Species-area functions revisited

Numerous functions have been proposed to describe the species-area relationship but despite almost a century of curve-fitting there is little agreement on which is best. We aimed to rationalize the list of proposed functions and to discuss appropriate methodology for fitting and comparing the alternatives. Data from the British Isles were used for model comparisons. Sixteen functions that have been proposed as models of the species-area relationship were compared algebraically and reformulated into a consistent format. Each was parameterized to enable their use as link functions to model the combined effects of area and other factors (covariates) on S (species number). Using data on the number of plant species on 41 British islands, we examined the effects of ignoring important covariates on the choice of the best-fitting function. The methods used in some recent studies that compared alternative functions were examined. Many of the 16 species-area functions are special cases of others, some are identical, and two arose as a result of transcription errors. The 16 functions were reduced to a set of nine general functions. The empirical comparison showed that including covariates in addition to area resulted in a different best-fitting function, and that different functions identified different covariates as important. Previous studies that have compared alternative functions suffered from three shortcomings: (1) too much emphasis was placed on maximizing goodness-of-fit between S and A (area), ignoring the effects of other factors, (2) most made implicit or untested assumptions about the distribution of S, and (3) some repeated the mispractice of using R² to compare models with different numbers of parameters or differing error distributions. The generalized linear model is a framework with which to fit alternative species-area functions, and the information-theoretic approach provides one suitable method with which to compare their fit. Ignoring the effects of important covariates may result in an incorrect choice of the best-fitting function. The choice of function may also affect which covariates are found to be important. Determining an appropriate statistical model with which to relate species number to area and other covariates requires careful consideration of many issues, not just of the functional relationship between species number and area.