Producing and scrounging can have stabilizing effects at multiple levels of organization

Abstract

This study shows, for the first time, that the evolution of a simple behavior, scrounging, at the individual level can have effects on populations, food chains, and community structure. In particular, the addition of scrounging in consumer populations can allow multiple consumers to coexist while exploiting a single prey. Also, scrounging in the top predator of a tritrophic food chain can stabilize interactions between the top predator, its prey, and its prey's prey. This occurs because the payoffs to scrounging for food in a population are negative frequency dependent, allowing scroungers to invade a population and to coexist with producers at a frequency which is density-dependent. The presence of scroungers, who do not search for resources but simply use those found by others (producers) reduces the total amount of resource acquired by the group. As scrounging increases with group size, this leads to less resource acquired per individual as the group grows. Ultimately, this limits the size of the group, its impact on its prey, and its ability to outcompete other species. These effects can promote stability and thus increase species diversity. I will further suggest that prey may alter their spatial distribution such that scrounging will be profitable among their predators thus reducing predation rate on the prey.

Keywords: adaptive dynamics; biodiversity; competition; density dependence; food chain; predation; producing; scrounging; stability.

Figure 1

The effect of the finder's share (a/F, the proportion of food in a patch which is consumed by the finder before scroungers arrive) and other model parameters on the equilibrium abundance (number of animals in the population) of the top predator in a tritrophic food chain with scrounging in the top predator. Note that the smaller the finder's share the more scrounging will occur. Whenever the top predator has a positive equilibrium abundance, the herbivore and the resource (not shown here for the sake of simplicity) also have positive equilibria. (a) Finder's share and the growth rate ($r$) of the resource; (b) finder's share and the number of groups of the top predator ($g$); (c) finder's share and the encounter rate of herbivores with resources ($\propto$); and (d) finder's share and the encounter rate of top predators with herbivores. Thick lines in (a), (c), and (d) indicate population sizes below which groups cannot form and thus this model will not apply. Parameter values used for these graphs are $F$ = 50, $e$ = 1/10, $e_p$=1/7, $\mu$ = 1/10, $\vartheta$ = 1/10, $r$ = 3 (except in a), $g$ = 5 (except in b), $\propto$ = 1/250 (except in c), and $\beta$ = 1/500 (except in d)

Figure 2

The effect of some model parameters on the proportion of scrounging necessary to allow stable coexistence of three species consuming just one resource. (Stable coexistence occurs only above and to the right of the lines in the figure.) (a) Growth rate of the resource; (b) the number of groups in the population of the most efficient consumer; (c) the encounter rate of the most efficient consumer with resources; and (d) the encounter rate of the second most efficient consumer with resources. (The previous two species both have scrounging while the least efficient species does not.) Note that the most scrounging will occur when the finder's share is smallest. (Jagged lines occur in this figure because the finder's advantages ($a_1$ and $a_2$) take on only integer values in this analysis.) Parameter values used for these graphs are $F$ = 50, $e_1$ = 1/10, $e_2$ = 1/10, $e_3$ = 1/7, $\mu$ = 1/10, $\vartheta$ = 1/8, $\rho$ = 1/7, $r$ = 3 (except in a), $g_1$ = 5 (except in b), $g_2$ = 7, ${\propto }_1$ = 1/100 (except in c), ${\propto }_2$ = 1/200 (except in d), and ${\propto }_3$ = 1/250. (Note that species 1 forages more efficiently than species 2 which in turn forages more efficiently than species 3)