How Important Is Budding Speciation for Comparative Studies?

The acknowledgment of evolutionary dependence among species has fundamentally changed how we ask biological questions. Phylogenetic models became the standard approach for studies with 3 or more lineages, in particular those using extant species. Most phylogenetic comparative methods (PCMs) translate relatedness into covariance, meaning that evolutionary changes before lineages split should be interpreted together whereas after the split lineages are expected to change independently. This clever realization has shaped decades of research. Here, we discuss one element of the comparative method often ignored or assumed as unimportant: if nodes of a phylogeny represent the dissolution of the ancestral lineage into two new ones or if the ancestral lineage can survive speciation events (i.e., budding). Budding speciation is often reported in paleontological studies, due to the nature of the evidence for budding in the fossil record, but it is surprisingly absent in comparative methods. Here, we show that many PCMs assume that divergence happens as a symmetric split, even if these methods do not explicitly mention this assumption. We discuss the properties of trait evolution models for continuous and discrete traits and their adequacy under a scenario of budding speciation. We discuss the effects of budding speciation under a series of plausible evolutionary scenarios and show when and how these can influence our estimates. We also propose that long-lived lineages that have survived through a series of budding speciation events and given birth to multiple new lineages can produce evolutionary patterns that challenge our intuition about the most parsimonious history of trait changes in a clade. We hope our discussion can help bridge comparative approaches in paleontology and neontology as well as foster awareness about the assumptions we make when we use phylogenetic trees.

Reducing the biases in false correlations between discrete characters

The correlation between two characters is often interpreted as evidence that there exists a significant and biologically important relationship between them. However, Maddison and FitzJohn (2015) recently pointed out that evidence of correlated evolution between two categorical characters is often spurious, particularly, when the dependent relationship stems from a single replicate deep in time. Here we will show that there may, in fact, be a statistical solution to the problem posed by Maddison and FitzJohn (2015) naturally embedded within the expanded model space afforded by the hidden Markov model (HMM) framework. We demonstrate that the problem of single unreplicated evolutionary events manifests itself as rate heterogeneity within our models and that this is the source of the false correlation. Therefore, we argue that this problem is better understood as model misspecification rather than a failure of comparative methods to account for phylogenetic pseudoreplication. We utilize HMMs to develop a multi-rate independent model which, when implemented, drastically reduces support for correlation. The problem itself extends beyond categorical character evolution, but we believe that the practical solution presented here may lend itself to future extensions in other areas of comparative biology.

A new automatic forecasting method based on a new input significancy test of a single multiplicative neuron model artificial neural network

The model adequacy and input significance tests have not been proposed as features for the specification of a single multiplicative neuron model artificial neural networks in the literature. Moreover, there is no systematic approach based on hypothesis tests for using single multiplicative neuron model artificial neural networks for forecasting purposes like classical time series forecasting methods. In this study, new methods are proposed to solve these problems. The performance of the proposed test procedures is investigated in a simulation study. According to simulation results, the proposed tests have very good performance. Moreover, the test procedures are illustrated by using two real-world examples. The second contribution of the paper is that an automatic forecasting method is proposed based on input significance and model adequacy tests and the particle swarm optimization-based learning algorithm. The proposed automatic forecasting method is applied to M4 competition hourly data sets, and it is the best pure machine learning method among others in the competition. The proposed automatic forecasting method is more accurate than all benchmarks, such as MLP, RNN, and ETS, which were proposed by the competition organizers.

Assessing model adequacy leads to more robust phylogeographic inference

Phylogeographic studies base inferences on large data sets and complex demographic models, but these models are applied in ways that could mislead researchers and compromise their inference. Researchers face three challenges associated with the use of models: (i) 'model selection', or the identification of an appropriate model for analysis; (ii) 'evaluation of analytical results', or the interpretation of the biological significance of the resulting parameter estimates, delimitations, and topologies; and (iii) 'model evaluation', or the use of statistical approaches to assess the fit of the model to the data. The field collectively invests most of its energy in point (ii) without considering the other points; we argue that attention to points (i) and (iii) is essential to phylogeographic inference.

