Fitting and evaluating univariate and multivariate models of within-lineage evolution

The nature of phenotypic evolution within lineages is central to many unresolved questions in paleontology and evolutionary biology. Analyses of evolutionary time-series of ancestor-descendant populations in the fossil record are likely to make important contributions to many of these debates. However, the limited number of models that have been applied to these types of data may restrict our ability to interpret phenotypic evolution in the fossil record. Using uni- and multivariate models of trait evolution that make different assumptions regarding the dynamics of the adaptive landscape, I evaluate contrasting hypotheses to explain evolution of size in the radiolarian Eucyrtidium calvertense and armor in the stickleback Gaserosteus doryssus. Body size evolution in E. calvertense is best explained by a model where the lineage evolves as a consequence of a shift in the adaptive landscape that coincides with the initiation of neosympatry with its sister lineage. Multivariate evolution of armor traits in a stickleback lineage (Gasterosteus doryssus) show evidence of adaptation towards independent optima on the adaptive landscape at the same time as traits change in a correlated fashion. The fitted models are available in a the R package evoTS, which builds on the commonly used paleoTS framework.

Conceptual and empirical bridges between micro- and macroevolution

Explaining broad molecular, phenotypic and species biodiversity patterns necessitates a unifying framework spanning multiple evolutionary scales. Here we argue that although substantial effort has been made to reconcile microevolution and macroevolution, much work remains to identify the links between biological processes at play. We highlight four major questions of evolutionary biology whose solutions require conceptual bridges between micro and macroevolution. We review potential avenues for future research to establish how mechanisms at one scale (drift, mutation, migration, selection) translate to processes at the other scale (speciation, extinction, biogeographic dispersal) and vice versa. We propose ways in which current comparative methods to infer molecular evolution, phenotypic evolution and species diversification could be improved to specifically address these questions. We conclude that researchers are in a better position than ever before to build a synthesis to understand how microevolutionary dynamics unfold over millions of years.

Cross-disciplinary information for understanding macroevolution

Many different macroevolutionary models can produce the same observations. Despite efforts in building more complex and realistic models, it may still be difficult to distinguish the processes that have generated the biodiversity we observe. In this opinion we argue that we can make new progress by reaching out across disciplines, relying on independent data and theory to constrain macroevolutionary inference. Using mainly paleontological insights and data, we illustrate how we can eliminate less plausible or implausible models, and/or parts of parameter space, while applying comparative phylogenetic approaches. We emphasize that such cross-disciplinary insights and data can be drawn between many other disciplines relevant to macroevolution. We urge cross-disciplinary training, and collaboration using common-use databases as a platform for increasing our understanding.

Causes and Consequences of Apparent Timescaling Across All Estimated Evolutionary Rates

Evolutionary rates play a central role in connecting micro- and macroevolution. All evolutionary rate estimates, including rates of molecular evolution, trait evolution, and lineage diversification, share a similar scaling pattern with time: The highest rates are those measured over the shortest time interval. This creates a disconnect between micro- and macroevolution, although the pattern is the opposite of what some might expect: Patterns of change over short timescales predict that evolution has tremendous potential to create variation and that potential is barely tapped by macroevolution. In this review, we discuss this shared scaling pattern across evolutionary rates. We break down possible explanations for scaling into two categories, estimation error and model misspecification, and discuss how both apply to each type of rate. We also discuss the consequences of this ubiquitous pattern, which can lead to unexpected results when comparing ratesover different timescales. Finally, after addressing purely statistical concerns, we explore a few possibilities for a shared unifying explanation across the three types of rates that results from a failure to fully understand and account for how biological processes scale over time.

