Effects of models of rate evolution on estimation of divergence dates with special reference to the metazoan 18S ribosomal RNA phylogeny

The molecular clock, i.e., constancy of the rate of evolution over time, is commonly assumed in estimating divergence dates. However, this assumption is often violated and has drastic effects on date estimation. Recently, a number of attempts have been made to relax the clock assumption. One approach is to use maximum likelihood, which assigns rates to branches and allows the estimation of both rates and times. An alternative is the Bayes approach, which models the change of the rate over time. A number of models of rate change have been proposed. We have extended and evaluated models of rate evolution, i.e., the lognormal and its recent variant, along with the gamma, the exponential, and the Ornstein-Uhlenbeck processes. These models were first applied to a small hominoid data set, where an empirical Bayes approach was used to estimate the hyperparameters that measure the amount of rate variation. Estimation of divergence times was sensitive to these hyperparameters, especially when the assumed model is close to the clock assumption. The rate and date estimates varied little from model to model, although the posterior Bayes factor indicated the Ornstein-Uhlenbeck process outperformed the other models. To demonstrate the importance of allowing for rate change across lineages, this general approach was used to analyze a larger data set consisting of the 18S ribosomal RNA gene of 39 metazoan species. We obtained date estimates consistent with paleontological records, the deepest split within the group being about 560 million years ago. Estimates of the rates were in accordance with the Cambrian explosion hypothesis and suggested some more recent lineage-specific bursts of evolution.     

Morphological disparity and evolutionary rates of cranial and postcranial characters in sloths (Mammalia,Pilosa, Folivora)

Sloth morphological evolution has been widely studied qualitatively, with comparative anatomy and morpho-functional approaches, or through quantitative assessments of morphological variation using morphometrics. Only recently, however, have folivoran morphological disparity and evolutionary rates begun to be evaluated using discrete character data. Nonetheless, patterns of morphological evolution in separate character partitions have not been investigated, neither the relative influence of, on the one hand, phylogeny, and on the other, dietary and locomotory adaptations of sloths. Here we evaluate those patterns using a phylomorphospace approach, quantifying morphological disparity and evolutionary rates, and investigating possible drivers of morphological evolution for cranial and postcranial characters in Folivora. The evolution of the morphology in those partitions is associated with distinct patterns of disparity among clades and ecological groups, even though the two partitions do not differ substantially in overall evolutionary tempo. Historical processes shaped the morphological evolution of sloths more consistently than ecological ones, although changes in postcranial characters also seem to be associated with locomotory adaptations, in which morphological convergences were much more common. We also discuss important methodological trade-offs in investigations of partitioned datasets mostly composed of fossil taxa.     

Inferring and testing hypotheses of cladistic character dependence by using character compatibility

The notion that two characters evolve independently is of interest for two reasons. First, theories of biological integration often predict that change in one character requires complementary change in another. Second, character independence is a basic assumption of most phylogenetic inference methods, and dependent characters might confound attempts at phylogenetic inference. Previously proposed tests of correlated character evolution require a model phylogeny and therefore assume that nonphylogenetic correlation has a negligible effect on initial tree construction. This paper develops "tree-free" methods for testing the independence of cladistic characters. These methods can test the character independence model as a hypothesis before phylogeny reconstruction, or can be used simply to test for correlated evolution. We first develop an approach for visualizing suites of correlated characters by using character compatibility. Two characters are compatible if they can be used to construct a tree without homoplasy. The approach is based on the examination of mutual compatibilities between characters. The number of times two characters i and j share compatibility with a third character is calculated, and a pairwise shared compatibility matrix is constructed. From this matrix, an association matrix analogous to a dissimilarity matrix is derived. Eigenvector analyses of this association matrix reveal suites of characters with similar compatibility patterns. A priori character subsets can be tested for significant correlation on these axes. Monte Carlo tests are performed to determine the expected distribution of mutual compatibilities, given various criteria from the original data set. These simulated distributions are then used to test whether the observed amounts of nonphylogenetic correlation in character suites can be attributed to chance alone. We have applied these methods to published morphological data for caecilian amphibians. The analyses corroborate instances of dependent evolution hypothesized by previous workers and also identify novel partitions. Phylogenetic analysis is performed after reducing correlated suites to single characters. The resulting cladogram has greater topological resolution and implies appreciably less change among the remaining characters than does a tree derived from the raw data matrix.     

