Stochastic Character Mapping, Bayesian Model Selection, and Biosynthetic Pathways Shed New Light on the Evolution of Habitat Preference in Cyanobacteria.

Cyanobacteria are the only prokaryotes to have evolved oxygenic photosynthesis paving the way for complex life. Studying the evolution and ecological niche of cyanobacteria and their ancestors is crucial for understanding the intricate dynamics of biosphere evolution. These organisms frequently deal with environmental stressors such as salinity and drought, and they employ compatible solutes as a mechanism to cope with these challenges. Compatible solutes are small molecules that help maintain cellular osmotic balance in high-salinity environments, such as marine waters. Their production plays a crucial role in salt tolerance, which, in turn, influences habitat preference. Among the 5 known compatible solutes produced by cyanobacteria (sucrose, trehalose, glucosylglycerol, glucosylglycerate, and glycine betaine), their synthesis varies between individual strains. In this study, we work in a Bayesian stochastic mapping framework, integrating multiple sources of information about compatible solute biosynthesis in order to predict the ancestral habitat preference of Cyanobacteria. Through extensive model selection analyses and statistical tests for correlation, we identify glucosylglycerol and glucosylglycerate as the most significantly correlated with habitat preference, while trehalose exhibits the weakest correlation. Additionally, glucosylglycerol, glucosylglycerate, and glycine betaine show high loss/gain rate ratios, indicating their potential role in adaptability, while sucrose and trehalose are less likely to be lost due to their additional cellular functions. Contrary to previous findings, our analyses predict that the last common ancestor of Cyanobacteria (living at around 3180 Ma) had a 97% probability of a high salinity habitat preference and was likely able to synthesize glucosylglycerol and glucosylglycerate. Nevertheless, cyanobacteria likely colonized low-salinity environments shortly after their origin, with an 89% probability of the first cyanobacterium with low-salinity habitat preference arising prior to the Great Oxygenation Event (2460 Ma). Stochastic mapping analyses provide evidence of cyanobacteria inhabiting early marine habitats, aiding in the interpretation of the geological record. Our age estimate of ~2590 Ma for the divergence of 2 major cyanobacterial clades (Macro- and Microcyanobacteria) suggests that these were likely significant contributors to primary productivity in marine habitats in the lead-up to the Great Oxygenation Event, and thus played a pivotal role in triggering the sudden increase in atmospheric oxygen.

Full Bayesian Comparative Phylogeography from Genomic Data.

A challenge to understanding biological diversification is accounting for community-scale processes that cause multiple, co-distributed lineages to co-speciate. Such processes predict non-independent, temporally clustered divergences across taxa. Approximate-likelihood Bayesian computation (ABC) approaches to inferring such patterns from comparative genetic data are very sensitive to prior assumptions and often biased toward estimating shared divergences. We introduce a full-likelihood Bayesian approach, ecoevolity, which takes full advantage of information in genomic data. By analytically integrating over gene trees, we are able to directly calculate the likelihood of the population history from genomic data, and efficiently sample the model-averaged posterior via Markov chain Monte Carlo algorithms. Using simulations, we find that the new method is much more accurate and precise at estimating the number and timing of divergence events across pairs of populations than existing approximate-likelihood methods. Our full Bayesian approach also requires several orders of magnitude less computational time than existing ABC approaches. We find that despite assuming unlinked characters (e.g., unlinked single-nucleotide polymorphisms), the new method performs better if this assumption is violated in order to retain the constant characters of whole linked loci. In fact, retaining constant characters allows the new method to robustly estimate the correct number of divergence events with high posterior probability in the face of character-acquisition biases, which commonly plague loci assembled from reduced-representation genomic libraries. We apply our method to genomic data from four pairs of insular populations of Gekko lizards from the Philippines that are not expected to have co-diverged. Despite all four pairs diverging very recently, our method strongly supports that they diverged independently, and these results are robust to very disparate prior assumptions.

Insights from a general, full-likelihood Bayesian approach to inferring shared evolutionary events from genomic data: Inferring shared demographic events is challenging.

