Abstract

Selection is expected to cause parents to adjust the sex of their offspring when the environment is predictable during development, and it is expected to affect each sex differently. When several offspring compete for limited resources, the environmental conditions acting on the brood are not a good predictor of the conditions affecting individual offspring. There is evidence for some species that, regardless of any bias in brood sex ratio, the sex of individual offspring within a brood may be related to its position in the hatching/birth/weight rank, in ways that might correlate with the expected share of available resources. Here I propose that parents may be selected to adjust offspring sex within the brood, provided that some depreciable environmental quality is unequally distributed among siblings in a predictable manner. I call this the “intrabrood sharing-out” hypothesis and present a graphical model to derive predictions about the relationship between offspring sex and positions within the brood. The model considers that sibling competition not only produces differences in the mean share of resources among siblings, but it also increases the predictability of the share obtained by high-ranking sibs and decreases the predictability of the share for low-ranking ones. Consequently, parents should be selected to deal with such a distribution by promoting the conditions to make it more predictable and then adaptively adjust the sex of particular siblings, especially in high-ranking positions within the brood, rather than to modify the sex ratio of the brood as a whole.

In species with sexual reproduction, parents should divide their parental investment into the production of sons and daughters. Several theories predict that natural selection should cause parents to adaptively adjust the sex of offspring according to predictable conditions (reviews in Charnov, 1982; Clutton-Brock, 1991; Frank, 1990; Godfray and Werren, 1996; Hardy, 1997). For example, in polygynous animals with sexual size dimorphism, males may have higher reproductive potential than females, although sons may be costlier to produce than daughters (Andersson, 1994; Clutton-Brock, 1991). For these species, Trivers and Willard (1973) reasoned that investing in a high-quality son might yield higher reproductive return than investing in a high-quality daughter, while, conversely, a low-quality daughter would over-reproduce a low-quality son. Thus they predicted that high-quality mothers should bias their investment toward the sex with the higher reproductive return (usually males).

The Trivers-Willard effect was originally considered a consequence of sexual selection acting on polygynous males. However, the environment can produce other sex-specific effects on fitness. For instance, there is evidence in parasitoid wasps that female offspring can increase survival and future fecundity from being reared in high-quality hosts, and females tend to lay either male or female eggs depending on host quality (Charnov, 1982; Charnov et al., 1981; Godfray, 1994, Hardy, 1994). The relationship between offspring environment and sex-specific fitness may differ from case to case, and, indeed, theory makes opposing predictions. For instance, dominant mothers should produce sons (Clutton-Brock et al., 1984) or daughters (e.g., Hiraiwa-Hasegawa, 1993) depending on species, and the progeny produced early in the breeding season should be biased toward males (Velando et al., 2002; Wright et al., 1995) or toward females (Cordero et al., 2001; Sheldon, 1998). Other theories predict sex ratio biases for different causes such as group structure and sex differences in dispersal (Clark, 1978; Hamilton, 1967; Hoogland, 1981; Silk, 1984), and even the Fisherian equilibrium of investment in both sexes (Fisher, 1930) requires some sex adjustment away from the meiotic 1:1 sex ratio when sons and daughters have different cost (Charnov, 1982).

All these theories on adaptive sex-manipulation must assume that parental influence on offspring sex is translated into fitness return. Since fitness return depends on the conditions of the offspring's environment during its development, predictability of such conditions should be a key factor favoring selection for parental ability to adjust offspring sex (see e.g., West and Sheldon, 2002; West et al., 2002). This idea is clearly incorporated into the Trivers-Willard–type or environmental hypotheses (Charnov and Bull, 1977; Charnov et al., 1981; Clutton-Brock, 1991; Frank, 1990; Hardy, 1997), although predictability of returns can potentially affect selection for any type of sex adjustment.

Many species produce several offspring per reproductive attempt, and these offspring share some limited resources or other conditions affecting the brood. In these cases, parental condition or environmental factors affecting the brood as a whole may not be good predictors of the conditions and returns associated with every offspring. Therefore, it is likely that predictions from most theories about sex adjustment should be modified to be applicable to individual offspring within broods.

Only in the case of the hypothesis proposed by Trivers and Willard (1973) was it suggested that species with large broods may not fit the predictions because the relationship between maternal condition and offspring condition would be less clear when the mother must divide the parental expenditure between several offspring. Later works stated that the original Trivers-Willard predictions cannot be applied to litter or brood sizes greater than one, mainly because when both the sex ratio and the number of offspring should be adjusted simultaneously, good-quality parents may gain more by increasing the number of offspring than by adjusting the sex ratio of the brood (Frank, 1987, 1990; Gosling, 1986; McGinley, 1984; Williams, 1979). Moreover, Frank (1990) argued that adjusting the sex of individual offspring may not be favored by selection as brood size increases. In spite of these considerations, many recent works have applied sex-ratio predictions to broods without dealing with these problems, which has probably contributed to increasing confusion in the current debate about the evidence for sex-ratio adjustment (see, e.g., Cockburn et al., 2002; West and Sheldon, 2002; West et al., 2002).

