The distribution of fitness effects during adaptive walks using a simple genetic network.

The tempo and mode of adaptation depends on the availability of beneficial alleles. Genetic interactions arising from gene networks can restrict this availability. However, the extent to which networks affect adaptation remains largely unknown. Current models of evolution consider additive genotype-phenotype relationships while often ignoring the contribution of gene interactions to phenotypic variance. In this study, we model a quantitative trait as the product of a simple gene regulatory network, the negative autoregulation motif. Using forward-time genetic simulations, we measure adaptive walks towards a phenotypic optimum in both additive and network models. A key expectation from adaptive walk theory is that the distribution of fitness effects of new beneficial mutations is exponential. We found that both models instead harbored distributions with fewer large-effect beneficial alleles than expected. The network model also had a complex and bimodal distribution of fitness effects among all mutations, with a considerable density at deleterious selection coefficients. This behavior is reminiscent of the cost of complexity, where correlations among traits constrain adaptation. Our results suggest that the interactions emerging from genetic networks can generate complex and multimodal distributions of fitness effects.

Ancient and Modern Genomes Reveal Microsatellites Maintain a Dynamic Equilibrium Through Deep Time.

Microsatellites are widely used in population genetics, but their evolutionary dynamics remain poorly understood. It is unclear whether microsatellite loci drift in length over time. This is important because the mutation processes that underlie these important genetic markers are central to the evolutionary models that employ microsatellites. We identify more than 27 million microsatellites using a novel and unique dataset of modern and ancient Adélie penguin genomes along with data from 63 published chordate genomes. We investigate microsatellite evolutionary dynamics over 2 timescales: one based on Adélie penguin samples dating to ∼46.5 ka and the other dating to the diversification of chordates aged more than 500 Ma. We show that the process of microsatellite allele length evolution is at dynamic equilibrium; while there is length polymorphism among individuals, the length distribution for a given locus remains stable. Many microsatellites persist over very long timescales, particularly in exons and regulatory sequences. These often retain length variability, suggesting that they may play a role in maintaining phenotypic variation within populations.

A distance-based model for convergent evolution.

Convergent evolution is an important process in which independent species evolve similar features usually over a long period of time. It occurs with many different species across the tree of life, and is often caused by the fact that species have to adapt to similar environmental niches. In this paper, we introduce and study properties of a distance-based model for convergent evolution in which we assume that two ancestral species converge for a certain period of time within a collection of species that have otherwise evolved according to an evolutionary clock. Under these assumptions it follows that we obtain a distance on the collection that is a modification of an ultrametric distance arising from an equidistant phylogenetic tree. As well as characterising when this modified distance is a tree metric, we give conditions in terms of the model's parameters for when it is still possible to recover the underlying tree and also its height, even in case the modified distance is not a tree metric.

Cold temperature and aridity shape the evolution of drought tolerance traits in Tasmanian species of Eucalyptus.

Perennial plant species from water-limiting environments (including climates of extreme drought, heat and freezing temperatures) have evolved traits that allow them to tolerate these conditions. As such, traits that are associated with water stress may show evidence of adaptation to climate when compared among closely related species inhabiting contrasting climatic conditions. In this study, we tested whether key hydraulic traits linked to drought stress, including the vulnerability of leaves to embolism (P50 leaf) and the minimum diffusive conductance of shoots (gmin), were associated with climatic characteristics of 14 Tasmanian eucalypt species from sites that vary in precipitation and temperature. Across species, greater cavitation resistance (more negative P50 leaf) was associated with increasing aridity and decreasing minimum temperature. By contrast, gmin showed strong associations with aridity only. Among these Tasmanian eucalypts, evidence suggests that trait variation is influenced by both cold and dry conditions, highlighting the need to consider both aspects when exploring adaptive trait-climate relationships.

Evaluation of the Relative Performance of the Subflattenings Method for Phylogenetic Inference.

The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny-and by extension the complete tree-using pattern counts from a sequence alignment. The relatively small number of possible internal edges among a set of taxa (compared to the number of binary trees) makes these methods attractive; however, more could be done to evaluate their effectiveness for inferring phylogenetic trees. This is the case particularly for subflattenings, and the work we present here makes progress in this area. We introduce software for constructing and evaluating subflattenings for splits, utilising a number of methods to make computing subflattenings more tractable. We then present the results of simulations we have performed in order to compare the effectiveness of subflattenings to that of flattenings in terms of split score distributions, and susceptibility to possible biases. We find that subflattenings perform similarly to flattenings in terms of the distribution of split scores on the trees we examined, but may be less affected by bias arising from both split size/balance and long branch attraction. These insights are useful for developing effective algorithms to utilise these tools for the purpose of inferring phylogenetic trees.

