Towards greater realism in inclusive fitness models: the case of worker reproduction in insect societies

Abstract

The conflicts over sex allocation and male production in insect societies have long served as an important test bed for Hamilton's theory of inclusive fitness, but have for the most part been considered separately. Here, we develop new coevolutionary models to examine the interaction between these two conflicts and demonstrate that sex ratio and colony productivity costs of worker reproduction can lead to vastly different outcomes even in species that show no variation in their relatedness structure. Empirical data on worker-produced males in eight species of Melipona bees support the predictions from a model that takes into account the demographic details of colony growth and reproduction. Overall, these models contribute significantly to explaining behavioural variation that previous theories could not account for.

Keywords: inclusive fitness; sex allocation; social insects; worker policing; worker reproduction.

Figure 1.

Areas of parameter space (defined by the proportion of the queen's eggs that are female f and sister–sister relatedness r) that allow invasion of worker reproduction and policing in a population where worker reproduction is initially absent (ψ ≈ 0) (cf. table 1). The results are shown for (a) Model 1a, where colonies are founded by lone queens and worker-laid eggs randomly compete with male- and gyne-destined queen-laid eggs; (b) Model 1b, where colonies reproduce by swarming and worker-laid eggs randomly compete with male-, gyne- and worker-destined queen-laid eggs (graph is shown for parameter values appropriate for Melipona stingless bees: b = 0.044, q = 0.0847, μ = 0.024; see electronic supplementary material, tables S2–S4); and (c–f) Model 2, where the workers manipulate the sex ratio towards their own optimum via the killing of less related brothers and reinvesting freed-up resources into more related sisters with efficiencies E = 0.3, 0.5, 0.8 and ≈1. The areas in the parameter space are green, no worker reproduction; blue, worker reproduction selected for, but potentially inhibited by worker policing; red, uninhibited worker reproduction. The optimal proportion of female eggs laid by the queen f is indicated with a dashed yellow line. In Models 1a and 1b, two alternative equilibria can be reached depending on initial conditions (initial f greater or smaller than the critical value indicated with the white dotted line, which is here drawn for n = 10; see electronic supplementary material, figure S4).

Figure 2.

ESS proportions of the males that are workers' sons (ψ) predicted by collective worker interests in colonies headed by a single monandrous queen (r = 3/4) as a function of the proportion of the queen's eggs that are female (f) according to (i) Model 1a (blue curves), where colonies are founded by lone queens and worker-laid eggs randomly compete with male- and gyne-destined queen-laid eggs and (ii) Model 1b (red curves), where colonies reproduce by swarming and worker-laid eggs randomly compete with male-, gyne- as well as worker-destined queen-laid eggs, thereby impacting colony productivity. The curve for Model 1b is drawn for parameter values appropriate for Melipona stingless bees (b = 0.044, q = 0.0847, μ = 0.024, see electronic supplementary material, tables S2–S4), and the dots are observed values in eight species of Melipona (see the electronic supplementary material, table S4). Curves are drawn for the case where n = 1 (dotted lines), 2 (dashed lines) or 10 (full lines) workers would reproduce in a colony.