This paper distinguishes four recognisably different geographical processes in principle causing species to die out. One of these processes, the one we dub ¿range eclipse¿, holds that one range expands at the expense of another one, thereby usurping it. Channell and Lomolino (2000a, Journal of Biogeography 27: 169¿179; 2000b, Nature 403: 84¿87; see also Lomolino and Channell, 1995, Journal of Mammalogy 76: 335¿347) measured the course of this process in terms of the proportion of the total range remaining in its original centre, thereby essentially assuming a homogeneous distribution of animals over the range. However, part of their measure seems mistaken. By giving a general, analytical formulation of eclipsing ranges, we estimate the exact course of this process. Also, our formulation does not partition a range into two spatially equal parts, its core and its edge, but it assumes continuity. For applying this model to data on the time evolution of species, individual time series should be available for each of them. For practical purposes we give an alternative way of plotting and interpreting such time series. Our approach, being more sensitive than Channell and Lomolino¿s, gives a less optimistic indication of range eclipses than theirs once these have started.
- geographical ranges