Angiosperm divergence times: the effect of genes, codon positions, and time constraints

An understanding of the evolution of modern terrestrial ecosystems requires an understanding of the dynamics associated with angiosperm evolution, including the timing of their origin and diversification into their extraordinary present-day diversity. Molecular estimates of angiosperm age have varied widely, and many substantially predate the Early Cretaceous fossil appearance of the group. In this study, the effect of different genes, codon positions, and chronological constraints on node ages are examined on divergence time estimates across seed plants, with a special focus on angiosperms. Penalized likelihood was used to estimate divergence times on a phylogenetic hypothesis for seed plants derived from Bayesian analysis, with branch lengths estimated with maximum likelihood. The plastid genes atpB, psaA, psbB, and rbcL were used individually and in combination, using first and second, third, and the three codon positions, including and excluding age constraints on 20 nodes derived from a critical examination of the land-plant fossil record. The optimal level of rate smoothing according to each unconstrained and constrained dataset was obtained with penalized likelihood. Tests for a molecular clock revealed significantly unclocklike rates in all datasets. Addition of fossil constraints resulted in even greater departures from constancy. Consistently with significant deviations from a clock, estimated optimal smoothing values were low, but a strict correlation between rate heterogeneity and optimal smoothing value was not found. Age estimates for nodes across the phylogeny varied, sometimes substantially, with gene and codon position. Nevertheless, estimates based on the four concatenated genes are very similar to the mean of the four individual gene estimates. For any given node, unconstrained age estimates are more variable than constrained estimates and are frequently younger than well-substantiated fossil members of the clade. Constrained estimates of ages of clades are older than unconstrained estimates and oldest fossil representatives, sometimes substantially so. Angiosperm age estimates decreased as rate smoothing increased. Whereas the range of unconstrained angiosperm age estimates spans the fossil age of the clade, the range of constrained estimates is narrower (and older) than the earliest angiosperm fossils. Results unambiguously indicate the relevance of constraints in reducing the variability of ages derived from different partitions of the data and diminishing the effect of the smoothing parameter. Constrained optimizations of divergence times and substitution rates across the phylogeny suggest appreciably different evolutionary dynamics for angiosperms and for gymnosperms. Whereas the gymnosperm crown group originated shortly after the origin of seed plants, a long time elapsed before the origin of crown group angiosperms. Although absolute age estimates of angiosperms and angiosperm clades are older than their earliest fossils, the estimated pace of phylogenetic diversification largely agrees with the rapid appearance of angiosperm lineages in stratigraphic sequences.     

INCREASED RATES OF MOLECULAR EVOLUTION IN AN EQUATORIAL PLANT CLADE: AN EFFECT OF ENVIRONMENT OR PHYLOGENETIC NONINDEPENDENCE?

A recent study of environmental effects on rates of molecular evolution in the plant subgenus Mearnsia shows that species occurring in more equatorial latitudes have higher rates of substitution in rDNA sequences as compared to their more southerly congeners (Wright et al. 2003). However, we believe that the statistical approach employed by Wright et al. (2003) insufficiently accounts for the phylogenetic nonindependence of the species examined, given that all six equatorial species of Mearnsia form a clade. To distinguish between the effect of latitude and that of phylogenetic nonindependence, we have employed a variety of comparative approaches that use independent contrasts to test for an effect of environment across this entire subgenus. We find very little evidence for an effect of latitude on rate of molecular evolution using these approaches and believe that the shared evolutionary history of the clade is a plausible explanation of the apparent rate difference between equatorial and subequatorial Mearnsia species.     

A computer-generated supercoiled model of the pUC19 plasmid

DNA models have become a powerful tool in the simulation of radiation-induced molecular damage. Here, a computer code was developed which calculates the coordinates of individual atoms in supercoiled plasmid DNA. In this prototype study, the known base-pair sequence of the pUC19 plasmid has been utilized. The model was built in a three-step process. Firstly, a Monte Carlo simulation was performed to shape a segment chain skeleton. Checks on elastic energy, distance and unknotting were applied. The temperature was considered in two different ways: (1) it was kept constant at 293 K and (2) it was gradually reduced from 350 K to less than 10 K. Secondly, a special smoothing procedure was introduced here to remove the edges from the segment chain without changing the total curve length while avoiding the production of overshooting arcs. Finally, the base pair sequence was placed along the smoothed segment chain and the positions of all the atoms were calculated. As a first result, a few examples of the supercoiled plasmid models will be presented, demonstrating the strong influence of appropriate control of the system temperature.     

Statistical analysis of temporal evolution in single-neuron firing rates

A fundamental methodology in neurophysiology involves recording the electrical signals associated with individual neurons within brains of awake behaving animals. Traditional statistical analyses have relied mainly on mean firing rates over some epoch (often several hundred milliseconds) that are compared across experimental conditions by analysis of variance. Often, however, the time course of the neuronal firing patterns is of interest, and a more refined procedure can produce substantial additional information. In this paper we compare neuronal firing in the supplementary eye field of a macaque monkey across two experimental conditions. We take the electrical discharges, or 'spikes', to be arrivals in a inhomogeneous Poisson process and then model the firing intensity function using both a simple parametric form and more flexible splines. Our main interest is in making inferences about certain characteristics of the intensity, including the timing of the maximal firing rate. We examine data from 84 neurons individually and also combine results into a hierarchical model. We use Bayesian estimation methods and frequentist significance tests based on a nonparametric bootstrap procedure. We are thereby able to conclude that a substantial fraction of the neurons exhibit important temporal differences in firing intensity across the two conditions, and we quantify the effect across the population of neurons.     

On Gibbs sampling for state space models

We show how to use the Gibbs sampler to carry out Bayesian inferenceon a linear state space model with errors that are a mixtureof normals and coefficients that can switch over time. Our approachsimultaneously generates the whole of the state vector giventhe mixture and coefficient indicator variables and simultaneouslygenerates all the indicator variables conditional on the statevectors. The states are generated efficiently using the Kalmanfilter. We illustrate our approach by several examples and empiricallycompare its performance to another Gibbs sampler where the statesare generated one at a time. The empirical results suggest thatour approach is both practical to implement and dominates theGibbs sampler that generates the states one at a time.     

Assessing the adequacy of variance function in heteroscedastic regression models

Heteroscedastic data arise in many applications. In heteroscedastic regression analysis, the variance is often modeled as a parametric function of the covariates or the regression mean. We propose a kernel-smoothing type nonparametric test for checking the adequacy of a given parametric variance structure. The test does not need to specify a parametric distribution for the random errors. It is shown that the test statistic has an asymptotical normal distribution under the null hypothesis and is powerful against a large class of alternatives. We suggest a simple bootstrap algorithm to approximate the distribution of the test statistic in finite sample size. Numerical simulations demonstrate the satisfactory performance of the proposed test. We also illustrate the application by the analysis of a radioimmunoassay data set.