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.