On predicting species yields in multispecies communities: Quantifying the accuracy of the linear Lotka-Volterra generalized model

Abstract

The linear generalized Lotka–Volterra equations (LGLVE) constitute the simplest theoretical framework for ecological communities involving different kinds of interspecific interactions ―e.g. competition, facilitation. These equations have been often criticized as being too simple to model real systems.This study has two main goals: First, to test the LGLVE as a quantitative tool for describing/explaining/predicting the equilibrium species abundances. That is, how accurately the LGLVE predict the yields of S interacting species? Second, to show analyze which quantitative predictions are possible with an incomplete knowledge of the LGLVE parameters.With this aim I compiled from the literature 33 experiments, most of them for plants, which measured species yields in monoculture, biculture and in mixtures of S >2 species.I found that, by obtaining the LGLVE parameters from the yields in monoculture and biculture experiments, the LGLVE can accurately predict the majority of the equilibrium species yields in the mixtures of S >2 species for most of the experiments.However, in many natural communities, e.g. tropical forests or plankton, S can be of the order of hundreds and estimating all the model parameters from empirical data is unfeasible. But, by estimating the mean interaction coefficient from the yields of an incomplete set of monoculture and biculture experiments, the LGLVE still can make accurate predictions. Firstly, it is possible to derive simple formulas which are able to predict the relative yield total and mean relative yield. Secondly, when we are interested in the fate or performance of a particular species, we can use a more refined approximation to predict the yield of this focal species with accuracy comparable to the one obtained when using the full set of LGLVE.