New paper: Sexual antagonism in sequential hermaphrodites

Hitchcock TJ & Gardner A (2023) Sexual antagonism in sequential hermaphrodites. Proceedings of the Royal Society of London Series B – Biological Sciences 290, 20232222.

Image: Wikimedia Commons

Females and males may have distinct phenotypic optima, but share essentially the same complement of genes, potentially leading to trade-offs between attaining high fitness through female versus male reproductive success. Such sexual antagonism may be particularly acute in hermaphrodites, where both reproductive strategies are housed within a single individual. While previous models have focused on simultaneous hermaphroditism, we lack theory for how sexual antagonism may play out under sequential hermaphroditism, which has the additional complexities of age-structure. Here, we develop a formal theory of sexual antagonism in sequential hermaphrodites. First, we construct a general theoretical overview of the problem, then consider different types of sexually antagonistic and life-history trade-offs, under different modes of genetic inheritance (autosomal or cytoplasmic), and different forms of sequential hermaphroditism (protogynous, protoandrous or bidirectional). Finally, we provide a concrete illustration of these general patterns by developing a two-stage two-sex model, which yields conditions for both invasion of sexually antagonistic alleles and maintenance of sexually antagonistic polymorphisms.

New paper: A geometric approach to the evolution of altruism

Gardner A (in press) A geometric approach to the evolution of altruism. Journal of Theoretical Biology

Fisher’s geometric model provides a powerful tool for making predictions about key properties of Darwinian adaptation. Here, I apply the geometric model to predict differences between the evolution of altruistic versus nonsocial phenotypes. I recover Kimura’s prediction that probability of fixation is greater for mutations of intermediate size, but I find that the effect size that maximises probability of fixation is relatively small in the context of altruism and relatively large in the context of nonsocial phenotypes, and that the overall probability of fixation is lower for altruism and is higher for nonsocial phenotypes. Accordingly, the first selective substitution is expected to be smaller, and to take longer, in the context of the evolution of altruism. These results strengthen the justification for employing streamlined social evolutionary methodologies that assume adaptations are underpinned by many genes of small effect.

[New paper] R. A. Fisher on J. A. Cobb’s The problem of the sex-ratio

Gardner A (2023) R. A. Fisher on J. A. Cobb’s The problem of the sex-ratio. Notes and Records

The logic of the rarer-sex effect, concerning how natural selection acts to balance the sex ratio among newborns, was long supposed to have originated with Ronald Aylmer Fisher in his 1930 book The genetical theory of natural selection. However, the principle is now understood to have originated with John Austin Cobb in his 1914 paper ‘The problem of the sex-ratio’. Fisher did not provide a citation of Cobb’s sex-ratio paper, and it has been unclear whether he was aware of its existence. Here, I show that Fisher was indeed aware of Cobb’s paper in 1930, as revealed by him citing it elsewhere that same year. Fisher’s willingness to highlight Cobb’s sex-ratio work lends support to the view that his failure to mention it in his book reflects the less stringent citation standards of the time rather than an attempt to deceive readers as to the provenance of the rarer-sex effect.

[New paper] Kin selection of time travel

Twyman KZ & Gardner A (2023) Kin selection of time travel: the social evolutionary causes and consequences of dormancy. Proceedings of the Royal Society of London Series B – Biological Sciences 290, 20231247.


A basic mechanism of kin selection is limited dispersal, whereby individuals remain close to their place of origin such that even indiscriminate social interaction tends to modify the fitness of genealogical kin. Accordingly, the causes and consequences of dispersal have received an enormous amount of attention in the social evolution literature. This work has focused on dispersal of individuals in space, yet similar logic should apply to dispersal of individuals in time (e.g. dormancy). We investigate how kin selection drives the evolution of dormancy and how dormancy modulates the evolution of altruism. We recover dormancy analogues of key results that have previously been given for dispersal, showing that: (1) kin selection favours dormancy as a means of relaxing competition between relatives; (2) when individuals may adjust their dormancy behaviour to local density, they are favoured to do so, resulting in greater dormancy in high-density neighbourhoods and a concomitant ‘constant non-dormant principle’; (3) when dormancy is constrained to be independent of density, there is no relationship between the rate of dormancy and the evolutionary potential for altruism; and (4) when dormancy is able to evolve in a density-dependent manner, a greater potential for altruism is expected in populations with lower dormancy.


[New paper] W. D. Hamilton and the golden sex ratio

Gardner A (in press) W. D. Hamilton and the golden sex ratio. Journal of Theoretical Biology. doi: 10.1016/j.jtbi.2023.111599

In his famous two-part paper, published in Journal of Theoretical Biology in 1964, W. D. Hamilton predicted that natural selection acting in male-haploid populations favours a ratio of males to females that is in accordance with the golden ratio. This prediction has found its way into the pages of one of the best-selling books of all time, Dan Brown’s 2003 novel The da Vinci Code, and is therefore in the running for the most widely known quantitative result in the history of evolutionary biology. Unfortunately, this golden-ratio result is wrong, and was later corrected by Hamilton, who showed that natural selection actually favours an unbiased sex ratio in this setting. But it has been unclear exactly how Hamilton arrived at the golden-ratio result in the first place. Here I show that the solution to this puzzle is found in unpublished work held in the British Library’s W. D. Hamilton collection. Specifically, in addition to employing a faulty method for calculating relatedness, Hamilton had also employed a faulty method for calculating reproductive value, considering only genetic contributions to the next generation rather than to the distant future. Repeating both mistakes recovers his erroneous golden-ratio result.


