The Tree of Life, Ranked: How a Branch-Length Sum Decides Which Species Live

Every time a species disappears, it takes with it a slice of evolutionary history that can never be re-run. But not all extinctions are created equal. Lose a species whose lineage stretches back 100 million years with no living close relatives—think of the Chinese alligator, a living fossil—and you erase a branch of the Tree of Life that nothing else carries. Lose a common mouse, and you barely dent the canopy. For three decades, conservation biologists have been trying to turn this intuition into hard numbers: how much unique evolutionary history does each species hold, and which ones should we spend our scarce conservation dollars on first?

The most famous answer is Faith's phylogenetic diversity (PD), a metric that simply adds up the total length of the branches connecting a chosen set of species to their shared ancestor. It sounds almost too simple to matter. Yet PD, and the family of indices built on top of it, now underpins one of the most successful conservation prioritization programs in the world: the EDGE of Existence initiative, which has supported over 120 conservation projects targeting evolutionarily distinct, threatened species across the globe (Wicke & Mooers, 2026). This review chapter, by mathematicians Kristina Wicke and Arne Mooers, traces how a 1990s idea about summing branch lengths grew into a sophisticated toolkit—one that now borrows from game theory, account for extinction risk in probabilistic terms, and even extends beyond trees to the messier webs of evolutionary networks.

The Science

The story begins in the early 1990s, when several research groups independently converged on the same realization: counting species wasn't enough. Two species in the same genus share almost all their evolutionary history; two species at the opposite ends of a family tree share almost none. If you want to preserve the broadest range of evolutionary "features"—the traits, genes, and adaptations that evolution has accumulated—you should prioritize the tree's most distinct branches, not just its most numerous tips.

Faith captured this in a single quantity: phylogenetic diversity, defined as the sum of the edge lengths of the minimal subtree connecting a chosen set of leaves to the root of a phylogenetic tree (Faith, 1992). In plain terms, add up the length of every branch needed to connect your selected species to their common ancestor, and you have a measure of how much evolutionary history that set of species represents. The term "edge length" can mean evolutionary time, genetic change, or the accumulation of features along a lineage—a flexibility that has let PD serve multiple purposes.

But PD answers the question "how much history does this set of species contain?" Conservation managers more often ask a different question: "which individual species should I save first?" That shift in framing—from ranking sets to ranking species—spawned a family of indices. The two simplest are the equal splits (ES) and fair proportion (FP) indices. Both hand out the tree's total edge length to individual species, but they divide each branch differently. The fair proportion index splits each edge's length equally among all the species that descend from it (Redding & Mooers, 2006). The equal splits index instead divides edge length as you walk up the tree, splitting at each branching point.

These two indices produce slightly different rankings, and the difference matters in practice. Consider a short internal edge that sits beneath a clade of three species. Fair proportion splits it three ways; equal splits might split it based on how the branching events are ordered. For a leaf A sitting at the end of a particular branch, this yields $F{P}_T(A)={\ell }_1+\frac{{\ell }_8}{2}+\frac{{\ell }_{11}}{3}$, whereas the equal splits version assigns $E{S}_T(A)={\ell }_1+\frac{{\ell }_8}{2}+\frac{{\ell }_{11}}{4}$. A small algebraic distinction, but one that reshuffles the priority list of which species get saved.

A striking theoretical result ties this to economics. The fair proportion index turns out to be exactly the Shapley value—a famous concept from cooperative game theory that apportions a coalition's total payoff fairly among its members based on their marginal contributions (Fuchs & Jin, 2015). This isn't a coincidence of numbering; it's a deep equivalence. The fair proportion index, which a zoo program adopted because it was intuitive, is provably the "fairest" way to distribute the value of evolutionary history among species, satisfying the four axiomatic properties (efficiency, symmetry, dummy player, and additivity) that make the Shapley value unique.

What They Found

The real-world payoff of these indices is the EDGE framework, launched by the Zoological Society of London. The EDGE score combines a species' evolutionary distinctiveness with its extinction risk: $EDGE(x)=\ln (1+FP(x))+GE(x)\cdot \ln (2)$, where $GE(x)$ is an IUCN Red List category weight. A species qualifies as an EDGE species if it falls in a threatened category (vulnerable, endangered, or critically endangered) and has an above-median fair proportion score within its clade (Isaac et al., 2007). This has generated priority lists for mammals, amphibians, birds, corals, reptiles, gymnosperms, and sharks and rays—and has translated, directly, into conservation action.

EDGE species identified by the Zoological Society of London, by taxonomic group

Label	Value
Mammals	579
Amphibians	1,759
Birds	999
Corals	235
Reptiles	1,303
Gymnosperms	428
Sharks & rays	258

EDGE species counts across taxonomic groups; values are representative of programme scope.

But the original indices had a blind spot: they treated the tree as fixed and ignored extinction risk among relatives. The fair proportion index, for all its elegance, can produce rankings that reverse completely when a species is removed from the tree (Spillner et al., 2020; Wicke & Steel, 2020). Since extinctions are rarely random—threatened species tend to cluster on particular branches—this instability is more than a mathematical footnote. It motivated a second generation of metrics that fold extinction probabilities directly into the calculation.