The macroevolutionary consequences of phenotypic integration: from development to deep time

Phenotypic integration is a pervasive characteristic of organisms. Numerous analyses have demonstrated that patterns of phenotypic integration are conserved across large clades, but that significant variation also exists. For example, heterochronic shifts related to different mammalian reproductive strategies are reflected in postcranial skeletal integration and in coordination of bone ossification. Phenotypic integration and modularity have been hypothesized to shape morphological evolution, and we extended simulations to confirm that trait integration can influence both the trajectory and magnitude of response to selection. We further demonstrate that phenotypic integration can produce both more and less disparate organisms than would be expected under random walk models by repartitioning variance in preferred directions. This effect can also be expected to favour homoplasy and convergent evolution. New empirical analyses of the carnivoran cranium show that rates of evolution, in contrast, are not strongly influenced by phenotypic integration and show little relationship to morphological disparity, suggesting that phenotypic integration may shape the direction of evolutionary change, but not necessarily the speed of it. Nonetheless, phenotypic integration is problematic for morphological clocks and should be incorporated more widely into models that seek to accurately reconstruct both trait and organismal evolution.     

Particulate versus integrated evolution of the upper body in late pleistocene humans: A test of two models

Evolutionary biologists are largely polarized in their approaches to integrating microevolutionary and macroevolutionary processes. Neo-Darwinians typically seek to identify population-level selective and genetic processes that culminate in macroevolutionary events. Epigeneticists and structuralists, on the other hand, emphasize developmental constraints on the action of natural selection, and highlight the role of epigenetic shifts in producing evolutionary change in morphology. Accordingly, the ways in which these paradigms view and address morphological contrasts between classes of related organisms differ. These paradigms, although seldomly explicitly stated, emerge in paleoanthropology as well. Considerations of postcranial morphological contrasts between archaic and modern humans typically fall into one of two broad interpretive models. The first derives from the neo-Darwinian perspective and holds that evolution in the postcranial skeleton was largely mosaic (operating in a particulate manner), and that temporal change in specific traits informs us about behavioral shifts or genetic evolution affecting isolated anatomical regions (i.e., adaptive behavioral inferences can be made from comparative studies of individual trait complexes). The alternative model follows from the epigeneticist paradigm and sees change in specific postcranial traits as correlated responses to change in overall body form (involving shifts in regulation of skeletal growth, or selective and developmental responses to broad adaptive shifts). By this view, integration of functional systems both constrains and directs evolution of various traits, and morphological contrasts inform us about overall change in body form related to change in such things as overall growth patterns, climatic adaptation, and technological dependency. These models were tested by confirmatory factor analysis using measures of upper body form and upper limb morphological traits in Eurasian Neandertal and early modern fossils and recent human samples. Results indicate (1) a model of morphological integration fits the data better than a model of no integration, but (2) this integration accounts for less than half of the variance in upper limb traits, suggesting a high degree of tolerance for particulate evolution in the context of an integrated upper body plan. Significant relationships were detected between joint shapes and body size, between humeral shaft shape and body size and chest shape, and between measures of biomechanical efficiency and robusticity. The observed morphological differences between late archaic and early modern humans reflect particulate evolution in the context of constraints imposed by genetic and morphological integration. While particulate approaches to interpreting the fossil record appear to be justified, attention must also be paid to delineating the nature and extent of morphological integration and its role in both constraining and producing observed patterns of variation between groups. Confirmatory factor analysis provides a means of examining trait covariance matrices, and serves as a useful method of identifying patterns of integration in morphology. © 1996 Wiley-Liss, Inc.     

Character space restrictions and boundary conditions in the evolution of quantitative multistate characters

The effects of restrictions of available character space on the mean morphological distance between living members of evolutionary phylads are examined by Monte Carlo simulation. The approach involves specifying the degree to which ancestor-descendant species may differ and limiting the range of attainable character states within a phylad. Morphological evolution is modeled as a Markovian process involving quantitative multistate characters. States for a given character are allowed to evolve at time-dependent or speciation-dependent rates.The final distributions of morphological distance for a given trait among members of a phylad depend on the number of species in the phylad, the rate and pattern of evolution of new character states, and the existence of boundary conditions indicating possible selective constraints on the trait. When morphological change is proportional to time, increasing restrictions on character evolution tend to (a) lower mean distance between species and (b) leave the ratio of mean distances ($\text{D}{}_{\mathrm{R}}\text{D}{}_{\mathrm{p}}$) in species-rich vs. species-poor phylads of comparable evolutionary age near one. When change is proportional to rate of speciation, similar restrictions tend to (a) limit mean distance only in phylads in which the number of speciations exceeds the range of attainable character states and (b) permit $\text{D}{}_{\mathrm{R}}\text{D}{}_{\mathrm{p}}$ to be considerably greater than one, except in extreme cases. Implications of these results for the current phyletic gradualism-rectangular evolution controversy are considered.     

