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.Comment: 19 pages, 2 figure

Computing quadratic entropy in evolutionary trees

We note here that quadratic entropy, a measure of biological diversity introduced by Rao, is a variant of the weighted Wiener index, a graph invariant intensively studied in mathematical chemistry. This fact allows us to deduce some efficient algorithms for computing the quadratic entropy in the case of given tip weights, which may be useful for community biodiversity measures. Furthermore, on ultrametric phylogenetic trees, the maximum of quadratic entropy is a measure of pairwise evolutionary distinctness in conservation biology, introduced by Pavoine. We present an algorithm that maximizes this quantity in linear time, offering a significant improvement over the currently used quadratic programming approaches

Computing quadratic entropy in evolutionary trees

We note here that quadratic entropy, a measure of biological diversity introduced by Rao, is a variant of the weighted Wiener index, a graph invariant intensively studied in mathematical chemistry. This fact allows us to deduce some efficient algorithms for computing the quadratic entropy in the case of given tip weights, which may be useful for community biodiversity measures. Furthermore, on ultrametric phylogenetic trees, the maximum of quadratic entropy is a measure of pairwise evolutionary distinctness in conservation biology, introduced by Pavoine. We present an algorithm that maximizes this quantity in linear time, offering a significant improvement over the currently used quadratic programming approaches

Računanje kvadratične entropije v evolucijskih drevesih

Kvadratična entropija, ki jo je vpeljal Rao, je mera za biološko raznolikost. V članku opazimo, da je kvadratična entropija inačica uteženega Wienerjevega indeksa, ki je po drugi strani intenzivno raziskovana grafovska invarianta v matematični kemiji. To dejstvo omogoča izpeljavo nekaj učinkovitih algoritmov za izračunavanje kvadratične entropije v primeru danih listnih uteži. Na ultrametričnih drevesih je Pavoine vpeljal maksimum kvadratičnih entropij kot mero za paroma evolucijsko različnost v ohranitveni biologiji. Predstavljamo algoritem, ki maksimizira to količino v linearnem času, kar je pomembna izboljšava glede na obstoječe kvadratične programske pristope.We note here that quadratic entropy, a measure of biological diversity introduced by Rao, is a variant of the weighted Wiener index, a graph invariant intensively studied in mathematical chemistry. This fact allows us to deduce some efficient algorithms for computing the quadratic entropy in the case of given tip weights, which may be useful for community biodiversity measures. Furthermore, on ultrametric phylogenetic trees, the maximum of quadratic entropy is a measure of pairwise evolutionary distinctness in conservation biology, introduced by Pavoine. We present an algorithm that maximizes this quantity in linear time, offering a significant improvement over the currently used quadratic programming approaches

Evolucijsko posebne vrste običajno predstavljajo več filogenetske raznolikosti, kot je pričakovano

Evolucijska posebnost meri, koliko se določena vrsta evolucijsko razlikuje v svoji filogenetski veji. Nedavno so bile za določanje prioritet pri ohranjanju biotske raznolikosti predlagane mere, ki so eksplicitno vključujejo časovno komponento. Vendar ugotavljamo, da se takšne mere kakovostno razlikujejo glede na to, kako dobro zaobjamejo skupno evolucijo (poimenovano kot filogenetsko raznolikost), ki jo predstavlja izbrana množica vrst. S pomočjo simulacij in preproste teorije grafov smo raziskali ta odnos glede na obliko filogenetskega drevesa. Pokazali smo, da mere posebnosti zaobjamejo več filogenetske raznolikosti na neuravnoteženih drevesih in na drevesih z veliko cepitvami blizu sedanjosti. Vrstni red glede na mero posebnosti je bil robusten neodvisno od oblike dreves, pri čemer so se proporcionalne mere obnašale bolje od mer, osnovanih na vozlišcih dreves. Enak vzorec se je izkazal na primeru 50 ultrametričnih dreves iz literature. Tako lahko zaključimo, da so mere posebnosti lahko koristen dodatni indikator pri določanju prioritet ohranjanja vrst. Najenostavnejša mera, starost vrste, se v tem kontekstu izkaže presenetljivo dobro, kar nakazuje da nove mere, ki se osredotočijo na obliko drevesa pri konicah, lahko zagotovijo transparentno alternativo za bolj zapletene pristope, ki obravnavajo polna drevesa.Evolutionary distinctiveness measures of how evolutionarily isolated a speciesis relative to other members of its clade. Recently, distinctiveness metrics that explicitly incorporate time have been proposed for conservation prioritization. However, we found that such measures differ qualitatively in how well they capture the total amount of evolution (termed phylogenetic diversity, or PD) represented by a set of species. We used simulation and simple graph theory to explore this relationship with reference to phylogenetic tree shape. Overall, the distinctiveness measures capture more PD on more unbalanced trees and on trees with many splits near the present. The rank order of performance was robust across tree shapes, with apportioning measures performing best and node-based measures performing worst. A sample of 50 ultrametric trees from the literature showed the same patterns. Taken together, this suggests that distinctiveness metrics may be a useful addition to other measures of value for conservation prioritization of species. The simplest measure, the age of a species, performed surprisingly well, suggesting that new measures that focus on tree shape near the tips may provide a transparent alternative to more complicated full-tree approaches