Estimating Fitness Differences
In the MCT framework, fitness refers to a population’s growth rate in the absence of competition. This can be derived from differences in species’ competitive abilities (Letten et al. 2017; Wainwrightet al. 2019), or, more directly, reproductive outputs (Adleret al. 2010; HilleRisLambers et al. 2012). For mammals, fitness (and other key life history processes) is frequently evaluated with the parameter R max - the maximum intrinsic growth rate of a species (Fryxell et al. 2014). We estimateR max for the 12 species in our data following two methods. The first relied on allometric relationships betweenR max and body mass from 35 herbivore species published in the literature (Duncan et al. 2007). The second used Cole’s (1954) equation, based on species’ fecundity, and age at first and last reproduction (see Tables S4 and S5, and accompanying text of the supplementary material for details). Our results were consistent for both methods.
The inequality described by equation 1 was visualized by plottingR max ratios\(\left(\frac{R_{\max,j}}{R_{\max,i}}\right)\) of each pair of interacting species as a function of Oij . To quantify the strength of the stabilizing effect of niche partitioning, we compared observed overlaps (Oij ) with theoretical possible minima (O *) beyond which stable coexistence would be impossible. From equation 1, it follows that
\begin{equation} O^{*}=\min\left(\frac{R_{\max,j}}{R_{\max,i}};\frac{R_{\max,i}}{R_{\max,j}}\right)\nonumber \\ \end{equation}
We calculated the degree of stabilization as the proportion by whichOij could theoretically be increased while still allowing species to coexist stably, i.e.\(\frac{O^{*}-\ O_{\text{ij}}}{O^{*}}\): positive values for this metric indicate over-stabilization, whereas negative values imply exclusion.