The Eclipse of Species Ranges
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Department of Mathematical and Statistical Methods, Biometris, Wageningen University, P.O. Box 100, 6700 AC Wageningen, The Netherlands. Email: [email protected] 2 Institute of Ecological Science, Vrije Universiteit, De Boelelaan 1085, 1081 HV, Amsterdam, The Netherlands. 3 Department of Ecology and Environment, Alterra, P.O. Box 47, 6700 AA, Wageningen, The Netherlands. 4 Westfalen 10, 3524 KG, Utrecht, The Netherlands. Received 26 June 2006; accepted 16 January 2007
ABSTRACT 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: 169179; 2000b, Nature 403: 8487; see also Lomolino and Channell, 1995, Journal of Mammalogy 76: 335347) 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 LomolinoÕs, gives a less optimistic indication of range eclipses than theirs once these have started.
Key Words: range, biogeography, conservation, extinction
1. INTRODUCTION Decreases in the extent of geographical species distributions are of main concern to present-day conservation biology, because species are (dynamically) distributed non-homogeneously over their (dynamical) ranges, when responding to ecological conditions. The size of a range is delimited by energetic requirements, by interactions with other organisms or climate, or by other factors (for a more extensive review see Hengeveld, 1990; Rodrı´ guez, 1999; Case et al., 2005). Range limits are, however, only part of the problem. They are extreme values of the general response of the species to varying ecological conditions that determine the density profile over the speciesÕ entire range. The dynamics of this profile in an expanding or contracting range are described in Hengeveld and Hemerik (2002) in Acta Biotheoretica (2006) 54:255266 DOI: 10.1007/s10441-007-9001-7
Springer 2007
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Lia Hemerik et al.
terms of an extension of an invasion model formulated previously (Bosch et al., 1990, 1992). Ranges can also be determined by special combinations of ecological factors (Haeck and Hengeveld, 1981) making these either both small, rare and ecologically vulnerable, or large, abundant and more or less stable. In
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