Understanding mammalian evolution using Bayesian phylogenetic inference

1. Phylogenetic trees are critical in addressing evolutionary hypotheses; however, the reconstruction of a phylogeny is no easy task. This process has recently been made less arduous by using a Bayesian statistical approach. This method offers the advantage that one can determine the probability of some hypothesis (i.e. a phylogeny), conditional on the observed data (i.e. nucleotide sequences). 2. By reconstructing phylogenies using Bayes’ theorem in combination with Markov chain Monte Carlo, phylogeneticists are able to test hypotheses more quickly compared with using standard methods such as neighbour-joining, maximum likelihood or parsimony. Critics of the Bayesian approach suggest that it is not a panacea, and argue that the prior probability is too subjective and the resulting posterior probability is too liberal compared with maximum likelihood. 3. These issues are currently debated in the arena of mammalian evolution. Recently, proponents and opponents of the Bayesian approach have constructed the mammalian phylogeny using different methods under different conditions and with a variety of parameters. These analyses showed the robustness (or lack of) of the Bayesian approach. In the end, consensus suggests that Bayesian methods are robust and give essentially the same answer as maximum likelihood methods but in less time. 4. Approaches based on fossils and molecules typically agree on ordinal-level relationships among mammals but not on higher-level relationships, as Bayesian analyses recognize the African radiation, Afrotheria, and the two Laurasian radiations, Laurasiatheria and Euarchontoglires, whereas fossils did not predict Afrotheria.     

Bayesian inference of character evolution

Much recent progress in evolutionary biology is based on the inference of ancestral states and past transformations in important traits on phylogenetic trees. These exercises often assume that the tree is known without error and that ancestral states and character change can be mapped onto it exactly. In reality, there is often considerable uncertainty about both the tree and the character mapping. Recently introduced Bayesian statistical methods enable the study of character evolution while simultaneously accounting for both phylogenetic and mapping uncertainty, adding much needed credibility to the reconstruction of evolutionary history.     

Evolution of the mammalian middle ear.

The structure and evolution of the mandible, suspensorium, and stapes of mammal-like reptiles and early mammals are examined in an attempt to determine how, why, and when in phylogeny the precursors of the mammalian tympanic bone, malleus, and incus (postdentary jaw elements and quadrate) came to function in the reception of air-borne sound. The following conclusions are reached: It is possible that at no stage in mammalian phylogeny was there a middle ear similar to that of "typical" living reptiles, with a postquadrate tympanic membrane contracted by an extrastapes. The aquamosal sulcus of cynodonts and other therapsids, usually thought to have housed a long external acoustic meatus, possibly held a depressor mandibulae muscle. In therapsids an air-filled chamber (recessus mandibularis of Westoll) extended deep to the reflected lamina and into the depression (external fossa) on the outer aspect of the angular element. A similar chamber was present in sphenacodontids but pterygoideus musculature occupied the small external fossa. The thin tissues superficial to the recessus mandibularis served as eardrum. Primitively, vibrations reached the stapes mainly via the anterior hyoid cornu, but in dicynodonts, therocephalians, and cynodants vibrations passed mainly or exclusively from mandible to quadrate to stapes and the reflected lamina was a component of the eardrum. In the therapsid phase of mammalian phylogeny, auditory adaptation was an important aspect of jaw evolution. Auditory efficiency, and sensitivity to higher sound frequencies were enhanced by diminution and loosening of the postdentary elements and quadrate, along with transference of musculature from postdentary elements to the dentary. These changes were made possible by associated modifications, including posterior expansion of the dentary. Establishment of a dentary-squamosal articulation permitted continuation of these trends, leading to the definitive mammalian condition, with no major change in auditory mechanism except that in most mammals (not monotremes) the angular, as tympanic, eventually bcame a non-vibrating structure.     

Ear ossicle morphology of the Jurassic euharamiyidan Arboroharamiya and evolution of mammalian middle ear

The middle ear bones of Mesozoic mammals are rarely preserved as fossils and the morphology of these ossicles in the earliest mammals remains poorly known. Here, we report the stapes and incus of the euharamiyidan Arboroharamiya from the lower Upper Jurassic (～160 Ma) of northern China, which represent the earliest known mammalian middle ear ossicles. Both bones are miniscule in relation to those in non‐mammalian cynodonts. The skull length/stapedial footplate diameter ratio is estimated as 51.74 and the stapes length as the percentage of the skull length is 4%; both numbers fall into the stapes size ranges of mammals. The stapes is “rod‐like” and has a large stapedial foramen. It is unique among mammaliaforms in having a distinct posterior process that is interpreted as for insertion of the stapedius muscle and homologized to the ossified proximal (stapedial) end of the interhyal, on which the stapedius muscle attached. The incus differs from the quadrate of non‐mammalian cynodonts such as morganucodontids in having small size and a slim short process. Along with lack of the postdentary trough and Meckelian groove on the medial surface of the dentary, the ossicles suggest development of the definitive mammalian middle ear (DMME) in Arboroharamiya. Among various higher‐level phylogenetic hypotheses of mammals, the one we preferred places “haramiyidans” within Mammalia. Given this phylogeny, development of the DMME took place once in the allotherian clade containing euharamiyidans and multituberculates, probably independent to those of monotremes and therians. Thus, the DMME has evolved at least three times independently in mammals. Alternative hypothesis that placed “haramiyidans” outside of Mammalia would require independent acquisition of the DMME in multituberculates and euharamiyidans as well as parallel evolution of numerous derived similarities in the dentition, occlusion pattern, mandibles, cranium, and postcranium between the two groups and between “haramiyidans” and other mammals. J. Morphol. 279:441–457, 2018. © 2016 Wiley Periodicals, Inc.     

