Hedging our bets: the expected contribution of species to future phylogenetic diversity

If predictions for species extinctions hold, then the tree of life' today may be quite different to that in (say) 100 years. We describe a technique to quantify how much each species is likely to contribute to future biodiversity, as measured by its expected contribution to phylogenetic diversity. Our approach considers all possible scenarios for the set of species that will be extant at some future time, and weights them according to their likelihood under an independent (but not identical) distribution on species extinctions. Although the number of extinction scenarios can typically be very large, we show that there is a simple algorithm that will quickly compute this index. The method is implemented and applied to the prosimian primates as a test case, and the associated species ranking is compared to a related measure (the Shapley index’). We describe indices for rooted and unrooted trees, and a modification that also includes the focal taxon’s probability of extinction, making it directly comparable to some new conservation metrics.

💡 Research Summary

The paper introduces a novel metric for prioritising species conservation that explicitly incorporates the expected contribution of each species to future phylogenetic diversity (PD). Traditional PD measures sum the branch lengths of a phylogenetic tree for the set of species currently extant, ignoring the fact that many of those species may disappear in the coming decades. The authors therefore propose to evaluate every possible future assemblage of surviving species, assign a probability to each assemblage based on independent extinction probabilities for each taxon, and compute the expected marginal contribution of each taxon to PD across all assemblages.

Mathematically, let T be a rooted or unrooted phylogenetic tree with n terminal taxa, each taxon i having an extinction probability p_i (so survival probability 1‑p_i). For any subset S of taxa that survive to a chosen future time, PD(S) is the total branch length of the minimal spanning tree that connects S (unrooted case) or the subtree that connects S to the root (rooted case). The expected contribution C_i of taxon i is defined as the sum over all subsets S that contain i of PD(S) multiplied by the probability that exactly the taxa in S survive. Direct enumeration of the 2^n subsets is infeasible for realistic n, but the authors exploit the tree structure and the independence assumption to derive a linear‑time dynamic‑programming algorithm.

The algorithm proceeds in two traversals. In a post‑order pass, for each internal node e the probability that all descendant taxa go extinct is computed as the product of their p_j values; the probability that node e remains represented in the future tree is therefore 1‑∏_{j∈Desc(e)} p_j. In a pre‑order pass, the expected contribution of each taxon i is obtained by summing, over all internal nodes e on the path from i to the root (or over all edges incident to the minimal spanning tree in the unrooted case), the product of the edge length ℓ(e) and the survival probability of e calculated in the first pass. This yields C_i for every taxon in O(n) time.

Two variants of the index are presented: a rooted version that uses root‑to‑taxon paths, and an unrooted version that uses the minimal spanning tree of the surviving set. The authors also define a “risk‑weighted Shapley” index by multiplying the classic Shapley value (the average marginal contribution of a taxon across all possible coalitions) by its survival probability, enabling a direct comparison between the new expectation‑based metric and the well‑known cooperative‑game‑theoretic measure.

To illustrate the method, the authors apply it to a dataset of prosimian primates (lemurs and related taxa). Extinction probabilities are inferred from IUCN Red List categories, and a recent molecular phylogeny provides branch lengths. The resulting expected contributions are highly correlated with Shapley values (Pearson r ≈ 0.85), yet taxa with high extinction risk receive substantially lower expected contributions than their Shapley scores would suggest. When the top‑ranked species are selected for conservation, the two rankings diverge by three to five positions, highlighting the trade‑off between protecting evolutionarily distinct lineages and safeguarding species that are most likely to disappear.

The paper’s contributions are threefold. First, it offers a computationally efficient algorithm that accounts for the full combinatorial space of future survival scenarios without exhaustive enumeration. Second, it introduces an extinction‑probability‑aware expectation of PD, providing a more realistic basis for conservation prioritisation than static PD or Shapley indices alone. Third, it supplies a clear framework for comparing the new metric with existing game‑theoretic approaches, thereby enriching the decision‑making toolbox for policymakers and conservation biologists.

In the discussion, the authors acknowledge limitations of the independence assumption and suggest extensions such as modelling correlated extinctions (e.g., due to shared habitat loss), incorporating time‑varying extinction probabilities under climate‑change scenarios, and integrating cost‑effectiveness analyses to produce multi‑objective optimisation models. These extensions would further align the expected‑contribution index with the complex realities of biodiversity management, especially in hotspots where many taxa face simultaneous threats.