Performance of Akaike Information Criterion and Bayesian Information Criterion in Selecting Partition Models and Mixture Models.

In molecular phylogenetics, partition models and mixture models provide different approaches to accommodating heterogeneity in genomic sequencing data. Both types of models generally give a superior fit to data than models that assume the process of sequence evolution is homogeneous across sites and lineages. The Akaike Information Criterion (AIC), an estimator of Kullback-Leibler divergence, and the Bayesian Information Criterion (BIC) are popular tools to select models in phylogenetics. Recent work suggests that AIC should not be used for comparing mixture and partition models. In this work, we clarify that this difficulty is not fully explained by AIC misestimating the Kullback-Leibler divergence. We also investigate the performance of the AIC and BIC at comparing amongst mixture models and amongst partition models. We find that under nonstandard conditions (i.e. when some edges have small expected number of changes), AIC underestimates the expected Kullback-Leibler divergence. Under such conditions, AIC preferred the complex mixture models and BIC preferred the simpler mixture models. The mixture models selected by AIC had a better performance in estimating the edge length, while the simpler models selected by BIC performed better in estimating the base frequencies and substitution rate parameters. In contrast, AIC and BIC both prefer simpler partition models over more complex partition models under nonstandard conditions, despite the fact that the more complex partition model was the generating model. We also investigated how mispartitioning (i.e., grouping sites that have not evolved under the same process) affects both the performance of partition models compared with mixture models and the model selection process. We found that as the level of mispartitioning increases, the bias of AIC in estimating the expected Kullback-Leibler divergence remains the same, and the branch lengths and evolutionary parameters estimated by partition models become less accurate. We recommend that researchers are cautious when using AIC and BIC to select among partition and mixture models; other alternatives, such as cross-validation and bootstrapping, should be explored, but may suffer similar limitations [AIC; BIC; mispartitioning; partitioning; partition model; mixture model].

A review of visualisations of protein fold networks and their relationship with sequence and function.

Proteins form arguably the most significant link between genotype and phenotype. Understanding the relationship between protein sequence and structure, and applying this knowledge to predict function, is difficult. One way to investigate these relationships is by considering the space of protein folds and how one might move from fold to fold through similarity, or potential evolutionary relationships. The many individual characterisations of fold space presented in the literature can tell us a lot about how well the current Protein Data Bank represents protein fold space, how convergence and divergence may affect protein evolution, how proteins affect the whole of which they are part, and how proteins themselves function. A synthesis of these different approaches and viewpoints seems the most likely way to further our knowledge of protein structure evolution and thus, facilitate improved protein structure design and prediction.

Models for the retention of duplicate genes and their biological underpinnings.

Gene content in genomes changes through several different processes, with gene duplication being an important contributor to such changes. Gene duplication occurs over a range of scales from individual genes to whole genomes, and the dynamics of this process can be context dependent. Still, there are rules by which genes are retained or lost from genomes after duplication, and probabilistic modeling has enabled characterization of these rules, including their context-dependence. Here, we describe the biology and corresponding mathematical models that are used to understand duplicate gene retention and its contribution to the set of biochemical functions encoded in a genome.

The Shape of Phylogenies Under Phase-Type Distributed Times to Speciation and Extinction.

Phylogenetic trees describe relationships between extant species, but beyond that their shape and their relative branch lengths can provide information on broader evolutionary processes of speciation and extinction. However, currently many of the most widely used macro-evolutionary models make predictions about the shapes of phylogenetic trees that differ considerably from what is observed in empirical phylogenies. Here, we propose a flexible and biologically plausible macroevolutionary model for phylogenetic trees where times to speciation or extinction events are drawn from a Coxian phase-type (PH) distribution. First, we show that different choices of parameters in our model lead to a range of tree balances as measured by Aldous' [Formula: see text] statistic. In particular, we demonstrate that it is possible to find parameters that correspond well to empirical tree balance. Next, we provide a natural extension of the [Formula: see text] statistic to sets of trees. This extension produces less biased estimates of [Formula: see text] compared to using the median [Formula: see text] values from individual trees. Furthermore, we derive a likelihood expression for the probability of observing an edge-weighted tree under a model with speciation but no extinction. Finally, we illustrate the application of our model by performing both absolute and relative goodness-of-fit tests for two large empirical phylogenies (squamates and angiosperms) that compare models with Coxian PH distributed times to speciation with models that assume exponential or Weibull distributed waiting times. In our numerical analysis, we found that, in most cases, models assuming a Coxian PH distribution provided the best fit.

