Monthly Archives: December 2013

The Evolution of Parental Care in the Context of Sexual Selection: A Critical Reassessment of Parental Investment Theory (2002) Wade MJ and Shuster SM

Previously discussed papers: Bateman 1948,Trivers 1972, Emlen & Oring 1977 and Arnold & Duvall (1994)

As we arrive at the fifth paper on the topic of mating systems, most of the themes highlighted in the discussion of Trivers’ 1972 paper have made an appearance: timing of investment, risks and rewards of mating strategies, and the influence of female choice. Again, these themes are common throughout Wade and Shuster’s paper, which emphasizes early gamete investment and its latent effects on the behaviour of males and females. Gametes are the first form of investment in offspring, and it is almost always females that invest in gametes the most heavily. Because males invest comparatively little in gametes, they can benefit from mating with multiple females, whereas females have little to gain from multiple sexual encounters, other than possibly an increased chance of successful fertilisation.

Wade and Shuster examine a classic paper by Maynard Smith (1977), which describes an Evolutionarily Stable Strategy (ESS) model. Through this model, Maynard Smith tried to formalize the ideas first articulated by Bateman (linked above); his model involves a nondescript species with typical sex roles, and assumes that re-mating within this species has both costs and benefits.

Maynard Smith’s ESS model shows that under some conditions it is possible to find both males that care for their offspring and females that desert theirs, despite the prevalence of indiscriminate mating in males and choosy behaviour in females. Past ESS models have shown that polymorphic traits, including polymorphisms in mating behaviour, can only evolve in a system if they offer equal fitness to one another. In the context of Maynard Smith’s model, this means that if atypically raised offspring (e.g. deserted by the female, cared for by the male) and those raised only by females (with deserting males) are exactly as viable as one another, the alternative mating behaviours will both be evolutionarily stable and remain.
Wade and Shuster take the ESS model by Maynard Smith and attempt to modify it in light of the state of evolutionary theory in the early 2000s.

In their paper, they argue that Maynard Smith’s model made some critical invalid assumptions. For example, the original model did not take into account how male re-mating could affect female fitness (such as through withdrawal of care for the purpose of remating). To illustrate the problem with such an assumption, they demonstrate that under Maynard-Smith’s model, when the sex ratio was equal, deserting males would be unable to breed with multiple females – either that or deserting males could not exist when the sex ratio was 1:1.

Wade and Shuster added several components to the model to overcome these problems. They add a ‘payoff matrix’ into the model, in which deserters may have more offspring, but these offspring are less likely to reach adulthood, and sacrificing future reproduction to care for current offspring is an opportunity cost. Their model also takes into account the reduced number of available females when deserting males mate multiple times. It therefore considers females a limited resource, meaning deserting males shift the operational sex ratio. Wade and Shuster were able to simplify the model to a single equation.
The deserting strategy would become more common than the caring strategy when:
/2 < p
s is offspring survivorship, and p is the probability of male mating.)

Because each offspring only has half of a parent’s DNA, strategic allocation to care (which increases offspring survivorship, s) must be scaled by half when assessing its value relative to male re-mating opportunities (p). When s/2 < p, desertion should be more prevalent (because fitness returns from re-mating outweigh those of caring), while care should be more prevalent when s/2 > p.

Wade and Shuster note that this solution satisfies the requirement of population genetic theory that male and female fitness should be equal, an important improvement over Maynard-Smith’s original ESS model.

In closing, they note that the presence of polygamous males and caring females under some conditions shows that sex roles can be the cause of differences in parental investment, rather than a consequence of initial differences in investment that are reflected in anisogamy, and that this inversion of the classic understanding “stands parental investment theory on its head”. While this may be a fair synthesis with respect to the conventional shorthand view, it is worth noting Trivers’ acknowledgement of the complex, reinforcing relationship between parental investment and sexual selection. Is this complex, bidirectional, causal relationship ultimately responsible for uncertainty about the causes of diversity in sexual differences among taxa? Maybe subsequent posts can help clarify this…

The, Selfish Gene, The

A popular science article causing something of a furore right now is journalist David Dobbs’ latest offering, ‘Die, Selfish Gene, Die‘. Dobbs attempts to lay out the case for the ‘extended modern synthesis’ as proposed by researchers such as Massimo Pigliucci, but – to me, at least – tries to cover too much ground and fails to make a coherent argument. Beware also the ‘controversial’ statements made to pique the reader’s interest; here, even the sub-heading claims that the content will overturn the central idea of Richard Dawkins’ famous book:

The selfish gene is one of the most successful science metaphors ever invented. Unfortunately, it’s wrong.

