Many social Hymenoptera species have morphologically sterile worker castes. It is proposed that the evolutionary routes to this obligate sterility must pass through a ‘monogamy window’, because inclusive fitness favours individuals retaining their reproductive totipotency unless they can rear full siblings. Simulated evolution of sterility, however, finds that ‘point of view’ is critically important. Monogamy is facilitating if sterility is expressed altruistically (i.e. workers defer reproduction to queens), but if sterility results from manipulation by mothers or siblings, monogamy may have no effect or lessen the likelihood of sterility. Overall, the model and data from facultatively eusocial bees suggest that eusociality and sterility are more likely to originate through manipulation than by altruism, casting doubt on a mandatory role for monogamy. Simple kin selection paradigms, such as Hamilton's rule, can also fail to account for significant evolutionary dynamics created by factors, such as population structure, group-level effects or non-random mating patterns. The easy remedy is to always validate apparently insightful predictions from Hamiltonian equations with life-history appropriate genetic models.
The key character of eusociality is reproductive division of labour within collaborative groups. One or a limited number of individuals (queens) produce most or all of the offspring, while ‘workers’ forego reproduction for group beneficial activities. Colonies in eusocial species are primarily composed of relatives, although whether high genetic relatedness is essential to evolving reproductive castes or merely a by-product of group formation is hotly debated [1–4]. If close kinship does matter, then monogamy would be a facilitating preadaptation for subsequent eusocial evolution by creating cohorts of full siblings. Support for this monogamy hypothesis comes from several phylogenetic analyses, that find cooperative breeding or eusociality in mammals, birds and Hymenoptera probably evolved from solitary ancestors that were either monogamous or with reduced promiscuity [5–7].
The monogamy hypothesis for eusociality is less consistently supported theoretically when the evolution of ‘helping’ is compared across full and half-sib offspring cohorts. Differing models produce a variety of outcomes: (i) polygamy is generally more facilitating for spreading eusociality in populations ; (ii) both monogamy and haplodiploidy facilitate eusociality more than polygamy and diploidy  and (iii) relative advantage from monogamy or polygamy depends on the degree of local resource competition between siblings . Boomsma  points out that these models consider facultative helping in totipotent offspring rather than testing the original monogamy hypothesis for evolution of obligately sterile social insect castes. Hence, the model here assumes a species that has evolved to a level of stable eusociality where reproductive success requires the presence of both a queen and offspring workers. In such species, virgin queens can never initiate or successfully head a colony because they cannot produce workers. Also in such species workers cannot inherit nests because, although they retain some ability to reproduce, they are physiologically limited and cannot become highly fecund queens. Nonacs  focused on these two issues relative to the evolution of facultative helping and, therefore, they are not reconsidered here in order to test the monogamy hypothesis in its most straightforward formulation .
2. Material and methods
I simulate natural selection  acting on worker reproductive behaviour by tracking changes in frequency of ‘obligate sterility’ alleles in hypothetical haplodiploid Hymenopteran populations. Independent from the genetic model, kin-selective calculations of inclusive fitness can a priori predict whether allele frequencies should increase or decrease in the simulations. This, however, requires specifying where the alleles act. One possibility is that sterility alleles create manipulating mothers, where queens impose sterility on their offspring through diet, physical suppression or pheromonal signals [12,13]. A second possibility is through offspring altruism, where alleles cause workers to cede their reproduction to their mother. The final possibility is sibsocial , where workers assume manipulating roles and enforce sterility on other siblings.
By Hamilton's rule, obligate sterility should be favoured  whenever benefit (b) provided to kin exceeds the cost (c) to self, or rgb > rlc (r values = probability of being identical by descent for relatives gained (g) or lost (l)). Obligate sterility, therefore, is predicted when b/c > rl/rg with the r value ratios depending on the point-of-view of who ‘controls’ sterility (table 1). That the controlling party can be either the mother, the worker themselves, or the cohort of non-reproductive siblings yields a separate Hamiton's rule for each. Calculating the r ratios for monogamy and polygamy shows that: (i) number of mates should have no effect on the predicted spread of sterility if based on manipulation by mothers; (ii) altruistic sterility by workers is more likely favoured through monogamy and (iii) sterility due sibsocial actions is more favoured through polygamy.
The genetic simulations examined whether or not a trait for obligate sterility would spread to fixation in populations that varied in mate number and benefit for worker sterility (full details of the model are presented in the electronic supplementary material). In colonies, a given worker had one of two phenotypes: (i) a worker that reproduced one offspring of their own or (ii) a worker that had ceded reproduction to its mother. Ceding reproduction could positively affect colony-level productivity, such as a large effect of two queen-produced offspring instead of the worker's single one. Thus, by Hamilton's rule the benefit of sterility here is twice its cost (b = 2, c = 1). A small effect creates a 10% increased queen productivity (b/c = 1.1). Finally, no additional benefit (b/c = 1) is also examined. A worker's phenotype depended on the genetic make-up of the colony. For maternal manipulation, obligate sterility was imposed on all workers as determined by the queen's genotype. For offspring altruism, a given worker's reproductive behaviour depended on whether or not it had a sterility-inducing genotype. For sibsocial effects, a given worker's phenotype was a probabilistic function of the frequency of sterility alleles across the entire worker population.