When fossil clades 'compete': local dominance, global diversification dynamics and causation

Examining the supposition that local-scale competition drives macroevolutionary patterns has become a familiar goal in fossil biodiversity studies. However, it is an elusive goal, hampered by inadequate confirmation of ecological equivalence and interactive processes between clades, patchy sampling, few comparative analyses of local species assemblages over long geological intervals, and a dearth of appropriate statistical tools. We address these concerns by reevaluating one of the classic examples of clade displacement in the fossil record, in which cheilostome bryozoans surpass the once dominant cyclostomes. Here, we analyse a newly expanded and vetted compilation of 40 190 fossil species occurrences to estimate cheilostome and cyclostome patterns of species proportions within assemblages, global genus richness and genus origination and extinction rates while accounting for sampling. Comparison of time-series models using linear stochastic differential equations suggests that inter-clade genus origination and extinction rates are causally linked to each other in a complex feedback relationship rather than by simple correlations or unidirectional relationships, and that these rates are not causally linked to changing within-assemblage proportions of cheilostome versus cyclostome species.

Fast likelihood calculation for multivariate Gaussian phylogenetic models with shifts

Phylogenetic comparative methods (PCMs) have been used to study the evolution of quantitative traits in various groups of organisms, ranging from micro-organisms to animal and plant species. A common approach has been to assume a Gaussian phylogenetic model for the trait evolution along the tree, such as a branching Brownian motion (BM) or an Ornstein-Uhlenbeck (OU) process. Then, the parameters of the process have been inferred based on a given tree and trait data for the sampled species. At the heart of this inference lie multiple calculations of the model likelihood, that is, the probability density of the observed trait data, conditional on the model parameters and the tree. With the increasing availability of big phylogenetic trees, spanning hundreds to several thousand sampled species, this approach is facing a two-fold challenge. First, the assumption of a single Gaussian process governing the entire tree is not adequate in the presence of heterogeneous evolutionary forces acting in different parts of the tree. Second, big trees present a computational challenge, due to the time and memory complexity of the model likelihood calculation. Here, we explore a sub-family, denoted G_LInv, of the Gaussian phylogenetic models, with the transition density exhibiting the properties that the expectation depends Linearly on the ancestral trait value and the variance is Invariant with respect to the ancestral value. We show that G_LInv contains the vast majority of Gaussian models currently used in PCMs, while supporting an efficient (linear in the number of nodes) algorithm for the likelihood calculation. The algorithm supports scenarios with missing data, as well as different types of trees, including trees with polytomies and non-ultrametric trees. To account for the heterogeneity in the evolutionary forces, the algorithm supports models with "shifts" occurring at specific points in the tree. Such shifts can include changes in some or all parameters, as well as the type of the model, provided that the model remains within the G_LInv family. This contrasts with most of the current implementations where, due to slow likelihood calculation, the shifts are restricted to specific parameters in a single type of model, such as the long-term selection optima of an OU process, assuming that all of its other parameters, such as evolutionary rate and selection strength, are global for the entire tree. We provide an implementation of this likelihood calculation algorithm in an accompanying R-package called PCMBase. The package has been designed as a generic library that can be integrated with existing or novel maximum likelihood or Bayesian inference tools.

Testing eco-evolutionary predictions using fossil data: Phyletic evolution following ecological opportunity

Fossil sequences provide observations of phenotypes within a lineage over time and represent essential data for increasing our understanding of phyletic evolution beyond microevolutionary timescales. I investigate if fossil time series of the diatom Stephanodiscus niagarae/yellowstonensis follow evolutionary dynamics compatible with hypotheses for how the adaptive landscape changes when a population enters a new environment. The lineage-which has a remarkably detailed stratigraphic record-invaded Yellowstone Lake immediately after recession of ice from the basin 14,000 years ago. Several phyletic models portraying different types of evolutionary dynamics-both compatible and not compatible with changes in the adaptive landscape following ecological opportunity-were fitted to the fossil times-series of S. niagarae/yellowstonensis. Different models best describe the three analyzed traits. Two of the models (a new model of decelerated evolution and an Ornstein-Uhlenbeck model) capture trait dynamics compatible with an event of ecological opportunity, whereas the third model (random walk) does not. Entering a new environment may accordingly affect trait dynamics for thousands of years, but the effects can vary across phenotypes. However, tests of model adequacy reveal shortcomings in all three models explaining the trait dynamics, suggesting model development is needed to more fully understand the phyletic evolution in S. niagarae/yellowstonensis.

