Electronic Supplementary Material 1
ESM 1 - Theoretical examples of phylogenetic entropy decomposition
To illustrate extreme cases, we propose two simple decompositions. Let us consider two
artificial regional pools (regions 1 and 2) having the same three species (A, B, and C)
distributed in two sites (C1 and C2) (Fig. 1a, b within the article).
We first focus on region 1. According to equation (2), we evaluate the local (α)
phylogenetic entropy of each site: HαC1=1.57 and HαC2=2.57 (Fig. 1c from the main text). The
phylogenetic entropy is higher in site C2 because species C, which is the most distant from
the others, has a higher abundance than in C1, which provides a more even distribution of
relative abundances along the phylogenetic tree (Allen et al. 2009). At the regional scale,
phylogenetic entropy, Hγ, equals 2.18 (Fig. 1c). We could try to apply different weights to
each community, but C1 and C2 have the same proportion of individuals (i.e. w=0.5). Hence,
the mean local biodiversity is Hᾱ=(1.57+2.57)/2=2.07. Finally, we replace Hγ and Hᾱ in the
equation: Hβ = Hγ ‒ Hᾱ or Hβst=1-(Hᾱ/Hγ) to express the turnover as a proportion (βst),
resulting in Hβst=0.05=5%. The biological turnover is very low, which is intuitive. Actually,
C1 and C2 are sites sharing the same species and where the same two closely related species
A and B are dominant. Unsurprisingly, there is a low phylogenetic turnover.
We apply the same procedure to region 2. We find the following values of phylogenetic
entropy: HαC1=0.35, HαC2=0.28, and Hγ=3.64 (Fig. 1c). The two communities are highly
dissimilar: community C1 consists of tightly related species whereas a singular species
dominates community C2. Thus, C1 and C2 are poorly diversified, leading to low local
phylogenetic diversities. However, the two communities are complementary in their
phylogenetic relatedness. Thus, abundance distribution along branches is very even at the
regional scale, resulting in a high γ-diversity value (3.64). We then estimate the mean ᾱdiversity and βst we obtain Hᾱ=(0.35+0.28)/2=0.315 and Hβst=1-(0.315/3.64)=0.91=91% (Fig.
1c). Here, the turnover of 91% between communities is easily explained by the high degree of
complementarity in the phylogenetic structure and in the distribution of relative abundances
along branches between the two local sites.
Our two theoretical examples highlight that the range of turnover values fulfils the 0–1
interval. In addition, it highlights that both phylogenetic composition and abundance
distribution among species (and branches) influence α-, β-, and γ-diversity values.
References
Allen, B., Kon, M. & Bar-Yam, Y. 2009 A New Phylogenetic Diversity Measure Generalizing
the Shannon Index and Its Application to Phyllostomid Bats. Am. Nat. 174, 236-243.
(doi: 10.1086/600101)