Natural distribution

Log-normal distributions describe data from diverse disciplines of science. However, the fundamental basis of log-normal distributions is unknown. We suggest that the skewed distributions are outcomes of natural processes i.e. they result from the principle of increasing entropy. Fluctuations during the course of evolution toward more probable states yield multiplicative variations about the mean. The non-linear dispersion of thermodynamic states, i.e. matter and energy defined by chemical potentials, underlies the skew. Cumulative curves of skewed distributions without integrable analytical forms are characteristic of natural processes.     

Rates of morphological evolution are correlated with species richness in salamanders

The tempo and mode of species diversification and phenotypic evolution vary widely across the tree of life, yet the relationship between these processes is poorly known. Previous tests of the relationship between rates of phenotypic evolution and rates of species diversification have assumed that species richness increases continuously through time. If this assumption is violated, simple phylogenetic estimates of net diversification rate may bear no relationship to processes that influence the distribution of species richness among clades. Here, we demonstrate that the variation in species richness among plethodontid salamander clades is unlikely to have resulted from simple time-dependent processes, leading to fundamentally different conclusions about the relationship between rates of phenotypic evolution and species diversification. Morphological evolutionary rates of both size and shape evolution are correlated with clade species richness, but are uncorrelated with simple estimators of net diversification that assume constancy of rates through time. This coupling between species diversification and phenotypic evolution is consistent with the hypothesis that clades with high rates of morphological trait evolution may diversify more than clades with low rates. Our results indicate that assumptions about underlying processes of diversity regulation have important consequences for interpreting macroevolutionary patterns.     

Effects of Distribution Choice on the Modeling of Life Cycle Inventory Uncertainty: An Assessment on the Ecoinvent v2.2 Database

Life cycle inventory data have multiple sources of uncertainty. These data uncertainties are often modeled using probability density functions, and in the ecoinvent database the lognormal distribution is used by default to model exchange uncertainty values. The aim of this article is to systematically measure the effect of this default distribution by changing from the lognormal to several other distribution functions and examining how this change affects the uncertainty of life cycle assessment results. Using the ecoinvent 2.2 inventory database, data uncertainty distributions are switched from the lognormal distribution to the normal, triangular, and gamma distributions. The effect of the distribution switching is assessed for both impact assessment results of individual products system, as well as comparisons between product systems. Impact assessment results are generated using 5,000 Monte Carlo iterations for each product system, using the Intergovernmental Panel on Climate Change (IPCC) 2001 (100‐year time frame) method. When comparing the lognormal distribution to the alternative default distributions, the difference in the resulting median and standard deviation values range from slight to significant, depending on the distributions used by default. However, the switch shows practically no effect on product system comparisons. Yet, impact assessment results are sensitive to how the data uncertainties are defined. In this article, we followed what we believe to be ecoinvent standard practice and preserved the “most representative” value. Practitioners should recognize that the most representative value can depart from the average of a probability distribution. Consistent default distribution choices are necessary when performing product system comparisons.     

Identifying heterogeneity in rates of morphological evolution: discrete character change in the evolution of lungfish (Sarcopterygii; Dipnoi)

Quantifying rates of morphological evolution is important in many macroevolutionary studies, and critical when assessing possible adaptive radiations and episodes of punctuated equilibrium in the fossil record. However, studies of morphological rates of change have lagged behind those on taxonomic diversification, and most authors have focused on continuous characters and quantifying patterns of morphological rates over time. Here, we provide a phylogenetic approach, using discrete characters and three statistical tests to determine points on a cladogram (branches or entire clades) that are characterized by significantly high or low rates of change. These methods include a randomization approach that identifies branches with significantly high rates and likelihood ratio tests that pinpoint either branches or clades that have significantly higher or lower rates than the pooled rate of the remainder of the tree. As a test case for these methods, we analyze a discrete character dataset of lungfish, which have long been regarded as "living fossils" due to an apparent slowdown in rates since the Devonian. We find that morphological rates are highly heterogeneous across the phylogeny and recover a general pattern of decreasing rates along the phylogenetic backbone toward living taxa, from the Devonian until the present. Compared with previous work, we are able to report a more nuanced picture of lungfish evolution using these new methods.     

