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Scrounging by foragers can resolve the paradox of enrichment

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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.


Relationship between the profitability of the less-profitable prey ε2/h2 and the amplitude of oscillation defined by the difference between the maximum and the minimum abundance of the more-profitable prey X1. The dashed line shows the cases in which the finder’s advantage f/F is either 0.21 or 0.51. The solid line shows the case in which the finder’s advantage f/F is 0.81. The numerical solution is obtained using the following parameter values: r1=15, r2=10, a1=a2=1, ε1=ε2=0.5, h1=1, α12=0.1, α21=0.4, b=1, d=0.25, K1=K2=4, F=1, g=3.
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RSOS160830F3: Relationship between the profitability of the less-profitable prey ε2/h2 and the amplitude of oscillation defined by the difference between the maximum and the minimum abundance of the more-profitable prey X1. The dashed line shows the cases in which the finder’s advantage f/F is either 0.21 or 0.51. The solid line shows the case in which the finder’s advantage f/F is 0.81. The numerical solution is obtained using the following parameter values: r1=15, r2=10, a1=a2=1, ε1=ε2=0.5, h1=1, α12=0.1, α21=0.4, b=1, d=0.25, K1=K2=4, F=1, g=3.

Mentions: Figure 3 shows the magnitude of oscillation relative to the profitability of the less profitable prey-2 ε2/h2. For simplicity, here I set f=f1=f2 and F=F1=F2. When the finder’s advantage f/F is small (i.e. f/F=0.21 or 0.51), the system is always stable regardless of the profitability of prey-2 ε2/h2. When the finder’s advantage is large (i.e. f/F=0.81), however, the system oscillates under a range of conditions as shown in the basal model without the PS game [43]. Note that, when the finder’s advantage is very large (i.e. f/F≈1), the proportion of the producers is almost always one and the model equation (3.1) becomes identical to the basal Genkai-Kato & Yamamura’s model [43].Figure 3.


Scrounging by foragers can resolve the paradox of enrichment
Relationship between the profitability of the less-profitable prey ε2/h2 and the amplitude of oscillation defined by the difference between the maximum and the minimum abundance of the more-profitable prey X1. The dashed line shows the cases in which the finder’s advantage f/F is either 0.21 or 0.51. The solid line shows the case in which the finder’s advantage f/F is 0.81. The numerical solution is obtained using the following parameter values: r1=15, r2=10, a1=a2=1, ε1=ε2=0.5, h1=1, α12=0.1, α21=0.4, b=1, d=0.25, K1=K2=4, F=1, g=3.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSOS160830F3: Relationship between the profitability of the less-profitable prey ε2/h2 and the amplitude of oscillation defined by the difference between the maximum and the minimum abundance of the more-profitable prey X1. The dashed line shows the cases in which the finder’s advantage f/F is either 0.21 or 0.51. The solid line shows the case in which the finder’s advantage f/F is 0.81. The numerical solution is obtained using the following parameter values: r1=15, r2=10, a1=a2=1, ε1=ε2=0.5, h1=1, α12=0.1, α21=0.4, b=1, d=0.25, K1=K2=4, F=1, g=3.
Mentions: Figure 3 shows the magnitude of oscillation relative to the profitability of the less profitable prey-2 ε2/h2. For simplicity, here I set f=f1=f2 and F=F1=F2. When the finder’s advantage f/F is small (i.e. f/F=0.21 or 0.51), the system is always stable regardless of the profitability of prey-2 ε2/h2. When the finder’s advantage is large (i.e. f/F=0.81), however, the system oscillates under a range of conditions as shown in the basal model without the PS game [43]. Note that, when the finder’s advantage is very large (i.e. f/F≈1), the proportion of the producers is almost always one and the model equation (3.1) becomes identical to the basal Genkai-Kato & Yamamura’s model [43].Figure 3.

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.