Bayesian phylogenetics using an RNA substitution model applied to early mammalian evolution

We study the phylogeny of the placental mammals using molecular data from all mitochondrial tRNAs and rRNAs of 54 species. We use probabilistic substitution models specific to evolution in base paired regions of RNA. A number of these models have been implemented in a new phylogenetic inference software package for carrying out maximum likelihood and Bayesian phylogenetic inferences. We describe our Bayesian phylogenetic method which uses a Markov chain Monte Carlo algorithm to provide samples from the posterior distribution of tree topologies. Our results show support for four primary mammalian clades, in agreement with recent studies of much larger data sets mainly comprising nuclear DNA. We discuss some issues arising when using Bayesian techniques on RNA sequence data.     

Gene networks inference using dynamic Bayesian networks

This article deals with the identification of gene regulatory networks from experimental data using a statistical machine learning approach. A stochastic model of gene interactions capable of handling missing variables is proposed. It can be described as a dynamic Bayesian network particularly well suited to tackle the stochastic nature of gene regulation and gene expression measurement. Parameters of the model are learned through a penalized likelihood maximization implemented through an extended version of EM algorithm. Our approach is tested against experimental data relative to the S.O.S. DNA Repair network of the Escherichia coli bacterium. It appears to be able to extract the main regulations between the genes involved in this network. An added missing variable is found to model the main protein of the network. Good prediction abilities on unlearned data are observed. These first results are very promising: they show the power of the learning algorithm and the ability of the model to capture gene interactions.     

Probable diphyletic formation of the mammalian middle ear: Monotremata and Theria

The first steps in the formation of the middle ear of the mammalian type, with the tympanum and three auditory ossicles, have only been passed by higher cynodonts. They have an incipient malleus, which developed from the anterior process of the articulare rather than the retroarticular process, which is rudimentary in cynodonts. The tympanic bone is formed of the anterior projections of the angulare. In some gorgonopians, the retroarticular process is elongated and curved anteriorly, resembling the malleus of mammals; however, this is only convergent similarity.     

Bayesian inference of recent migration rates using multilocus genotypes

A new Bayesian method that uses individual multilocus genotypes to estimate rates of recent immigration (over the last several generations) among populations is presented. The method also estimates the posterior probability distributions of individual immigrant ancestries, population allele frequencies, population inbreeding coefficients, and other parameters of potential interest. The method is implemented in a computer program that relies on Markov chain Monte Carlo techniques to carry out the estimation of posterior probabilities. The program can be used with allozyme, microsatellite, RFLP, SNP, and other kinds of genotype data. We relax several assumptions of early methods for detecting recent immigrants, using genotype data; most significantly, we allow genotype frequencies to deviate from Hardy-Weinberg equilibrium proportions within populations. The program is demonstrated by applying it to two recently published microsatellite data sets for populations of the plant species Centaurea corymbosa and the gray wolf species Canis lupus. A computer simulation study suggests that the program can provide highly accurate estimates of migration rates and individual migrant ancestries, given sufficient genetic differentiation among populations and sufficient numbers of marker loci.     

Bayesian inference of biochemical kinetic parameters using the linear noise approximation

Background  

Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data.     

Bayesian inference on protective antibody levels using case-control data

In the study of immune responses to infectious pathogens, the minimum protective antibody concentration (MPAC) is a quantity of great interest. We use case-control data to estimate the posterior distribution of the conditional risk of disease given a lower bound on antibody concentration in an at-risk subject. The concentration bound beyond which there is high credibility that infection risk is zero or nearly so is a candidate for the MPAC. A very simple Gibbs sampling procedure that permits inference on the risk of disease given antibody level is presented. In problems involving small numbers of patients, the procedure is shown to have favorable accuracy and robustness to choice/misspecification of priors. Frequentist evaluation indicates good coverage probabilities of credibility intervals for antibody-dependent risk, and rules for estimation of the MPAC are illustrated with epidemiological data.     