Dawkins has responded to this ‘adversarial journalism’ on his own blog; meanwhile, Jerry Coyne at ‘Why Evolution is True’ has written two lengthy pieces which go into rather more detail on the science:

Part 1

Part 2

Dobbs himself has written another two posts on the subject on his own blog, the first being a ‘clarification’ of his original piece. The second is a more direct response to Coyne’s writing. PZ Myers has also weighed in on Dobbs’ side, expanding on the science while claiming that pushback is from ‘people who don’t quite get the concept‘.

It’s worth reading all these to get a feel for the different ideas flying around, although reading ‘The Selfish Gene’ itself (or Dawkins’ later book, ‘The Extended Phenotype’) should be on your xmas list if you don’t own them already.

I also tried to follow a twitter conversation between the likes of Richard Lenski, Razib Khan, Josh Witten, Karen James, Emily Willingham, Joel McGlothlin, Aylwyn Scally… among others… but it all got a bit too intense for me! Hopefully someone will gather those tweets together under one internet roof, but that someone certainly isn’t going to be me.

I’m pretty sure we haven’t heard the last of this, so I’ll try to keep adding links as I find them. In the meantime, feel free to weigh in below in the comments section…

Update: 15/12/13

I’m also covering this on my own blog, so the update is copied verbatim from there:

It wouldn’t be a scientific debate on Twitter without a blaze of capslock hulkspeak. SMASH LINK TO READ

‘Die, Selfish Gene, Die’ has evolved: David Dobbs has, rather wonderfully, published a revised version of his article. While I’m sure many will still take issue with the ideas contained within it, it’s fantastic that he has taken all of the criticism and comments onboard and updated his article. The original version still exists online, and I’ve changed the link at the top of this post so that it is linked there. There is also another (!) version of the revised article with links inserted by Dobbs to show his sources.

Finally (for today, at least), I just saw a great post by Sergio Graziosi on the whole affair, discussing both the public understanding of evolution and the technical points of Dobbs’ article. It’s well worth a read.

Arnold & Duvall (1994) Animal Mating Systems: A Synthesis Based on Selection Theory

Arnold & Duvall (1994) use mathematical modeling and statistical analysis of classic data such as those collected by Bateman (1984) to analyse how the strength of sexual selection can be used to explain diversity in mating systems.

The previous papers (by Bateman 1948, Trivers 1972, and Emlen & Oring 1977), discussed in previous posts, had set the stage for more empirical and theoretical work attempting to explain the evolution of mating systems. Arnold & Duvall (1994) suggested that although there had been many important articles contributing to different aspects of mating system theory, including Bateman’s classic work on the relationship between fecundity and mating success, there was no formal theoretical and analytical framework that integrated all the research.

The authors reaffirm that the relationship between mating success and fecundity (based on Bateman’s original work) is a key driver of mating system evolution.  One of the paper’s main themes is based on a now well-accepted idea articulated in the early 1980’s (Lande and Arnold 1983), that selection can be seen as the statistical relationship between certain traits and fitness. To integrate this analytic approach with the study of mating systems, Arnold and Duvall propose a 4 tiered hierarchical framework including the traits that influence fitness. This conceptual model illustrates the direct and indirect relationships between traits and fitness measures, and allows formal testing of the pathways that affect fitness components. Traits that have the most direct effect on fitness are assigned rank one, while more indirect agents have higher ranks (2, 3 or 4) depending on the number of presumed mediating factors that relate them with fitness (Figure 1.).

Luc noted that creating thought maps or path diagrams similar to this figure, which describe the important relationships or factors within a system, could be very useful in allowing us to visualize and understand the important questions in our own research. These conceptual diagrams often further allow one to make the statistical associations between correlated components of a system more explicit.

