Testing the water-energy theory on American palms (Arecaceae) using geographically weighted regression

Abstract

Water and energy have emerged as the best contemporary environmental correlates of broad-scale species richness patterns. A corollary hypothesis of water-energy dynamics theory is that the influence of water decreases and the influence of energy increases with absolute latitude. We report the first use of geographically weighted regression for testing this hypothesis on a continuous species richness gradient that is entirely located within the tropics and subtropics. The dataset was divided into northern and southern hemispheric portions to test whether predictor shifts are more pronounced in the less oceanic northern hemisphere. American palms (Arecaceae, n = 547 spp.), whose species richness and distributions are known to respond strongly to water and energy, were used as a model group. The ability of water and energy to explain palm species richness was quantified locally at different spatial scales and regressed on latitude. Clear latitudinal trends in agreement with water-energy dynamics theory were found, but the results did not differ qualitatively between hemispheres. Strong inherent spatial autocorrelation in local modeling results and collinearity of water and energy variables were identified as important methodological challenges. We overcame these problems by using simultaneous autoregressive models and variation partitioning. Our results show that the ability of water and energy to explain species richness changes not only across large climatic gradients spanning tropical to temperate or arctic zones but also within megathermal climates, at least for strictly tropical taxa such as palms. This finding suggests that the predictor shifts are related to gradual latitudinal changes in ambient energy (related to solar flux input) rather than to abrupt transitions at specific latitudes, such as the occurrence of frost.

Figure 1. Inherent spatial autocorrelation of local GWR results.

Moran's I correlogram of the amount of variation in American palm species richness locally explained by water and energy in geographically weighted regression. The black line shows the kernel function of the GWR analysis for comparison, a bi-square function with a bandwidth of 1200 km. Distance in km.

Figure 2. Variation in American palm species richness locally explained by water and energy.

Local R² values obtained from geographically weighted regression (GWR) of palm species richness on annual precipitation, precipitation of the driest month, and water deficit (A) and mean annual temperature, minimum temperature of the coldest month, and potential evapotranspiration (B). Fraction of variation uniquely explained by the water variables (C) and energy variables (D) obtained from variation partitioning. The green circle in (A) shows the GWR bandwidth for a cell situated at the equator.

Figure 3. Latitudinal trends in the ability of water and energy to explain American palm species richness.

The amount of variation in palm species richness locally explained by energy variables (A–D) and water variables (E–G) plotted against latitude. A, B: total energy (R_e). C, D: pure energy (R_pe). E, F: total water (R_w). G, H: pure water (R_pw). Regression lines obtained from OLS regression (black) and SAR regression (red).