The key concept is expected PD loss. An internal edge in a tree is only lost to extinction if all the species beneath it die. So the expected loss of an edge is its length multiplied by the product of the extinction probabilities of every species that subtends it. Sum these across all edges and you get the expected loss of evolutionary history. This logic underpins the heightened evolutionary distinctiveness (HED) index, which measures a species' expected contribution to future PD given that its relatives may vanish (Redding et al., 2008).

Here's the counterintuitive insight: a species whose close relatives face high extinction risk carries more responsibility for preserving shared history than a species whose relatives are safe. Lose a species' sole close relative and the surviving species suddenly becomes the last carrier of a long branch. HED captures this "heightened" value—it is typically larger than a species' pendant edge length precisely because the loss of relatives inflates its future contribution. This is the logic that bakes into the updated EDGE2 protocol (proposed in 2023), which explicitly incorporates uncertainty in both tree topology and extinction risk (Gumbs et al., 2023).

Rising complexity of phylogeny-based conservation indices

Label	Value
Pre-EDGE (FP only)	1
EDGE (FP + threat)	3
EDGE2 (expected PD + uncertainty)	6

Generic illustration of framework evolution; no specific numerical dataset implied beyond framework categories.

The framework also extended sideways, to abundance-weighted measures that account for how many individuals or how much biomass a species contributes. Rao's quadratic entropy and phylogenetic Hill numbers let researchers move beyond "which species are most distinct" toward "which communities harbor the most evolutionary and ecological diversity simultaneously." And it extended into more exotic mathematical territory: phylogenetic networks, which allow for reticulate events like hybridization and horizontal gene transfer, where the clean branching-tree metaphor breaks down and PD must be redefined.

Development milestones in phylogeny-based conservation metrics

Label	Value
Protected areas chosen to maximize PD	1
Early 1990s metric development	1
HED / extinction-aware indices	1

Schematic timeline of framework milestones, not a measured quantitative series.

Why This Changes Things

The shift from "count species" to "measure evolutionary history" has real, on-the-ground consequences. The EDGE of Existence program has supported over 120 conservation projects worldwide, targeting species that rank at the top of evolutionary distinctiveness and threat. The choice to prioritize a solitary, ancient lineage over a cluster of closely related species is a genuine value judgment—and it's one that PD makes explicit and defensible. When resources are limited, every dollar spent on one species is a dollar not spent on another, and having a transparent, quantitative basis for ranking is not a luxury; it's a necessity.

Yet the underlying assumption deserves scrutiny. PD's power rests on a claim that edge lengths predict feature diversity—that a longer branch really does carry more distinct genes, traits, and adaptations. Faith's original formulation measured edge lengths as the number of inferred character changes, and summing those gave the same total as counting features directly. But this coincidence holds only under specific conditions (Pardi & Goldman, 2005). In general, PD is a proxy, not a direct measurement. This is not a fatal flaw—no conservation metric could directly count all of a lineage's features—but it means the field has to keep testing how well branch lengths predict the things we actually care about, like functional diversity and resilience.

There's also a computational honesty that the review brings to the foreground. The clean case—choose the k species that maximize PD—solves efficiently with a greedy algorithm thanks to PD's submodularity (Steel, 2005). But real conservation problems are messier: species come with heterogeneous costs, budgets are fixed, and species interact through food webs and dependence networks. Under those realistic conditions, maximizing PD becomes NP-hard—the kind of problem where no efficient algorithm exists and optimal solutions are, in practice, intractable as problems scale. The species-ranking approach (ES, FP, EDGE, HED) sidesteps this: instead of chasing a provably optimal protected-area design, it ranks individual species and funds from the top down. This is a pragmatic trade, but the review is honest about its limits: ranking species one at a time does not guarantee a globally optimal conservation portfolio.

What's Next

Three frontiers stand out in the review's closing analysis. First, the field is actively reconciling the "classic" PD framework with network structures. Hybridization and horizontal gene transfer are not rare curiosities—they happen across plant families, microbial communities, and beyond—and a tree that forces a single genealogy onto these species silently misrepresents their evolutionary history. Generalizing PD and its indices to networks is an active, technically rich area, and one where the mathematics is still catching up to the biology.

Second, the interpretation of edge lengths remains a live question. If edge lengths represent time, PD measures how much history is held; if they represent feature accumulation, PD measures how much distinct functional material is held. These are different quantities with different conservation implications, and the choice of inference method shapes which one you're actually measuring. The review flags this as a place where the community could be more self-aware.

Third, and most practically, the move toward EDGE2-style metrics—explicitly probabilistic, uncertainty-aware, extinction-informed—is where the next decade of conservation prioritization is heading. The original EDGE framework was a triumph of simplicity; EDGE2 is a bet that the complexity is worth it. By incorporating uncertainty in tree inference and species-specific extinction risk, these updated metrics promise priorities that are both more accurate and more honest about what we don't know.

The deeper lesson of this chapter is that a good conservation metric does two things at once: it quantifies something we value, and it forces us to articulate why we value it. PD and its descendants made the case that evolutionary history is worth preserving in its own right—not just because a genetically diverse ecosystem might be more resilient, but because the Tree of Life is, quite literally, a record of every successful experiment evolution has ever run. The 120 projects funded, the endangered alligators, the last-of-their-line amphibians—these are the places where abstract branch-length sums become actual, living species saved. The mathematics has grown elaborate, but the goal it serves has never been simpler: don't let the oldest branches fall.