Only one hypothesis exists on sex allocation within broods (Williams, 1979). Williams suggested that maternal ability to provide parental care should be related to a sequence of brood composition that combines the demands of litter size and offspring sex (for instance, from small female-biased broods to large male-biased ones), but with unisexual broods of either sex along the sequence. This would result in a nonlinear variation in the brood sex ratio along the sequence of broods, so that the quality of the mother or the environment of the brood may not correlate with the sex ratio of the brood. Williams' hypothesis has received some support, mainly from studies of species producing few offspring per reproductive attempt (e.g., Cassinello and Gomendio, 1996).

Williams' hypothesis predicts combinations of brood sizes and sex ratios but treats every position within the brood as equivalent regarding sex-ratio adjustment. In contrast, an increasing number of studies in birds (Ankney, 1982; Badyaev et al., 2002; Bednarz and Hayden, 1991; Bortolotti, 1986; Clutton-Brock, 1986; Ryder, 1983; Velando et al., 2002) and mammals (Gosling et al., 1984; Fernández-Llario et al., 1999; Vanderbergh and Hugget, 1994) have noted that offspring sex is not independent of positions within the brood, and it appears to be associated with the hatching/birth/weight rank in ways that might correlate with some environmental feature at the level of individual offspring.

The situation within a brood, when different offspring share current resources, may be different from other cases because the environmental conditions affecting each offspring not only depend on the conditions affecting the brood as a whole but also depend on the interactions among siblings (for instance, their competition for the share of resources; Mock and Parker, 1997). One consequence of these interactions is that the mean share of resources as well as its predictability may differ according to positions within the brood—related, for instance, to the dominance hierarchy between siblings. But moreover, selection may favor parental strategies to increase the predictability of the interactions among offspring. The final arrangement within the brood may lead to conditions favoring one sex or another, or even to no sex adjustment, depending on the relative position of each offspring with respect to other siblings and the predictability of its environment. Here I present a mostly graphical model to derive predictions for sex adjustment in species where several offspring share current resources.

The model

Consider that some depreciable (sensu Clutton-Brock, 1991) environmental quality at the level of one individual offspring (resources, r) positively influences offspring success; the relationship between r and fitness return is a function ϕ(r) for a female offspring and μ(r) for a male offspring.

Resource r may be regarded as parental expenditure if provided by parents (Clutton-Brock, 1991). In other cases, parents may simply release propagules into an environment, but even in these cases they can theoretically influence r—for instance, by choosing the place and time of release. For the purpose of this model, r is considered in its wider sense including not only the resources allocated into propagule size before release, but also those obtained by the offspring during its development thanks to parental effect (Mousseau and Fox, 1998).

Assume that parents influence the value of r by allocating parental effort, so that the evolutionarily stable amount of parental expenditure per female offspring is given by the value of r = f* where ϕo(r)/r is maximized, henceforth ϕ( f*)/f*. This can be represented by the straight line with the highest slope that touches the fitness curve (Lloyd, 1987; Smith and Fretwell, 1974). Likewise, optimum expenditure into male offspring (i.e., highest fitness return per unit r) occurs at r = m* (Figure 1). If investing in one of the sexes becomes more profitable, as denoted by the slope of the straight line that indicates the rate of return per unit r, then the production of this sex will be favored. Contrary to females, the return curve for males depends on their competitive success and is thus very sensitive to the sex ratio. Consequently, as one sex becomes overproduced, the mean reproductive success and the return curve for males should change (Fisher, 1930). The evolutionarily stable equilibrium can be reached when both slopes equalize at  

formula

Available resources for an individual offspring (r) might be for any reason constrained to any amount different from m* or f*. In all cases, the sex with highest reproductive return will be favored for r values higher than a critical value, rc, above which μ(r) − ϕ(r) > 0, as implicitly stated by Trivers and Willard (1973; see also Carranza, 2002). The difference between the fitness return after producing a son minus the fitness return after producing a daughter is expected to be proportional to the magnitude of the selection component (S) for sex adjustment for every value of r, of either sex according to sign.  

formula
Note that male has been taken here as the sex with higher reproductive return when receiving extra resources, but the opposite situation is equally possible.

Lifetime reproductive success in iteroparous organisms scale with the number of offspring. In a large population at the sex ratio equilibrium, parents will keep the same rate of return per unit of expenditure by producing offspring of either sex, provided that they allocate the sex-specific optimal amount of resources to individual offspring (Frank, 1990; Kolman, 1960). Any departure from such amount of resources per individual would decrease the rate of return regardless the sex and number of offspring.

Let us now consider the case when several offspring are produced in a single reproductive attempt. This includes brood sizes >1, but it also applies to other cases when offspring from different births share limited resources, such as for humans. When several offspring are produced per reproductive attempt, the available amount of resources for the brood is likely to be much higher than the optimum for one offspring of the costliest sex. Hence, even a parent in rather poor condition can theoretically produce a good offspring of the costlier sex, provided that the expenditure in other offspring is adequately reduced (McGinley, 1984; Williams, 1979). Conversely, some individual offspring from a breeder in good condition (or good brood environment) may receive less resources than some others from a parent in poor condition if resources are unequally distributed within the brood. It follows that sex-adjustment predictions based on brood environment may not hold because offspring sex should be related to the expected share of resources.

