Methods and models for identifying thresholds of habitat loss

There is mounting evidence that many taxa respond in non-linear ways to perturbation (i.e. deviations from a natural trajectory brought on by an external agent), and many statistical, physical and ecological methods have been developed to detect the critical points or thresholds of perturbation. The majority of these methods define thresholds as the perturbation points causing abrupt ecological response, but in reality most species or ecosystems do not show a break point response but more gradual transitional change to perturbation. We develop a new method which delineates thresholds as a region in which the slope of the relationship between ecological response (y) and perturbation (x; e.g. habitat loss) is larger than 1: vertical bar|dy/dx vertical bar >= 1, where both x-and y-axes are scaled to (0, 1) range. The lower end of threshold zones so defined is of particular ecological interest because it is the smallest x that may trigger impending catastrophic response to a small change in x. We derived two landscape models (edge length and the number of patches of species distribution) and two biodiversity models (endemics-area relationship and half-population curve) to test this method. We applied our zonal thresholding method to these four models fit to empirical data of two forest plots to detect thresholds of species distribution to habitat loss. The two landscape metric models predict that no species could tolerate more than 40% of habitat loss and these thresholds can be much lower for relatively rare species with occupancy <0.4 and for aggregated habitat loss compared to random habitat loss. The half-population model leads to a similar threshold level of 40% habitat loss. Overall, we suggest the maximum permissible habitat loss threshold to be between 0-40%, depending on the pre-disturbed occupancy (or abundance) of a species. This habitat loss threshold falls within the otherwise wide range of thresholds calculated from conventional methods. Our study contributes novel methods and models to quantify the effect of habitat loss on species distribution and diversity in landscapes with potential for conservation applications.