Heterogeneous communities with lognormal species abundance distribution: Species-area curves and sustainability

Heterogeneous species abundance models are models in which the dynamics differ between species, described by variation among parameters defining the dynamics. Using a dynamic and heterogeneous species abundance model generating the lognormal species abundance distribution it is first shown that different degrees of heterogeneity may result in equivalent species abundance distributions. An alternative to Preston's canonical lognormal model is defined by assuming that reduction in resources, for example reduction in available area, increases the density regulation of each species. This leads to species-individual curves and species-area curves that are approximately linear in a double logarithmic plot. Preston's canonical parameter gamma varies little along these curves and takes values in the neighborhood of one. Quite remarkably, the curves, which define the sensitivity of the community to area reductions, are independent of the heterogeneity among species for this model. As a consequence, the curves can be estimated from a single sample from the community using the Poisson lognormal distribution. It is shown how to perform sensitivity analysis with respect to over-dispersion in sampling relative to the Poisson distribution as well as sampling intensity, that is, the fraction of the community sampled. The method is exemplified by analyzing three simulated data sets.     

A likelihood method for detecting trait-dependent shifts in the rate of molecular evolution

Rate heterogeneity within groups of organisms is known to exist even when closely related taxa are examined. A wide variety of phylogenetic and dating methods have been developed that aim either to test for the existence of rate variation or to correct for its bias. However, none of the existing methods track the evolution of features that account for observed rate heterogeneity. Here, we present a likelihood model that assumes that rate variation is caused, in part, by species' intrinsic characteristics, such as a particular life-history trait, morphological feature, or habitat association. The model combines models of sequence and character state evolution such that rates of sequence change depend on the character state of a lineage at each point in time. We test, using simulations, the power and accuracy of the model to determine whether rates of molecular evolution depend on a particular character state and demonstrate its utility using an empirical example with halophilic and freshwater daphniids.     

MODULARITY AND RATES OF EVOLUTIONARY CHANGE IN A POWER‐AMPLIFIED PREY CAPTURE SYSTEM

The dynamic interplay among structure, function, and phylogeny form a classic triad of influences on the patterns and processes of biological diversification. Although these dynamics are widely recognized as important, quantitative analyses of their interactions have infrequently been applied to biomechanical systems. Here we analyze these factors using a fundamental biomechanical mechanism: power amplification. Power‐amplified systems use springs and latches to generate extremely fast and powerful movements. This study focuses specifically on the power amplification mechanism in the fast raptorial appendages of mantis shrimp (Crustacea: Stomatopoda). Using geometric morphometric and phylogenetic comparative analyses, we measured evolutionary modularity and rates of morphological evolution of the raptorial appendage's biomechanical components. We found that “smashers” (hammer‐shaped raptorial appendages) exhibit lower modularity and 10‐fold slower rates of morphological change when compared to non‐smashers (spear‐shaped or undifferentiated appendages). The morphological and biomechanical integration of this system at a macroevolutionary scale and the presence of variable rates of evolution reveal a balance between structural constraints, functional variation, and the “roles of development and genetics” in evolutionary diversification.     

A statistical study of the interspike-interval distribution of cortical neurons]

Spontaneous activity was recorded extracellularly by glass microelectrodes from 54 neurons of the Gyrus sigmoideus posterior of unnarcotized and gallamine-immobilazed cats, and the sequential and nonsequential interspike-interval histograms were determined using the multi-channel analyzer CAT 400 C. The interval distributions were characterized by graphic criteria, and it was attempted to describe these distributions mathematically by four biparametric distributions, the Weibull, lognormal, gamma and normal distributions. 80% of the frequency distributions of type I (exponential), II (left skew, gamma-similar) and IV (almost symmetrical) could be assigned to these distributions, namely 43% of the lognormal distribution, 32% of the Weibull distribution, and 5% of the gamma distribution. The interval histograms of the type III (left skew, steep) and V (bimodal) could not be described by any of the distributions selected.     

