Bayesian methods for comparing species physiological and ecological response curves

Abstract Many ecological questions require information on species' optimal conditions or critical limits along environmental gradients. These attributes can be compared to answer questions on niche partitioning, species coexistence and niche conservatism. However, these comparisons are unconvincing when existing methods do not quantify the uncertainty in the attributes or rely on assumptions about the shape of species' responses to the environmental gradient. The aim of this study was to develop a model to quantify the uncertainty in the attributes of species response curves and allow them to be tested for substantive differences without making assumptions about the shape of the responses. We developed a model that used Bayesian penalised splines to produce and compare response curves for any two given species. These splines allow the data to determine the shape of the response curves rather than making a priori assumptions. The models were implemented using the R2OpenBUGS package for R, which uses Markov Chain Monte Carlo simulation to repetitively fit alternative response curves to the data. As each iteration produces a different curve that varies in optima, niche breadth and limits, the model estimates the uncertainty in each of these attributes and the probability that the two curves are different. The models were tested using two datasets of mosses from Antarctica. Both datasets had a high degree of scatter, which is typical of ecological research. This noise resulted in considerable uncertainty in the optima and limits of species response curves, but substantive differences were found. Schistidium antarctici was found to inhabit wetter habitats than Ceratodon purpureus , and Polytrichastrum alpinum had a lower optimal temperature for photosynthesis than Chorisodontium aciphyllum under high light conditions. Our study highlights the importance of considering uncertainty in physiological optima and other attributes of species response curves. We found that apparent differences in optima of 7.5 °C were not necessarily substantive when dealing with noisy ecological data, and it is necessary to consider the uncertainty in attributes when comparing the curves for different species. The model introduced here could increase the robustness of research on niche partitioning, species coexistence and niche conservatism.