We may first assume that parents are able to equally distribute brood resources among the offspring of each sex according to the optimum for that sex. In this case, the predictions may agree with that of Williams (1979; i.e., a combination of sexes that yields maximum return for resources available for the brood). However, equal allocation by parents according to sex may not be possible. Although selection acting on offspring may promote different extraction rates by males and females within a brood, sibling rivalry often leads to unequal distribution of resources both between and within sexes (Mock and Parker, 1997) and hence to suboptimal allocation per offspring from the point of view of the parents.

We can rank the siblings within a brood according to the share of resources received. This arrangement may be determined, for instance, by the existence of a dominance hierarchy among them, but also by any differential access to some environmental quality. I will refer to positions within the brood to mean those determining the relative share on any depreciable environmental quality among siblings. Then, resources (r) per offspring as a function of rank-decreasing positions within the brood might follow any pattern depending on the sharing-out mode of brood resources, which may result from degrees of intensity of sibling competition, from parental strategies of resource distribution among offspring, or from the interaction between both. The optimum total return for parents will be obtained by allocating to each position the sex yielding the highest return as predicted by S(r) at this position. This leads to the prediction that the costlier sex should be allocated at rank positions above the critical value, rc, and the other sex down the rank. Any departure from this arrangement should decrease the slope which represents the rate of return per unit r and hence the total return for parents. Note that extreme cases are particular. In a theoretical case where all sibs would always receive the same share, there would be no point for intrabrood sex adjustment. In the opposite extreme case of very high competition and siblicide, the second position may be expected to receive too little share of resources. Then total fitness return could be higher by producing two rather suboptimal offspring than a single optimal one. Under such conditions parental strategies to reduce sibling competition are expected, including the reduction of size differences between siblings by reversing the relationship between hatching order and sex-specific size.

However, parental abilities for sex adjustment may not be favored by selection with the same strength at every position within the brood. So far, we have considered the share of resources as moving downward in the sibling hierarchy, but we have assumed them to be fixed amounts for every position. The degree of sibling competition differs between species from almost equal distribution of parental resources to siblicide. In addition, competition may vary within a species according to total available resources (i.e., the environmental conditions affecting the whole brood). This dependence on the environment introduces a stochastic factor which, in the case of a brood, affects each offspring differently, depending on its rank within the brood. Empirical information indicates that stochastic environmental factors affect rear positions in the sibling hierarchy more strongly (Lack, 1954; Ricklefs, 1968), but that at the same time low-ranking sibs can buffer the effect of variable conditions over high-ranking sibs (Drummond and García, 1989; Mock and Parker, 1997). Therefore, as we go down the rank, the mean of r decreases and, most important, its variance increases (Figure 2).

We may consider that an offspring cannot survive with an amount of resources below certain minimum value, r = rmin. As the variance of r increases, the probability of rrmin augments. In addition, unpredictable events such as predation or any other environmental stressing factors are likely to affect lower ranking sibs more strongly, despite a considerable amount of parental effort probably having been already invested into them. Actually, mortalities may be disproportionately higher in smallest pups or last-hatched chicks (Clutton-Brock, 1991; Lack, 1954; Ricklefs, 1968).

Thus, let αp(r) be the survival probability of an offspring at position (p) that expects to receive a mean amount of resources (r). For any sharing-out mode, there is a family of probability functions, each of them corresponding to a particular position within the brood, like, for example, those represented in Figure 3.

The selection component (S) acting on parents to adjust the sex of offspring should be proportional to the difference between male and female fitness but devaluated by the survival function for every position.  

formula
When S > 0 selection favors the production of males and conversely females, and selection is weaker at lower ranking positions within the brood (Figure 4).

Finally, besides the benefits of adjusting the sex of particular offspring according to their individual environments, we can assume that selection might act on parents to produce a general bias in the sex ratio of the brood. This may happen, for instance, for reasons such as the first-cohort advantage (Wright et al., 1995), local resource competition or enhancement (Emlen et al., 1986; Gowaty, 1993) or simply by Fisherian selection toward the rare sex (Fisher, 1930). In terms of the present model, this means that one sex will have increased returns. We may start simply by elevating the return function of one of the sexes in Figure 1. Although the slopes for the population will tend to equalize, they do not need to equalize for every parent and at every moment. For instance, early fledged males may outcompete late fledged ones with the same body mass (Daan et al., 1996). In the present model this simply means that the critical point, rc, is displaced, but intrabrood positions are still relevant. Likewise, if some low-ranking positions have low survival expectancies, they will contribute slightly to the final sex ratio of the brood, and hence selection for sex adjustment at these positions will be weak.

