Strong asymmetries in parental care, with one sex providing more care than the other, are widespread across the animal kingdom. At present, two factors are thought to ultimately cause sex differences in care: certainty of parentage and sexual selection. By contrast, we here show that the coevolution of care and the ability to care can result in strong asymmetries in both the ability to care and the level of care, even in the absence of these factors. While the coevolution of care and the ability to care does not predict which sex evolves to care more than the other, once other factors give rise to even the slightest differences in the cost and benefits of care between the sexes (e.g. differences in certainty in parentage), a clear directionality emerges; the sex with the lower cost or higher benefit of care evolves both to be more able to care and to provide much higher levels of care than the other sex. Our findings suggest that the coevolution of levels of care and the ability to care may be a key factor underlying the evolution of sex differences in care.
Parental care involves one of the fundamental conflicts of interest between the sexes [1–6]. Care by either partner is beneficial to both partners as it increases the fitness prospects of the common young. At the same time, providing care is costly only to the caring individual. As a consequence, each partner does best in a situation where most of the care is provided by the other partner—an outcome that is clearly impossible. What thus determines the outcome of this ‘battle of the sexes′ ? Put differently, what are the eco-evolutionary factors underlying the patterns of parental care observed in nature [8,9], ranging from uniparental care (e.g. in many mammals) to male/female-biased care to biparental care (e.g. in many birds)?
Adaptive explanations of the levels of parental care are based on the relative costs and benefits of care to males and females . If there are no differences between the partners, equal care is expected. Differences in care, in turn, are explained by differences in the costs and benefits of caring. At present, two factors are considered to be the key drivers of such differences [10–15]: certainty of parentage (decreasing the benefit of care for the less certain sex) and sexual selection (increasing the cost of care for the sex that can remate faster). By contrast, we here use a modelling approach to show that even in the complete absence of these factors, substantial differences in care are to be expected. In particular, as we show below, sex differences in both the ability to care and levels of care are prone to spontaneously evolve as a result of the sexual conflict of interest over parental care and the coevolutionary interaction between levels of care and ability to care—even in the complete absence of both sexual selection and differences in certainty in parentage.
While the coevolution of care and the ability to care thus predicts strong sex differences in care to emerge, it does not predict which sex is more likely to care more than the other. However, as we show below, once other factors that give rise to even the slightest differences in the costs and benefits of care between the sexes are included in the analysis (e.g. differences in certainty in parentage), a clear directionality emerges, where that sex with the lower cost or higher benefit of care evolves to provide higher levels of care. Importantly, while both the traditional approach (fixed ability to care) as well as our approach (taking into account the coevolution of care and ability to care) predict sex differences in care in the presence of differences in the costs and benefits of care, the predicted patterns of these sex differences in care differ substantially between these two scenarios. While scenarios with fixed ability to care give rise to outcomes where both sexes provide a substantial amount of care, scenarios with coevolution of levels of care and the ability to care promote much more extreme outcomes, where one sex provides almost all the care.
2. Model and results
We start by considering the classic model of parental care, the Houston–Davies game . Let, ei, 0 ≤ ei ≤ 1, (i = m, f) denote the parental efforts of the male and female. The benefit from their common young is then given by B(em + ef), while the costs to the male and female are given by K(ei) (i = m, f). The fitness Wi of the male and female is thus given by 2.1
In this formulation, the cost of care is the loss in future reproductive success as a result of the effort expended in care. In our analysis, we first explore the consequences of a given fixed cost function. In reality, costs are not fixed but emerge from a consistent account of the entire life history of the organism, and change as the population evolves. We later take this into account in our evolutionary simulations. Costs can operate in a variety of ways. Here, we envisage the cost of increased effort as due to additional mortality after the current breeding season, so that increased effort reduces the probability that the individual will survive until the next breeding season. Other forms of cost, such as the loss of opportunity to remate in the current breeding season, could also be considered, although a different evolutionary simulation would be required to provide a fully consistent account of this form of cost (cf. ).
