Testing for heterogeneous rates of discrete character evolution on phylogenies

Many hypotheses in the field of phylogenetic comparative biology involve specific changes in the rate or process of trait evolution. We present a method designed to test whether the rate of evolution of a discrete character has changed in one or more clades, lineages, or time periods. This method differs from other related approaches (such as the 'covarion' model) in that the 'regimes' in which the rate or process is postulated to have changed are specified a priori by the user, rather than inferred from the data. Similarly, it differs from methods designed to model a correlation between two binary traits in that the regimes mapped onto the tree are fixed. We apply our method to investigate the rate of dewlap color and/or caudal vertebra number evolution in Caribbean and mainland clades of the diverse lizard genus Anolis. We find little evidence to support any difference between mainland and island evolution in either character. We also examine the statistical properties of the method more generally and show that it has acceptable type I error, parameter estimation, and power. Finally, we discuss the relationship of our method to existing models of heterogeneity in the rate of discrete character evolution on phylogenies.

The BNSR-invariants of the Stein group 𝐹2,3

The Stein group F 2 , 3 F_{2,3} is the group of orientation-preserving piecewise linear homeomorphisms of the unit interval with slopes of the form 2 p ⁢ 3 q 2^{p}3^{q} ( p , q ∈ Z p,q\in\mathbb{Z} ) and breakpoints in Z ⁢ [ 1 6 ] \mathbb{Z}[\frac{1}{6}] . This is a natural relative of Thompson’s group 𝐹. In this paper, we compute the Bieri–Neumann–Strebel–Renz (BNSR) invariants Σ m ⁢ ( F 2 , 3 ) \Sigma^{m}(F_{2,3}) of the Stein group for all m ∈ N m\in\mathbb{N} . A consequence of our computation is that (as with 𝐹) every finitely presented normal subgroup of F 2 , 3 F_{2,3} is of type F ∞ \operatorname{F}_{\infty} . Another, more surprising, consequence is that (unlike 𝐹) the kernel of any map F 2 , 3 → Z F_{2,3}\to\mathbb{Z} is of type F ∞ \operatorname{F}_{\infty} , even though there exist maps F 2 , 3 → Z 2 F_{2,3}\to\mathbb{Z}^{2} whose kernels are not even finitely generated. In terms of BNSR-invariants, this means that every discrete character lies in Σ ∞ ⁢ ( F 2 , 3 ) \Sigma^{\infty}(F_{2,3}) , but there exist (non-discrete) characters that do not even lie in Σ 1 ⁢ ( F 2 , 3 ) \Sigma^{1}(F_{2,3}) . To the best of our knowledge, F 2 , 3 F_{2,3} is the first group whose BNSR-invariants are known exhibiting these properties.

(2, 2) Scattering and the celestial torus

Analytic continuation from Minkowski space to (2, 2) split signature spacetime has proven to be a powerful tool for the study of scattering amplitudes. Here we show that, under this continuation, null infinity becomes the product of a null interval with a celestial torus (replacing the celestial sphere) and has only one connected component. Spacelike and timelike infinity are time-periodic quotients of AdS3. These three components of infinity combine to an S3 represented as a toric fibration over the interval. Privileged scattering states of scalars organize into SL(2, ℝ)L×SL(2, ℝ)R conformal primary wave functions and their descendants with real integral or half-integral conformal weights, giving the normally continuous scattering problem a discrete character.

Evaluating Results

This chapter explores the tools used to evaluate the quality and plausibility of results of phylogenetic analyses. The term “fit” has been widely used in the phylogenetic literature to indicate the degree to which data conform to (or are explained by) a cladogram. The most commonly used measure of fit applied to discrete character data is the consistency index, or ci. Meanwhile, measures of synapomorphy are less frequently reported than the consistency index. The chapter then considers the resolution of branches; multiple equally parsimonious cladograms; successive approximations weighing; and data decisiveness. It also differentiates between total evidence and consensus, before describing supertrees. Finally, the chapter looks at approaches for evaluating support or stability of phylogenetic results, including branch support, jackknifing, bootstrapping, randomization tests, and sensitivity analysis.

The patterns and modes of the evolution of disparity in Mesozoic birds

The origin of birds from non-avian theropod dinosaurs is one of the greatest transitions in evolution. Shortly after diverging from other theropods in the Late Jurassic, Mesozoic birds diversified into two major clades—the Enantiornithes and Ornithuromorpha—acquiring many features previously considered unique to the crown group along the way. Here, we present a comparative phylogenetic study of the patterns and modes of Mesozoic bird skeletal morphology and limb proportions. Our results show that the major Mesozoic avian groups are distinctive in discrete character space, but constrained in a morphospace defined by limb proportions. The Enantiornithines, despite being the most speciose group of Mesozoic birds, are much less morphologically disparate than their sister clade, the Ornithuromorpha—the clade that gave rise to living birds, showing disparity and diversity were decoupled in avian history. This relatively low disparity suggests that diversification of enantiornithines was characterized in exhausting fine morphologies, whereas ornithuromorphs continuously explored a broader array of morphologies and ecological opportunities. We suggest this clade-specific evolutionary versatility contributed to their sole survival of the end-Cretaceous mass extinction.