A Penalized Likelihood Framework for High-Dimensional Phylogenetic Comparative Methods and an Application to New-World Monkeys Brain Evolution

Working with high-dimensional phylogenetic comparative data sets is challenging because likelihood-based multivariate methods suffer from low statistical performances as the number of traits $p $ approaches the number of species $n $ and because some computational complications occur when $p $ exceeds $n$. Alternative phylogenetic comparative methods have recently been proposed to deal with the large $p $ small $n $ scenario but their use and performances are limited. Herein, we develop a penalized likelihood (PL) framework to deal with high-dimensional comparative data sets. We propose various penalizations and methods for selecting the intensity of the penalties. We apply this general framework to the estimation of parameters (the evolutionary trait covariance matrix and parameters of the evolutionary model) and model comparison for the high-dimensional multivariate Brownian motion (BM), Early-burst (EB), Ornstein-Uhlenbeck (OU), and Pagel's lambda models. We show using simulations that our PL approach dramatically improves the estimation of evolutionary trait covariance matrices and model parameters when $p$ approaches $n$, and allows for their accurate estimation when $p$ equals or exceeds $n$. In addition, we show that PL models can be efficiently compared using generalized information criterion (GIC). We implement these methods, as well as the related estimation of ancestral states and the computation of phylogenetic principal component analysis in the R package RPANDA and mvMORPH. Finally, we illustrate the utility of the new proposed framework by evaluating evolutionary models fit, analyzing integration patterns, and reconstructing evolutionary trajectories for a high-dimensional 3D data set of brain shape in the New World monkeys. We find a clear support for an EB model suggesting an early diversification of brain morphology during the ecological radiation of the clade. PL offers an efficient way to deal with high-dimensional multivariate comparative data.

Inference of Adaptive Shifts for Multivariate Correlated Traits

To study the evolution of several quantitative traits, the classical phylogenetic comparative framework consists of a multivariate random process running along the branches of a phylogenetic tree. The Ornstein-Uhlenbeck (OU) process is sometimes preferred to the simple Brownian motion (BM) as it models stabilizing selection toward an optimum. The optimum for each trait is likely to be changing over the long periods of time spanned by large modern phylogenies. Our goal is to automatically detect the position of these shifts on a phylogenetic tree, while accounting for correlations between traits, which might exist because of structural or evolutionary constraints. We show that, in the presence of shifts, phylogenetic Principal Component Analysis fails to decorrelate traits efficiently, so that any method aiming at finding shifts needs to deal with correlation simultaneously. We introduce here a simplification of the full multivariate OU model, named scalar OU, which allows for noncausal correlations and is still computationally tractable. We extend the equivalence between the OU and a BM on a rescaled tree to our multivariate framework. We describe an Expectation-Maximization (EM) algorithm that allows for a maximum likelihood estimation of the shift positions, associated with a new model selection criterion, accounting for the identifiability issues for the shift localization on the tree. The method, freely available as an R-package (PhylogeneticEM) is fast, and can deal with missing values. We demonstrate its efficiency and accuracy compared to another state-of-the-art method ($\ell$1ou) on a wide range of simulated scenarios and use this new framework to reanalyze recently gathered data sets on New World Monkeys and Anolis lizards.

Common species link global ecosystems to climate change: dynamical evidence in the planktonic fossil record

Common species shape the world around us, and changes in their commonness signify large-scale shifts in ecosystem structure and function. However, our understanding of long-term ecosystem response to environmental forcing in the deep past is centred on species richness, neglecting the disproportional impact of common species. Here, we use common and widespread species of planktonic foraminifera in deep-sea sediments to track changes in observed global occupancy (proportion of sampled sites at which a species is present and observed) through the turbulent climatic history of the last 65 Myr. Our approach is sensitive to relative changes in global abundance of the species set and robust to factors that bias richness estimators. Using three independent methods for detecting causality, we show that the observed global occupancy of planktonic foraminifera has been dynamically coupled to past oceanographic changes captured in deep-ocean temperature reconstructions. The causal inference does not imply a direct mechanism, but is consistent with an indirect, time-delayed causal linkage. Given the strong quantitative evidence that a dynamical coupling exists, we hypothesize that mixotrophy (symbiont hosting) may be an ecological factor linking the global abundance of planktonic foraminifera to long-term climate changes via the relative extent of oligotrophic oceans.