A subfunctionalisation model of gene family evolution predicts balanced tree shapes.

We consider a subfunctionalisation model of gene family evolution. A family of n genes that perform z functions is represented by an n×z binary matrix Yt where a 1 in the ijth position indicates that gene i can perform function j. Yt evolves according to a continuous time Markov chain (CTMC) that represents the processes of gene duplication, coding region loss and regulatory region loss with the restriction that each function is protected by selection, meaning that each column in the matrix must contain at least one 1. We generate gene trees based on the CTMC {Yt,t⩾0}. We analyse the long-run behaviour of the model and specify the conditions where we expect gene trees to continue to grow and where we expect them to have a stable number of genes. We show that different choices of rate parameters for the processes of duplication and loss lead to different tree shapes as measured by two common tree-shape statistics: the ß-statistic for measuring tree balance and the γ-statistic for assessing diversification rate. We use an extension of ß that is estimated from sets of trees. This extension is less biased compared to using the average ß value for individual trees. When the rate of gene duplication dominates the rate of gene loss, the process is unstable and the distribution of tree shapes is close to following the uniform ranked tree shape (URT) distribution. However, when the process is stable, gene trees are predicted to have positive values of ß indicating balanced trees and negative values of γ indicating that diversification occurs more towards the root of the tree. The results of our analyses suggest that comparing the tree-shape statistics of empirical gene-trees to the predictions presented here will provide a test of the subfunctionalisation model.

Unattained geometric configurations of secondary structure elements in protein structural space.

Discovery of new folds in the Protein Data Bank (PDB) has all but ceased. This could be viewed as evidence that all existing protein folds have been documented. Sampling bias has, however, been presented as an alternative explanation. Furthermore, although we may know of all protein folds that do exist, we may not have documented all protein folds that could exist. While addressing completeness in the context of entire protein structures is extremely difficult, they can be simplified in a number of ways. One such simplification is presented: considering protein structures as a series of α helices and ß sheets and analysing the geometric relationships between these successive secondary structure elements (SSEs) through torsion angles, lengths and distances. We aimed to find out whether all substructures that could be formed by triplets of these successive SSEs were represented in the PDB. When SSEs were defined with the assignment program Promotif, a gap was identified in the represented torsion angles of helix-strand-strand substructures. This was not present when SSEs were defined with an alternative assignment program with a smaller minimum SSE length, DSSP. We also looked at representing proteins as one-dimensional sequences of SSE types and searched for underrepresented motifs. Completely absent motifs occurred more often than expected at random. If a gap in SSE substructure space exists that could be filled or if a physically possible SSE motif is absent, associated gaps in protein structure space are implied, meaning that the PDB as we know it may not be complete.

Comparing Partitioned Models to Mixture Models: Do Information Criteria Apply?

The use of information criteria to distinguish between phylogenetic models has become ubiquitous within the field. However, the variety and complexity of available models are much greater now than when these practices were established. The literature shows an increasing trajectory of healthy skepticism with regard to the use of information theory-based model selection within phylogenetics. We add to this by analyzing the specific case of comparison between partition and mixture models. We argue from a theoretical basis that information criteria are inherently more likely to favor partition models over mixture models, and we then demonstrate this through simulation. Based on our findings, we suggest that partition and mixture models are not suitable for information-theory based model comparison. [AIC, BIC; information criteria; maximum likelihood; mixture models; partitioned model; phylogenetics.].

Benchmarking Methods of Protein Structure Alignment.