Model adequacy tests for probabilistic models of chromosome-number evolution

Chromosome number is a central feature of eukaryote genomes. Deciphering patterns of chromosome-number change along a phylogeny is central to the inference of whole genome duplications and ancestral chromosome numbers. ChromEvol is a probabilistic inference tool that allows the evaluation of several models of chromosome-number evolution and their fit to the data. However, fitting a model does not necessarily mean that the model describes the empirical data adequately. This vulnerability may lead to incorrect conclusions when model assumptions are not met by real data. Here, we present a model adequacy test for likelihood models of chromosome-number evolution. The procedure allows us to determine whether the model can generate data with similar characteristics as those found in the observed ones. We demonstrate that using inadequate models can lead to inflated errors in several inference tasks. Applying the developed method to 200 angiosperm genera, we find that in many of these, the best-fitting model provides poor fit to the data. The inadequacy rate increases in large clades or in those in which hybridizations are present. The developed model adequacy test can help researchers to identify phylogenies whose underlying evolutionary patterns deviate substantially from current modelling assumptions and should guide future methods development.

Macroevolutionary and macroecological approaches to understanding the evolution of stress tolerance in plants

Environmental stress response in plants has been studied using a wide range of approaches, from lab-based investigation of biochemistry and genetics, to glasshouse studies of physiology and growth rates, to field-based trials and ecological surveys. It is also possible to investigate the evolution of environmental stress responses using macroevolutionary and macroecological analyses, analysing data from many different species, providing a new perspective on the way that environmental stress shapes the evolution and distribution of biodiversity. "Macroevoeco" approaches can produce intriguing results and new ways of looking at old problems. In this review, we focus on studies using phylogenetic analysis to illuminate macroevolutionary patterns in the evolution of environmental stress tolerance in plants. We follow a particular thread from our own research-evolution of salt tolerance-as a case study that illustrates a macroevolutionary way of thinking that opens up a range of broader questions on the evolution of environmental stress tolerances. We consider some potential future applications of macroevolutionary and macroecological analyses to understanding how diverse groups of plants evolve in response to environmental stress, which may allow better prediction of current stress tolerance and a way of predicting the capacity of species to adapt to changing environmental stresses over time.

New Statistical Criteria Detect Phylogenetic Bias Caused by Compositional Heterogeneity

In statistical phylogenetic analyses of DNA sequences, models of evolutionary change commonly assume that base composition is stationary through time and across lineages. This assumption is violated by many data sets, but it is unclear whether the magnitude of these violations is sufficient to mislead phylogenetic inference. We investigated the impacts of compositional heterogeneity on phylogenetic estimates using a method for assessing model adequacy. Based on a detailed simulation study, we found that common frequentist criteria are highly conservative, such that the model is often rejected when the phylogenetic estimates do not show clear signs of bias. We propose new criteria and provide guidelines for their usage. We apply these criteria to genome-scale data from 40 birds and find that loci with severely non-homogeneous base composition are uncommon. Our results show the importance of using well-informed diagnostic statistics when testing model adequacy for phylogenomic analyses.

The Validation of a Beta-Binomial Model for Overdispersed Binomial Data

The beta-binomial model has been widely used as an analytically tractable alternative that captures the overdispersion of an intra-correlated, binomial random variable, X. However, the model validation for X has been rarely investigated. As a beta-binomial mass function takes on a few different shapes, the model validation is examined for each of the classified shapes in this paper. Further, the mean square error (MSE) is illustrated for each shape by the maximum likelihood estimator (MLE) based on a beta-binomial model approach and the method of moments estimator (MME) in order to gauge when and how much the MLE is biased.

Assessing the performance of DNA barcoding using posterior predictive simulations

Accurate estimates of biodiversity are required for research in a broad array of biological subdisciplines including ecology, evolution, systematics, conservation and biodiversity science. The use of statistical models and genetic data, particularly DNA barcoding, has been suggested as an important tool for remedying the large gaps in our current understanding of biodiversity. However, the reliability of biodiversity estimates obtained using these approaches depends on how well the statistical models that are used describe the evolutionary process underlying the genetic data. In this study, we utilize data from the Barcode of Life Database and posterior predictive simulations to assess the performance of DNA barcoding under commonly used substitution models. We demonstrate that the success of DNA barcoding varies widely across DNA substitution models and that model choice has a substantial impact on the number of operational taxonomic units identified (changing results by ~4-31%). Additionally, we demonstrate that the widely followed practice of a priori assuming the Kimura 2-parameter model for DNA barcoding is statistically unjustified and should be avoided. Using both data-based and inference-based test statistics, we detect variation in model performance across taxonomic groups, clustering algorithms, genetic divergence thresholds and substitution models. Taken together, these results illustrate the importance of considering both model selection and model adequacy in studies quantifying biodiversity.

