Constructing random matrices to represent real ecosystems

TY - JOUR

T1 - Constructing random matrices to represent real ecosystems

AU - James, Alex

AU - Plank, Michael J.

AU - Rossberg, Axel G.

AU - Beecham, Jonathan

AU - Emmerson, Mark

AU - Pitchford, Jonathan W.

PY - 2015/5

Y1 - 2015/5

N2 - Models of complex systems with n components typically have order n2 parameters because each component can potentially interact with every other. When it is impractical to measure these parameters, one may choose random parameter values and study the emergent statistical properties at the system level. Many influential results in theoretical ecology have been derived from two key assumptions: that species interact with random partners at random intensities and that intraspecific competition is comparable between species. Under these assumptions, community dynamics can be described by a community matrix that is often amenable to mathematical analysis. We combine empirical data with mathematical theory to show that both of these assumptions lead to results that must be interpreted with caution. We examine 21 empirically derived community matrices constructed using three established, independent methods. The empirically derived systems are more stable by orders of magnitude than results from random matrices. This consistent disparity is not explained by existing results on predator-prey interactions. We investigate the key properties of empirical community matrices that distinguish them from random matrices. We show that network topology is less important than the relationship between a species’ trophic position within the food web and its interaction strengths. We identify key features of empirical networks that must be preserved if random matrix models are to capture the features of real ecosystems.

AB - Models of complex systems with n components typically have order n2 parameters because each component can potentially interact with every other. When it is impractical to measure these parameters, one may choose random parameter values and study the emergent statistical properties at the system level. Many influential results in theoretical ecology have been derived from two key assumptions: that species interact with random partners at random intensities and that intraspecific competition is comparable between species. Under these assumptions, community dynamics can be described by a community matrix that is often amenable to mathematical analysis. We combine empirical data with mathematical theory to show that both of these assumptions lead to results that must be interpreted with caution. We examine 21 empirically derived community matrices constructed using three established, independent methods. The empirically derived systems are more stable by orders of magnitude than results from random matrices. This consistent disparity is not explained by existing results on predator-prey interactions. We investigate the key properties of empirical community matrices that distinguish them from random matrices. We show that network topology is less important than the relationship between a species’ trophic position within the food web and its interaction strengths. We identify key features of empirical networks that must be preserved if random matrix models are to capture the features of real ecosystems.

KW - Community matrix

KW - Complexity

KW - Food web

KW - Interaction strength

KW - Predator-prey interaction

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=84928473798&partnerID=8YFLogxK

U2 - 10.1086/680496

DO - 10.1086/680496

M3 - Article

AN - SCOPUS:84928473798

SN - 0003-0147

VL - 185

SP - 680

EP - 692

JO - The American Naturalist

JF - The American Naturalist

IS - 5

ER -