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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.


Effect of enrichment with different finder’s advantages (dotted lines: f/F= 0.3, dashed lines: f/F=0.5, and solid lines: f/F=0.6). The degree of enrichment is represented by the magnitude of the prey carrying capacity K (=K1=K2). (a) Relation between enrichment and the amplitude of the oscillation. Note that the dotted line is hidden behind the dashed line. (b–d) Relation of prey enrichment with (b) the minimum density of the more-profitable prey X1, with (c) that of the less-profitable prey X2, and with (d) that of predator Y . The same parameter values are used as in figure 3 except for h2, as h2=2.2 (i.e. ε2/h2=0.227).
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RSOS160830F5: Effect of enrichment with different finder’s advantages (dotted lines: f/F= 0.3, dashed lines: f/F=0.5, and solid lines: f/F=0.6). The degree of enrichment is represented by the magnitude of the prey carrying capacity K (=K1=K2). (a) Relation between enrichment and the amplitude of the oscillation. Note that the dotted line is hidden behind the dashed line. (b–d) Relation of prey enrichment with (b) the minimum density of the more-profitable prey X1, with (c) that of the less-profitable prey X2, and with (d) that of predator Y . The same parameter values are used as in figure 3 except for h2, as h2=2.2 (i.e. ε2/h2=0.227).

Mentions: Finally, I investigated how the system responds to prey enrichment. For simplicity, I set K=K1=K2. Figure 5a shows that the system remains stable when the finder’s advantage is small (i.e. f/F=0.3 or 0.5). When the finder’s advantage is large (i.e. f/F=0.6), however, the system becomes unstable as K increases. When the system is stable, minimum densities of all three species increase with an increase in K (figure 5b–d). Therefore, the paradox of enrichment is resolved when the finder’s advantage is small. Interestingly, however, the increase of the minimum density of the predator is weak when f/F is small compared with when it is at an intermediate-level (see the dotted versus dashed line in figure 5d). This is because, when the finder’s advantage f/F is small, too low a proportion of the predator individuals capture prey (due to the low proportion of the producers), and hence the net energetic gain of the entire predator population is diminished.Figure 5.


Scrounging by foragers can resolve the paradox of enrichment
Effect of enrichment with different finder’s advantages (dotted lines: f/F= 0.3, dashed lines: f/F=0.5, and solid lines: f/F=0.6). The degree of enrichment is represented by the magnitude of the prey carrying capacity K (=K1=K2). (a) Relation between enrichment and the amplitude of the oscillation. Note that the dotted line is hidden behind the dashed line. (b–d) Relation of prey enrichment with (b) the minimum density of the more-profitable prey X1, with (c) that of the less-profitable prey X2, and with (d) that of predator Y . The same parameter values are used as in figure 3 except for h2, as h2=2.2 (i.e. ε2/h2=0.227).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSOS160830F5: Effect of enrichment with different finder’s advantages (dotted lines: f/F= 0.3, dashed lines: f/F=0.5, and solid lines: f/F=0.6). The degree of enrichment is represented by the magnitude of the prey carrying capacity K (=K1=K2). (a) Relation between enrichment and the amplitude of the oscillation. Note that the dotted line is hidden behind the dashed line. (b–d) Relation of prey enrichment with (b) the minimum density of the more-profitable prey X1, with (c) that of the less-profitable prey X2, and with (d) that of predator Y . The same parameter values are used as in figure 3 except for h2, as h2=2.2 (i.e. ε2/h2=0.227).
Mentions: Finally, I investigated how the system responds to prey enrichment. For simplicity, I set K=K1=K2. Figure 5a shows that the system remains stable when the finder’s advantage is small (i.e. f/F=0.3 or 0.5). When the finder’s advantage is large (i.e. f/F=0.6), however, the system becomes unstable as K increases. When the system is stable, minimum densities of all three species increase with an increase in K (figure 5b–d). Therefore, the paradox of enrichment is resolved when the finder’s advantage is small. Interestingly, however, the increase of the minimum density of the predator is weak when f/F is small compared with when it is at an intermediate-level (see the dotted versus dashed line in figure 5d). This is because, when the finder’s advantage f/F is small, too low a proportion of the predator individuals capture prey (due to the low proportion of the producers), and hence the net energetic gain of the entire predator population is diminished.Figure 5.

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.