Challenges in the estimation of extinction from molecular phylogenies: A response to Beaulieu and O'Meara

Time-calibrated phylogenies that contain only living species have been widely used to study the dynamics of speciation and extinction. Concerns about the reliability of phylogenetic extinction estimates were raised by Rabosky (2010), where I suggested that unaccommodated heterogeneity in speciation rate could lead to positively biased extinction estimates. In a recent article, Beaulieu and O'Meara (2015a) correctly point out several technical errors in the execution of my 2010 study and concluded that phylogenetic extinction estimates are robust to speciation rate heterogeneity under a range of model parameters. I demonstrate that Beaulieu and O'Meara underestimated the magnitude of speciation rate variation in real phylogenies and consequently did not incorporate biologically meaningful levels of rate heterogeneity into their simulations. Using parameter values drawn from the recent literature, I find that modest levels of heterogeneity in speciation rate result in a consistent, positive bias in extinction estimates that are exacerbated by phylogenetic tree size. This bias, combined with the inherent lack of information about extinction in molecular phylogenies, suggests that extinction rate estimates from phylogenies of extant taxa only should be treated with caution.

Evaluating the Adequacy of Molecular Clock Models Using Posterior Predictive Simulations

Molecular clock models are commonly used to estimate evolutionary rates and timescales from nucleotide sequences. The goal of these models is to account for rate variation among lineages, such that they are assumed to be adequate descriptions of the processes that generated the data. A common approach for selecting a clock model for a data set of interest is to examine a set of candidates and to select the model that provides the best statistical fit. However, this can lead to unreliable estimates if all the candidate models are actually inadequate. For this reason, a method of evaluating absolute model performance is critical. We describe a method that uses posterior predictive simulations to assess the adequacy of clock models. We test the power of this approach using simulated data and find that the method is sensitive to bias in the estimates of branch lengths, which tends to occur when using underparameterized clock models. We also compare the performance of the multinomial test statistic, originally developed to assess the adequacy of substitution models, but find that it has low power in identifying the adequacy of clock models. We illustrate the performance of our method using empirical data sets from coronaviruses, simian immunodeficiency virus, killer whales, and marine turtles. Our results indicate that methods of investigating model adequacy, including the one proposed here, should be routinely used in combination with traditional model selection in evolutionary studies. This will reveal whether a broader range of clock models to be considered in phylogenetic analysis.

Substitution Model Adequacy and Assessing the Reliability of Estimates of Virus Evolutionary Rates and Time Scales

Determining the time scale of virus evolution is central to understanding their origins and emergence. The phylogenetic methods commonly used for this purpose can be misleading if the substitution model makes incorrect assumptions about the data. Empirical studies consider a pool of models and select that with the highest statistical fit. However, this does not allow the rejection of all models, even if they poorly describe the data. An alternative is to use model adequacy methods that evaluate the ability of a model to predict hypothetical future observations. This can be done by comparing the empirical data with data generated under the model in question. We conducted simulations to evaluate the sensitivity of such methods with nucleotide, amino acid, and codon data. These effectively detected underparameterized models, but failed to detect mutational saturation and some instances of nonstationary base composition, which can lead to biases in estimates of tree topology and length. To test the applicability of these methods with real data, we analyzed nucleotide and amino acid data sets from the genus Flavivirus of RNA viruses. In most cases these models were inadequate, with the exception of a data set of relatively closely related sequences of Dengue virus, for which the GTR+Γ nucleotide and LG+Γ amino acid substitution models were adequate. Our results partly explain the lack of consensus over estimates of the long-term evolutionary time scale of these viruses, and indicate that assessing the adequacy of substitution models should be routinely used to determine whether estimates are reliable.

A graphical method to assess distribution assumption in group-based trajectory models

Group-based trajectory models had a rapid development in the analysis of longitudinal data in clinical research. In these models, the assumption of homoscedasticity of the residuals is frequently made but this assumption is not always met. We developed here an easy-to-perform graphical method to assess the assumption of homoscedasticity of the residuals to apply especially in group-based trajectory models. The method is based on drawing an envelope to visualize the local dispersion of the residuals around each typical trajectory. Its efficiency is demonstrated using data on CD4 lymphocyte counts in patients with human immunodeficiency virus put on antiretroviral therapy. Four distinct distributions that take into account increasing parts of the variability of the observed data are presented. Significant differences in group structures and trajectory patterns were found according to the chosen distribution. These differences might have large impacts on the final trajectories and their characteristics; thus on potential medical decisions. With a single glance, the graphical criteria allow the choice of the distribution that best capture data variability and help dealing with a potential heteroscedasticity problem.