Evolution of Aggression in Consumer-Resource Models

In both cases, we also calculate the proportion of Hawks in the population as the population size approaches its limit.

We numerically solved model (7) for 20,000 time steps. Then, using the final abundances as initial conditions, we numerically solved the model for an additional 20,000 time steps. Using this solution, we integrated the average proportion of Hawks over this time.

This prediction assumes that the value of the resource V is less than the cost of fighting C. Otherwise, the Hawk–Dove game predicts all individuals will be aggressive.

A similar model was studied in Křivan et al. [17]. In Sect. 4 of their paper, they interpreted the Hawk–Dove model as a model of contest competition. Resources were nesting sites, and the number of nesting sites was fixed. They showed that Hawks would outcompete Doves, thus occupying all of the available nesting sites. This underscores a major difference between how aggression might evolve under scramble competition or contest competition.

Bistability was also observed in Auger et al. [3] and can be related to similar dynamics in models of intraguild predation [cf.,  5, 23, 13, 16] if we conceive of Hawks as intraguild predators and Doves as intraguild “prey.” This is because both Hawks and Doves compete for the common resource, but Hawks also obtain energy from Doves through pair-wise interactions when they capture the resource that a Dove is handling. In both situations, Hawks reduce the Doves’ net growth rate, albeit in our case Hawks do not kill Doves but they collect the Doves’ resource. Holt et al. [11] showed that intraguild predators and intraguild prey can coexist only if the resource environmental carrying capacity is intermediate and the intraguild predators are inferior to the intraguild prey at exploiting a common resource. Otherwise, the intraguild prey is outcompeted. We observe a similar pattern in our model too. First, Hawks are weaker competitors because of the additional cost C. Second, Fig. 1b shows that when m is large enough (i.e., \(m>C/8\)), Doves are outcompeted from the system at high environmental resource carrying capacity. At lower mortality rates we observe bistability at high values of K where Doves are either outcompeted, or they coexist with Hawks at the equilibrium proportion \(p_2\).

Exploitation and interference competition are also known, respectively, as scramble and contest competition.