Estimating the fundamental niche: Accounting for the uneven availability of existing climates in the calibration area

Studies that question important conceptual and methodological aspects of the field of ecological niche modeling (and species distribution modeling) have cast doubts on whether it is possible to estimate the fundamental niche of a species using presence-only data. The main limitation in niche estimation is that presence data come from the realized niche, which is only a subset of the fundamental niche. Most of the existing methods lack the ability to overcome this limitation and therefore fit niches that resemble the realized niche. To obtain a more accurate estimate of the fundamental niche, we propose using the geographic region that is accessible to a species (based on its dispersal ability) to determine a sampling distribution, in environmental space, from which we can quantify the likelihood of observing a particular environmental combination in a sample of presence points. We incorporate this sampling distribution into a multivariate normal model (i.e., a Mahalanobis distance model) by creating a weight function that modifies the probabilities of observing different environmental combinations in a sample of presences. This modification accounts for the uneven availability of environmental conditions. We show that the parameters of this weighted-normal model can be approximated with a maximum likelihood estimation approach; and then used to draw ellipsoids (confidence regions) that represent the fundamental niche of the species. We illustrate the application of our model with two worked examples. First, we use presence data for an invasive species and an accessible area that includes only its native range to evaluate whether the fitted model predicts confirmed establishments of the species outside its native range. Second, we use presence data for closely related species with known accessible areas to demonstrate how the different dispersal abilities of the species constrain a classic Mahalanobis distance model. Overall, we show that accounting for the distribution of environmental conditions that are accessible to a species indeed affects the estimation of the ellipsoids used to model its fundamental niche.