Combining marine macroecology and palaeoecology in understanding biodiversity: microfossils as a model

There is growing interest in the integration of macroecology and palaeoecology towards a better understanding of past, present, and anticipated future biodiversity dynamics. However, the empirical basis for this integration has thus far been limited. Here we review prospects for a macroecology-palaeoecology integration in biodiversity analyses with a focus on marine microfossils [i.e. small (or small parts of) organisms with high fossilization potential, such as foraminifera, ostracodes, diatoms, radiolaria, coccolithophores, dinoflagellates, and ichthyoliths]. Marine microfossils represent a useful model system for such integrative research because of their high abundance, large spatiotemporal coverage, and good taxonomic and temporal resolution. The microfossil record allows for quantitative cross-scale research designs, which help in answering fundamental questions about marine biodiversity, including the causes behind similarities in patterns of latitudinal and longitudinal variation across taxa, the degree of constancy of observed gradients over time, and the relative importance of hypothesized drivers that may explain past or present biodiversity patterns. The inclusion of a deep-time perspective based on high-resolution microfossil records may be an important step for the further maturation of macroecology. An improved integration of macroecology and palaeoecology would aid in our understanding of the balance of ecological and evolutionary mechanisms that have shaped the biosphere we inhabit today and affect how it may change in the future.

Ecological interactions on macroevolutionary time scales: clams and brachiopods are more than ships that pass in the night

Competition among organisms has ecological and evolutionary consequences. However, whether the consequences of competition are manifested and measureable on macroevolutionary time scales is equivocal. Marine bivalves and brachiopods have overlapping niches such that competition for food and space may occur. Moreover, there is a long-standing debate over whether bivalves outcompeted brachiopods evolutionarily, because brachiopod diversity declined through time while bivalve diversity increased. To answer this question, we estimate the origination and extinction dynamics of fossil marine bivalve and brachiopod genera from the Ordovician through to the Recent while simultaneously accounting for incomplete sampling. Then, using stochastic differential equations, we assess statistical relationships among diversification and sampling dynamics of brachiopods and bivalves and five paleoenvironmental proxies. None of these potential environmental drivers had any detectable influence on brachiopod or bivalve diversification. In contrast, elevated bivalve extinction rates causally increased brachiopod origination rates, suggesting that bivalves have suppressed brachiopod evolution.

A novel Bayesian method for inferring and interpreting the dynamics of adaptive landscapes from phylogenetic comparative data

Our understanding of macroevolutionary patterns of adaptive evolution has greatly increased with the advent of large-scale phylogenetic comparative methods. Widely used Ornstein-Uhlenbeck (OU) models can describe an adaptive process of divergence and selection. However, inference of the dynamics of adaptive landscapes from comparative data is complicated by interpretational difficulties, lack of identifiability among parameter values and the common requirement that adaptive hypotheses must be assigned a priori. Here, we develop a reversible-jump Bayesian method of fitting multi-optima OU models to phylogenetic comparative data that estimates the placement and magnitude of adaptive shifts directly from the data. We show how biologically informed hypotheses can be tested against this inferred posterior of shift locations using Bayes Factors to establish whether our a priori models adequately describe the dynamics of adaptive peak shifts. Furthermore, we show how the inclusion of informative priors can be used to restrict models to biologically realistic parameter space and test particular biological interpretations of evolutionary models. We argue that Bayesian model fitting of OU models to comparative data provides a framework for integrating of multiple sources of biological data-such as microevolutionary estimates of selection parameters and paleontological timeseries-allowing inference of adaptive landscape dynamics with explicit, process-based biological interpretations.