Arnold and Duvall explain how the ‘selection gradients’ illustrated as arrows in Figure 1 can be quantified using multiple regression of fitness on estimates of the traits presumed to be under selection. Each aforementioned selection gradient is the partial standardized regression coefficient in a multiple regression including other aspects of the phenotype. Multiple regression can therefore be used to estimate the total combined selection on all the various traits affecting fitness, including the sexual selection component that affects reproductive fitness.

The authors explain that linear regression is appropriate in the estimation of selection gradients even if the fits are nonlinear. This is now an accepted convention when trying to measure strength of selection on a trait, however Luc suggested that, notwithstanding Arnold and Duvall’s logic about the nature of evolutionary genetic change and its relationship with the well-established body of work on selection analysis, we should neverthelessalways question exactly what coefficients mean when they come from a model that might have a poor fit.

The authors further discuss how estimates of selection gradients can be used to test sexual selection theory, by integrating different aspects of mating systems such as nuptial gifts or parental care, to examine the strength of selection on males and females. They argue that their approach quantifies differences in the strength of selection (regression slopes) between males and females, which is useful for testing theory on mating systems.

They illustrate their analysis using several examples of mating systems, including one in which males provide nuptial gifts to females. In this case, models showed that there should be a small increase in female’s selection gradient (strength of sexual selection) for each multiple mating (as a result of the benefits to gaining extra gifts and therefore nutrition), and that the greater the nutritional benefit of the gift, the greater the strength of sexual selection will be.

Arnold and Duvall finally use models involving encounter rate, similar to the ideas proposed by Emlen and Oring (1977), and show that these can also be used to measure the strength of selection on fitness based traits. They do however contest Emlen and Oring’s (1977) assertion about the most useful metric for describing or determining mating systems. Whereas Emlen and Oring argue that the operational sex ratio (the average over time of the number of sexually active males to the number of females capable of insemination) is the most useful indicator of the mating system, Arnold and Duvall reason that the breeding sex ratio (the ratio of breeding males to breeding females, including the zero fecundity class for each sex) is more appropriate. This may be something to think about for some members of our lab who are looking at malaise trap samples to determine the adult operational sex ratios and mating rates of dance flies.

Ultimately the authors claim that it is the disparity in selection gradients that determines which sex competes for access to the other. While sexual selection due to competition will therefore determine a species’ mating system, it seems logical that a species mating system will also influence the level of selection in a cyclical fashion. This reminds us of Trivers (1972), who noted the cyclical relationship between mate competition and parental investment in his own analysis of what determines the sex roles.

Emlen & Oring 1977: Ecology, Sexual Selection, and the Evolution of Mating Systems

The previous posts from our discussions on classic mating systems papers have shown how both empirical work and theory advanced knowledge of sex differences in the returns from relative investment in reproduction. In their 1977 paper, Emlen & Oring attempted to bring natural history observations and ecology into a general theory of mating systems evolution, and to discuss the ecological factors and selective forces that shape polygamous mating systems. Of particular relevance here is Trivers’ work on parental care, as the prevalence of polygamy is often related to whether one sex is freed from parental care duties (and thus have excess time and energy to seek additional mates).

‘Ecology, Sexual Selection, and the Evolution of Mating Systems’ was published 2 years after E. O. Wilson’s ‘Sociobiology’ had hit the shelves, and Emlen & Oring are careful to note early on that understanding mating systems requires the reader to abandon any thoughts of group- or species-level ‘adaptiveness’. Fitness is a measure of the reproductive success of an individual (or genotype) relative to other individuals (or genotypes) in the same or other populations, and so we must consider selection to be operating at the level of the individual . Intraspecific competition is a crucial aspect of sexual selection: essentially, when one sex becomes a limiting factor for the other, the result is an increase in intrasexual competition among members of the available sex for access to mates of the limiting sex. The authors hypothesise that an important cause of the differing intensities of sexual selection found both across species and between populations of the same species is “the ability of a portion of the population to control the access of others to potential mates”. This control may be enforced through physically excluding other members of the same sex from potential mates, or through controlling critical resources. Central to Emlen & Oring’s argument is a cost-benefit analysis: under what environmental circumstances is the defending of multiple mates, or of those resources necessary for gaining multiple mates, economically viable?

