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Scrounging by Foragers Can Resolve the Paradox of Enrichment

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Scrounging by Foragers Can Resolve the Paradox of Enrichment bioRxiv preprint doi: https://doi.org/10.1101/077537; this version posted September 26, 2016. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-ND 4.0 International license. Scrounging by foragers can resolve the paradox of enrichment Wataru Toyokawa1,2,* 1School of Biology, University of St Andrews, St Andrews, Fife, UK, KY16 9TH 2Japan Society for the Promotion of Science, Kojimachi, Chiyoda-ku, Tokyo, Japan *e-mail address: [email protected] 1 bioRxiv preprint doi: https://doi.org/10.1101/077537; this version posted September 26, 2016. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-ND 4.0 International license. 1 Abstract 2 Theoretical models of predator-prey system predict that sufficient enrichment of 3 prey can generate large amplitude limit cycles, paradoxically causing a high risk of 4 extinction (the paradox of enrichment). While real ecological communities contain 5 many gregarious species whose foraging behaviour should be influenced by socially 6 transmitted information, few theoretical studies have examined the possibility that 7 social foraging might be a resolution of the paradox. I considered a predator pop- 8 ulation in which individuals play the producer-scrounger foraging game both in 9 a one-prey-one-predator system and a two-prey-one-predator system. I analysed 10 the stability of a coexisting equilibrium point in the former one-prey system and 11 that of non-equilibrium dynamics of the latter two-prey system. The result showed 12 that social foraging can stabilise both systems and thereby resolves the paradox of 13 enrichment when scrounging behaviour is prevalent in predators. This suggests a 14 previously neglected mechanism underlying a powerful effect of group-living animals 15 on sustainability of ecological communities. 16 Keywords: paradox of enrichment, community stability, predator-prey, producer- 17 scrounger game, kleptoparasitism, social foraging 2 bioRxiv preprint doi: https://doi.org/10.1101/077537; this version posted September 26, 2016. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-ND 4.0 International license. 18 1 Introduction 19 Understanding how complex biological communities can sustainably persist has been 20 an essential theme in ecology. Community ecologists have tried for decades to reveal 21 mechanisms that maintain or destroy the persistence of natural communities [1{3]. One 22 of the most intriguing predictions from classical predator-prey models is that a sufficient 23 enrichment of prey (i.e., increasing prey carrying capacity) can destabilise the commu- 24 nity, causing a high risk of extinction [2]. This is called the paradox of enrichment. 25 Although this hypothesis was supported in simple predator-prey systems [4{6], it has 26 been rejected by a number of empirical studies (e.g. [7{10]). 27 The bulk of theoretical studies have identified ecologically relevant mechanisms that 28 can explain the scarcity of the paradox of enrichment in field conditions. Generally 29 speaking, mechanisms that reduce the per predator consumption rate as predator den- 30 sity increases are thought to weaken the paradox of enrichment [11]. For instance, both 31 inducible defensive morphs or predator-avoidance behaviour in prey [12,13], and aggres- 32 sive mutual interference or "prudence" in predators [14, 15] are depicted as potential 33 resolutions of the paradox in simple predator-prey systems. Also, as for more complex 34 communities including multiple prey populations, theory predicts that imperfection of 35 the optimal menu switching by predator [16] and diversity in interaction types between 36 species [17] can help the community to persist. 37 However, most of the previous predator-prey studies have considered an asocial for- 38 ager that searches for food resources without using socially transmitted information. 3 bioRxiv preprint doi: https://doi.org/10.1101/077537; this version posted September 26, 2016. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-ND 4.0 International license. 39 Assuming asocial foraging is simple and mathematically tractable, and it might be a 40 suitable assumption for some communities such as phytoplankton-zooplankton systems 41 (e.g. [6]). However, ecological communities actually contain many gregarious species, 42 whose foraging behaviour should be influenced by information that comes from other 43 conspecifics. 