Can Rapoport's rule be rescued? Modeling causes of the latitudinal gradient in species richness

The latitudinal gradient in species richness, wherein species richness peak s near the equator and declines toward the poles, is a widely recognized ph enomenon that holds true for many taxa in all habitat types. Understanding the causative mechanism or mechanisms that generate the latitudinal gradien t in species richness (LGSR) has been a major challenge, and the gradient r emains unexplained. A different latitudinal trend (named "Rapoport's rule") , in which the mean size of species geographical ranges tends to decline to ward 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 s ustained by immigration. The Stevens hypothesis is now commonly cited as a potential explanation for the LGSR and has provoked numerous empirical stud ies in macroecology and biogeography. However, important aspects of the hyp othesis 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 simulat ion models that test the logical structure of the Stevens hypothesis, exami ne effects on global patterns of species richness produced by the mechanism s (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 t he equator. The same qualitative result (a "reverse" LGSR) appears when res cue-effect regions, as described by Stevens, are added to the model. Buildi ng upon Stevens's verbal model, we then develop an explicit version of comp etition and show that competition alone tends to equalize species richness across all latitudes. However, when both Rapoport's rule and competition ar e included in the model, we find that a qualitatively correct LGSR is produ ced. Unlike previous hypotheses regarding the LGSR, this version of the mod el 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 wi th regional, not local, sampling. In contrast, when competition is explicit ly added to the model with both Rapoport's rule and the rescue effect, an L GSR that is qualitatively consistent with that. of the real world does appe ar in both local and regional samples. This expanded version of the Stevens hypothesis potentially could explain the real-world LGSR, but all three el ements (Rapoport's rule, the rescue effect, and competition) are crucial an d must operate sufficiently strongly and in specific ways. The LGSR becomes apparent in the model only when parameter values for Rapoport's rule and t he rescue effect are large, possibly unrealistically so, and when all paint s on Earth are filled to the competitively defined "community species satur ation level." These findings highlight the complexity of the hypothesis and the need to consider all three of its components during empirical tests.