Two of the crucial components of this concept of an environment’s ‘polygamy potential’ are illustrated by the figure below, in which the height of the shaded area perpendicular to each diagonal line indicates the environmental potential for polygamy in relation to the spatial distribution of resources (on the x-axis) and the temporal availability of receptive mates (on the y-axis). Resource ‘clumping’ in space means individuals can monopolise critical resources, which always increases the potential for polygamy. Asynchrony of mate availability is required for polygamy, else the time to locate, attract or copulate will mean that other potential mates are no longer available. However, too much asynchrony means the cost of continual defence outweighs the benefits of gaining additional mates.


The environmental potential for polygamy, relative to the spatial distribution of resources and temporal availability of receptive mates. Taken from Emlen & Oring (1977).

Another crucial piece of the sexual selection intensity puzzle is the realisation that the overall ratio of males to females in the population is less important than the operational sex ratio (OSR): the average ratio of fertilisable females to sexually active males at any point. The OSR is affected by spatial and temporal clumping of the limiting sex; the example given is of continuous long periods of male sexual activity alongside brief, asynchronous periods of female receptivity, producing a strong skew in the OSR.

The bulk of the paper outlines an ecological classification of mating systems, concentrating on whether and how access to potential mates and resources are controlled, and the effects of temporal and spatial clumping on the OSR. Detailed examples of mating system types are illustrated using examples of avian mating biology. Emlen & Oring also consider how changes in ecological parameters might disrupt the environmental potential for polygamy, and indicate that their framework should enable predictions of the form of mating system plasticity that occurs.

Trivers 1972: Parental investment and sexual selection

Continuing the series of classic papers on mating systems, Hazel and I lead some discussion on Bob Trivers’ book chapter on how parental investment relates to the sex roles. Bateman (1948) had already suggested that the difference between the sexes in the returns on investment might be related to anisogamy (the difference in gamete size across the sexes), but Trivers examined (using formal theory rather than empirical experiments) the possible effects of investment in all stages of offspring (not just the gametes themselves). He reasoned that since all kids have two parents, the sex that invests more becomes limiting to the other one. The relative investment of the sexes in their young is therefore the key variable controlling sexual selection.

Trivers was careful to point out that although “investment” can be energetic or metabolic, it doesn’t need to be for his theory to work. For example, risky behaviour like hunting or singing (which could lead to predation or parasitism) is also a form of investment and needs to be part of any calculations comparing the sexes.

Trivers also was careful to notes the circular nature of the relationship between investment and mating system, a theme that will undoubtedly resurface as we continue our tour through classic papers on mating systems: parental investment affects sexual selection (e.g., by controlling which sex is in short supply), but sexual selection also affects parental investment (e.g., by determining how much energy is left for care, for example).

The paper also pointed out a few features of the natural history of mating in animals that were likely to be important (observations whose importance we might be able to confirm with the benefit of hindsight). Here are a few haphazardly selected points that will probably feature in future discussions:

  1. The timing of investment (females usually invest substantially in gametes before mating) creates asymmetry between mating partners in the risk of desertion: males may have invested comparatively little in a clutch after mating and so they risk little by deserting, whereas a female may be trapped into caring for the young or losing all of her investment. Conversely, the risk of cuckoldry is asymmetrical in the opposite direction, because males can rarely be completely certain about paternity in the same way that females can trust their relationship to eggs.
  2. The differential risks and returns on parental investment have important implications for sexual differences in mortality. Trivers spent some time arguing that differences in mortality are not simply a consequence of chromosomal differences (i.e., the fact that in most mammals males are heterogametic), but rather imply adaptive differences in investment in longevity. Whether sexual differences in lifespan are generally adaptive is a continuing focus of quite a lot of research, including by our own Tom H.
  3. Female choice is probably related to some important aspects of paternal investment. Research over the past twenty years on the relative importance of direct and indirect benefits owes much to this initial analysis.
  4. In his closing sentence, Trivers reaffirms one of the fundamental insights that has shaped sexual selection research since this paper:

“Throughout, I emphasize that sexual selection favors different male and female reproductive strategies and that even when ostensibly cooperating in a joint task male and female interests are rarely identical.”

This recognition of sexual conflict would have to wait some time to be fully appreciated, in part because the empirical literature had plenty of work to do in testing Trivers’ theory on how parental investment affects sexual selection. In future posts, perhaps we can assess how much of that work remains to be done.