Elucidating the relationship between species niche and its geographical distribution is one of the fundamental problems in biogeography, with direct implications for our conceptual understanding of how life is distributed on the biosphere. In his seminal work, Grinnell (1917) argued that species occur where the abiotic conditions meet the biophysical requirements of the organism. However, Hutchinson (1957) later pointed out that a species may not realizes its Grinnellian niche, which he referred to as the fundamental niche. For example, Pulliam (1988) showed that dispersal from source habitats may maintain the population in sink habitats with suboptimal growth conditions, thereby allowing the species to realize niche space that is greater than its fundamental niche. This reciprocal relationship between the abstract fundamental niche space and the realized environmental conditions over which the species is geographically distributed is referred to as the Hutchinson’s duality. However, we do not know the operational relationship between the fundamental and realizes niche spaces, which is an important precursor to develop predictive methods for determining species ranges.
Results/Conclusions
Using a two-dimensional reaction-diffusion model, we develop a simple mechanistic model to relate the fundamental and realized niches of a vagile species. We show that the range limit of the species is not only determined by the fundamental niche limit but also by the geometrical shape of the niche contours. Surprisingly, we find that sources can not only maintain sinks, but sink can drive sources to local extinction. Using non-dimensional analysis, we show that the ratio of the fundamental and realized niche for any species is given by a non-dimensional area with is a function of species life-history traits and geometrical properties of the range limit. Our analysis provides a first analytical relationship that theoretically explores the Hutchinson’s duality for a vagile species.