44 Scrounging (or kleptoparasitism) is a well-known consequence of social information 45 use in predation [18]. Assume that an individual in a group engages in predation by 46 using either of two different tactics: searching their environment for food clumps (or 47 divisible prey) by itself ("producing"), or attending to other foragers' clump discoveries 48 and sequestering some food at each clump found by a producer ("scrounging"). Note 49 that scrounging does not require any aggressive interferences between predators, and can 50 occur even in mere aggregations of animals which do not consist of social structures or 51 genetic relations between individuals [18]. Rather, social foraging can potentially exist in 52 any circumstances under which animals search for divisible food and information that an 53 individual has found/captured a food clump is available to other conspecifics. For this 54 reason, social foraging should be a very common phenomenon in ecological communities. 55 The game theoretic model of this producer-scrounger (PS) behavioural dynamics 56 predicts that both producer and scrounger tactics can stably coexist at the equilibrium 57 [18{22]. The equilibrium proportion of the two tactics may have a substantial influence 58 on the predator-prey dynamics, because prey are discovered only by producing predators. 59 The proportion of producers in the predator population should, therefore, crucially affect 60 the predation pressure (i.e., predator-prey encounter rate). 4 bioRxiv preprint doi: https://doi.org/10.1101/077537; this version posted September 26, 2016. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-ND 4.0 International license. 61 Conversely, population dynamics may affect the equilibrium proportion between 62 producers and scroungers. In the basic PS game, each producer exclusively obtains 63 a ”finder’s advantage", that is a portion f out of the total value of a prey item F 64 (0 ≤ f ≤ F ), before scroungers arrive. Once a producer capture a prey, all of the 65 scroungers arrive and divide the remaining F − f value equally among the individuals 66 present (i.e., all the scroungers and the producer). Scrounging provides more rewards 67 when scroungers are rare (i.e., producers are common) while it becomes less rewardable 68 when they are common. This negative frequency dependence generates an evolutionary ∗ 69 stable mixed equilibrium [23] at which the producers' proportion is q = f=F + 1=G, 70 where G is a group size [19]. Note that the equilibrium proportion of producers is re- 71 duced by an increase in the group size G which might be influenced by the population 72 size. Therefore, the model predicts that the proportion of producing would be influenced 73 not only by the finder’s advantage, but also by population dynamics. 74 Although both the paradox of enrichment and producer-scrounger dynamics have 75 separately received huge attention by ecologists, the relationship between them remains 76 largely unclear. A notable exception was a Coolen et al. [24] study, which showed that 77 scrounging behaviour in predators can stabilise the oscillation of the classical Lotka- 78 Volterra predator-prey model. As mentioned above, an increase of predator population 79 density (i.e., group size) reduces the proportion of producing, and reduction of producer 80 proportion should reduce the per capita predation rate. Therefore, predation pressure 81 becomes mitigated as the predator population grows, and thereby the Lotka-Volterra 82 system is stabilised [24]. Although the Lotka-Volterra model is too simple to understand 5 bioRxiv preprint doi: https://doi.org/10.1101/077537; this version posted September 26, 2016. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-ND 4.0 International license. 83 complex communities and does not contain the paradox of enrichment because of the 84 absence of prey carrying capacity, Coolen et al. [24] suggests that the PS game in predator 85 is a strong candidate for the resolution of the paradox of enrichment in more complex 86 predator-prey systems. 87 In this article, I extend the model of Coolen et al. [24] to standard one-prey-one- 88 predator systems (i.e., Rosenzweig-MacArthur model [1]) as well as more complex two- 89 prey-one-predator systems [25{28]. Both of these systems are known to show the paradox 90 of enrichment. Here I demonstrate that the producer-scrounger dynamics in the predator 91 resolves the paradox under a broad range of conditions. 92 2 One prey - one predator system 93 2.1 The model 94 First, I investigated a standard predator-prey model consisting of a prey population X 95 and a predator population Y [1].
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