The effect of topology on estimates of among-site rate variation

Among-site rate variation, as quantified by the gamma-distribution shape parameter,a or , and the ratio of transition rate to transversion rate (Ts/Tv) influence phylogenetic inference. We examine the effect of topology on estimates of these two parameters in 12S rRNA sequences from nine species of mice belonging to the generaOnychomys andPeromyscus by generating 100 random topologies and estimating these parameters using parsimony and maximum-likelihood methods for each of the random topologies. The parsimony-based estimate ofTs/Tv from the well-corroborated topology falls within the distribution of estimates based on random topologies, whereas the maximum-likelihood estimate ofTs/Tv based on the well-corroborated topology lies well outside the distribution of estimates derived from random topologies. TheTs/Tv ratio derived via maximumlikelihood estimation is three times the parsimony-based estimate, suggesting that parsimony-based estimates are severe underestimates even when the correct topology is used. Both parsimony- and likelihood-based estimates of the gamma-distribution shape parameter () are sensitive to topology because the best estimates based on the well-corroborated topology are well outside the distributions of estimates derived from random topologies for both methods. We show that the reason for topology dependence is the presence of long internal branches in the underlying topology.     

The effects of nucleotide substitution model assumptions on estimates of nonparametric bootstrap support

The use of parameter-rich substitution models in molecular phylogenetics has been criticized on the basis that these models can cause a reduction both in accuracy and in the ability to discriminate among competing topologies. We have explored the relationship between nucleotide substitution model complexity and nonparametric bootstrap support under maximum likelihood (ML) for six data sets for which the true relationships are known with a high degree of certainty. We also performed equally weighted maximum parsimony analyses in order to assess the effects of ignoring branch length information during tree selection. We observed that maximum parsimony gave the lowest mean estimate of bootstrap support for the correct set of nodes relative to the ML models for every data set except one. For several data sets, we established that the exact distribution used to model among-site rate variation was critical for a successful phylogenetic analysis. Site-specific rate models were shown to perform very poorly relative to gamma and invariable sites models for several of the data sets most likely because of the gross underestimation of branch lengths. The invariable sites model also performed poorly for several data sets where this model had a poor fit to the data, suggesting that addition of the gamma distribution can be critical. Estimates of bootstrap support for the correct nodes often increased under gamma and invariable sites models relative to equal rates models. Our observations are contrary to the prediction that such models cause reduced confidence in phylogenetic hypotheses. Our results raise several issues regarding the process of model selection, and we briefly discuss model selection uncertainty and the role of sensitivity analyses in molecular phylogenetics.     

Turn designation, sampling rate and the misidentification of power laws in movement path data using maximum likelihood estimates

Many authors have claimed to observe animal movement paths that appear to be Lévy walks, i.e. a random walk where the distribution of move lengths follows an inverse power law. A Lévy walk is known to be the optimal search strategy of a particular class of random walks in certain environments; hence, it is important to distinguish correctly between Lévy walks and other types of random walks in observed animal movement paths. Evidence of a power law distribution in the step length distribution of observed animal movement paths is often used to classify a particular movement path as a Lévy walk. However, there is some doubt about the accuracy of early studies that apparently found Lévy walk behaviour. A recently accepted method to determine whether a movement path truly exhibits Lévy walk behaviour is based on an analysis of move lengths with a maximum likelihood estimate using Akaike weights. Here, we show that simulated (non-Lévy) random walks representing different types of animal movement behaviour (a composite correlated random walk; pooled data from a set of random walks with different levels of correlation and three-dimensional correlated random walks projected into one dimension) can all show apparent power law behaviour typical of Lévy walks when using the maximum likelihood estimation method. The probability of the movement path being identified as having a power law step distribution is related to both the sampling rate used by the observer and the way that ‘turns’ or ‘reorientations’ in the movement path are designated. However, identification is also dependent on the nature and properties of the simulated path, and there is currently no standard method of observation and analysis that is robust for all cases. Our results indicate that even apparently robust maximum likelihood methods can lead to a mismatch between pattern and process, as paths arising from non-Lévy walks exhibit Lévy-like patterns.     

