Hutchinson and MacArthur (1959) argued that the number of available habitats and thus the number of species should decrease with body size. May (1978) presented an estimate of species number as a function of body length for all terrestrial animals, and he interpreted his data to be more or less in accord with the prediction of Hutchinson and MacArthur (1959; see also Morse et al. 1985). However, recent analysis showed that the smallest organisms are not the most diverse and that global body size distributions among species are humped and right-skewed even on a logscale (Brown and Nicoletto 1991, Blackburn and Gaston 1994a, Barlow 1994; Fig. 1). If a variety of factors acts in a multiplicative way then a lognormal distribution would be expected (May 1975). Thus, the central issue is, why body size distributions deviate from a lognormal shape and show a considerable right-skew (for a review see Blackburn and Gaston 1994b). Based on an energetic definition of fitness, Brown et al. (1993) developed a model which predicts not only the right-skewed shape of the frequency distribution but also an optimal body size. This model simplifies the physiological processes of reproduction and uses scaling functions derived for mammals. It was successful in predicting the optimal body size of mammals and the body size shifts of mammals on islands. However, predictions for other taxa remain obscure because it is unclear whether the scaling functions are valid for other taxa. Another approach to predict a right-skew of body size distributions applies size-biased extinction and speciation rates (Dial and Marzluff 1988, Maurer et al. 1992). There is a complex and scattered literature on speciation rates in correlation to body size (e.g. Bush 1993, Fenchel 1993) with the general conclusion that speciation rates decrease with body size. Thus, the higher speciation rates of small animal species can generate a right-skewed pattern. Maurer et al. (1992), however, conclude that a right-skewed distribution needs size-biased speciation and extinction rates. Until now the relationship between extinction risk and body size is equivocal. In general, population persistence is more likely when fluctuations in numbers are small and the recovery from low numbers is fast. Lawton (1995) notes that these factors can be correlated with body size but not necessarily in ways that act consistently to either promote or reduce the risk of extinction. Pimm et al. (1988) argued that large-bodied organisms are at greater disadvantage in a stochastic environment due to their small growth rates and thus long recovery times from population crashes. This generates a positive relationship between extinction risk and body size (see also Brown and Maurer 1986, Lawton 1989, Blackburn et al. 1990, Gaston and Blackburn 1995). However, Cook and Hanski (1995) found an opposite pattern in shrews. They argued that smallbodied species are more sensitive to environmental fluctuations than large-bodied species (see also Tracy and George 1992). Thus, small-bodied species fluctuate more likely to extinction. Furthermore, in a stable environment large organisms are favoured because they may achieve dominance over resources (Dial and Marzluff 1988). The above discussion shows that the relationship between body size and species' vulnerability to extinction is poorly understood and a unifying approach is badly needed. Using a simulation model we explore how extinction risk of populations in a stochastic environment may depend on body size. We distinguish between two different types of environmental perturbations: fluctuations (frequent, weak perturbations) and catastrophes (rare, strong perturbations). We hypothesize that species respond to environmental fluctuations along different timescales and with different sensitivities, both assumed to be correlated with body size. Catastrophes, however, are special strong perturbations that cause sudden major declines of the population size of all species independent of their biological characteristics and thus independent of body size. We will show that these different types of perturbations translate into a relationship of extinction risk versus body size, which is U-shaped with a skew depending on the actual environmental perturbations and the biological traits of the species. Therefore, even under the assumption of a

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