Making the competitive exclusion principle operational at the biogeographical scale using fuzzy logic

Abstract

In biogeography the competitive exclusion principle (CEP) has been confirmed in some cases but not in others. This has fueled an unresolved debate between those advocating niche theory or the neutral theory in biodiversity and biogeography. We suggest that this situation mainly arises from the use of crisp logic, where the CEP is defined as either completely true or false. We propose the application of the fuzzy concepts of favorability (the degree to which environmental conditions are propitious for the occurrence of individual species) and favorableness (the degree to which environmental conditions are simultaneously favorable for competing species) to operationalize a fuzzy version of the CEP. Favorability was obtained by performing species distribution models applying favorability functions, while favorableness was derived from the application of the fuzzy intersection between the favorability for competing species. Then we plotted individual favorability values along the gradient of favorableness. Two potentially competing species would coexist in high-favorableness locations, as the demands of both species would be well fulfilled. In locations of low favorableness, the result would be either autecological exclusion of both species or autecological segregation, as abiotic conditions are unfavorable for at least one of the species. Competitive exclusion would occur at the intermediate stretch of the favorableness gradient, as the conditions would be good enough for persistence of each species separately but not enough for permanent coexistence. According to this theoretical framework, the observed probability that a location belongs to the intermediate favorableness area given that the two species co-occur in this location should be lower than expected according to the environmental probability models for the two species. We tested this prediction on published data about the distribution of pairs of native and introduced deer species in Great Britain, using a Bayesian approach. In two thirds of comparisons between a native and an introduced deer species the predictions of the fuzzy CEP were corroborated, which suggests that these are the pairs of species and the specific geographical areas affected by competitive exclusion. This is important both theoretically and for biodiversity conservation planning.