Predicting The Yields Of Species Occupying A Single Trophic Level With Incomplete Information: Two Approximations Based On The Lotka-Volterra Generalized Equations

The linear Lotka-Volterra generalized equations (LLVGE) serve for describing the dynamics of communities of species connected by negative as well as positive interspecific interactions. Here we particularize these LLVGE to the case of a single trophic level community with S >2 species, either artificial or natural. In this case, by estimating the LLVGE parameters from the yields in monoculture and biculture experiments, the LLVGE are able to produce quite accurate predictions for species yields. However, a common situation we face is that we don't know all the parameters appearing in the LLVGE. Indeed, for large values of S, only a fraction of the experiments necessary for estimating the model parameters is commonly carried out. We then analyze which quantitative predictions are possible with an incomplete knowledge of the parameters. We discuss two approximations that allow using these LLVGE as a quantitative tool. First, when we only know a fraction of the model parameters, the mean field approximation allows making predictions on aggregate or average quantities. Second, for cases in which all the interaction parameters involving a particular species are available, we have the focal species approximation for predicting the yield of this focal species.