[New paper] A simulation test of the prediction that density-dependent dispersal promotes female-biased sex allocation in viscous populations

Chokechaipaisarn C & Gardner A (2023) A simulation test of the prediction that density-dependent dispersal promotes female-biased sex allocation in viscous populations. microPublication Biology doi: 10.17912/micropub.biology.000821

A classic result of sex-allocation theory is that the sex ratio is predicted to be invariant with respect to the rate of dispersal. However, a recent mathematical analysis has suggested that if individuals are able to adjust their probability of dispersal according to the local density of their neighbourhood, then a lower rate of dispersal will be associated with greater female-bias. Here, we perform a computer simulation test of this prediction. Our simulation data provide strong qualitative support for the prediction, and a Monte Carlo randomization test of significance allows us to reject the null hypothesis of the invariance relationship.

[New paper] Kin selection favours religious traditions: ancestor worship as a cultural descendant-leaving strategy

Stucky K & Gardner A (in press) Kin selection favours religious traditions: ancestor worship as a cultural descendant-leaving strategy Religion, Brain & Behavior doi: 10.1080/2153599X.2023.2215854

Recent years have seen renewed interest in the role of religious systems as drivers of the evolution of cooperation in human societies. One suggestion is that a cultural tradition of ancestor worship might have evolved as a “descendant-leaving strategy” of ancestors by encouraging increased altruism particularly between distant kin. Specifically, Coe and others have suggested a mechanism of cultural transmission exploiting social learning biases, whereby ancestors have been able to establish parental manipulation of kin recognition and perceived relatedness as a traditional behavior, leading to increased altruism among co-descendants and thereby maximizing the ancestor’s long-term inclusive fitness. Here, we develop a demographically explicit model in order to quantify the resulting increase in altruism and concomitant “ancestor-descendant conflict”, and to determine the evolutionary feasibility of religiously motivated cultural norms that promote altruism among co-descendants. Our analysis reveals that such norms could indeed drive an overall increase in altruism with potential for ancestor-descendant conflict, particularly in low-dispersal settings. Moreover, we find that natural selection can favor traditions encouraging increased altruism towards co-descendants under a range of conditions, with the inclusive-fitness costs of enacting an inappropriately high level of altruism being offset by inclusive-fitness benefits derived from the cultural tradition facilitating kin recognition.

[New paper] The rarer-sex effect

Gardner A (2023) The rarer-sex effect. Philosophical Transactions of the Royal Society B 378, 20210500.

The study of sex allocation—that is, the investment of resources into male versus female reproductive effort—yields among the best quantitative evidence for Darwinian adaptation, and has long enjoyed a tight and productive interplay of theoretical and empirical research. The fitness consequences of an individual’s sex allocation decisions depend crucially upon the sex allocation behaviour of others and, accordingly, sex allocation is readily conceptualized in terms of an evolutionary game. Here, I investigate the historical development of understanding of a fundamental driver of the evolution of sex allocation—the rarer-sex effect—from its inception in the writing of Charles Darwin in 1871 through to its explicit framing in terms of consanguinity and reproductive value by William D. Hamilton in 1972. I show that step-wise development of theory proceeded through refinements in the conceptualization of the strategy set, the payoff function and the unbeatable strategy.

[New paper] The geometry of evolutionary conflict

Rautiala P & Gardner A (2023) The geometry of evolutionary conflict. Proceedings of the Royal Society of London Series B – Biological Sciences 290, 20222423.

Conflicts of interest abound not only in human affairs but also in the biological realm. Evolutionary conflict occurs over multiple scales of biological organization, from genetic outlawry within genomes, to sibling rivalry within nuclear families, to collective-action disputes within societies. However, achieving a general understanding of the dynamics and consequences of evolutionary conflict remains an outstanding challenge. Here, we show that a development of R. A. Fisher’s classic ‘geometric model’ of adaptation yields novel and surprising insights into the dynamics of evolutionary conflict and resulting maladaptation, including the discoveries that: (i) conflict can drive evolving traits arbitrarily far away from all parties’ optima and, indeed, if all mutations are equally likely then contested traits are more often than not driven outwith the zone of actual conflict (hyper-maladaptation); (ii) evolutionary conflicts drive persistent maladaptation of orthogonal, non-contested traits (para-maladaptation); and (iii) modular design greatly ameliorates conflict-driven maladaptation, thereby facilitating major transitions in individuality.

[New paper] Density-dependent dispersal promotes female-biased sex allocation in viscous populations

Chokechaipaisarn C & Gardner A (2022) Density-dependent dispersal promotes female-biased sex allocation in viscous populations. Biology Letters 18, 20220205.

A surprising result emerging from the theory of sex allocation is that the optimal sex ratio is predicted to be completely independent of the rate of dispersal. This striking invariance result has stimulated a huge amount of theoretical and empirical attention in the social evolution literature. However, this sex-allocation invariant has been derived under the assumption that an individual’s dispersal behaviour is not modulated by population density. Here, we investigate how density-dependent dispersal shapes patterns of sex allocation in a viscous-population setting. Specifically, we find that if individuals are able to adjust their dispersal behaviour according to local population density, then they are favoured to do so, and this drives the evolution of female-biased sex allocation. This result obtains because, whereas under density-independent dispersal, population viscosity is associated not only with higher relatedness—which promotes female bias—but also with higher kin competition—which inhibits female bias—under density-dependent dispersal, the kin-competition consequences of a female-biased sex ratio are entirely abolished. We derive analytical results for the full range of group sizes and costs of dispersal, under haploid, diploid and haplodiploid modes of inheritance. These results show that population viscosity promotes female-biased sex ratios in the context of density-dependent dispersal.