To summarize, the model makes two assumptions: (1) two of more siblings share some depreciable environmental quality or resources effected by their parents, and (2) offspring of one sex will increase its fitness return comparatively more than those of the other sex by receiving extra resources. Then, the model makes the following predictions. (1) Parents will be selected to develop strategies to increase the predictability of resource sharing between offspring, so that initial asymmetries are expected, which relate to the expected share of resources, in the form of differences in birth weight or hatching asynchrony, for example. (2) The sex of individual offspring will be related to positions within the brood, so that the sex with higher reproductive return will be associated with positions obtaining a higher proportion of resources. (3) The increase of general environmental quality (e.g., maternal condition) is expected to produce biases toward the costlier sex from the highest down to the lowest positions of rank within the brood. For example, for males costlier than females, offspring in the best position may be a male even for poor-condition mothers, and subsequent positions will change from female to male bias down the rank of positions as we consider mothers in better condition. (4) Selection on mothers to adjust offspring sex is expected to be stronger at highest positions and weaker down the rank of positions within the brood. Sex adjustment in lower positions would be favored only if environmental predictability is high enough; otherwise primary sex ratio should tend to unity for last positions within the brood in spite of the bias to the cheaper sex that could occur at independence in these positions due to sex-differential mortality. (5) Extreme sib competition, including siblicide, may promote parental strategies to reduce the differences between siblings by reversing the relationship between expected resources and sex at positions within the brood, thus resulting in exceptions to the general arrangement predicted in the model. (6) Selection for sex-ratio adjustment of the brood as a whole (e.g., related to first-cohort advantages, repayment, or Fisherian equilibrium), which favor one sex over the other, will also be weaker at producing sex adjustment in last positions within the brood.

The predictions outlined above are neither independent nor equivalent. Whether parents can effectively control/predict the outcome of interactions between offspring (prediction 1) will affect the remaining predictions. A certain level of parental certainty is required to allow intrabrood sex adjustment, since otherwise there would be no positions within the brood in the sense of this model. But also, extreme reduction of sib interactions may lead to the production of independent offspring instead of broods. For the remaining predictions, 1–4 are more general provided the two basic assumptions are met, while 5 and 6 refer to particular circumstances. Regarding prediction 6, note that a bias of brood sex ratio toward the smaller sex affecting all except the very low-ranking positions is compatible with the predominance of the larger sex in first positions.

DISCUSSION

Implications of the model on sex ratio studies

Contradictory results in sex ratio studies (Clutton-Brock, 1991; Clutton-Brock and Iason, 1986; Festa-Bianchet, 1996; Frank, 1990; Godfray and Werren, 1996; Hardy, 1997) may be influenced either by constraints of parental ability to adjust offspring sex (e.g., Krackov, 1995; Mittwoch, 1996) or by the complexity of predictions (sometimes opposite) on the adaptive value of parental decisions about the sex of offspring (Frank, 1990; Hardy, 1997; West and Sheldon, 2002). Recent works (e.g., Oddie, 1998; West et al., 2002) and meta-analysis results (West and Sheldon, 2002) indicate that sex ratio adjustment occurs in taxa with very different sex determination mechanisms (and presumably different kinds of proximal constraints) and stress the role of the predictability of offspring's environment and its sex-specific effects on fitness return. The model presented here highlights two main points about predictions on the relationship between environment and offspring sex. First, the model stresses the role of environmental conditions at the level of the individual offspring, instead of at the level of the mother or the brood as a whole. Second, the model emphasizes the differences of environmental predictability at different positions within the brood, affecting selection for sex adjustment.

Conditions at the level of the individual offspring

Literature on sex ratio acknowledges that relevant conditions for selection on sex adjustment are those at the level of individual offspring. The Trivers-Willard (1973) hypothesis was a particular case when offspring conditions largely depend on maternal condition. In many cases, however, mothers can influence the environment of individual sons and daughters regardless of their condition—for instance, by placing offspring at different sites (e.g., parasitoid wasps; Charnov, 1982; Godfray, 1994) or by modifying the environment for each offspring (e.g., sex differentials in mass provisioning wasps; Strohm and Lisenmair, 2000), with the result that the environments may be highly different among siblings. A common feature in all these cases is that the environment of a given offspring is largely independent from that of other offspring.

When interactions between siblings occur, they may affect individual conditions. For example, in gregarious parasitoid wasps (where more than one offspring develops within a single host), sibling competition may promote different parental strategies, including reduced clutch size for one or both sexes and single-sex clutches (Godfray, 1986; Rosenheim, 1993). However, models on interactions within broods usually assume that resources are shared equally between siblings, at least within the same sex (Charnov and Donover, 1995; Godfray, 1986). This may not be the case, and inequality of resource share may increase in larger broods (Mayhew, 1998) even if they are unisexual (West et al., 2001). Assuming that fitness return differ between sexes, the present model proposes (prediction 1) that mothers will develop strategies to increase predictability of positions within the brood to adjust offspring sex. If the existence of predictable positions is somehow constrained, the remaining predictions are not applicable. Alternative strategies may be to produce independent offspring at least for one (perhaps most sensitive) of the sexes. It would be worth exploring whether it can contribute, for example, to explain the occurrence of clutches with both sexes versus unisexual clutches, as well as single-male clutches in parasitoid wasps (Godfray, 1994; West et al., 2001).

