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- LITERATURE CITED
- Appendix A
- Appendix B
Cooperative breeding is a system in which certain individuals facilitate the production of offspring by others. The ecological constraints hypothesis states that ecological conditions deter individuals from breeding independently, and so individuals breed cooperatively to make the best of a bad situation. Current theoretical support for the ecological constraints hypothesis is lacking. We formulate a mathematical model that emphasizes the underlying ecology of cooperative breeders. Our goal is to derive theoretical support for the ecological constraints hypothesis using an ecological model of population dynamics. We consider a population composed of two kinds of individuals, nonbreeders (auxiliaries) and breeders. We suppose that help provided by an auxiliary increases breeder fecundity, but reduces the probability with which the auxiliary becomes a breeder. Our main result is a condition that guarantees success of auxiliary help. We predict that increasing the cost of dispersal promotes helping, in agreement with verbal theory. We also predict that increasing breeder mortality can either hinder helping (at high population densities), or promote it (at low population densities). We conclude that ecological constraints can exert influence over the evolution of auxiliary help when population dynamics are considered; moreover, that influence need not coincide with direct fitness benefits as previously found.
In many cooperatively breeding species, nonbreeding individuals (i.e., auxiliary individuals) postpone or forgo their own reproduction to increase the fecundity of others. Cooperative breeders include a taxonomically broad set of species that occur in a wide range of environments (Jennions and MacDonald 1994; Cockburn 1998; Leadbeater et al. 2011; Wong and Balshine 2011). Thus, the help provided by nonbreeding auxiliaries represents one of the most diverse forms of cooperation in nature.
The adaptive significance of auxiliary help is often explained in terms of its direct and indirect fitness benefits (Wiley and Rabenold 1984; Brown 1987; Heinsohn and Legge 1999; Clutton-Brock 2002; Griffin and West 2002). Direct benefits of help accrue through the production of descendant offspring. These are realized, for example, when a helpful auxiliary gains valuable parenting experience (Skutch 1961), or when a helpful auxiliary contributes to the formation of a larger, more productive group that it will inherit at some later date (Wiley and Rabenold 1984; Kokko et al. 2001; Clutton-Brock 2002). Indirect benefits of help accrue through increased production of related, nondescendant offspring. For indirect benefits to play a role in the emergence and maintenance of auxiliary help, helpers must be able to associate with breeding kin (Griffin and West 2002). While both direct and indirect fitness benefits likely promote the evolution of helpful behavior in cooperatively breeding species (Clutton-Brock 2009), we choose to focus on indirect benefits here.
The indirect fitness benefits of auxiliary help can be realized in a number of ways, but the most prominent explanation of how they accumulate is given by the ecological constraints hypothesis (ECH). The ECH proposes that the provision of help by auxiliaries is motivated by the relatively small direct-fitness returns that come from independent breeding attempts. In this way, the ECH views an auxiliary's decision to postpone independent reproduction to help relatives as simply making the best out of a bad situation (Dickinson and Hatchwell 2004). Importantly, the ECH predicts that the selective advantage of auxiliary help is promoted by the high cost of dispersal, low probability of establishing a breeding territory, and low expected fecundity of independent breeders (Emlen 1982a, b).
While there is substantial empirical evidence to support the ECH (Hannon et al. 1985; Pruett-Jones and Lewis 1990; Komdeur 1992; Dickinson 2004; Schoepf and Schradin 2012), comprehensive theoretical support is lacking. Early theoretical work supported the hypothesis (Emlen 1982b; Motro 1993; Reeve and Ratnieks 1993), but did not embed key ecological features in a population-dynamic context. Consequently, the predictions made by these early models do not necessarily correspond to any ecologically plausible scenario. Pen and Weissing (2000a) were the first to address this limitation by modeling the evolution of cooperative breeding with explicit population dynamics. However, they found that in the absence of other effects, such as territory inheritance, the evolution of cooperative breeding was independent of ecological constraints (Pen and Weissing 2000a). Not only does this result run counter to empirical findings, but also suggests that the indirect fitness effects that feature in the ECH only act to supplement the more important direct fitness benefits associated with territory inheritance. Our goal is to reverse this view of the ECH, and show that ecological constraints alone can influence the emergence of auxiliary help—and ultimately cooperative breeding—when explicit population dynamics are taken into account.
We use a mathematical model to investigate the role played by ecological constraints in the emergence of auxiliary help. We find that the ecological constraints associated with the cost of dispersal, probability of establishment, and independent breeding success all play a role in the emergence of cooperative breeding. As a result, we are able to provide ecologically consistent theoretical support for an explanation of cooperative breeding that is widely used in biology. We also provide interpretations of our results in terms of inclusive fitness and equilibrium population densities to make our predictions amenable to experimental testing.
- Top of page
- LITERATURE CITED
- Appendix A
- Appendix B
The ECH is an empirically well-supported explanation for the adaptive significance of cooperative breeding (Hannon et al. 1985; Pruett-Jones and Lewis 1990; Komdeur 1992; Dickinson 2004; Schoepf and Schradin 2012). By contrast, theoretical support for the hypothesis is equivocal. Early theoretical work that supported the ECH treated key ecological parameters as fixed quantities, effectively neglecting the ecological underpinnings of the natural systems in which cooperative breeding occurs (Emlen 1982b; Motro 1993; Reeve and Ratnieks 1993). More recent work has taken ecological dynamics into consideration, and has found that the emergence of auxiliary help is independent of the ecological constraints featured in the ECH, when auxiliary territory inheritance is absent (Pen and Weissing 2000a). This more recent result suggests that ecological constraints are of secondary importance to other explanations.