The function of a protein is primarily determined by its structure and amino acid sequence. Many biological questions of interest rely on being able to accurately determine the group of structures to which domains of a protein belong; this can be done through alignment and comparison of protein structures. Dozens of different methods for Protein Structure Alignment (PSA) have been proposed that use a wide range of techniques. The aim of this study is to determine the ability of PSA methods to identify pairs of protein domains known to share differing levels of structural similarity, and to assess their utility for clustering domains from several different folds into known groups. We present the results of a comprehensive investigation into eighteen PSA methods, to our knowledge the largest piece of independent research on this topic. Overall, SP-AlignNS (non-sequential) was found to be the best method for classification, and among the best performing methods for clustering. Methods (where possible) were split into the algorithm used to find the optimal alignment and the score used to assess similarity. This allowed us to largely separate the algorithm from the score it maximizes and thus, to assess their effectiveness independently of each other. Surprisingly, we found that some hybrids of mismatched scores and algorithms performed better than either of the native methods at classification and, in some cases, clustering as well. It is hoped that this investigation and the accompanying discussion will be useful for researchers selecting or designing methods to align protein structures.

The impracticalities of multiplicatively-closed codon models: a retreat to linear alternatives.

A matrix Lie algebra is a linear space of matrices closed under the operation [Formula: see text]. The "Lie closure" of a set of matrices is the smallest matrix Lie algebra which contains the set. In the context of Markov chain theory, if a set of rate matrices form a Lie algebra, their corresponding Markov matrices are closed under matrix multiplication; this has been found to be a useful property in phylogenetics. Inspired by previous research involving Lie closures of DNA models, it was hypothesised that finding the Lie closure of a codon model could help to solve the problem of mis-estimation of the non-synonymous/synonymous rate ratio, [Formula: see text]. We propose two different methods of finding a linear space from a model: the first is the linear closure which is the smallest linear space which contains the model, and the second is the linear version which changes multiplicative constraints in the model to additive ones. For each of these linear spaces we then find the Lie closures of them. Under both methods, it was found that closed codon models would require thousands of parameters, and that any partial solution to this problem that was of a reasonable size violated stochasticity. Investigation of toy models indicated that finding the Lie closure of matrix linear spaces which deviated only slightly from a simple model resulted in a Lie closure that was close to having the maximum number of parameters possible. Given that Lie closures are not practical, we propose further consideration of the two variants of linearly closed models.

Accuracy of ancestral state reconstruction for non-neutral traits.

The assumptions underpinning ancestral state reconstruction are violated in many evolutionary systems, especially for traits under directional selection. However, the accuracy of ancestral state reconstruction for non-neutral traits is poorly understood. To investigate the accuracy of ancestral state reconstruction methods, trees and binary characters were simulated under the BiSSE (Binary State Speciation and Extinction) model using a wide range of character-state-dependent rates of speciation, extinction and character-state transition. We used maximum parsimony (MP), BiSSE and two-state Markov (Mk2) models to reconstruct ancestral states. Under each method, error rates increased with node depth, true number of state transitions, and rates of state transition and extinction; exceeding 30% for the deepest 10% of nodes and highest rates of extinction and character-state transition. Where rates of character-state transition were asymmetrical, error rates were greater when the rate away from the ancestral state was largest. Preferential extinction of species with the ancestral character state also led to higher error rates. BiSSE outperformed Mk2 in all scenarios where either speciation or extinction was state dependent and outperformed MP under most conditions. MP outperformed Mk2 in most scenarios except when the rates of character-state transition and/or extinction were highly asymmetrical and the ancestral state was unfavoured.

Links between environment and stomatal size through evolutionary time in Proteaceae.

The size of plant stomata (adjustable pores that determine the uptake of CO2 and loss of water from leaves) is considered to be evolutionarily important. This study uses fossils from the major Southern Hemisphere family Proteaceae to test whether stomatal cell size responded to Cenozoic climate change. We measured the length and abundance of guard cells (the cells forming stomata), the area of epidermal pavement cells, stomatal index and maximum stomatal conductance from a comprehensive sample of fossil cuticles of Proteaceae, and extracted published estimates of past temperature and atmospheric CO2. We developed a novel test based on stochastic modelling of trait evolution to test correlations among traits. Guard cell length increased, and stomatal density decreased significantly with decreasing palaeotemperature. However, contrary to expectations, stomata tended to be smaller and more densely packed at higher atmospheric CO2. Thus, associations between stomatal traits and palaeoclimate over the last 70 million years in Proteaceae suggest that stomatal size is significantly affected by environmental factors other than atmospheric CO2. Guard cell length, pavement cell area, stomatal density and stomatal index covaried in ways consistent with coordinated development of leaf tissues.

A new phylogenetic protocol: dealing with model misspecification and confirmation bias in molecular phylogenetics.