Differences in environmental quality affecting individual offspring that share limited resources are not necessarily determined by direct competition between siblings. For example, the hierarchical arrangement from positions 1 to n may be equivalent to distances from a central or inner place outward along a transect in a clutch with many offspring, provided that either the mean or the variance of some key environmental quality differs along the transect. This makes a parallel with some forms of environmental sex determination (Shine, 1999) but could also be expected in species with genetic sex determination.

The intrabrood approach at the level of individual offspring may also affect predictions on sex-ratio variance among families. Kolman (1960) proposed that intrabrood variance in sex ratio was a neutral trait under selection based on Fisher equilibrium that would also apply to Trivers-Willard conditions (Frank, 1990; Williams, 1979). This leads to the prediction of higher-than-binomial variances in the sex ratio among broods. This prediction has received little support, however (see, e.g., Hardy, 1997). One implicit assumption in Kolman's model is that parents can allocate the appropriate amount of resources to every offspring they produce in a brood. Thus, selection would maintain Fisher equilibrium equally well by families investing in males and females or by an adequate proportion of families investing in unisexual broods of either sex. Likewise, a mother in good condition in the Trivers-Willard model would do well by producing unisexual male broods, and mother in a poor condition should produce unisexual female broods. The model presented here considers position-specific differences in the amount or resources that each sib can obtain. Thus, because parents are not able to allocate the sex-optimal amount of resources to each offspring by producing unisexual broods, and provided that they can promote predictable positions within the brood, the expected variance in sex ratio among broods should be lower (i.e., closer to binomial), than previously expected.

Environmental predictability and offspring sex

The approach in this model agrees with the generalization that selection on sex adjustment depends on the predictability of offspring environment (West and Sheldon, 2002) and translates this to the individual level. Most important, the model incorporates the assumption that sibling competition and interactions between intrabrood positions can modify the predictability of conditions for individual offspring, mainly reducing it for low-ranking sibs, but at the same time increasing it for high-ranking sibs. This can explain (1) the presence of runts of any sex, more likely when interactions between siblings/positions are possible, and (2) higher concordance between expected and observed sex at first positions (e.g., Fernández-Llario et al., 1999; Komdeur et al., 2002; Velando et al., 2002). As a consequence, parents should be selected not only to adjust the sex of offspring related to positions, but also to influence the predictability of the resource share at positions, and give up (i.e., weaker selection for sex adjustment) when there is unpredictability and/or low survival expectancies.

Evidence so far

Most studies on sex ratio during the last three decades have investigated the sex of whole broods or singletons according to predictions from existing theories (Frank, 1990; Godfray and Werren, 1996; Hardy, 1997). Whether they found any relationship on brood sex ratios or not, further intrabrood adjustments may have occurred as well, although probably many of these studies have simply not looked at positions within the brood. In fact, clearest evidence for adaptive sex ratio adjustment according to mother or environmental conditions (Charnov, 1982; Trivers and Willard, 1973) comes from species where every single offspring develops quite independently from other siblings, such as many parasitoid wasps (Charnov, 1982; Godfray, 1994), red deer (Cervus elaphus; Clutton-Brock et al., 1984), or Seychelles warblers (Acrocephalus seichellensis; Komdeur et al., 1997; see also Emlen, 1997).

We should note that the occurrence of differential returns according to sex may favor independence between developing offspring in agreement with prediction 1, and, conversely, many species producing broods may not have sex-differential returns and hence not be selected to vary the sex of individual offspring according to conditions. For example, for mammals, Carranza (1996) has shown that increases in sexual dimorphism across the phylogeny are accompanied by decreases in the number of offspring per litter, with many taxa reaching the limit of bearing singletons. It is also expected, therefore, that predictions of the type of sex adjustment according to conditions (Trivers and Willard, 1973) should be less likely for species producing litters.

Slagsvold et al. (1986) reported a positive relationship between sexual size-dimorphism and hatching asynchrony in birds and interpreted it as a mechanism to cope with the Fisher (1930) equal-allocation principle. In the light of the present model, this finding agrees with prediction 1 that in dimorphic species, where return curves differ between the sexes, selection will act on parents to produce initial asymmetries for intrabrood sex adjustment.

Most reported examples that meet the assumptions of differential return according to sex and the production of broods where siblings must share limited resources so far are from endotherms, although there is no reason that these conditions cannot apply to other organisms, including plants (see below).

An increasing number of studies on birds provide clear evidence on the relationship between hatching order and sex ratio, and we have experimental evidence that females can control the sex of individual eggs throughout the laying sequence (e.g., Kalmbach et al., 2001) on the basis of preovulation control mechanisms (Komdeur et al., 2002). In lesser snow geese (Chen caeruleslens caerulescens), Ankney (1982) reported that the first two eggs laid produced more males (64%) than the last two (28%), although a larger sample of the same species failed to find any relationship (Cooke and Harmsen, 1983). Ryder (1983) found for ring-billed gulls (Larus delawarensis) that during three reproductive seasons the first egg in the brood consistently produced more males (63.7% of males, 3 years of combined data), the second one produced more females (38.8% of males), and the sex ratio of the third laid egg did not differ from unity (43.1% of males), in agreement of predictions 2 and 4 of the present model.

