Density outbursts in a food web model with a closed nutrient cycle

Szwabiński, Janusz

doi:10.1016/j.physa.2013.03.047

Cited by 3 publications

(8 citation statements)

References 38 publications

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“…Apart from mobility of animals, the present model differs from the one considered in [39][40][41] in several other aspects. Organisms forming a trophic level have now individual characteristics, their fate (eating, proliferation) is determined by local conditions and they may die of hunger if they do not find food fast enough.…”

Section: Introductionmentioning

confidence: 89%

“…It is interesting to check how the model with diffusion differs from the static one [39][40][41]. To recall, in the latter model all agents stayed localized, i.e.…”

Section: More On Interspecific Interactionsmentioning

confidence: 99%

“…In our recent studies [39][40][41] a food web model with a detritus path and a spatial dynamics was analysed by means of Monte Carlo simulations. The model consists of three trophic levels, each of which is populated by animals of one distinct species.…”

Section: Introductionmentioning

confidence: 99%

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Role of detritus in a spatial food web model with diffusion

Pękalski

Szwabiński

2014

Phys. Rev. E

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One of the central themes in modern ecology is the enduring debate on whether there is a relationship between the complexity of a biological community and its stability. In this paper, we focus on the role of detritus and spatial dispersion on the stability of ecosystems. Using Monte Carlo simulations we analyze two three level models of food webs: a grazing one with the basal species (i.e. primary producers) having unlimited food resources and a detrital one in which the basal species uses detritus as a food resource. While the vast majority of theoretical studies neglects detritus, from our results it follows that the detrital food web is more stable than its grazing counterpart, because the interactions mediated by detritus damp out fluctuations in species' densities. Since the detritus model is the more complex one in terms of interaction patterns, our results provide new evidence for the advocates of the complexity as one of the factors enhancing stability of ecosystems.

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Section: Introductionmentioning

confidence: 89%

“…It is interesting to check how the model with diffusion differs from the static one [39][40][41]. To recall, in the latter model all agents stayed localized, i.e.…”

Section: More On Interspecific Interactionsmentioning

confidence: 99%

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Role of detritus in a spatial food web model with diffusion

Pękalski

Szwabiński

2014

Phys. Rev. E

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“…But recently, the function of detritus has been considered in the food web models [1,[9][10][11][12][13]23]. In these articles, it is proved that both the intermediate and top level species play crucial roles in maintaining the structure of the system [11][12][13]. And it also indicates that a food web with detritus is more stable [1].…”

Section: Introductionmentioning

confidence: 99%

A species invasion model with detritus

Peng¹,

Qin²,

Hou³

et al. 2017

ams

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We present a lattice model of food web with alien plants invasion and analyze the model via Monte Carlo simulations and Mean Field Theory. The original food web contains herbivore, plant and detritus. Our results reveal that the alien species invasion will cause different consequences under different conditions. There are five kinds of phenomenon at most in our experiment. The system's status could be only detritus exists, only alien plants exists, all plants exist harmoniously, initial plants die out while other ingredients still be alive with the alien plants, or the alien plants become extinct while the original system keeps working. In these consequences, people should pay attention to the system collapse caused by the unsuccessful species invasion. Probably it is the reason to some ecosystems break down.

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“…the average heel size) when moving to relatively higher status locations, but mostly ignore new local norms when moving to relatively lower status locations [10]. Our claim is that we do not need to introduce any exogenous factors to obtain recurring cycles, a fact acknowledged in the population dynamics literature [46, 47]. …”

Section: Introductionmentioning

confidence: 99%

The Hunt Opinion Model—An Agent Based Approach to Recurring Fashion Cycles

et al. 2016

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We study a simple agent-based model of the recurring fashion cycles in the society that consists of two interacting communities: “snobs” and “followers” (or “opinion hunters”, hence the name of the model). Followers conform to all other individuals, whereas snobs conform only to their own group and anticonform to the other. The model allows to examine the role of the social structure, i.e. the influence of the number of inter-links between the two communities, as well as the role of the stability of links. The latter is accomplished by considering two versions of the same model—quenched (parameterized by fraction L of fixed inter-links) and annealed (parameterized by probability p that a given inter-link exists). Using Monte Carlo simulations and analytical treatment (the latter only for the annealed model), we show that there is a critical fraction of inter-links, above which recurring cycles occur. For p ≤ 0.5 we derive a relation between parameters L and p that allows to compare both models and show that the critical value of inter-connections, p*, is the same for both versions of the model (annealed and quenched) but the period of a fashion cycle is shorter for the quenched model. Near the critical point, the cycles are irregular and a change of fashion is difficult to predict. For the annealed model we also provide a deeper theoretical analysis. We conjecture on topological grounds that the so-called saddle node heteroclinic bifurcation appears at p*. For p ≥ 0.5 we show analytically the existence of the second critical value of p, for which the system undergoes Hopf’s bifurcation.

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Density outbursts in a food web model with a closed nutrient cycle

Cited by 3 publications

References 38 publications

Role of detritus in a spatial food web model with diffusion

Role of detritus in a spatial food web model with diffusion

A species invasion model with detritus

The Hunt Opinion Model—An Agent Based Approach to Recurring Fashion Cycles

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