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Time-dependent birth-death sampling models have been used in numerous studies for inferring past evolutionary dynamics in different areas, e.g. speciation and extinction rates in macroevolutionary studies, or effective reproductive number in epidemiological studies. These models are branching processes where lineages can bifurcate, die, or be sampled with time-dependent birth, death, and sampling rates and generate phylogenetic trees. It has recently been shown that in some subclasses of such models, different sets of rates can result in the same distributions of reconstructed phylogenetic trees, and therefore the rates become unidentifiable from the trees regardless of their size. Here we show that widely used time-dependent fossilised birth-death (FBD) models are identifiable. This subclass of models makes more realistic assumptions about the fossilisation process and certain infectious disease transmission processes than the unidentifiable birth-death sampling models. Namely, FBD models assume that sampled lineages stay in the process rather than being immediately removed upon sampling. Identifiability of the time-dependent FBD model ensures that statistical methods that implement this model infer the true underlying temporal diversification or epidemiological dynamics from phylogenetic trees or directly from molecular or other comparative data. We further show that the time-dependent birth-death model with an extra parameter, the removal after sampling probability, is unidentifiable. This implies that in scenarios where we do not know how sampling affects lineages we are unable to infer this extra parameter together with birth, death, and sampling rates solely from trees.
Time-dependent birth-death sampling models have been used in numerous studies for inferring past evolutionary dynamics in different areas, e.g. speciation and extinction rates in macroevolutionary studies, or effective reproductive number in epidemiological studies. These models are branching processes where lineages can bifurcate, die, or be sampled with time-dependent birth, death, and sampling rates and generate phylogenetic trees. It has recently been shown that in some subclasses of such models, different sets of rates can result in the same distributions of reconstructed phylogenetic trees, and therefore the rates become unidentifiable from the trees regardless of their size. Here we show that widely used time-dependent fossilised birth-death (FBD) models are identifiable. This subclass of models makes more realistic assumptions about the fossilisation process and certain infectious disease transmission processes than the unidentifiable birth-death sampling models. Namely, FBD models assume that sampled lineages stay in the process rather than being immediately removed upon sampling. Identifiability of the time-dependent FBD model ensures that statistical methods that implement this model infer the true underlying temporal diversification or epidemiological dynamics from phylogenetic trees or directly from molecular or other comparative data. We further show that the time-dependent birth-death model with an extra parameter, the removal after sampling probability, is unidentifiable. This implies that in scenarios where we do not know how sampling affects lineages we are unable to infer this extra parameter together with birth, death, and sampling rates solely from trees.
A phylogenetic tree has three types of attributes: size, shape (topology), and branch lengths. Phylody-namic studies are often motivated by questions regarding the size of clades, nevertheless, nearly all of the inference methods only make use of the other two attributes. In this paper, we ask whether there is additional information if we consider tree size more explicitly in phylodynamic inference methods. To address this question, we first needed to be able to compute the expected tree size distribution under a specified phylodynamic model; perhaps surprisingly, there is not a general method for doing so — it is known what this is under a Yule or constant rate birth-death model but not for the more complicated scenarios researchers are often interested in. We present three different solutions to this problem: using i) the deterministic limit; ii) master equations; and iii) an ensemble moment approximation. Using simulations, we evaluate the accuracy of these three approaches under a variety of scenarios and alternative measures of tree size (i.e., sampling through time or only at the present; sampling ancestors or not). We then use the most accurate measures for the situation, to investigate the added informational content of tree size. We find that for two critical phylodynamic questions — i) is diversification diversity dependent? and, ii) can we distinguish between alternative diversification scenarios? — knowing the expected tree size distribution under the specified scenario provides insights that could not be gleaned from considering the expected shape and branch lengths alone. The contribution of this paper is both a novel set of methods for computing tree size distributions and a path forward for richer phylodynamic inference into the evolutionary and epidemiological processes that shape lineage trees.
Using phylogenies of present‐day species to estimate diversification rate trajectories—speciation and extinction rates over time—is a challenging task due to non‐identifiability issues. Given a phylogeny, there exists an infinite set of trajectories that result in the same likelihood; this set has been coined a congruence class. Previous work has developed approaches for sampling trajectories within a given congruence class, with the aim to assess the extent to which congruent scenarios can vary from one another. Based on this sampling approach, it has been suggested that rapid changes in speciation or extinction rates are conserved across the class. Reaching such conclusions requires to sample the broadest possible set of distinct trajectories. We introduce a new method for exploring congruence classes that we implement in the R package CRABS. Whereas existing methods constrain either the speciation rate or the extinction rate trajectory, ours provides more flexibility by sampling congruent speciation and extinction rate trajectories simultaneously. This allows covering a more representative set of distinct diversification rate trajectories. We also implement a filtering step that allows selecting the most parsimonious trajectories within a class. We demonstrate the utility of our new sampling strategy using a simulated scenario. Next, we apply our approach to the study of mammalian diversification history. We show that rapid changes in speciation and extinction rates need not be conserved across a congruence class, but that selecting the most parsimonious trajectories shrinks the class to concordant scenarios. Our approach opens new avenues both to truly explore the myriad of potential diversification histories consistent with a given phylogeny, embracing the uncertainty inherent to phylogenetic diversification models, and to select among these different histories. This should help refining our inference of diversification trajectories from extant data.
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