Matrix models for quantifying competitive intransitivity.
Assessing the relative importance of intransitive competition networks in nature has been difficult because it requires a large number of pairwise competition experiments linked to observed field abundances of interacting species. Here we introduce metrics and statistical tests for evaluating the contribution of intransitivity to community structure using two kinds of data: competition matrices derived from the outcomes of pairwise experimental studies (Cmatrices) and species abundance matrices. We use C matrices to develop patch transition matrices (P) that predict community structure in a simple Markov chain model. We propose a randomization test to evaluate the degree of intransitivity from thesePmatrices in combination with empirical or simulatedCmatrices. Benchmark tests revealed that the methods could correctly detect intransitive competition networks, even in the absence of direct measures of pairwise competitive strength. These tests represent the first tools for estimating the degree of intransitivity in competitive networks from observational datasets. They can be applied to both spatio-temporal data sampled in homogeneous environments or across environmental gradients, and to experimental measures of pairwise interactions. To illustrate the methods, we analyzed empirical data matrices on the colonization of slug carrion by necrophagous flies and their parasitoids.
Chair of Ecology and Biogeography Nicolaus Copernicus University in Toruń Lwowska1, 87-100 Toruń, Poland.
Werner
W
Ulrich
Área de Biodiversidad y Conservación Departamento de Biología y Geología Escuela Superior de Ciencias Experimentales y Tecnología Universidad Rey Juan Carlos, 28933 Móstoles, SPAIN.
Santiago
S
Soliveres
Faculty of Mathematics and Informatics Nicolaus Copernicus University in Toruń Chopina 12/18, 87-100 Toruń, Poland.
Wojciech
W
Kryszewski
Área de Biodiversidad y Conservación Departamento de Biología y Geología Escuela Superior de Ciencias Experimentales y Tecnología Universidad Rey Juan Carlos, 28933 Móstoles, SPAIN.
Fernando T
FT
Maestre
Department of Biology University of Vermont Burlington, VT 05405 USA.
Nicholas J
NJ
Gotelli
Ecological abundance matrix; competition; diversity; meta-community; variance decomposition