Quantitative Proteomics Comparison of Total Expressed Proteomes of Anisakis simplex Sensu Stricto, A. pegreffii, and Their Hybrid Genotype

The total proteomes of Anisakis simplex s.s., A. pegreffii and their hybrid genotype have been compared by quantitative proteomics (iTRAQ approach), which considers the level of expressed proteins. Comparison was made by means of two independent experiments considering four biological replicates of A. simplex and two each for A. pegreffii and hybrid between both species. A total of 1811 and 1976 proteins have been respectively identified in the experiments using public databases. One hundred ninety-six proteins were found significantly differentially expressed, and their relationships with the nematodes’ biological replicates were estimated by a multidimensional statistical approach. Results of pairwise Log2 ratio comparisons among them were statistically treated and supported in order to convert them into discrete character states. Principal component analysis (PCA) confirms the validity of the method. This comparison selected thirty seven proteins as discriminant taxonomic biomarkers among A. simplex, A. pegreffii and their hybrid genotype; 19 of these biomarkers, encoded by ten loci, are specific allergens of Anisakis (Ani s7, Ani s8, Ani s12, and Ani s14) and other (Ancylostoma secreted) is a common nematodes venom allergen. The rest of the markers comprise four unknown or non-characterized proteins; five different proteins (leucine) related to innate immunity, four proteolytic proteins (metalloendopeptidases), a lipase, a mitochondrial translocase protein, a neurotransmitter, a thyroxine transporter, and a structural collagen protein. The proposed methodology (proteomics and statistical) solidly characterize a set of proteins that are susceptible to take advantage of the new targeted proteomics.

Body size correlates with discrete-character morphological proxies

Principal coordinates analysis (PCoA) is a statistical ordination technique commonly applied to morphology-based cladistic matrices to study macroevolutionary patterns, morphospace occupation, and disparity. However, PCoA-based morphospaces are dissociated from the original data; therefore, whether such morphospaces accurately reflect body-plan disparity or extrinsic factors, such as body size, remains uncertain. We collated nine character–taxon matrices of dinosaurs together with body-mass estimates for all taxa and tested for relationships between body size and both the principal axis of variation (i.e., PCo1) and the entire set of PCo scores. The possible effects of body size on macroevolutionary hypotheses derived from ordinated matrices were tested by reevaluating evidence for the accelerated accumulation of avian-type traits indicated by a strong directional shift in PCo1 scores in hypothetical ancestors of modern birds. Body mass significantly accounted for, on average, approximately 50% and 16% of the phylogenetically corrected variance in PCo1 and all PCo scores, respectively. Along the avian stem lineage, approximately 30% of the morphological variation is attributed to the reconstructed body masses of each ancestor. When the effects of body size are adjusted, the period of accelerated trait accumulation is replaced by a more gradual, additive process. Our results indicate that even at low proportions of variance, body size can noticeably affect macroevolutionary hypotheses generated from ordinated morphospaces. Future studies should thoroughly explore the nature of their character data in association with PCoA-based morphospaces and use a residual/covariate approach to account for potential correlations with body size.

Dental characters used in phylogenetic analyses of mammals show higher rates of evolution, but not reduced independence

Accurate reconstructions of phylogeny are essential for studying the evolution of a clade, and morphological characters are necessarily used for the reconstruction of the relationships of fossil organisms. However, variation in their evolutionary modes (for example rate variation and character non-independence) not accounted for in analyses may be leading to unreliable phylogenies. A recent study suggested that phylogenetic analyses of mammals may be suffering from a dominance of dental characters, which were shown to have lower phylogenetic signal than osteological characters and produced phylogenies less congruent with molecularly-derived benchmarks. Here we build on this previous work by testing five additional morphological partitions for phylogenetic signal and examining what aspects of dental and other character evolution may be affecting this, by fitting models of discrete character evolution to phylogenies inferred and time calibrated using molecular data. Results indicate that the phylogenetic signal of discrete characters correlate most strongly with rates of evolution, with increased rates driving increased homoplasy. In a dataset covering all Mammalia, dental characters have higher rates of evolution than other partitions. They do not, however, fit a model of independent character evolution any worse than other regions. Primates and marsupials show different patterns to other mammal clades, with dental characters evolving at slower rates and being more heavily integrated (less independent). While the dominance of dental characters in analyses of mammals could be leading to inaccurate phylogenies, the issue is not unique to dental characters and the results are not consistent across datasets. Molecular benchmarks (being entirely independent of the character data) provide a framework for examining each dataset individually to assess the evolution of the characters used.

A Bayesian Approach for Inferring the Impact of a Discrete Character on Rates of Continuous-Character Evolution in the Presence of Background-Rate Variation

Understanding how and why rates of character evolution vary across the Tree of Life is central to many evolutionary questions; for example, does the trophic apparatus (a set of continuous characters) evolve at a higher rate in fish lineages that dwell in reef versus nonreef habitats (a discrete character)? Existing approaches for inferring the relationship between a discrete character and rates of continuous-character evolution rely on comparing a null model (in which rates of continuous-character evolution are constant across lineages) to an alternative model (in which rates of continuous-character evolution depend on the state of the discrete character under consideration). However, these approaches are susceptible to a “straw-man” effect: the influence of the discrete character is inflated because the null model is extremely unrealistic. Here, we describe MuSSCRat, a Bayesian approach for inferring the impact of a discrete trait on rates of continuous-character evolution in the presence of alternative sources of rate variation (“background-rate variation”). We demonstrate by simulation that our method is able to reliably infer the degree of state-dependent rate variation, and show that ignoring background-rate variation leads to biased inferences regarding the degree of state-dependent rate variation in grunts (the fish group Haemulidae). [Bayesian phylogenetic comparative methods; continuous-character evolution; data augmentation; discrete-character evolution.]

Genetic-Mathematical Modelling of Mutational Processes in a Population

Processes of genetic-mathematical modeling of a population development are considered. A basic distinction in the mathematical description of a family tree and a population is shown. In a family tree alternation of generations has discrete character. In a population there is a continuous alternation of generations. The method of the differential equations is applied for the description of a population. It is shown that mutational process in a population can be described with use of a Green’s function. For radiating influence on a population the universal evolutionary law is found.