Limits...
Scrounging by foragers can resolve the paradox of enrichment

View Article: PubMed Central - PubMed

ABSTRACT

Theoretical models of predator–prey systems predict that sufficient enrichment of prey can generate large amplitude limit cycles, paradoxically causing a high risk of extinction (the paradox of enrichment). Although real ecological communities contain many gregarious species, whose foraging behaviour should be influenced by socially transmitted information, few theoretical studies have examined the possibility that social foraging might resolve this paradox. I considered a predator population in which individuals play the producer–scrounger foraging game in one-prey-one-predator and two-prey-one-predator systems. I analysed the stability of a coexisting equilibrium point in the one-prey system and that of non-equilibrium dynamics in the two-prey system. The results revealed that social foraging could stabilize both systems, and thereby resolve the paradox of enrichment when scrounging behaviour (i.e. kleptoparasitism) is prevalent in predators. This suggests a previously neglected mechanism underlying a powerful effect of group-living animals on the sustainability of ecological communities.

No MeSH data available.


Phase-plane diagrams. Hump shaped solid lines are prey isoclines with different carrying capacities (light grey: K=10, grey: K=15, black: K=60). Dashed lines are predator isoclines, when (a) the finder’s advantage is small (f/F≤dh/b) and (b) the finder’s advantage is large (f/F>dh/b). The intersections of the isoclines are coexistence equilibria. The predator isocline is the same for all carrying capacity levels. Parameters were set to the following values: r=15, a=1, b=0.5, h=1, d=0.25, F=1, g=5, f=0.48 for (a) and f=0.52 for (b).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5383828&req=5

RSOS160830F2: Phase-plane diagrams. Hump shaped solid lines are prey isoclines with different carrying capacities (light grey: K=10, grey: K=15, black: K=60). Dashed lines are predator isoclines, when (a) the finder’s advantage is small (f/F≤dh/b) and (b) the finder’s advantage is large (f/F>dh/b). The intersections of the isoclines are coexistence equilibria. The predator isocline is the same for all carrying capacity levels. Parameters were set to the following values: r=15, a=1, b=0.5, h=1, d=0.25, F=1, g=5, f=0.48 for (a) and f=0.52 for (b).

Mentions: Figure 2a,b shows both predator and prey isoclines of the model (equation (2.1)). When the finder’s advantage is sufficiently small (i.e. f/F<dh/b; figure 2a), the predator isocline is concave-down and never intersects to the left side of the hump in the prey isocline (appendix A); consequently, the predator and prey can stably coexist regardless of prey enrichment. Figure 2a also shows that the equilibrium densities of both species increase with enrichment when f/F<dh/b. Therefore, the paradox of enrichment disappears if scrounging behaviour is prominent in the predator population.Figure 2.


Scrounging by foragers can resolve the paradox of enrichment
Phase-plane diagrams. Hump shaped solid lines are prey isoclines with different carrying capacities (light grey: K=10, grey: K=15, black: K=60). Dashed lines are predator isoclines, when (a) the finder’s advantage is small (f/F≤dh/b) and (b) the finder’s advantage is large (f/F>dh/b). The intersections of the isoclines are coexistence equilibria. The predator isocline is the same for all carrying capacity levels. Parameters were set to the following values: r=15, a=1, b=0.5, h=1, d=0.25, F=1, g=5, f=0.48 for (a) and f=0.52 for (b).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5383828&req=5

RSOS160830F2: Phase-plane diagrams. Hump shaped solid lines are prey isoclines with different carrying capacities (light grey: K=10, grey: K=15, black: K=60). Dashed lines are predator isoclines, when (a) the finder’s advantage is small (f/F≤dh/b) and (b) the finder’s advantage is large (f/F>dh/b). The intersections of the isoclines are coexistence equilibria. The predator isocline is the same for all carrying capacity levels. Parameters were set to the following values: r=15, a=1, b=0.5, h=1, d=0.25, F=1, g=5, f=0.48 for (a) and f=0.52 for (b).
Mentions: Figure 2a,b shows both predator and prey isoclines of the model (equation (2.1)). When the finder’s advantage is sufficiently small (i.e. f/F<dh/b; figure 2a), the predator isocline is concave-down and never intersects to the left side of the hump in the prey isocline (appendix A); consequently, the predator and prey can stably coexist regardless of prey enrichment. Figure 2a also shows that the equilibrium densities of both species increase with enrichment when f/F<dh/b. Therefore, the paradox of enrichment disappears if scrounging behaviour is prominent in the predator population.Figure 2.

View Article: PubMed Central - PubMed

ABSTRACT

Theoretical models of predator&ndash;prey systems predict that sufficient enrichment of prey can generate large amplitude limit cycles, paradoxically causing a high risk of extinction (the paradox of enrichment). Although real ecological communities contain many gregarious species, whose foraging behaviour should be influenced by socially transmitted information, few theoretical studies have examined the possibility that social foraging might resolve this paradox. I considered a predator population in which individuals play the producer&ndash;scrounger foraging game in one-prey-one-predator and two-prey-one-predator systems. I analysed the stability of a coexisting equilibrium point in the one-prey system and that of non-equilibrium dynamics in the two-prey system. The results revealed that social foraging could stabilize both systems, and thereby resolve the paradox of enrichment when scrounging behaviour (i.e. kleptoparasitism) is prevalent in predators. This suggests a previously neglected mechanism underlying a powerful effect of group-living animals on the sustainability of ecological communities.

No MeSH data available.