Bayesian inference of fine-scale recombination rates using population genomic data

Recently, several statistical methods for estimating fine-scale recombination rates using population samples have been developed. However, currently available methods that can be applied to large-scale data are limited to approximated likelihoods. Here, we developed a full-likelihood Markov chain Monte Carlo method for estimating recombination rate under a Bayesian framework. Genealogies underlying a sampling of chromosomes are effectively modelled by using marginal individual single nucleotide polymorphism genealogies related through an ancestral recombination graph. The method is compared with two existing composite-likelihood methods using simulated data.Simulation studies show that our method performs well for different simulation scenarios. The method is applied to two human population genetic variation datasets that have been studied by sperm typing. Our results are consistent with the estimates from sperm crossover analysis.     

Environmental influences in the evolution of tetrapod hearing sensitivity and middle ear tuning

Vertebrates inhabit and communicate acoustically in most natural environments. We review the influence of environmental factors on the hearing sensitivity of terrestrial vertebrates, and on the anatomy and mechanics of the middle ears. Evidence suggests that both biotic and abiotic environmental factors affect the evolution of bandwidth and frequency of peak sensitivity of the hearing spectrum. Relevant abiotic factors include medium type, temperature, and noise produced by nonliving sources. Biotic factors include heterospecific, conspecific, or self-produced sounds that animals are selected to recognize, and acoustic interference by sounds that other animals generate. Within each class of tetrapods, the size of the middle ear structures correlates directly to body size and inversely to frequency of peak sensitivity. Adaptation to the underwater medium in cetaceans involved reorganization of the middle ear for novel acoustic pathways, whereas adaptation to subterranean life in several mammals resulted in hypertrophy of the middle ear ossicles to enhance their inertial mass for detection of seismic vibrations. The comparative approach has revealed a number of generalities about the effect of environmental factors on hearing performance and middle ear structure across species. The current taxonomic sampling of the major tetrapod groups is still highly unbalanced and incomplete. Future expansion of the comparative evidence should continue to reveal general patterns and novel mechanisms.     

A Bayesian approach to the inference of diploid genotypes using haploid genotypes

Morris and Spieth (1978) described a method of calculating unbiased estimates of diploid genotype frequencies given information on the genotypes of haploid cells derived from diploid individuals. They concluded that three haploids per diploid would minimize sampling variance of genotype frequencies, given a fixed total number of haploids examined. If the identity of individual diploid genotypes is needed, Morris and Spieth (1978) stated that more haploids should be collected per diploid. We extend this work by showing from a Bayesian perspective that the probability of misclassification of individuals depends not only on the number of haploids sampled, but also on the genetic structure of the population since misclassification error will increase as the frequency of heterozygotes increases. Since information on the genetic structure (allele frequencies, inbreeding coefficient) of a population is rarely known prior to the initiation of an empirical study, the usefulness of our Bayesian approach is in experimental design, by revealing the magnitude of possible misclassification errors given a particular choice of number of haploids.     

Estimating Neospora caninum prevalence in wildlife populations using Bayesian inference

Prevalence of disease in wildlife populations, which is necessary for developing disease models and conducting epidemiologic analyses, is often understudied. Laboratory tests used to screen for diseases in wildlife populations often are validated only for domestic animals. Consequently, the use of these tests for wildlife populations may lead to inaccurate estimates of disease prevalence. We demonstrate the use of Bayesian latent class analysis (LCA) in determining the specificity and sensitivity of a competitive enzyme‐linked immunosorbent assay (cELISA; VMRD^®, Inc.) serologic test used to identify exposure to Neospora caninum (hereafter N. caninum) in three wildlife populations in southeastern Ohio, USA. True prevalence of N. caninum exposure in these populations was estimated to range from 0.1% to 3.1% in American bison (Bison bison), 51.0% to 53.8% in Père David's deer (Elaphurus davidianus), and 40.0% to 45.9% in white‐tailed deer (Odocoileus virginianus). The accuracy of the cELISA in American bison and Père David's deer was estimated to be close to the 96% sensitivity and 99% specificity reported by the manufacturer. Sensitivity in white‐tailed deer, however, ranged from 78.9% to 99.9%. Apparent prevalence of N. caninum from the test results is not equal to the true prevalence in white‐tailed deer and Père David's deer populations. Even when these species inhabit the same community, the true prevalence in the two deer populations differed from the true prevalence in the American bison population. Variances in prevalence for some species suggest differences in the epidemiology of N. caninum for these colocated populations. Bayesian LCA methods could be used as in this example to overcome some of the constraints on validating tests in wildlife species. The ability to accurately evaluate disease status and prevalence in a population improves our understanding of the epidemiology of multihost pathogen systems at the community level.     

Bayesian inference for stochastic kinetic models using a diffusion approximation

This article is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a diffusion approximation (or stochastic differential equation approach) where a white noise term models stochastic behavior and the model is identified using equispaced time course data. The estimation framework involves the introduction of m- 1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters. The methodology is applied to the estimation of parameters in a prokaryotic autoregulatory gene network.