“Nature is much more complicated” than predicted in theoretical models. In the Early View Paper “Matrix models for quantifying competitive intransitivity from species abundance data”, Werner Ulrich and colleagues try to fill a gap between models and mother nature when it comes to competition interactions.
Below is their summary of the study:
Ecologists have devoted much effort to inferring competitive processes from observed patterns of species abundances, morphology, and particularly from changes in the spatio-temporal distribution, (i.e. species co-occurrences). Classic assembly rules models, derived from the principle of competitive exclusion, predict that differences in competitive abilities should cause non-random patterns of species occurrences among sites and generate inequalities in species abundances within sites. Competitively inferior species are predicted to occur less frequently and at lower abundance, and an important and largely unresolved question is how such species can persist in a community over long time periods (also known as Darwin’s paradox and nicely explained in http://www.wbez.org/blog/clever-apes/2011-11-22/clever-apes-22-paper-covers-rock-94295) .
Simple competition models assume that species can be ranked unequivocally (A>B>C…>Z) according to their competitive strength. However, nature is much more complicated and intransitive competitive networks can generate loops in the competitive hierarchy (e.g. the rock-scissors-paper game, in which A>B>C>A). Importantly, such loops allow weak competitors to coexist with strong ones. Additionally, the structure of such loops might be modulated by environmental factors. Experimentally competitive strength can be tested with simple two-species systems. Testing competitive interactions in many-species systems requires an increasing number of species exclusion experiments.
Up to now no comprehensive theoretical framework existed to infer competitive loops from observed patterns of species abundances. Existing mathematical models based on presences and absences of species (on perfect competitive exclusion) have rarely been applied to empirical data. Our new paper in Oikos seeks to fill this gap in our knowledge. We introduce a statistical framework for evaluating the contribution of intransitivity to community structure using species abundance matrices that are commonly generated from replicated sampling of species assemblages. We use a stochastic back-engineering procedure to find a transition probability matrix that predicts best observed distributions of abundances in an ordinary Markov chain approach. We then use a probabilistic argument to convert this transition matrix into a pairwise competition matrix that contains the information of competitive strength between all species in the community. Our approach can be used for abundance data, time series, and abundances in combination with environmental data. Our case study on necrophagous flies and their hymenopteran parasitoids revealed strong hints towards instable competitive hierarchies. In other words the competitive outcome in these communities (having at least five species) strongly depended on environmental conditions but also on the spatial structure of fly and parasitoid occurrence.
We hope that our new approach sparks a fresh new look at competitive interactions in ecological communities and helps to assess and appreciate the importance of intransitivity for the coexistence of species in natural communities. We fell the need for joint approaches that link existing methods using the temporal and spatial co-variation in species abundances and occurrences with methods (like our) that reconstruct competitive hierarchies.