Distribution of phylogenetic diversity under random extinction

Abstract

Abstract. Phylogenetic diversity is a measure for describing how much of an evolutionary tree is spanned by a subset of species. If one applies this to the (unknown) subset of current species that will still be present at some future time, then this 'future phylogenetic diversity' provides a measure of the impact of various extinction scenarios in biodiversity conservation. In this paper we study the distribution of future phylogenetic diversity under a simple model of extinction (a generalized 'field of bullets' model). We show that the distribution of future phylogenetic diversity converges to a normal distribution as the number of species grows (under mild conditions, which are necessary). We also describe an algorithm to compute the distribution efficiently, provided the edge lengths are integral, and briefly outline the significance of our findings for biodiversity conservation.

Phylogenetically Clustered Extinction Risks Do Not Substantially Prune the Tree of Life

“…To simulate these scenarios, we used the original p(ext) distribution (with mean value of 0.5) and transformed (using simple division and/or multiplication) their values to produce other distributions with mean values of 0.25 and 0.75, respectively. We then assigned the extinction vulnerabilities to the corresponding taxa and calculated the expected future PD [E(PD)] of each tree under the “generalized field of bullets” model or the g-FOB model [2]:The term represents the length of an edge i , while represents the probability of extinction for the corresponding subtended j th taxa in a reference phylogeny.…”

“…In order to answer our main question, we compared E(PD) on the modeled p(ext) values with E(PD) obtained from the identical tree with shuffled p(ext) values, representing a useful extension of the uniform p(ext) FOB model reported by Nee and May [3] (see also [2]). We report the results [E(PD) and p(ext) distribution] for each set of 1000 trees, at different strengths of phylogenetic clustering and mean extinction risk.…”

“…The edge lengths of these trees represent accrued change or temporal accounts of diversification events [1], [2]. The sum of the edge lengths has been referred to as “evolutionary history” [EH; 3].…”

Markovian log-supermodularity, and its applications in phylogenetics

“…Given a subset Y of X , the phylogenetic diversity (PD) of Y , denoted ϕ Y , is the sum of the lengths of the edges of the minimal subtree of T connecting the root and the leaves in Y . Under various possible interpretations of the λ values, PD has been widely used as a measure for quantifying present and expected future biodiversity [8][9][10].…”

“…For each species x ∈ X let E x denote the event that species x is extinct at some future time t. Then the expected phylogenetic diversity of the species that are extant at time t, referred to as expected future PD and denoted E[ϕ], is given by: where C v denotes the subset of X that is separated from the root by v. A simple model, referred to as the generalized field of bullets model (g-FOB) in [9] (generalizing an earlier model from [10]), assumes that the events E x are independent. Then, if we let p x = P(E x ), the value of P( x∈C v E x ) in (5) (the probability of the extinction of all the species descended from v) is given by:…”