In roseate terns (Sterna dougallii), Szczys et al. (2001) reported a general bias to female chicks both at hatching and fledging. The adaptive reason for such a bias is not certain, but provided that it exists, the outcome agrees with the present model. Clutch size is usually two, but only the first egg laid shows a bias toward females. Chicks from the second egg have higher mortality, and the sex ratio of these eggs is not biased (Szczys et al., 2001).

In bird species with sexual dimorphism in favor of females (Andersson, 1994), parents should be selected to provide the conditions for a higher investment in the heaviest sex, for which intrabrood positions may be relevant. Accordingly, most such species studied produced more males down the hatching order (Clutton-Brock, 1986). However, there are some cases where females are larger than males, and the first egg laid appears to produce mostly males. An example of this pattern is Harris's hawk (Parabuteo unicintus) studied by Bednarz and Hayden (1991), where females are 46.7% larger than males. They found that nests where males hatch first produced more fledglings than those where females hatch first. The reason was the high probability of siblicide in these later nests due to the big size differences in favor of the female chick. Their observations agree with the idea (Bortolotti, 1986) that in species where sibling competition is very intense and there are big differences in size, brood reduction by siblicide is likely even in good years if the larger sex is produced first. By reversing the sexes as a function of the hatching order, or by producing unisexual broods (Edwards et al., 1988), parents may produce two medium-size offspring, thus obtaining rather suboptimal returns from both sexes although higher total return from the brood.

In zebra finches (Taenopygia guttata), weight at fledging influences reproductive success (Haywood and Perrins, 1992) and survival (de Kogel, 1997) of female offspring, but this seems not to be the case for male offspring (de Kogel, 1997; Kilner, 1998). Eggs laid first in this species tend to be females, with increased male bias down the hatching order (Kilner, 1998; but see Clotfelter, 1996, for a reverse pattern). Kilner (1998) experimentally changed the conditions of food availability and found that the first egg was female biased in all cases, the second egg changed from female to male bias as conditions got worse, the third one was male biased in all cases, and the results for the remaining eggs were predominately male-biased but more variable and less affected by food conditions.

A good example of the relevance of intrabrood sex adjustment in the context of two different sex ratio theories come from the European shag (Phalacrocorax aristotelis). It is a size-dimorphic seabird (adult males 22% heavier than females during the breeding season; Cramp and Simmons, 1977), for which body size is related to reproductive success, as bigger males obtain the best breeding sites and the best mates (Aebischer et al., 1995; Potts et al., 1980) and more extrapair fertilizations (Graves et al., 1993), so a Trivers-Willard effect is applicable. Parents are able to unequally distribute parental resources among siblings on the basis of hatching asynchrony, which promotes the dominance and prior access to resources by the first hatching bird (Velando et al., 2002), according to prediction 1. However, differential parental resources are translated into fitness increment of sons only if they are hatched early in the season, so first-cohort advantage (Wright et al., 1995) selects for producing males early and females late. In a colony of European shag studied in the Cíes Islands (northwestern Spain), pairs breeding early in the season produced more sons (63%), whereas late-breeding pairs produced more daughters (36% sons; Velando et al., 2002). But according to the present model, sex adjustment occurred mainly for the first egg laid, which was male biased (77%) in early broods and female biased (30% males) in late broods, while there was no significant bias in second and third eggs (Velando et al., 2002). Similarly, in crimson rosellas (Platycercus elegans), a socially monogamous Australian parrot, the sex ratio of offspring is female biased (41.8% males) at the population level, but such a bias is accomplished by early broods in the season. Within broods, only the first eggs followed the brood level pattern, whereas the sex of middle- and late-laid eggs did not change as the season progressed (Krebs et al., 2002).

Albrecht (2000) reported a female-biased sex ratio (27 out of 34) for the last-hatched chick within broods of house wrens (Troglodytes aedon). However, 32% (16 out of 50) of runt chicks died before blood sampling occurred, and sex was not determined for them, so an effect of higher male mortality cannot be fully discarded in this result. In contrast, Albrecht (2000) did not report any data on sex adjustment in the first or any other positions in the laying sequence. The intrabrood model would predict a male bias for the first position more strongly than a female bias for the last one. Another possibility, however, is that the house wren does not conform to the assumptions of the model because, although moderately polygynous, it is a size-monomorphic species for which fitness return for both sexes as a function of differences in parental expenditure may not differ.