Using the standard assumption  that the benefit of care is an increasing but decelerating function of the total amount of care (i.e. B’(x) > 0 and B″(x) < 0 for all x > 0) and that costs are increasing and accelerating (i.e. K’(e) > 0 and K″(e) > 0 for all e > 0), it is easy to show (electronic supplementary material, S1 and S2) that the game with pay-off function (2.1) has a unique Nash equilibrium () which is both convergent and evolutionary stable (figure 1a). Importantly, as long as the cost and benefits of a given level of parental effort is the same for males and females, these efforts are predicted to be identical, that is 2.2
To supplement this analysis, we have also performed evolutionary simulations (electronic supplementary material, S3). In each simulation, there is an annual breeding season. During a breeding season, males and females pair up to breed. Those that fail to pair skip reproduction that year. The probability that an individual survives until the following year is a decreasing function of the parental effort expended in the current year. Thus, assuming that the birth sex ratio is fixed, the sex ratio in the breeding population is skewed towards the sex that expends less effort in care, and as a consequence members of the sex that expends less effort may be unable to find a mate in a breeding season. In this model, consequences of care are specified, not costs. However, it is possible to interpret results in terms of costs. The cost of care is the probability an individual dies as a result of care times the expected future lifetime reproductive success had it survived. As this latter quantity depends on the behaviour of future mates and the population sex ratio, costs depend on what evolves and cannot be specified in advance. Thus, it is not possible to make the analytic model and the evolutionary simulation exactly equivalent. Nevertheless, our evolutionary simulations are fully in line with the prediction of our analytic model that males and females evolve to provide identical levels of parental effort (equation (2.2) and figure 1b).
We will now show that a simple and realistic extension of this basic model explains the emergence of sex differences in parental care, even in the complete absence of both sexual selection and differences in certainty in parentage. In particular, we now assume that the costs of parental effort are affected by morphological and physiological features of the organisms that can evolve (e.g. mammary glands, brooding structures). We thus assume that in addition to parental effort e, there is as second evolving trait θ which corresponds to the ability of an individual to provide parental care. Specifically, we will assume that the ability to care θ is associated with a cost a(θ) that increases with ability, that is a′(θ) > 0. The higher the ability to care θ, however, the lower the cost associated with a given level of effort, that is .
We thus consider a situation where both males and females are characterized by two evolving traits (ei, θi) (i = m,f) corresponding to effort and ability to care, respectively. The fitness Wi to the male and female is thus given by 2.3
At an evolutionary equilibrium, the ability to care of each parent should be optimally adjusted to its parental effort, such that a parent that provisions e should have an ability to care θ*(e) that minimizes . At this minimum, the effective cost to the parent providing effort e is 2.4
We can then regard this situation as one where both parents have this cost function. Thus, the cost of a given amount of effort is the same for both parents, and in particular there will be a symmetric Nash equilibrium at which efforts and the abilities to care are identical for both sexes ( and ). However, unlike the standard case outlined above, this does not mean we predict this symmetric equilibrium to evolve.
Figure 2 illustrates the dependence of on e for a range of values of θ. The effective cost function K(e) is the lower envelope curve in the figure. As can be seen, even though is an accelerating function of e for each possible fixed θ, K(e) is a decelerating function of e over most of its range. This has dramatic consequences. In particular, when K(e) is decelerating at the symmetric Nash equilibrium ( and ), it is easy to show (electronic supplementary material, S1) that there are (at least) three Nash equilibria for this game.
Figure 3a illustrates this for the particular case where the effective cost is that shown in figure 2. Importantly, the symmetric equilibrium () is no longer convergence stable as adaptive dynamics lead away from this point (electronic supplementary material, S2). Moreover, there are now two Nash equilibria with asymmetric efforts and asymmetric abilities to provide care ( and , i = m, f, j = m, f, i ≠ j). Importantly, these are now points of attraction under adaptive dynamics (electronic supplementary material, S2). Thus, we predict disruptive selection on the ability to provide care, with the evolution of one sex being more able to provide care than the other. Moreover, as the ability to care diverges, the levels of care also evolve to be unequal.
An intuition of why the symmetric Nash equilibrium with in figure 1a is an attractor can be gained from the following argument. Note that in the region of the symmetric equilibrium, the best response function of females (specifying their optimal effort as a function of fixed male effort) is less steep than the line of slope −1. Thus, if male effort were held fixed at some value, female effort would evolve to be closer to the effort than male effort. If female effort were now held fixed at this new value, male effort would then evolve to be closer still to , and so on. Of course, in reality both efforts coevolve together, but the result is the same: efforts evolve to . This intuition contrasts with that for figure 3a, for which the best response function of females is steeper than the line of slope −1 in the region of the symmetric equilibrium. Thus, if male effort were held fixed at some value, female effort would evolve to be further away from than male effort. If female effort were now held fixed at this new value, male effort would then evolve to be even further from , and so on. The result is evolution away from the symmetric Nash.
