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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 Here I show that the solution to this puzzle is found in unpublished work held in the British Library’s W. D. Hamilton collection.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.

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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

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.

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.

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.

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.

Hitchcock TJ & Gardner A (in press) Paternal genome elimination promotes altruism in viscous populations. Evolution https://doi.org/10.1111/evo.14585

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Population viscosity has long been thought to promote the evolution of altruism. However, in the simplest scenarios, the potential for altruism is invariant with respect to dispersal – a surprising result that holds for haploidy, diploidy, and haplodiploidy (arrhenotoky). Here we develop a kin-selection model to investigate how population viscosity affects the potential for altruism in species with male paternal genome elimination (PGE), exploring altruism enacted by both females and males, and both juveniles and adults. We find that: 1) PGE promotes altruistic behaviours relative to the other inheritance systems, and to a degree that depends on the extent of paternal genome expression. 2) Under PGE, dispersal increases the potential for altruism in juveniles and decreases it in adults. 3) The genetics of PGE can lead to striking differences in sex-specific potentials for altruism, even in the absence of any sex-differences in ecology.

Scots translation (by Ashley Douglas):

Paternal genome drap-oot forders altruism in stieve populations

Population stieveness has lang been thocht tae forder the evolution o altruism. Hooivver, in the maist straucht-forrit o scenarios, the potential fur altruism is invariant wi respeck tae skail – a stamagasterin ootcome that hauds fur haploidy, diploidy, and haplodiploidy (arrhenotoky). Here we pit forrit a kin-walin model fur tae airt-oot hoo population stieveness affects the potential fur altruism in species wi male paternal genome drap-oot (PGD), takkin tent o altruism enactit by baith females and males, forby baith young-anes and aulder-anes. We find that: 1) PGD forders altruistic ongauns relative tae the ither inheritance seestems, forby tae a degree that depends on the extent o paternal genome kythin. 2) Unner PGD, skail maks mair muckle the potential fur altruism amang young-anes and gars it less likely amang aulder-anes. 3) The genetics o PGD can lead tae kenspeckle differences in sex-specific potentials fur altruism, even wioot onie sex-differences in ecology.

Stucky K & Gardner A (2022) The evolution of religiosity by kin selection. Religion, Brain & Behavior

Despite religion’s apparent ubiquity, hypotheses about the selection pressures that may have shaped its cognitive foundations remain controversial. Here, we develop and analyze a mathematical model inspired by Crespi and Summers’ suggestion that parent-offspring conflict has driven the evolution of religious beliefs to explore the causes and consequences of these selection pressures. To this end, we employ kin selection methodology to investigate how selection may mold an individual’s propensity for religiosity and corresponding patterns of gene expression, revealing that the evolution of religiosity is modulated by genetic relatedness between social partners, that selection in relation to religiosity may depend on an individual’s age and sex, and that religiosity can foment intragenomic conflicts of interest that give rise to parent-of-origin specific patterns of gene expression and concomitant clinical disorders. More generally, we develop a formal, theoretical framework that enables the derivation of clear-cut, comparative predictions about adaptive as well as maladaptive religiosity phenotypes.

Kanwal JK & Gardner A (2022) Population viscosity promotes altruism under density-dependent dispersal Proceedings of the Royal Society of London Series B – Biological Sciences289, 20212668.

A basic mechanism of kin selection is population viscosity, whereby individuals do not move far from their place of birth and hence tend to be surrounded by relatives. In such circumstances, even indiscriminate altruism among neighbours will often involve interactions between kin, which has a promoting effect on the evolution of altruism. This has the potential to explain altruistic behaviour across the whole tree of life, including in taxa for which recognition of kin is implausible. However, population viscosity may also intensify resource competition among kin, which has an inhibitory effect on altruism. Indeed, in the simplest scenario, in which individuals disperse with a fixed probability, these two effects have been shown to exactly cancel such that there is no net impact of viscosity on altruism. Here, we show that if individuals are able to disperse conditionally upon local density, they are favoured to do so, with more altruistic neighbourhoods exhibiting a higher rate of dispersal and concomitant relaxation of kin competition. Comparing across different populations or species, this leads to a negative correlation between overall levels of dispersal and altruism. We demonstrate both analytically and using individual-based simulations that population viscosity promotes the evolution of altruism under density-dependent dispersal.