In mammals, although a number of studies have investigated sex ratio variation between litters, studies that pay attention to offspring sex according to positions within the litter are extremely scarce (but see Clark et al., 1993; Vanderbergh and Hugget, 1994). A recently reported mammalian example is that of the wild boar (Sus scrofa). It is a polygynous, dimorphic ungulate, which usually produces several offspring (median 4) per litter. Soon after birth, piglets compete among themselves for the best nipples (English and Smith, 1975; McBride, 1963). The unique neonatal dentition is specifically adapted to sibling competition: canines and third incisors are fully erupted several weeks before birth, with the anterior portion of the jaw rotated in such a way that the third incisors temporarily assume a caninelike orientation (Fraser and Thompson, 1991). Birth mass appears to be very important for this competition (Thompson and Fraser, 1986) and in survival (Fraser and Rushen, 1992; Le Dividich and Noblet, 1981). Mothers may influence the distribution of maternal resources among offspring by affecting intrauterine and hence birth mass. For a sample of litters from a population of wild boar of central Spain, it was found that the heaviest fetus was a male in 81% of litters, and the sex ratio was more female biased down the weight rank (Fernández-Llario et al., 1999). Also, data from different years showed that improvement of environmental conditions (higher rainfall) produced male biases down the rank according to prediction 3 (Fernández-Llario P, unpublished data). When birth mass stands out as the key variable to determine intrabrood positions, the evidence entails an unavoidable circularity: provided that there is some sexual dimorphism also at birth, the heaviest offspring in a brood is likely to be a male. In the wild boar, although intrauterine sib competition cannot be discarded, the mechanisms that the mother uses thereafter during development to maintain the initial arrangement strongly suggest that the initial asymmetries are favored (see Le Dividich and Noblet, 1981; Perry and Rowell, 1969; Rohde and Gonyou, 1988; Rossillon-Warnier and Paquay, 1984; Rushen and Fraser, 1989).

Humans are slightly dimorphic and moderately polygynous, and male reproductive potential is higher than that of females (Betzig et al., 1988; Daly and Wilson, 1983; Mace, 2000), so males might benefit more than females from receiving extra investment. Parental care in humans involves the sharing of parental resources by siblings from different births because children need a long-term parental investment. Human offspring should therefore be considered as litters of polytocous mammals regarding sex-ratio hypotheses (e.g., Frank, 1990). The share of parental resources might decrease as the number of offspring increases, so a first-born advantage can be expected. Some studies have shown that primiparous women deliver more boys than girls, the probability of boys decreasing with increasing birth order (Erickson, 1976; Rostron and James, 1977; James, 1987; Feitosa and Kreiger, 1993; Mace and Sear, 1997). However, evidence for humans appears too variable between populations and cultures to draw any general conclusion so far (James, 1996; Maconochie and Roman, 1997; Martin, 1994; Renkonen, 1970; Ulizzi and Zonta, 1995).

The approach in the present model may also be relevant for sex allocation in plants. Recent work on monoecious plants provides evidence for a trade-off in resource allocation to male and female structures (Campbell, 2000; Mazer and Dawson, 2001; Mazer et al., 1999). Also, fitness-return curves may differ between genders as a function of resources received (Campbell, 2000). Sex allocation is usually 1:1 between both sexual functions in those plants for which there is open competition between pollen from different individuals (Campbell, 2000; Mazer and Delesalle, 1998), but it is interesting that in some species, sexual structures are produced at places that predictably receive a different share of resources. For example, Mazer and Dawson (2001) investigated sex allocation in the annual herb Clarkia unguiculata, which produces bisexual flowers. Because resources can affect the fitness of female more than male functions, they predicted that flowers of bigger plants (supposedly of higher resource status) should invest proportionally more in female function. However, they found no bias in sex allocation related to plant size. Mazer and Dawson also predicted that flowers produced earlier, (i.e., at basal positions within a branch), which have access to a larger share of resources, should bias their investment to female function compared to more distal flowers. This relationship was highly significant and consistent among different maternal families. Moreover, although phenotypic variation in several floral traits was high among different maternal lines, the sex (pollen:ovule) ratio did not vary among families for flowers at positions 1–4 (basal to distal) and only varied for the last considered position (5). The concordances between these results and the predictions of the present model are straightforward.

Testing the predictions

The model presented here may help refine the predictions from other sex-ratio theories when applied to broods. For intrabrood predictions to be falsifiable, we need information on the relationships between rank positions, predictability of relevant conditions associated with them, and sex-specific effects on fitness.

A key issue is identifying the relevant positions—in other words, to determine which variable predicts the share of resources (or the environment) at the level of individual offspring. In altricial birds, egg size and/or hatching asynchrony commonly leads to constant differences among nestlings in resource share (e.g., O'Connor, 1978, 1984). In most mammals, however, parturition is not so long lasting as to produce relevant differences in birth order that could affect the hierarchical arrangement. In these cases, birth mass may be the key variable related to the expected share of subsequent parental resources. Another important question is how the sharing of critical resources affects offspring fitness and especially which sex is most favored, which may lead to opposite predictions. Likewise, relevant information includes the predictability of resource sharing or conditions at every position. Predictability at lower-ranking positions compared to higher-ranking ones may indicate to which extent we should expect sex adjustment in runts.