Hamilton's rule predicts that matedness levels have no effect on selection for sterility (table 1) and that under b/c ratios considered, sterility is always favoured. These predictions are upheld (figure 1a). With worker altruism, sterility is predicted to be spread under monogamy when b/c > 1, but under polygamy only with b/c = 2. These predictions are also upheld (figure 1b). The same qualitative relationships are expressed with diploidy (electronic supplementary material). With sibsocial effects, sterility spreads as predicted by Hamilton's rule with all three b/c values tested (figure 1c). If workers can produce males, obligate sterility also spreads as predicted by b/c > rg/rl (figure 1d: the inequality is always met with polygamy, but only when b/c = 2 with monogamy). Contrary to predictions from Hamilton's rule about sibsociality, however, obligate sterility increases faster with monogamy than with polygamy when b/c > rl/rg and the benefit-to-cost ratio is large.
Viscosity and other population-level processes can lead to faulty predictions from the simplest form of Hamilton's rule  illustrated here through predicted sibsocial outcomes being insensitive to group-level effects. Colonies with parents having sterility genotypes are more productive whenever b > 1. An example of how colony-level effects arise is apparent from examining the productivity of individual colonies in a sibsocial scenario when 50% of population alleles are for sterility (figure 2). The coefficient of variation in productivity across all colonies is greater with monogamy than with polygamy. Greater across-group variance with monogamy leads to stronger group-level selection. Therefore, sterility alleles that are favoured by kin selection can increase more rapidly with monogamy. This complementary effect of group-level selection appears in all figure 1 curves, where the fastest increases occur with intermediate frequencies of sterility alleles. Across-group variance is maximal at those frequencies and therefore, so is group-level selection.
Theoretically, obligately sterile worker castes need not always evolve through a narrow monogamy window. Monogamy is the favourable preadaptation if: (i) sterility evolves as a self-sacrificial behaviour in workers or (ii) sterility through manipulation of developing offspring by siblings can significantly increase queen reproduction. Conversely, neither monogamy nor polygamy makes sterility more likely to be selectively favoured if effects arise through maternal manipulation. Finally, polygamy is the more favourable preadaptation if worker reproduction is already restricted to producing only sons and its suppression leads to little or no gain in queen-produced offspring.
The results clearly emphasize the importance of the genetic mechanisms that create phenotypes. Under identical conditions of benefit, cost and mating biology, an allele for obligate sterility can spread if it affects maternal behaviour, but may not if it only affects worker behaviour. More broadly considered, if offspring sterility is favoured either as altruistic or sibsocial effects, it will be even more strongly favoured by mothers (i.e. compare slopes of curves in figure 1). This asymmetry in selective advantage suggests that the conceptual concentration on cooperation evolving through offspring maximizing their inclusive fitness may be misplaced or at least incomplete [1–4]. Instead, parental manipulation, effectively brought to bear on offspring, may more often drive the evolution of helping behaviour. Indeed, recent studies on facultative eusociality in the halictid bee, Megalopta genalis, strongly implicate mothers as being manipulative in causing daughters to become helpers [12,13]. Because the mothers control the amount and delivery of food, daughters may have no recourse but to acquiesce to manipulation.
In the models presented here, Hamiltonian inclusive fitness calculations accurately predict the general outcomes, such as when is obligate sterility selectively adaptive. Problems arise, however, if specific effects from genetic system dynamics, changing gene frequencies over time, population structure and group-level selection or non-random mating patterns are involved. A case in point is the disparate outcomes of two models on evolution of facultative helping behaviour. Nonacs  found that polygamy is often more facilitating for spreading cooperative behaviour and haploidiploidy versus diploidy has no effect. By contrast, Fromhage & Kokko  found that both monogamy and haploidiploidy are more facilitating for cooperative evolution. Resolving these two outcomes is quite simple: Nonacs's model allows nest inheritance by daughters and Fromhage & Kokko's model does not. Nest inheritance creates an asymmetric genetic effect whereby only helpers with the cooperative genotype reap this advantage. Because polygamy creates more nests with helping daughters, the inheritance occurs more often and cooperation spreads more rapidly. If nest inheritance is added to , or prevented in , the predictions become identical (P. Nonacs 2013, unpublished results). The monogamy and haplodiploidy bias for the evolution of cooperation is not because of higher within-nest relatedness, but because of another asymmetric genetic pattern. Again because only certain genotypes can become helpers, in nests with both helper and non-helper daughters, the former is removed from the pool of future reproductives to the benefit of the latter. Both monogamy and haplodiploidy reduce the relative proportion of nests in a population experiencing this asymmetry in selection, thereby facilitating helping to spread .
Thus, one must be wary of simple kin-selective generalities such as monogamy and close genetic relatedness always increase the likelihood that cooperative behaviour or obligate sterility are selectively advantageous. One need to also examine under what range of conditions an explicit genetic model supports the statement. The phenomenon under consideration may be deceptively complex and affected by ecological and genetic details, not captured by one single Hamiltonian inequality.
I thank K. Kapheim and anonymous reviewers for their helpful comments.
- Received January 30, 2014.
- Accepted February 25, 2014.
- © 2014 The Author(s) Published by the Royal Society. All rights reserved.