Unidentifiable divergence times in rates-across-sites models

The rates-across-sites assumption in phylogenetic inference posits that the rate matrix governing the Markovian evolution of a character on an edge of the putative phylogenetic tree is the product of a character-specific scale factor and a rate matrix that is particular to that edge. Thus, evolution follows basically the same process for all characters, except that it occurs faster for some characters than others. To allow estimation of tree topologies and edge lengths for such models, it is commonly assumed that the scale factors are not arbitrary unknown constants, but rather unobserved, independent, identically distributed draws from a member of some parametric family of distributions. A popular choice is the gamma family. We consider an example of a clock-like tree with three taxa, one unknown edge length, a known root state, and a parametric family of scale factor distributions that contains the gamma family. This model has the property that, for a generic choice of unknown edge length and scale factor distribution, there is another edge length and scale factor distribution which generates data with exactly the same distribution, so that even with infinitely many data it will be typically impossible to make correct inferences about the unknown edge length.     

ELEVATED RATES OF MORPHOLOGICAL AND FUNCTIONAL DIVERSIFICATION IN REEF‐DWELLING HAEMULID FISHES

The relationship between habitat complexity and species richness is well established but comparatively little is known about the evolution of morphological diversity in complex habitats. Reefs are structurally complex, highly productive shallow‐water marine ecosystems found in tropical (coral reefs) and temperate zones (rocky reefs) that harbor exceptional levels of biodiversity. We investigated whether reef habitats promote the evolution of morphological diversity in the feeding and locomotion systems of grunts (Haemulidae), a group of predominantly nocturnal fishes that live on both temperate and tropical reefs. Using phylogenetic comparative methods and statistical analyses that take into account uncertainty in phylogeny and the evolutionary history of reef living, we demonstrate that rates of morphological evolution are faster in reef‐dwelling haemulids. The magnitude of this effect depends on the type of trait; on average, traits involved in the functional systems for prey capture and processing evolve twice as fast on reefs as locomotor traits. This result, along with the observation that haemulids do not exploit unique feeding niches on reefs, suggests that fine‐scale trophic niche partitioning and character displacement may be driving higher rates of morphological evolution. Whatever the cause, there is growing evidence that reef habitats stimulate morphological and functional diversification in teleost fishes.     

How the worm got its pharynx: phylogeny, classification and Bayesian assessment of character evolution in Acoela

Acoela are marine microscopic worms currently thought to be the sister taxon of all other bilaterians. Acoels have long been used as models in evolutionary scenarios, and generalized conclusions about acoel and bilaterian ancestral features are frequently drawn from studies of single acoel species. There is no extensive phylogenetic study of Acoela and the taxonomy of the 380 species is chaotic. Here we use two nuclear ribosomal genes and one mitochondrial gene in combination with 37 morphological characters in an analysis of 126 acoel terminals (about one-third of the described species) to estimate the phylogeny and character evolution of Acoela. We present an estimate of posterior probabilities for ancestral character states at 31 control nodes in the phylogeny. The overall reconstruction signal based on the shape of the posterior distribution of character states was computed for all morphological characters and control nodes to assess how well these were reconstructed. The body-wall musculature appears more clearly reconstructed than the reproductive organs. Posterior similarity to the root was calculated by averaging the divergence between the posterior distributions at the nodes and the root over all morphological characters. Diopisthoporidae is the sister group to all other acoels and has the highest posterior similarity to the root. Convolutidae, including several "model" acoels, is most divergent. Finally, we present a phylogenetic classification of Acoela down to the family level where six previous family level taxa are synonymized.     

Positive correlations between molecular and morphological rates of evolution

The existence of positive associations between rates of molecular and morphological evolution (calculated from branch lengths of phylogenetic trees reconstructed using molecular and morphological characters, respectively) is important to issues of neutrality in sequence evolution, phylogenetic reconstructions assuming neutrality, and evolutionary genotype-phenotype mapping. Rates correlate positively when including branches leading to extant species (tips). Excluding tips, trends are similar, but statistical significances decrease systematically. This is due to (a) lower statistical power (excluding tips reduces sample sizes), and (b) rates are solely calculated from inaccurately reconstructed character states of extinct ancestral species, and this noise decreases correlation strengths. Correlations between molecular and morphological rates of evolution increase as more morphological characters are included for phylogenetic reconstruction. Sequence lengths apparently affect correlations along similar principles. Analyses of plant phylogenies confirm those from animals: sampling biases decrease correlations between molecular and morphological rates of evolution. Results confirm that genotype and phenotype are linked, and suggest adaptive components for molecular evolution. The discussion stresses the difficulties associated with analyses and conclusions based on data deduced from phylogenetic reconstruction.