Our analytic predictions are in line with our evolutionary simulations in which we allow male effort, male ability to care, female effort and females ability to care to all evolve together (figure 3b,c). As can be seen, the population rapidly evolves away from a symmetric care situation towards a situation where females are better able to care than males () (figure 3c) and also provide most of the care () (figure 3b). The one difference between the analytic predictions and the simulation is that the analytic model predicts no care by one sex, whereas the simulation predicts low, but non-zero levels by one sex. This is partly because there is mutation in the simulation model, so that zero levels of care can mutate to positive values. It is also because when one sex is providing most of the care, the sex ratio is biased towards the other sex (as survival until the following year is a decreasing function of the parental effort expended in the current year), so that members of this latter sex have a lower chance of finding a mate in the breeding season and thus a lower expected future reproductive success. This lowers their cost of care, so reducing the selection pressure to evolve zero care.
In this figure, we started our simulations in a situation where females and males are completely identical, that is, em = ef and θm = θf. As the situation is exactly symmetric between males and females, the fact that we evolved female care is due to random events (mutation and survival of offspring) that broke the symmetry; we would have been equally likely to evolve predominantly male care (see figure 4b and our discussion below). While the coevolution of care and the ability to care thus predicts the evolution of substantial differences in both care and the ability to care, even in the absence of both sexual selection and differences in certainty in parentage, it does not predict which of the sexes is more likely to care more than the other. This can be expected to change, however, as soon as other factors that give rise to even slight differences in the costs and benefits of care between the sexes are included into the analysis. Intuitively, it should be expected that, whenever these factors act in concert with the coevolution of ability to care and care, (i) the sex with the lower cost or higher benefits of care will evolve to provide higher levels of care, and (ii) compared with scenarios that neglect the coevolution of levels of care and the ability of care, differences in levels of care are substantially exaggerated, as levels of care and ability to care are coupled by a mutually reinforcing feedback.
In order to investigate this, we extended our above simulations for the coevolution of levels of care and the ability to care to allow for different degrees of certainty in parentage, and compared this with scenarios that do not take into account this coevolution (i.e. assume fixed ability to care). In particular, for each of these two scenarios (fixed ability to care, coevolution of levels of care and ability to care), and each of three different degrees of certainty of parentage for the males (1.0, 0.98 and 0.96), we ran 100 replicate simulations. Two key results emerge from these simulations (figure 4). First, as predicted from the analyses we have presented above, in the absence of sex differences in certainty in parentage (figure 4a,b), only the scenario taking into account the coevolution of levels of care and the ability to care (figure 4b) predicts sex differences in care. However, no directionality is predicted; that is, evolutionary outcomes where females provide almost all the care are equally likely as outcomes where males provide almost all the care (figure 4b). Importantly, this changes when we take into account sex differences in certainty of parentage between the sexes; here, a clear-cut directionality emerges, with females (i.e. the more certain sex) being substantially more likely to provide almost all the care than males (figure 4d,f). Second, with differences in certainty of parentage, both the scenarios with fixed ability to care (figure 4c,e) and those that take into account the coevolution of levels of care and the ability to care (figure 4d,f) predict the evolution of sex differences in levels of care. The observed patterns of these differences between the sexes, however, differ substantially between these scenarios. While scenarios with fixed ability to care give rise to outcomes where both sexes provide substantial amount of care (figure 4c,e), scenarios with coevolution of levels of care and the ability to care promote more extreme outcomes where one sex provides almost all the care (figure 4d,f). We stress that, while we have here investigated the consequences of extending our analysis with respect to one particular factor (differences in certainty of parentage), we expect qualitatively similar results for any other factor that gives rise to differences in the costs and benefits of levels of care between the sexes.
In this work, we have shown that sexual conflict over parental care promotes disruptive selection, resulting in the evolution of substantial differences in levels of parental care between the sexes. Our analysis thus predicts that differences in parental care emerge even in the absence of all other factors that induce differences in the costs and benefits of care between the sexes (e.g. certainty of parentage). Importantly, sex differences in parental care are caused by sexual conflict over care in combination with a coevolutionary interaction between levels of care and the ability to provide care. In contrast to current explanations of sex differences in parental care [10–14], which focus on factors ‘external′ to the individual (certainty in parentage and sexual selection), this novel explanation puts emphasis on the morphological and physiological features of organisms that affect the ability to provide care.