Factors that influence the distribution, abundance, and diversification of species can simultaneously affect multiple evolutionary lineages within or across communities. These include changes to the environment or inter-specific ecological interactions that cause ranges of multiple species to contract, expand, or fragment. Such processes predict temporally clustered evolutionary events across species, such as synchronous population divergences and/or changes in population size. There have been a number of methods developed to infer shared divergences or changes in population size, but not both, and the latter has been limited to approximate methods. We introduce a full-likelihood Bayesian method that uses genomic data to estimate temporal clustering of an arbitrary mix of population divergences and population-size changes across taxa. Using simulated data, we find that estimating the timing and sharing of demographic changes tends to be inaccurate and sensitive to prior assumptions, which is in contrast to accurate, precise, and robust estimates of shared divergence times. We also show that previous estimates of co-expansion among five Alaskan populations of three-spine sticklebacks (Gasterosteus aculeatus) were likely driven by prior assumptions and ignoring invariant characters. We conclude by discussing potential avenues to improve the estimation of synchronous demographic changes across populations.

Objective Bayesian Comparison of Constrained Analysis of Variance Models.

In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means [Formula: see text] through an analysis of variance (ANOVA), a model may specify that [Formula: see text], while another one may state that [Formula: see text], and finally a third model may instead suggest that all means are unrestricted. This is a challenging problem, because it involves a combination of nonnested models, as well as nested models having the same dimension. We adopt an objective Bayesian approach, requiring no prior specification from the user, and derive the posterior probability of each model under consideration. Our method is based on the intrinsic prior methodology, suitably modified to accommodate equality and inequality constraints. Focussing on normal ANOVA models, a comparative assessment is carried out through simulation studies. We also present an application to real data collected in a psychological experiment.

Implications of uniformly distributed, empirically informed priors for phylogeographical model selection: a reply to Hickerson et al.

Establishing that a set of population-splitting events occurred at the same time can be a potentially persuasive argument that a common process affected the populations. Recently, Oaks et al. () assessed the ability of an approximate-Bayesian model-choice method (msBayes) to estimate such a pattern of simultaneous divergence across taxa, to which Hickerson et al. () responded. Both papers agree that the primary inference enabled by the method is very sensitive to prior assumptions and often erroneously supports shared divergences across taxa when prior uncertainty about divergence times is represented by a uniform distribution. However, the papers differ about the best explanation and solution for this problem. Oaks et al. () suggested the method's behavior was caused by the strong weight of uniformly distributed priors on divergence times leading to smaller marginal likelihoods (and thus smaller posterior probabilities) of models with more divergence-time parameters (Hypothesis 1); they proposed alternative prior probability distributions to avoid such strongly weighted posteriors. Hickerson et al. () suggested numerical-approximation error causes msBayes analyses to be biased toward models of clustered divergences because the method's rejection algorithm is unable to adequately sample the parameter space of richer models within reasonable computational limits when using broad uniform priors on divergence times (Hypothesis 2). As a potential solution, they proposed a model-averaging approach that uses narrow, empirically informed uniform priors. Here, we use analyses of simulated and empirical data to demonstrate that the approach of Hickerson et al. () does not mitigate the method's tendency to erroneously support models of highly clustered divergences, and is dangerous in the sense that the empirically derived uniform priors often exclude from consideration the true values of the divergence-time parameters. Our results also show that the tendency of msBayes analyses to support models of shared divergences is primarily due to Hypothesis 1, whereas Hypothesis 2 is an untenable explanation for the bias. Overall, this series of papers demonstrates that if our prior assumptions place too much weight in unlikely regions of parameter space such that the exact posterior supports the wrong model of evolutionary history, no amount of computation can rescue our inference. Fortunately, as predicted by fundamental principles of Bayesian model choice, more flexible distributions that accommodate prior uncertainty about parameters without placing excessive weight in vast regions of parameter space with low likelihood increase the method's robustness and power to detect temporal variation in divergences.