Ecology Letters, (2015) 18: 74–84 doi: 10.1111/ele.12392 LETTER The risk-return trade-off between solitary and eusocial reproduction Abstract Feng Fu,1* Sarah D. Kocher2 and Social insect colonies can be seen as a distinct form of biological organisation because they func- Martin A. Nowak2,3,4 tion as superorganisms. Understanding how natural selection acts on the emergence and mainte- nance of these colonies remains a major question in evolutionary biology and ecology. Here, we explore this by using multi-type branching processes to calculate the basic reproductive ratios and the extinction probabilities for solitary vs. eusocial reproductive strategies. We find that eusociali- ty, albeit being hugely successful once established, is generally less stable than solitary reproduc- tion unless large demographic advantages of eusociality arise for small colony sizes. We also demonstrate how such demographic constraints can be overcome by the presence of ecological niches that strongly favour eusociality. Our results characterise the risk-return trade-offs between solitary and eusocial reproduction, and help to explain why eusociality is taxonomically rare: eusociality is a high-risk, high-reward strategy, whereas solitary reproduction is more conserva- tive. Keywords Ecology and evolution, eusociality, evolutionary dynamics, mathematical biology, social insects, stochastic process. Ecology Letters (2015) 18: 74–84 There have been a number of attempts to identify some of INTRODUCTION the key ecological factors associated with the evolution of Eusocial behaviour occurs when individuals reduce their life- eusociality. Several precursors for the origins of eusociality time reproduction to help raise their siblings (Wilson 1971). have been proposed based on comparative analyses among Eusocial colonies comprise two castes: one or a few reproduc- social insect species – primarily the feeding and defense of off- tive individuals and a (mostly) non-reproductive, worker spring within a nest (Andersson 1984). These behaviours are caste. These societies thus contain a reproductive division of also frequently associated with a subsocial life history, where labour where some individuals reproduce and others forage parents and offspring overlap and occupy the nest simulta- and provision the young (Holldobler} & Wilson 1990, 2009). neously (Michener 1974; Gadagkar 1990). Insect species that have reached this remarkable level of In contrast to the relatively few origins of eusociality, losses social complexity have proven to be vastly successful in nat- or reversions back to solitary behaviour appear to be much ure, and are thought to comprise nearly 50% of the world’s more common (a very rough estimate indicates a minimum of insect biomass (Wilson 1971). Despite the apparent success of nine losses within the bees – nearly twice the number of ori- this strategy, only 2% of described insect species are eusocial. gins; see Wcislo & Danforth 1997; Cardinal & Danforth Here, we use a mathematical approach to improve our under- 2011). This suggests that the evolution of eusociality is diffi- standing of why such a successful life history strategy so cult to both achieve and maintain. However, some taxa have rarely evolves. nonetheless evolved highly complex eusocial behaviours where Eusociality has originated only 12–15 times within the caste differentiation is determined during development and insects, and perhaps 20–25 times within the entire animal individuals no longer retain the ability to perform all of the kingdom (Wilson 1971). Most of these evolutionary origins tasks required to reproduce on their own (obligate eusociality) have occurred in the order Hymenoptera (the bees, ants and (Batra 1966; Crespi & Yanega 1995). In these cases, no rever- wasps) where there has been a single origin in the ants (Wil- sions to solitary behaviour have been observed, suggesting son 1971), 2–3 origins in the wasps (Hines et al. 2007), and 4– that these species have crossed a ‘point of no return’ where 5 origins in the bees (Cardinal & Danforth 2011; Gibbs et al. reversion to a solitary life history is no longer possible 2012). As a result, much focus has been placed on under- (Wilson & Holldobler€ 2005). standing the factors favouring or disfavouring the evolution Here we calculate the emergence and extinction probabilities of eusociality within the social insects (Andersson 1984; of eusocial vs. solitary reproductive strategies. We use the Crozier 2008). haploid version of a simple model of eusociality from Nowak 1Theoretical Biology, Institute of Integrative Biology, ETH Zurich,€ 8092,Zurich,€ 3Program for Evolutionary Dynamics, Harvard University, Cambridge, Switzerland MA,02138,USA 2Department of Organismic and Evolutionary Biology, Harvard University, 4Department of Mathematics, Harvard University, Cambridge, MA,02138,USA Cambridge, MA,02138,USA *Correspondence: E-mail: [email protected] © 2014 John Wiley & Sons Ltd/CNRS Letter The risk-return trade-off of eusociality 75 et al. (2010). In our model, solitary females produce offspring through the basic reproductive ratio, R0, and