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      Phylogenetic analysis accounting for age-dependent death and sampling with applications to epidemics

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          Abstract

          The reconstruction of phylogenetic trees based on viral genetic sequence data sequentially sampled from an epidemic provides estimates of the past transmission dynamics, by fitting epidemiological models to these trees. To our knowledge, none of the epidemiological models currently used in phylogenetics can account for recovery rates and sampling rates dependent on the time elapsed since transmission. Here we introduce an epidemiological model where infectives leave the epidemic, either by recovery or sampling, after some random time which may follow an arbitrary distribution. We derive an expression for the likelihood of the phylogenetic tree of sampled infectives under our general epidemiological model. The analytic concept developed in this paper will facilitate inference of past epidemiological dynamics and provide an analytical framework for performing very efficient simulations of phylogenetic trees under our model. The main idea of our analytic study is that the non-Markovian epidemiological model giving rise to phylogenetic trees growing vertically as time goes by, can be represented by a Markovian "coalescent point process" growing horizontally by the sequential addition of pairs of coalescence and sampling times. As examples, we discuss two special cases of our general model, namely an application to influenza and an application to HIV. Though phrased in epidemiological terms, our framework can also be used for instance to fit macroevolutionary models to phylogenies of extant and extinct species, accounting for general species lifetime distributions.

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          Reconciling molecular phylogenies with the fossil record.

          Historical patterns of species diversity inferred from phylogenies typically contradict the direct evidence found in the fossil record. According to the fossil record, species frequently go extinct, and many clades experience periods of dramatic diversity loss. However, most analyses of molecular phylogenies fail to identify any periods of declining diversity, and they typically infer low levels of extinction. This striking inconsistency between phylogenies and fossils limits our understanding of macroevolution, and it undermines our confidence in phylogenetic inference. Here, we show that realistic extinction rates and diversity trajectories can be inferred from molecular phylogenies. To make this inference, we derive an analytic expression for the likelihood of a phylogeny that accommodates scenarios of declining diversity, time-variable rates, and incomplete sampling; we show that this likelihood expression reliably detects periods of diversity loss using simulation. We then study the cetaceans (whales, dolphins, and porpoises), a group for which standard phylogenetic inferences are strikingly inconsistent with fossil data. When the cetacean phylogeny is considered as a whole, recently radiating clades, such as the Balaneopteridae, Delphinidae, Phocoenidae, and Ziphiidae, mask the signal of extinctions. However, when isolating these groups, we infer diversity dynamics that are consistent with the fossil record. These results reconcile molecular phylogenies with fossil data, and they suggest that most extant cetaceans arose from four recent radiations, with a few additional species arising from clades that have been in decline over the last ~10 Myr.
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            Diversity-dependence brings molecular phylogenies closer to agreement with the fossil record.

            The branching times of molecular phylogenies allow us to infer speciation and extinction dynamics even when fossils are absent. Troublingly, phylogenetic approaches usually return estimates of zero extinction, conflicting with fossil evidence. Phylogenies and fossils do agree, however, that there are often limits to diversity. Here, we present a general approach to evaluate the likelihood of a phylogeny under a model that accommodates diversity-dependence and extinction. We find, by likelihood maximization, that extinction is estimated most precisely if the rate of increase in the number of lineages in the phylogeny saturates towards the present or first decreases and then increases. We demonstrate the utility and limits of our approach by applying it to the phylogenies for two cases where a fossil record exists (Cetacea and Cenozoic macroperforate planktonic foraminifera) and to three radiations lacking fossil evidence (Dendroica, Plethodon and Heliconius). We propose that the diversity-dependence model with extinction be used as the standard model for macro-evolutionary dynamics because of its biological realism and flexibility.
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              The contour of splitting trees is a Lévy process

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                Author and article information

                Journal
                1306.3427

                Evolutionary Biology,Probability
                Evolutionary Biology, Probability

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