Expected length of pendant and interior edges of a Yule tree

The Yule (pure-birth) model is the simplest null model of speciation; each lineage gives rise to a new lineage independently with the same rate $\lambda$. We investigate the expected length of an edge chosen at random from the resulting evolutionary tree. In particular, we compare the expected length of a randomly selected edge with the expected length of a randomly selected pendant edge. We provide some exact formulae, and show how our results depend slightly on whether the depth of the tree or the number of leaves is conditioned on, and whether $\lambda$ is known or is estimated using maximum likelihood.Comment: 6 pages, 1 figur

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

Inferring Ancestral States without Assuming Neutrality or Gradualism Using a Stable Model of Continuous Character Evolution

Background The value of a continuous character evolving on a phylogenetic tree is commonly modelled as the location of a particle moving under one-dimensional Brownian motion with constant rate. The Brownian motion model is best suited to characters evolving under neutral drift or tracking an optimum that drifts neutrally. We present a generalization of the Brownian motion model which relaxes assumptions of neutrality and gradualism by considering increments to evolving characters to be drawn from a heavy-tailed stable distribution (of which the normal distribution is a specialized form). Results We describe Markov chain Monte Carlo methods for fitting the model to biological data paying special attention to ancestral state reconstruction, and study the performance of the model in comparison with a selection of existing comparative methods, using both simulated data and a database of body mass in 1,679 mammalian species. We discuss hypothesis testing and model selection. The stable model outperforms Brownian and Ornstein-Uhlenbeck approaches under simulations in which traits evolve with occasional large “jumps” in their value, but does not perform markedly worse for traits evolving under a truly Brownian process. Conclusions The stable model is well suited to a stochastic process with a volatile rate of change in which biological characters undergo a mixture of neutral drift and occasional evolutionary events of large magnitude

Linking Speciation to Extinction: Diversification Raises Contemporary Extinction Risk in Amphibians

Many of the traits associated with elevated rates of speciation, including niche specialization and having small and isolated populations, are similarly linked with an elevated risk of extinction. This suggests that rapidly speciating lineages may also be more extinction prone. Empirical tests of a speciation-extinction correlation are rare because assessing paleontological extinction rates is difficult. However, the modern biodiversity crisis allows us to observe patterns of extinction in real time, and if this hypothesis is true then we would expect young clades that have recently diversified to have high contemporary extinction risk. Here, we examine evolutionary patterns of modern extinction risk across over 300 genera within one of the most threatened vertebrate classes, the Amphibia. Consistent with predictions, rapidly diversifying amphibian clades also had a greater share of threatened species. Curiously, this pattern is not reflected in other tetrapod classes and may reflect a greater propensity to speciate through peripheral isolation in amphibians, which is partly supported by a negative correlation between diversification rate and mean geographic range size. This clustered threat in rapidly diversifying amphibian genera means that protecting a small number of species can achieve large gains in preserving amphibian phylogenetic diversity. Nonindependence between speciation and extinction rates has many consequences for patterns of biodiversity and how we may choose to conserve it

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

Anthropogenic activities have increased the rate of biological extinction many-fold. Recent empirical studies suggest that projected extinction may lead to extensive loss to the Tree of Life, much more than if extinction were random. One suggested cause is that extinction risk is heritable (phylogenetically patterned), such that entire higher groups will be lost. We show here with simulation that phylogenetically clustered extinction risks are necessary but not sufficient for the extensive loss of phylogenetic diversity (PD) compared to random extinction. We simulated Yule trees and evolved extinction risks at various levels of heritability (measured using Pagel\u27s ). At most levels of heritability ( in range of 0 to 10), mean values of extinction risk (range 0.25 to 0.75), tree sizes (64 to 128 tips), tree balance and temporal heterogeneity of diversification rates (Yule and coalescent trees), extinction risks do not substantially increase the loss of PD in these trees when compared to random extinction. The maximum loss of PD (20% above random) was only associated with the combination of extremely excessive values of phylogenetic signal, high mean species\u27 extinction probabilities, and extreme (coalescent) tree shapes. Interestingly, we also observed a decline in the rate of increase in the loss of PD at high phylogenetic clustering of extinction risks. Our results suggest that the interplay between various aspects of tree shape and a predisposition of higher extinction risks in species-poor clades is required to explain the substantial pruning of the Tree of Life

The expected length of pendant and interior edges of a Yule tree

AbstractThe Yule (pure-birth) model is the simplest null model of speciation; each lineage gives rise to a new lineage independently with the same rate λ. We investigate the expected length of an edge chosen at random from the resulting evolutionary tree. In particular, we compare the expected length of a randomly selected edge with the expected length of a randomly selected pendant edge. We provide some exact formulae, and show how our results depend slightly on whether the depth of the tree or the number of leaves is conditioned on, and whether λ is known or is estimated using maximum likelihood

Ranking Mammal Species for Conservation and the Loss of Both Phylogenetic and Trait Diversity

The \u27edge of existence\u27 (EDGE) prioritisation scheme is a new approach to rank species for conservation attention that aims to identify species that are both isolated on the tree of life and at imminent risk of extinction as defined by the World Conservation Union (IUCN). The self-stated benefit of the EDGE system is that it effectively captures unusual \u27unique\u27 species, and doing so will preserve the total evolutionary history of a group into the future. Given the EDGE metric was not designed to capture total evolutionary history, we tested this claim. Our analyses show that the total evolutionary history of mammals preserved is indeed much higher if EDGE species are protected than if at-risk species are chosen randomly. More of the total tree is also protected by EDGE species than if solely threat status or solely evolutionary distinctiveness were used for prioritisation. When considering how much trait diversity is captured by IUCN and EDGE prioritisation rankings, interestingly, preserving the highest-ranked EDGE species, or indeed just the most threatened species, captures more total trait diversity compared to sets of randomly-selected at-risk species. These results suggest that, as advertised, EDGE mammal species contribute evolutionary history to the evolutionary tree of mammals non-randomly, and EDGE-style rankings among endangered species can also capture important trait diversity. If this pattern holds for other groups, the EDGE prioritisation scheme has greater potential to be an efficient method to allocate scarce conservation effort

Prioritizing Populations for Conservation Using Phylogenetic Networks

In the face of inevitable future losses to biodiversity, ranking species by conservation priority seems more than prudent. Setting conservation priorities within species (i.e., at the population level) may be critical as species ranges become fragmented and connectivity declines. However, existing approaches to prioritization (e.g., scoring organisms by their expected genetic contribution) are based on phylogenetic trees, which may be poor representations of differentiation below the species level. In this paper we extend evolutionary isolation indices used in conservation planning from phylogenetic trees to phylogenetic networks. Such networks better represent population differentiation, and our extension allows populations to be ranked in order of their expected contribution to the set. We illustrate the approach using data from two imperiled species: the spotted owl Strix occidentalis in North America and the mountain pygmy-possum Burramys parvus in Australia. Using previously published mitochondrial and microsatellite data, we construct phylogenetic networks and score each population by its relative genetic distinctiveness. In both cases, our phylogenetic networks capture the geographic structure of each species: geographically peripheral populations harbor less-redundant genetic information, increasing their conservation rankings. We note that our approach can be used with all conservation-relevant distances (e.g., those based on whole-genome, ecological, or adaptive variation) and suggest it be added to the assortment of tools available to wildlife managers for allocating effort among threatened populations