Appendix 1: Additional methodological information associated with region delineation,
diversification rate estimation and the calculation of ecological divergence.
Regionalization based on maximizing dissimilarity
We first calculated the Simpson dissimilarity between assemblages over a 12,100 km2
equal-area grid. We then clustered this dissimilarity matrix using average-linkage
UPGMA (Unweighted Pair Group Method with Arithmetic Mean) clustering, which
allows defining k bioregions by cutting the resulting dendogram to produce k partitions.
Cells with bird or mammal richness below five were excluded before this clustering
procedure, as these cells (usually remote oceanic islands) tended to display idiosyncratic
clustering (however, the results remain similar when these cells were retained).
Diversification rates
We considered several ways of calculating DivRate. As version 1, we used the entire
phylogenetic tree (Jetz et al. 2012), but restrict the DivRate calculation to below the most
ancient node of species in the region. As this metric may conflate speciation and
extinction events that occur within a region with those outside, we also examined two
more restrictive alternatives: (2) Down-weighting the effect of ancient speciation events
by focusing only on diversification rates within the last X years, varying values of X from
3 to 30 million years BP; (3) A modified version of the method above in which we used
region-specific cutoffs determined by the time since the onset of the bioregion assessment
(see below). All methods returned similar results and exact DivRate metric specification
did not affect our main conclusions (Fig. S1).
In addition, we examined a version (4) of the DivRate metric in which all
calculations are restricted to only those species associated with a region. The DivRate
values based on this regional set of species are highly correlated with other measures of
diversification calculated for these regionally subset phylogenies, such as the Kendall
Moran estimator (r = 0.99 and 0.98; for birds and mammals, respectively) and a birthdeath model (r = 0.93 and 0.80). However, all these region-restricted measures of
diversification rate disregard speciations in which one of the descendants remains outside
the focal region. The degree to which such speciation events remain erroneously noncaptured increases with decreasing region richness and is thus expected to result in
spuriously high associations with Richness. This is confirmed in our results, but as we
show this did not alter substantially any of the focal associations in our study (Fig S2).
We therefore restrict our main presentation of results to version (1) of the DivRate
estimate as it requires neither an arbitrary temporal cutoff or external estimates of the
bioregion age nor is it biased by outside-region speciation.
Ecological divergence
Data. We closely follow Wilman et al. (2014) categorization, with the following
exceptions: (i) activity time is transformed to an ordinal variable with five categories (1 nocturnal, 2- nocturnal and crepuscular, 3- crepuscular or cathemeral, 4- diurnal and
crepuscular, 5- diurnal) to better represent variability in dial activity patterns. While
crepuscular and cathemeral (irregularly active at any time of night or day) represent very
different activity patterns, they are both intermediate between diurnal and nocturnal
patterns and hence are given an intermediate score. (ii) Bird foraging height data were
matched to those of mammals to include four ordinal categories (1 – ground level, 2scansorial/ low vegetation / understory, 3 – fully arboreal / canopy, 4- aerial). (iii) We
added an ordinal variable indicating the degree to which species forage in aquatic habitats
(1 - aquatic, 2 - semi-aquatic, 3 - terrestrial/non-aquatic).
Metric calculation. There is currently no consensus on the best way to quantify trait
diversity from a distance matrix (Mouchet et al. 2010; Schleuter et al. 2010). We thus
explored three methods. First, we used the sum of dendogram branch lengths , formed by
removing all terminal branches belonging to species not present in the assemblage or not
belonging to the taxon examined. The dendogram was based on UPGMA clustering of
the trait distance matrix (using the R function "hclust" from R package "stats"), which in
simulation studies has been shown to provide the best representation of the original
dissimilarities (Merigot et al. 2010). Indeed, we found the goodness-of-fit between the
original distance and the clustered distance [as measured by the 2-norm (Merigot et al.
2010)] to be better than the values obtained by alternative clustering methods (UPGMA:
= 81,347; WPGMA: 91,209; Neighbor joining: 262,871; Ward: 81,536,156). Using a
consensus tree from alternative clustering methods (Mouchet et al. 2008) was
computationally unfeasible given the number of species considered.
Second, we examined ‘functional attribute diversity’, which is simply the sum of
the pairwise distances between all species in an assemblage. The advantage of this
method is that it does not require the additional clustering stage, but results were
extremely similar to those found using the sum of dendogram branch lengths (the
correlation between rarefied dendogram-based and functional attribute trait diversity was
0.90 and 0.77 for birds and mammals, respectively).
Finally, we used the convex hull approach, using Principal Coordinates axes to
represent the dissimilarity matrix (Cornwell et al. 2006; Ricklefs 2012). However, for our
purposes we found it unsuitable as the convex hull approach is influenced by extreme
traits and is insensitive to variation in traits for species that do not possess extreme
values. Moreover, the calculation of convex hull over many trait axes for a large amount
of species is computationally challenging. Thus, for subsequent analyses we only show
the results obtained from the first method using the sum of dendogram branch lengths.
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