the extinction that leave the nest to reproduce individually, while eusocial probability, p, of a given lineage. These parameters are females produce a mix of offspring that remain in the natal described in detail below (Table S1). nest and others that disperse to establish new, eusocial nests. A solitary individual reproduces at rate b0, and dies at rate Those offspring that stay augment the size of the colony. We d0. Each offspring of a eusocial queen stays with their mother assume that the key reproductive parameters (oviposition rate, with probability q; otherwise she leaves to establish another successful raising of the young, and expected lifespan of new colony with probability 1 À q. A eusocial queen with col- reproductive females) increase with colony size. ony size i reproduces at rate bi and dies at rate di. bi and di Our focus is not on explaining the origins of eusociality, are sigmoid functions of the colony size i with the inflection which has already been modelled in Nowak et al. (2010). point being at the eusocial threshold m. For simplicity, let us Instead, we attempt to explain the phylogenetic rarity of this start with assuming bi and di to be step functions of i: for trait by calculating the extinction probabilities of solitary vs. i < m, bi = b0 and di = d0; for i ≥ m, bi = b and di = d. Thus, eusocial reproduction in a stochastic model based on the the- eusociality confers an enhanced reproductive rate and a ory of branching processes (Harris 2002). We calculate the reduced death rate for a queen whose colony size reaches the probability that a lineage starting from a single, solitary indi- eusocial threshold (i ≥ m): b > b0 and d < d0 (henceforth vidual faces extinction, and we compare this with the extinc- referred to as the ‘eusocial advantage’). Later on, we will ver- tion probability of a lineage that starts with a single, eusocial ify the robustness of our derived results using more general individual. sigmoid functions (online appendix). Intuitively, the eusocial lifestyle appears to be risky because A single foundress can either die or successfully start a line- the production of non-reproductive workers before reproduc- age by giving birth to another reproductive individual. Each tive offspring results in a delayed reproductive payoff. Fur- queen reproduces independently of one another. In the light thermore, there is an opportunity cost associated with the of this, we can use a multi-type branching process to calculate non-reproductive offspring that remain in the nest instead of the ultimate extinction probability, p, of the lineage initiated establishing their own lineages. It is largely unknown whether by a single founding female. This value represents the chance this initial risk associated with eusocial reproduction can later that a given lineage founded by a single female will go extinct be compensated with higher reproductive rewards. To address over time t?∞. The converse of this is the emergence probabil- this question, we perform a comprehensive assessment of the ity,1À p, or the chance that a lineage founded by a single risks of population extinction for solitary vs. eusocial repro- female will persist over time t?∞. ductive life histories. We explicitly take into account the Since the daughters who stay with their mother assist to demographic and ecological factors involved in this process. perform tasks for the colony, the whole colony (consisting of We calculate and compare the population extinction proba- a reproductive queen and non-reproductive workers) can be bilities and basic reproductive ratios for solitary and eusocial seen as a sort of superorganism which differs in size and life histories. We show that eusociality is typically a riskier reproductive capacity (bi,di). We thus construct the type space strategy than solitary reproduction unless significant eusocial using colony size i (Fig. 1). benefits arise for small colony sizes. We find that, when it is For an infinitesimal time interval, Dt, a colony of size i dies available, obligate eusociality is a more successful strategy with probability diDt, increases its size to i + 1 with probabil- than facultative eusociality. These results suggest that the evo- ity qbiDt, and gives rise to a new colony of size 1 with proba- lution of eusociality is difficult because it requires a high bility (1 À q)biDt. When a colony reaches the maximal size reproductive payoff generated by the immediate production of M, the subsequent offspring are required to leave the colony. a small number of workers. We also extend our model to Thus the colony of size M gives rise to a new colony of size 1 study population competition dynamics between solitary and with probability bMDt. For simplicity, we do not consider eusocial lineages under different ecological contexts, and we worker mortality. quantify the role that ecological niches play in facilitating the emergence and maintenance of eusociality. Altogether, these findings can explain both why origins of eusociality are rare bM but hugely successful and why reversions to solitary behaviour (1 q)b also occur.