Phase transition on the convergence rate of parameter estimation under an Ornstein-Uhlenbeck diffusion on a tree

Cécile Ané, Lam Si Tung Ho, Sebastien Roch
(Submitted on 6 Jun 2014)

Diffusion processes on trees are commonly used in evolutionary biology to model the joint distribution of continuous traits, such as body mass, across species. Estimating the parameters of such processes from tip values presents challenges because of the intrinsic correlation between the observations produced by the shared evolutionary history, thus violating the standard independence assumption of large-sample theory. For instance Ho and An\’e \cite{HoAne13} recently proved that the mean (also known in this context as selection optimum) of an Ornstein-Uhlenbeck process on a tree cannot be estimated consistently from an increasing number of tip observations if the tree height is bounded. Here, using a fruitful connection to the so-called reconstruction problem in probability theory, we study the convergence rate of parameter estimation in the unbounded height case. For the mean of the process, we provide a necessary and sufficient condition for the consistency of the maximum likelihood estimator (MLE) and establish a phase transition on its convergence rate in terms of the growth of the tree. In particular we show that a loss of n‾‾√-consistency (i.e., the variance of the MLE becomes Ω(n−1), where n is the number of tips) occurs when the tree growth is larger than a threshold related to the phase transition of the reconstruction problem. For the covariance parameters, we give a novel, efficient estimation method which achieves n‾‾√-consistency under natural assumptions on the tree.

Testing the Toxicofera: comparative reptile transcriptomics casts doubt on the single, early evolution of the reptile venom system

Adam D Hargreaves, Martin T Swain, Darren W Logan, John F Mulley

Background The identification of apparently conserved gene complements in the venom and salivary glands of a diverse set of reptiles led to the development of the Toxicofera hypothesis – the idea that there was a single, early evolution of the venom system in reptiles. However, this hypothesis is based largely on relatively small scale EST-based studies of only venom or salivary glands and toxic effects have been assigned to only some of these putative Toxcoferan toxins in some species. We set out to investigate the distribution of these putative venom toxin transcripts in order to investigate to what extent conservation of gene complements may reflect a bias in previous sampling efforts. Results We have carried out the first large-scale test of the Toxicofera hypothesis and found it lacking in a number of regards. Our quantitative transcriptomic analyses of venom and salivary glands and other body tissues in five species of reptile, together with the use of available RNA-Seq datasets for additional species shows that the majority of genes used to support the establishment and expansion of the Toxicofera are in fact expressed in multiple body tissues and most likely represent general maintenance or “housekeeping” genes. The apparent conservation of gene complements across the Toxicofera therefore reflects an artefact of incomplete tissue sampling. In other cases, the identification of a non-toxic paralog of a gene encoding a true venom toxin has led to confusion about the phylogenetic distribution of that venom component. Conclusions Venom has evolved multiple times in reptiles. In addition, the misunderstanding regarding what constitutes a toxic venom component, together with the misidentification of genes and the classification of identical or near-identical sequences as distinct genes has led to an overestimation of the complexity of reptile venoms in general, and snake venom in particular, with implications for our understanding of (and development of treatments to counter) the molecules responsible for the physiological consequences of snakebite.

Predicting evolution from the shape of genealogical trees

Richard A. Neher, Colin A. Russell, Boris I. Shraiman
(Submitted on 3 Jun 2014)

Given a sample of genome sequences from an asexual population, can one predict its evolutionary future? Here we demonstrate that the branching pattern of reconstructed genealogical trees contains information about the relative fitness of the sampled sequences and that this information can be used to infer the closest extant relative of future populations. Our approach is based on the assumption that evolution proceeds predominantly by accumulation of small effect mutations and does not require any species specific input. Hence, the resulting inference algorithm can be applied to any asexual population under persistent selection pressure. We demonstrate its performance using historical data on seasonal influenza A/H3N2 virus. We predict the progenitor lineage of the upcoming influenza season with near optimal performance in 30% of cases and makes informative predictions in 16 out of 18 years. Beyond providing a practical tool for prediction, our results suggest that continuous adaptation by small effect mutations is a major component of influenza virus evolution.