CAN RAPOPORT’S RULE BE RESCUED? MODELING CAUSES OF THE LATITUDINAL GRADIENT IN SPECIES RICHNESS

The latitudinal gradient in species richness, wherein species richness peaks near the equator and declines toward the poles, is a widely recognized phenomenon that holds true for many taxa in all habitat types. Understanding the causative mechanism or mechanisms that generate the latitudinal gradient in species richness (LGSR) has been a major challenge, and the gradient remains unexplained. A different latitudinal trend (named "Rapoport's rule"), in which the mean size of species geographical ranges tends to decline toward the equator, has been hypothesized by G. C. Stevens to play a key role in generating the LGSR when coupled with a version of the "rescue effect," in which local populations toward the fringes of geographical ranges are sustained by immigration. The Stevens hy- pothesis is now commonly cited as a potential explanation for the LGSR and has provoked numerous empirical studies in macroecology and biogeography. However, important aspects of the hypothesis are not obvious in Stevens's verbal model and may go unrecognized, despite their major implications for empirical work related to large-scale ecological and evolutionary processes. Here we present mathematical simulation models that test the logical structure of the Stevens hypothesis, examine effects on global patterns of species richness produced by the mechanisms (Rapoport's rule and the rescue effect) explicitly identified by Stevens, and investigate the additional effect of competition. We find that Rapoport's rule on its own generates an LGSR opposite that of the real world, with species richness peaking at the poles rather than at the equator. The same qualitative result (a "reverse" LGSR) appears when rescue-effect regions, as described by Stevens, are added to the model. Building upon Stevens's verbal model, we then develop an explicit version of competition and show that competition alone tends to equalize species richness across all latitudes. However, when both Rapoport's rule and competition are included in the model, we find that a qualitatively correct LGSR is produced. Unlike previous hypotheses regarding the LGSR, this version of the model does not rely on a latitudinal gradient in the intensity of competition to produce an LGSR. However, detection of this LGSR depends on the spatial scale at which species richness is sampled, with the LGSR appearing only with regional, not local, sampling. In contrast, when competition is explicitly added to the model with both Rapoport's rule and the rescue effect, an LGSR that is qualitatively consistent with that of the real world does appear in both local and regional samples. This expanded version of the Stevens hypothesis potentially could explain the real-world LGSR, but all three elements (Rapoport's rule, the rescue effect, and com- petition) are crucial and must operate sufficiently strongly and in specific ways. The LGSR becomes apparent in the model only when parameter values for Rapoport's rule and the rescue effect are large, possibly unrealistically so, and when all points on Earth are filled to the competitively defined "community species saturation level." These findings highlight the complexity of the hypothesis and the need to consider all three of its components during empirical tests.