We present an explicit account of population dynamics, and we use that account to derive an ecologically reasonable measure of helper fitness. We purposefully neglect local factors, such as territory inheritance, and direct benefits of helping, such as gained parenting experience, to focus solely on the importance of ecological constraints.
Our main result is an invasion condition that can be expressed in terms of quantities that relate directly to the ECH—specifically, cost of dispersal c and breeder mortality . We find that ecological constraints can influence the emergence of cooperative breeding without additional direct-fitness benefits, such as territory inheritance. In particular, we find that increased cost of dispersal acts as an incentive for auxiliary help, as originally suggested by Emlen (1982a, b). Changes to breeder mortality (equivalently, probability of establishment ψ, at equilibrium) have a variable effect that depends on the tension between the expected lifetime of breeder–auxiliary associations, on the one hand, and expected time spent in the auxiliary class, on the other hand. Lastly, we find that other life-history parameters, such as auxiliary dispersal rate (δ) and auxiliary mortality rate (), influence the emergence of cooperation; however, the effect of those parameters will depend heavily on the nature of the fitness costs of increased helping.
We framed our qualitative results concerning ecological constraints in terms of the occupancy rate of breeding territories (), and the density of auxiliaries (). Our results indicate that the cost of dispersal c exerts greatest influence in populations with low-to-moderate occupancy rates and low-to-moderate auxiliary densities. We also predict that increases to breeder mortality will inhibit the emergence of auxiliary help in populations with high territory occupancy rate and high breeder densities, and promote the emergence of auxiliary help as occupancy rates and auxiliary densities fall. Lastly, the complicated relationship among key ecological constraints featured in the ECH (particularly the probability of establishment ψ, unassisted lifetime reproductive success N, and territory occupancy rate ) indicates that the ECH is better framed in terms of more basic ecological features (e.g., mortality rates, or even birth rates when appropriate). Of course, what basic ecological features one accounts for will depend on what species is under consideration, and constraints beyond those accounted for here (e.g., constraints like spatial or temporal variability in habitat quality or food availability) will play a role, in general.
The main conclusion our analysis points to is that ecological constraints do not need to “piggy-back” on other features of a species' biology (e.g., territory inheritance or indeed any other feature that supplies helpers with a direct fitness benefit) to exert influence over the emergence of auxiliary help. This conclusion differs from conclusions made by other theoretical treatments of cooperative breeding that have—like us—incorporated population dynamics. The model proposed by Pen and Weissing (2000a) assumed that helpful and selfish auxiliaries alike had to pass through the same intermediary stage (a “waiter” or “floater” stage) before breeding could occur. Individuals were influenced by ecological constraints during the “waiter” stage, and since “waiting” occurred regardless of the level of help offered by an auxiliary, ecological constraints acting during that period of the life history necessarily cancelled from the invasion condition. By contrast, our model did not explicitly consider a “waiter” stage. Instead our model assumed that the life history of a helpful auxiliary diverged from that of a selfish auxiliary until such time as recruitment to the breeder class occurred. As a result, ecological constraints in our model could affect helpful and selfish auxiliaries differently, and were not fated to cancel out of our calculations. Since “waiters” or “floaters” are simply dispersers that have not yet secured a breeding territory (Koenig et al. 1992), our model does implicitly deal with these types of individuals. Indeed, the cost of dispersal c could be interpreted as a mortality rate suffered while “waiting” or “floating”.
There are many aspects of cooperative breeding not addressed by the work presented here. We chose to ignore many features of the biology of cooperative breeders (e.g., parenting experience, local competitive effects, territory inheritance, issues concerning variable levels of promiscuity) to focus on the ECH. Granted, some assumptions were made because we wished to keep the model as simple as possible. In particular, we chose to model cooperative breeders as hermaprhodites with an evolutionarily fixed pattern of sex allocation. Although the consequences of cooperative breeding for the evolution of sex allocation and the sex ratio are well understood (Emlen et al. 1986; Pen and Weissing 2000b; Wild 2006), the joint evolution of auxiliary help and sex allocation are not. In our model, the parent who produces an offspring (auxiliary) through female function receives help. This suggests that if we were to track the evolution of sex allocation strategies, we would find bias toward investment in female function (or, for a dioecious species, possibly a female-biased sex ratio). Nevertheless, allowing sex allocation or the sex ratio to evolve should not affect our main conclusion that ecological constraints exert a principal—rather than supplementary—influence on its emergence.
One key limitation of our work is that it does not address possible changes in breeder behavior with increasing help. In many cooperatively breeding birds, for example, breeders reduce their workload as helpers take on some of the burden (Hatchwell 1999; Heinsohn 2004; Russell et al. 2008; Santos and Macedo 2011). Adaptive changes like these would certainly detract from the size of the benefit required for auxiliary help to emerge, but should not affect our main conclusion.
A second key limitation of our work is that it only predicts when auxiliary help will emerge—it does not predict the ultimate level at which such help will be provisioned. By focusing on emergence only, we were able to ensure population dynamics could be described in two dimensions which made a powerful set of mathematical results available to us (the theory of planar dynamical systems; see Appendix A). Future work will go beyond the emergence of auxiliary help, and consider the maintenance of help.
Associate Editor: J. Wilkins