~, =s~2=s~2=.~. The sign of expression (1) will hence be determined by ( t t z - - t l l ) , which means that selection will favor the genotype that produces the highest number of surviving offspring. This will be the genotype whose original sex ratio equals .~ since its phenotype will, on average, kill the fewest children. Thus, selection favors a male-biased sex ratio (8) at birth, as was shown by Uyenoyama & Bengtsson (1979). Next, suppose family size is controlled strictly by laws or custom (t~w= tl2 = t22) and that some daughters are killed. Here, (1) reduces to (s12- sll)(l - 2slj)tjj, which is positive if and only if s[i < 1/2 and sl2>sll or sil > 1/2 and si2

Female infanticide and human sex ratio evolution.

The possible effect on the evolution of the human sex ratio of a preference for male children is examined in a genetic model. It is shown that the kil...
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