2015
DOI: 10.1038/ncomms8842
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Predicting the stability of large structured food webs

Abstract: The stability of ecological systems has been a long-standing focus of ecology. Recently, tools from random matrix theory have identified the main drivers of stability in ecological communities whose network structure is random. However, empirical food webs differ greatly from random graphs. For example, their degree distribution is broader, they contain few trophic cycles, and they are almost interval. Here we derive an approximation for the stability of food webs whose structure is generated by the cascade mo… Show more

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Cited by 133 publications
(149 citation statements)
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“…A popular model for food web structure is the cascade model [41], where species are rank ordered, and each species can exclusively prey upon lower-ranked species. The differential effects between predators and prey in the cascade model can be described using connectivity matrices with different statistics for entries above and below the diagonal [42]: Jij=μ(zi,zj)N+g(zi,zj)Jij0 with μ(zi,zj)=μaϴ(zizj)μbϴ(zjzi)g(zi,zj)=gaϴ(zizj)+gbϴ(zjzi) where Θ is the Heaviside step function. We use the convention Θ(0) = 0.…”
Section: An Example From Ecologymentioning
confidence: 99%
“…A popular model for food web structure is the cascade model [41], where species are rank ordered, and each species can exclusively prey upon lower-ranked species. The differential effects between predators and prey in the cascade model can be described using connectivity matrices with different statistics for entries above and below the diagonal [42]: Jij=μ(zi,zj)N+g(zi,zj)Jij0 with μ(zi,zj)=μaϴ(zizj)μbϴ(zjzi)g(zi,zj)=gaϴ(zizj)+gbϴ(zjzi) where Θ is the Heaviside step function. We use the convention Θ(0) = 0.…”
Section: An Example From Ecologymentioning
confidence: 99%
“…As shown here the dynamic dimensionality of an ecological community is determined by the distribution of the magnitudes of the eigenvalues of the community matrix. The magnitudes of these eigenvalues are themselves determined by network topology, types (predator-prey, mutualistic, competitive) and strengths of species interactions together with the demographic rates of species (May 1972, Neutel et al 2002, Allesina and Tang 2012, Tang et al 2014, Allesina et al 2015. This suggests that there exist relationships between dynamic dimensionality and patterns of interactions in ecological networks.…”
Section: Paper IImentioning
confidence: 99%
“…We 295 parameterised these interactions with draws from a bivariate normal distribution ( = −1, = 296 1, = 0.5, = 0.5, = −0.8) to create each trophic interaction matrix B, following Allesina et 297 al. 63 . This specification maintains an average interaction strength of 0 and an overall symmetry in 298 impacts between consumer and resource.…”
Section: Generating Trophic Network 292mentioning
confidence: 99%
“…Introducing TIMs to artificial trophic networks 63 We specified the interactions within artificial communities with a Jacobian matrix A from the 64 combination of two matrices specifying the trophic (B) and non-trophic (C) interactions (Figure 2). 65…”
mentioning
confidence: 99%