Our key modelling assumption is that the ability to care can coevolve with levels of care. This assumption is in line with the fact that sex differences in the ability to provide care are ubiquitous in the animal kingdom, and high ability in one sex is coupled with high levels of care in that sex. Examples range from pouches in female marsupials  to functional mammary glands in female mammals , brood structures in male seahorses and pipefishes , and increased brain size in the sex that provides sole parental care in fish [22,23] and carnivores . The fact that differences between the sexes are so pronounced is certainly consistent with the disruptive selection predicted by our analysis.
Note that spontaneous sex differences in levels of care and the ability to care are predicted to emerge for a wide range of cost and benefit functions, but do not emerge for other functions. An interesting question for future research is thus whether, for example, similar male and female care levels are more common in birds than mammals because the two groups tend to have systematic differences in these functions.
We have also seen that the coevolution of levels of care and ability to care has substantial effects on the evolutionary outcomes in scenarios where other factors induce difference in the costs and benefits of care between the sexes. We illustrated this with differences in certainty of parentage. As we have seen, for fixed (i.e. non-evolving) abilities to care, small differences in certainty of parentage give rise to evolutionary outcomes where the less certain sex provides less parental care, but both sexes provide substantial amounts of care. By contrast, once the coevolution of ability to care is taken into account, more extreme evolutionary outcomes are predicted, where one sex provides almost all the care. We stress that, while our analysis has focused on differences in certainty in parentage, we expect qualitatively similar results for any other factor that gives rise to differences in the costs and benefits of parental care between the sexes. Furthermore, one sex may be predisposed to giving more care if it is more likely to be physically near the young once they need care , and this initial asymmetry may initiate the subsequent coevolution. Thus, for example, in mammals, the female is always present when young are born, while the male may be absent, and our analysis suggests that these initial differences give rise to strong selection increasing both female ability to care and levels of care, and consequent selection on males to reduce care ability and levels of care.
Previous work on parental care has considered situations in which individuals are able to adopt strategic handicaps, that is actions or physiological/morphological features that decrease their ability to provide parental care. Such handicaps have been discussed, for example, in the context of a strategic reduction of energy reserves , and early moult in birds , where the sex that adopts the strategic handicap (e.g. reduction of energy reserves) may be able to ‘force′ its mate to provide more parental care. These handicaps operate in real time; in order for an individual to gain an advantage by a handicap, the partner needs to observe the handicap. In our model, handicaps work over evolutionary time rather than real time. As a result of the coevolutionary process, members of one sex evolve to be poor at care, which forces members of the other sex to compensate.
Our findings might also have implications for the ongoing debate about the evolution of anisogamy. According to an influential theory [28,29], anisogamy has evolved through disruptive selection on isogamous ancestral populations. More recently, this idea has been criticized  for one of its key assumptions, namely that zygote fitness increases disproportionately with the size of the fusing gametes. While we did not explicitly address the evolution of anisogamy with our modelling set-up, our results suggest that the coevolution of gamete size (‘parental effort′) with morphological and physiological traits that affect gamete production may easily give rise to disruptive selection on gamete size, thereby making evolution of anisogamy via disruptive selection a more likely scenario.
Finally, we would like to point out that our results are in line with accumulating evidence that seemingly innocent and minor changes in the model assumptions towards more realism can often have substantial effects for the predicted evolutionary outcomes. Here, we have shown that taking into account the physiological or morphological features associated with providing parental care can drastically change the predicted patterns of parental care derived from evolutionary analysis; similarly, we have recently shown that the outcome of frequency-dependent selection in a behavioural context depends crucially on whether or not the coevolving morphological or physiological architecture is taken into account . Both studies deal with scenarios where multiple traits within an individual affect the costs and benefits of each other (e.g. the cost of parental care depend on the ability to provide parental care) and suggest that approaches that neglect this complexity may easily result in misleading predictions. This underscores the importance of recent calls in the literature to systematically extend our modelling framework to take into account real world complexities [32–34].
M.W. was funded by the B-Types research project (SAW-2013-IGB-2) through the Leibniz Competition.
We thank Tim Fawcett, Michael Jennions and one anonymous referee for very constructive comments on a previous version of this manuscript.
- Received November 10, 2014.
- Accepted January 19, 2015.
- © 2015 The Author(s) Published by the Royal Society. All rights reserved.