An interesting source of evidence for intrabrood sex adjustment may occur in cases when environmental factors differ along a gradient within the brood. It is well known that in species with environmental sex determination, the conditions within the nest mechanistically affect offspring sex (Shine, 1999). But likewise, for species with genetic sex determination, if the environment or its predictability differ in a gradient within the nest, parents should be selected to control offspring sex according to positions. Similarly, sex allocation in plants may benefit from the analysis of positions and their associated means and variances of resource share and sex-specific fitness returns.

The model shows that hypotheses on the relationship between parental conditions (or brood conditions) and offspring sex should be tested for every position independently. Thus, ideally we should know how differences in parental (or brood) conditions are likely to affect each position. For instance, the first position may remain highly unaffected by the improvement of conditions, and the difference may affect other positions stepwise up to the rearmost ones in the most favorable circumstances. This allows quite straightforward qualitative predictions and comparisons, although quantitative predictions face several practical problems.

On one hand, relevant information includes the mean and the variance of the expected share at every position for different conditions affecting the whole brood. But on the other hand, fitness return curves for male and female offspring are far from being fixed curves. In fact, the relevant relationship from the point of view of the parents is not between resources (or parental expenditure) and fitness, but on parental investment and fitness. Because parental investment includes the costs for a particular individual, it should differ among individuals. This means that the critical point, rc, may occur at different amounts of resources, r, for every breeding individual. But even if we consider the fitness curves for female offspring as fixed ones, the curves for male offspring will still be highly dependent on the sex ratio of the population, which introduces further difficulties to make quantitative predictions.

We still have limited knowledge of the costs associated with sex adjustment (Oddie, 1998; West and Sheldon, 2002), and on how such costs can affect predictions on sex ratio (Pen and Weissing, 2002). In this context the effects of intrabrood positions must be taken into account, mostly because the ratio between benefits and costs should differ among them. Future meta-analyses should indicate the extent of intrabrood effects in sex ratio adjustment when more studies have approached the problem at the level of positions within broods. Likewise, experimental manipulation is a highly promising source of evidence for sex-ratio adjustment (Komdeur and Pen, 2002), which should certainly allow more precise tests of quantitative predictions on sex allocation within broods.

Sex-ratio theory is considered one of the areas in evolutionary biology that may show strongest concordance between predictions and observed evidence (West et al., 2002). This statement hardly applies to species producing broods, not only because of the limitations imposed by the discrete nature of broods (Frank, 1990; Komdeur and Pen, 2002; Williams, 1979), but especially because we need precise predictions at the level of intrabrood positions.

Figure 1

Fitness return for individual female and male offspring as a function of the amount of parental resources (r) received. Given the female curve ϕ(r), any μκ(r) (dashed curve) for male offspring is not an evolutionarily stable strategy unless μ(m*)/m* = ϕ( f*)f*, m* and f* being the optimum r value for each sex. rc is the critical r value for sex change. A case has been chosen for which male fitness gains more than female fitness from parental resources, although this does not need to be so in all cases

Figure 1

Fitness return for individual female and male offspring as a function of the amount of parental resources (r) received. Given the female curve ϕ(r), any μκ(r) (dashed curve) for male offspring is not an evolutionarily stable strategy unless μ(m*)/m* = ϕ( f*)f*, m* and f* being the optimum r value for each sex. rc is the critical r value for sex change. A case has been chosen for which male fitness gains more than female fitness from parental resources, although this does not need to be so in all cases

Figure 2

Hypothetical frequency distributions of parental expenditure (r) received by individual offspring at different positions within a brood. With decreasing rank, the mean of r decreases, but its standard deviation increases. Numbers over the curves indicate the rank positions within the brood

Figure 2

Hypothetical frequency distributions of parental expenditure (r) received by individual offspring at different positions within a brood. With decreasing rank, the mean of r decreases, but its standard deviation increases. Numbers over the curves indicate the rank positions within the brood

Figure 3

An example of how rank positions within a brood might affect the relationship between the parental expenditure that an offspring receives and its survival probability α(r). Survival decreases more steeply for rearmost positions due to stochastic factors differentially affecting mortality of subordinate sibs. Numbers at the curves indicate the rank positions within the brood

Figure 3

An example of how rank positions within a brood might affect the relationship between the parental expenditure that an offspring receives and its survival probability α(r). Survival decreases more steeply for rearmost positions due to stochastic factors differentially affecting mortality of subordinate sibs. Numbers at the curves indicate the rank positions within the brood

Figure 4

Selection component, Sp, corrected by survival probability, αp(r) for positions within the brood. Numbers at the curves indicate the rank positions within the brood. The outermost, light line indicates the selection component before it being corrected by the survival probability

Figure 4

Selection component, Sp, corrected by survival probability, αp(r) for positions within the brood. Numbers at the curves indicate the rank positions within the brood. The outermost, light line indicates the selection component before it being corrected by the survival probability

I am grateful to Pedro Fernández-Toledo, Pedro Fernández-Llario, Concha Mateos, Juliana Valencia, and Juan Gabriel Martínez for comments. During the preparation of this work the research of J.C. was supported by project 1FD97-1504 from Ministerio de Educación y Cultura and project REN2001-1524 from Ministerio de Ciencia y Tecnología of Spain.

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