A minimum model of prey-predator system with dormancy of predators and the paradox of enrichment

Kuwamura, Masataka; Nakazawa, Takefumi; Ogawa, Teiichiro

doi:10.1007/s00285-008-0203-1

Cited by 37 publications

(42 citation statements)

References 28 publications

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“…Dormancy is an adaptive response by the predator to a harsh environment, e.g. low prey density [16]. For copepods a feeding threshold was already known [22].…”

Section: Discussionmentioning

confidence: 99%

“…Indeed, many biological models that include more detail than the RM model seem to resolve the paradox by preventing destabilisation under nutrient enrichment. Among the underlying mechanisms are the division of the prey-population into two subpopulations one accessible, vulnerable or edible and one inaccessible, invulnerable or inedible [15,2], self-limitation of the prey [12], predator-induced defence mechanisms in the prey population [32], dormancy of the predators [16] and spatial heterogeneity [11,29,25]. Whether these mechanisms do cause stability depends on model specifics, as for example, adaptive defence of the prey can be both stabilizing [32] and destabilizing [1].…”

Section: Introductionmentioning

confidence: 99%

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Feeding Threshold for Predators Stabilizes Predator-Prey Systems

Bontje

Kooi

Voorn

et al. 2009

Math. Model. Nat. Phenom.

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Abstract. Since Rosenzweig showed the destabilisation of exploited ecosystems, the so called Paradox of enrichment, several mechanisms have been proposed to resolve this paradox. In this paper we will show that a feeding threshold in the functional response for predators feeding on a prey population stabilizes the system and that there exists a minimum threshold value above which the predator-prey system is unconditionally stable with respect to enrichment. Two models are analysed, the first being the classical Rosenzweig-MacArthur (RM) model with an adapted Holling type-II functional response to include a feeding threshold. This mathematical model can be studied using analytical tools, which gives insight into the mathematical properties of the two dimensional ODE system and reveals underlying stabilisation mechanisms. The second model is a mass-balance (MB) model for a predator-prey-nutrient system with complete recycling of the nutrient in a closed environment. In this model a feeding threshold is also taken into account for the predator-prey trophic interaction. Numerical bifurcation analysis is performed on both models. Analysis results are compared between models and are discussed in relation to the analytical analysis of the classical RM model. Experimental data from the literature of a closed system with ciliates, algae and a limiting nutrient are used to estimate parameters for the MB model. This microbial system forms the bottom trophic levels of aquatic ecosystems and therefore a complete overview of its dynamics is essential for understanding aquatic ecosystem dynamics.

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“…Dormancy is an adaptive response by the predator to a harsh environment, e.g. low prey density [16]. For copepods a feeding threshold was already known [22].…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Feeding Threshold for Predators Stabilizes Predator-Prey Systems

Bontje

Kooi

Voorn

et al. 2009

Math. Model. Nat. Phenom.

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“…Notice that (1.7) is reduced to (1.1) if mð pÞ 1 1 and a ¼ 0. Furthermore, as seen in [9], we suppose…”

Section: Introductionmentioning

confidence: 94%

“…Recently, we examined the population dynamics of prey-predator systems with dormancy of predators in a series of studies [7,8,9,10], which were motivated by empirical studies concerning phytoplankton-zooplankton preypredator systems; zooplankton produce resting eggs (dormant predator) to survive periods of harsh environmental conditions [6]. Moreover, [3] examined the population dynamics of a prey-predator system with di¤usive coupling to a quiescent phase.…”

Section: Introductionmentioning

confidence: 99%

“…In the next section, we give a proof of Theorem 1.3 by using the Routh-Hurwitz condition [5]. The proof of Theorem 1.3 is di¤erent from that of [9,Theorem 3.4]. In section 3, we numerically study the bifurcation structures of (1.7) with respect to K for given s and a under the Holling type II functional response (1.2) and the sigmoid type switching function (1.8).…”

Section: Introductionmentioning

confidence: 99%

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Stability of Coexisting Equilibrium of Prey-Predator Systems with Dormancy of Predators

Kuwamura

2014

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Predator Dormancy is a Stable Adaptive Strategy due to Parrondo's Paradox

et al. 2019

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Many predators produce dormant offspring to escape harsh environmental conditions, but the evolutionary stability of this adaptation has not been fully explored. Like seed banks in plants, dormancy provides a stable competitive advantage when seasonal variations occur, because the persistence of dormant forms under harsh conditions compensates for the increased cost of producing dormant offspring. However, dormancy also exists in environments with minimal abiotic variation—an observation not accounted for by existing theory. Here it is demonstrated that dormancy can out‐compete perennial activity under conditions of extensive prey density fluctuation caused by overpredation. It is shown that at a critical level of prey density fluctuations, dormancy becomes an evolutionarily stable strategy. This is interpreted as a manifestation of Parrondo's paradox: although neither the active nor dormant forms of a dormancy‐capable predator can individually out‐compete a perennially active predator, alternating between these two losing strategies can paradoxically result in a winning strategy. Parrondo's paradox may thus explain the widespread success of quiescent behavioral strategies such as dormancy, suggesting that dormancy emerges as a natural evolutionary response to the self‐destructive tendencies of overpredation and related biological phenomena.

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A minimum model of prey-predator system with dormancy of predators and the paradox of enrichment

Cited by 37 publications

References 28 publications

Feeding Threshold for Predators Stabilizes Predator-Prey Systems

Feeding Threshold for Predators Stabilizes Predator-Prey Systems

Stability of Coexisting Equilibrium of Prey-Predator Systems with Dormancy of Predators

Predator Dormancy is a Stable Adaptive Strategy due to Parrondo's Paradox

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