vol. 159, no. 3 the american naturalist march 2002 Species Richness and Altitude: A Comparison between Null Models and Interpolated Plant Species Richness along the Himalayan Altitudinal Gradient, Nepal John Arvid Grytnes 1,* and Ole R. Vetaas 2,† 1. Department of Botany, University of Bergen, Alle ´gaten 41, N-5007 Bergen, Norway; 2. Centre for Development Studies, University of Bergen, Stroemgaten 54, N-5007 Bergen, Norway Submitted June 15, 2000; Accepted August 16, 2001 abstract: We compare different null models for species richness patterns in the Nepalese Himalayas, the largest altitudinal gradient in the world. Species richness is estimated by interpolation of pres- ences between the extreme recorded altitudinal ranges. The number of species in 100-m altitudinal bands increases steeply with altitude until 1,500 m above sea level. Between 1,500 and 2,500 m, little change in the number of species is observed, but above this altitude, a decrease in species richness is evident. We simulate different null models to investigate the effect of hard boundaries and an assumed linear relationship between species richness and altitude. We also stimulate the effect of interpolation when incomplete sampling is assumed. Some modifications on earlier simulations are presented. We demonstrate that all three factors in combination may explain the observed pattern in species richness. Estimating species richness by interpolating species presence between maximum and minimum altitudes creates an artificially steep decrease in species richness to- ward the ends of the gradient. The addition of hard boundaries and an underlying linear trend in species richness is needed to simulate the observed broad pattern in species richness along altitude in the Nepalese Himalayas. Keywords: hard boundaries, interpolation, null model, unimodal relationship. The latitudinal decrease in species richness has been known for over a century (Wallace 1878; Pianka 1966; Brown and Lomolino 1998). This latitudinal pattern is commonly explained by a monotonic relationship with * Corresponding author; e-mail: jon.grytnes@bot.uib.no. † E-mail: ole.vetaas@bot.uib.no. Am. Nat. 2002. Vol. 159, pp. 294–304.  2002 by The University of Chicago. 0003-0147/2002/15903-0007$15.00. All rights reserved. climatic factors such as primary productivity or other energy-related factors (Richerson and Lum 1980; Turner et al. 1987; Currie 1991; Rohde 1992; Wright et al. 1993; Austin et al. 1996; Grytnes et al. 1999). Altitudinal trends in species richness are generally thought to mimic lati- tudinal trends in species richness, and the same factors are often used to explain this altitudinal pattern (MacArthur 1969, 1972; Begon et al. 1990; Rohde 1992; Rahbek 1997; Brown and Lomolino 1998; Givnish 1999). Several studies have found a decreasing trend in species richness with altitude (e.g., Yoda 1967; Alexander and Hilliard 1969; Kikkawa and Williams 1971; Hamilton 1975; Ha ˚gvar 1976; Wolda 1987; Gentry 1988; Kitayama 1992; Navarro 1992; Stevens 1992; Patterson et al. 1998; Vazquez and Givnish 1998; Odland and Birks 1999). Rahbek (1995) presented a critical literature review on species richness patterns in relation to altitude and showed that approximately half of the studies detected a mid- altitude peak in species richness. Studies finding a humped relationship between species richness and altitude include Whittaker (1960), Janzen (1973), Whittaker and Niering (1975), Shmida and Wilson (1985), McCoy (1990), Lie- berman et al. (1996), Gutie ´rrez (1997), Rahbek (1997), and Fleishman et al. (1998). A recently recognized factor that may contribute to a humped relationship between species richness and altitude is the geometric constraint on species ranges (Pineda 1993; Colwell and Hurtt 1994; Rahbek 1997; Pineda and Caswell 1998; Lees et al. 1999; Colwell and Lees 2000). The range of a species along an altitudinal gradient is geometrically constrained by sea level or the bottom of a valley as a lower boundary and the top of a mountain or an eco- physiological constraint as an upper boundary. If these boundaries present some degree of resistance to dispersal, they form so-called hard boundaries (Colwell and Lees 2000). Simulations and analytical modeling have shown that hard boundaries alone (given a random distribution of species) can cause a unimodal relationship between spe- cies richness and vertical or horizontal gradients (Colwell