Toward greater realism in inclusive fitness models: the case of caste fate conflict in insect societies

Abstract

In the field of social evolution, inclusive fitness theory has been successful in making a wide range of qualitative predictions on expected patterns of cooperation and conflict. Nevertheless, outside of sex ratio theory, inclusive fitness models that make accurate quantitative predictions remain relatively rare. Past models dealing with caste fate conflict in insect societies, for example, successfully predicted that if female larvae can control their own caste fate, an excess should opt to selfishly develop as queens. Available models, however, were unable to accurately predict levels of queen production observed in Melipona bees-a genus of stingless bees where caste is self-determined-as empirically observed levels of queen production are approximately two times lower than the theoretically predicted ones. Here, we show that this discrepancy can be resolved by explicitly deriving the colony-level cost of queen overproduction from a dynamic model of colony growth, requiring the incorporation of parameters of colony growth and demography, such as the per-capita rate at which new brood cells are built and provisioned, the percentage of the queen's eggs that are female, costs linked with worker reproduction and worker mortality. Our revised model predicts queen overproduction to more severely impact colony productivity, resulting in an evolutionarily stable strategy that is approximately half that of the original model, and is shown to accurately predict actual levels of queen overproduction observed in different Melipona species. Altogether, this shows how inclusive fitness models can provide accurate quantitative predictions, provided that costs and benefits are modeled in sufficient detail and are measured precisely.

Keywords: caste fate conflict; inclusive fitness theory; social evolution; stingless bees.

Figure 1.

Modelled colony-level cost of queen overproduction in terms of reduced swarm (A) and male production (B). Curves were obtained by plotting expected swarm (W_s, Equation 1) and male production (W_m, Equation 4) in function of levels of queen production (g) divided by the reproductive output if there was no queen overproduction (g = 0). For swarm production (A) and for empirically observed average parameter values (Table 2), the cost of queen overproduction is approximately twice as severe as originally assumed (Ratnieks, 2001; Wenseleers et al., 2003), with swarm production already dropping to zero when 45% of all female larvae develop as queens, as opposed to at 100%, assumed in the original models. Only in the absence of worker mortality (μ = 0) or with extremely high brood cell building rates (b → ∞) would the colony level cost in terms of reduced swarm production reduced to that assumed in the original caste conflict models (Ratnieks, 2001; Wenseleers et al., 2003), but this is evidently highly unrealistic. A similar cost function applies for species with high and low levels of worker reproduction (M. favosa: ψ = 94.9%, w = 16.39%, and f = 98.9%; M. beecheii: ψ = 0.909%, w = 0.909%, and f = 79.4%), due to the negative covariation between f and w (Wenseleers et al., 2013). By contrast, for male production, relative output would drop to a lower level when all females would develop as queens, but not to zero as was assumed in the original models (Ratnieks, 2001; Wenseleers et al., 2003), as the original workers that found a colony would still be able to raise males as long as they stayed alive. Hence, in the absence of worker mortality (μ = 0) or at very high rates of brood cell construction (b → ∞), relative male production would only drop to ln(2) instead of to zero. For further details, see Supplementary Material.

Figure 2.

Empirical test of ESS model predictions based on levels of queen production in stingless bees and honeybees with or without individual control over caste development. In Melipona stingless bee species queens are reared in worker cells, and caste is under individual control, which contrasts with species where queens are reared in larger royal cells and caste fate is socially enforced via differential feeding. In the group of stingless bee species shown in the middle, queens can be reared in both worker cells and royal cells, implying caste fate is under mixed control. In support of caste conflict theory and our new ESS model, self-determination of caste fate results in two orders of magnitude higher levels of queen production and queens therefore being produced in great excess of colony needs. The black vertical line and dark gray shaded area represent the observed overall average percentage of female larvae developing as queens in the 21 Melipona species and 95% confidence intervals (9.65% [8.07%−11.50%]). The gray vertical line and light gray shaded area represent the percentage of female larvae that would be expected to develop as queens, based on parameter estimates from eight Melipona species (Table 2) and our current ESS model and 95% population prediction intervals (9.97% [4.91%−13.48%]). Dashed black lines represent the percentage of female larvae that were expected to develop as queens according to the previous model of Ratnieks (2001) and Wenseleers et al. (2003), which was derived under the assumption of a linear, directly proportionate cost of queen overproduction. Earlier model predictions overestimated the % of females that should develop as queens by a factor of 2, while our current model, which accurately derives the expected colony-level cost function, closely matches empirical data. For details see Tables 2 and Supplementary Table S5. Picture credits: Tom Wenseleers.

Figure 3.

Predicted effect of model parameters on ESS level of queen production. Curves show the predicted partial effect of varying each individual parameter, holding constant the remaining parameters; points are estimates at average parameter values or at parameter values observed in species with high or low levels of worker reproduction (cf. Table 2). (A) A higher per capita daily cell building rate (b) results in a reduced colony-level cost of queen production and hence a higher ESS queen production, (B) queens laying a higher proportion of female eggs (f) results in the development of more workers and leads to a lower colony-level cost of queen overproduction and hence a higher ESS queen production, but with a more pronounced effect in species with high levels of worker reproduction, and (C) increased worker longevity (L = 1/µ) leads to a reduced colony-level cost of queen overproduction and hence a higher ESS queen production.