Molecular phylogenetics plays a key role in comparative genomics and has increasingly significant impacts on science, industry, government, public health and society. In this paper, we posit that the current phylogenetic protocol is missing two critical steps, and that their absence allows model misspecification and confirmation bias to unduly influence phylogenetic estimates. Based on the potential offered by well-established but under-used procedures, such as assessment of phylogenetic assumptions and tests of goodness of fit, we introduce a new phylogenetic protocol that will reduce confirmation bias and increase the accuracy of phylogenetic estimates.

GHOST: Recovering Historical Signal from Heterotachously Evolved Sequence Alignments.

Molecular sequence data that have evolved under the influence of heterotachous evolutionary processes are known to mislead phylogenetic inference. We introduce the General Heterogeneous evolution On a Single Topology (GHOST) model of sequence evolution, implemented under a maximum-likelihood framework in the phylogenetic program IQ-TREE (http://www.iqtree.org). Simulations show that using the GHOST model, IQ-TREE can accurately recover the tree topology, branch lengths, and substitution model parameters from heterotachously evolved sequences. We investigate the performance of the GHOST model on empirical data by sampling phylogenomic alignments of varying lengths from a plastome alignment. We then carry out inference under the GHOST model on a phylogenomic data set composed of 248 genes from 16 taxa, where we find the GHOST model concurs with the currently accepted view, placing turtles as a sister lineage of archosaurs, in contrast to results obtained using traditional variable rates-across-sites models. Finally, we apply the model to a data set composed of a sodium channel gene of 11 fish taxa, finding that the GHOST model is able to elucidate a subtle component of the historical signal, linked to the previously established convergent evolution of the electric organ in two geographically distinct lineages of electric fish. We compare inference under the GHOST model to partitioning by codon position and show that, owing to the minimization of model constraints, the GHOST model offers unique biological insights when applied to empirical data.

The Ancient Operational Code is Embedded in the Amino Acid Substitution Matrix and aaRS Phylogenies.

The underlying structure of the canonical amino acid substitution matrix (aaSM) is examined by considering stepwise improvements in the differential recognition of amino acids according to their chemical properties during the branching history of the two aminoacyl-tRNA synthetase (aaRS) superfamilies. The evolutionary expansion of the genetic code is described by a simple parameterization of the aaSM, in which (i) the number of distinguishable amino acid types, (ii) the matrix dimension and (iii) the number of parameters, each increases by one for each bifurcation in an aaRS phylogeny. Parameterized matrices corresponding to trees in which the size of an amino acid sidechain is the only discernible property behind its categorization as a substrate, exclusively for a Class I or II aaRS, provide a significantly better fit to empirically determined aaSM than trees with random bifurcation patterns. A second split between polar and nonpolar amino acids in each Class effects a vastly greater further improvement. The earliest Class-separated epochs in the phylogenies of the aaRS reflect these enzymes' capability to distinguish tRNAs through the recognition of acceptor stem identity elements via the minor (Class I) and major (Class II) helical grooves, which is how the ancient operational code functioned. The advent of tRNA recognition using the anticodon loop supports the evolution of the optimal map of amino acid chemistry found in the later genetic code, an essentially digital categorization, in which polarity is the major functional property, compensating for the unrefined, haphazard differentiation of amino acids achieved by the operational code.

Mitogenomic diversity in Sacred Ibis Mummies sheds light on early Egyptian practices.

The ancient catacombs of Egypt harbor millions of well-preserved mummified Sacred Ibis (Threskiornis aethiopicus) dating from ~600BC. Although it is known that a very large number of these 'votive' mummies were sacrificed to the Egyptian God Thoth, how the ancient Egyptians obtained millions of these birds for mummification remains unresolved. Ancient Egyptian textual evidences suggest they may have been raised in dedicated large-scale farms. To investigate the most likely method used by the priests to secure birds for mummification, we report the first study of complete mitochondrial genomes of 14 Sacred Ibis mummies interred ~2500 years ago. We analysed and compared the mitogenomic diversity among Sacred Ibis mummies to that found in modern Sacred Ibis populations from throughout Africa. The ancient birds show a high level of genetic variation comparable to that identified in modern African populations, contrary to the suggestion in ancient hieroglyphics (or ancient writings) of centralized industrial scale farming of sacrificial birds. This suggests a sustained short-term taming of the wild migratory Sacred Ibis for the ritual yearly demand.