Estimating the rate of gamergate turnover in the queenless ant Diacamma cyaneiventre using a maximum likelihood model

In monogynous ants, the death of the queen generally implies the death of the colony. However, queen replacement by either unrelated or related queen has been described in few species. In queenless ants from the genus Diacamma, the single reproductive worker (gamergate) is replaced by one of her daughters (or occasionally by a sister). From a long-term genetic survey of nests of D. cyaneiventre, we estimated the rate of gamergate turnover as well as the lifespan of workers and gamergate tenure using a maximum likelihood model developed for this purpose. We specifically compared the genotypes of two cohorts of workers sampled at 2 and 16 months interval from the same nests, using five microsatellite markers. To improve the accuracy of the estimates, we also used in the model the nests from the same population sampled only once and analysed by André et al. (2001). The model indicates that the possibility of the same nest not sheltering the same colony at two different sampling dates (colony turnover) was not significantly different from zero in our sample. The likelihood of the model was maximal for a probability of gamergate change p_γ = 0.005 per day (i.e. a gamergate tenure of 200 days) and a worker lifespan w=60 days, indicating that the gamergate ‘s tenure is about 3 times longer than workers’ expected lifespan in the population studied. Moreover, the genetic analysis of the gamergate and brood in three colonies excavated completely, reveals that colony fission can occur just after a gamergate replacement with the sister of the new gamergate reproducing in the new propagule. Received 12 October 2005; revised 7 December 2005; accepted 5 January 2006.     

The effect of branch lengths on phylogeny: an empirical study using highly conserved orthologs from mammalian genomes

Phylogenetic analyses were applied to 269 families of putative orthologs represented by a single member in the genomes of human, mouse, dog, and chicken. Five methods were used: maximum parsimony (NP), neighbor-joining (NJ) with Poisson and Gamma distances; and maximum likelihood (ML) with JTT and JTT+gamma models. When applied to the concatenated sequence of all families, all methods strongly supported a tree in which mouse branched before human and dog. In analyses of individual families, the same topology was supported more than any other. Although there was evidence of an increased rate of amino acid replacement in the mouse lineage in comparison to the other two mammals, there was no evidence that support for the mouse's basal position was due to long-branch attraction; rather, this topology was seen in the families with the lowest rate variation among the three mammalian branches. In families with highly divergent mouse sequences, ML with both JTT and JTT+gamma and NJ with the gamma distance tended to support a topology in which the dog, rather than the mouse, branched first. Thus, in these data, a tendency of long and short branches to cluster together ("opposite-branch attraction") seemed to be more of a problem than long-branch attraction.     

Stage‐specific probabilistic phenology model of Cydia pomonella (Lepidoptera: Tortricidae) using laboratory maximum likelihood parameter estimates

In this study, a probabilistic degree‐day phenology model has been developed for the codling moth, Cydia pomonella, and calibrated using data from laboratory growth studies. The model is further used to predict the succession and overlapping of certain biological events of C. pomonella in probabilistic‐physiological time scale in northern Greece fruit orchards. The model satisfactorily predicts the stage‐specific pest population dynamics, including egg laying and hatching, the occurrence of larvae and pupae stages and the emergence of adults. According to the model projections for the adult flights, there is a very high probability, p = 0.999, of observing adults of the first flight generation until 333 degree‐days (DD), but a very low probability of finding adults of the second flight generation. Moreover, at 575 DD, the probability of finding an individual to lay eggs is p = 0.15. However, there is nearly the same probability of egg hatch, p = 0.36, and larval completion p = 0.313, while at the same time, the probability of pupal completion is very low, p = 0.001. The above model predictions were validated using field data for the adult stage emergence as well as for the percentage of larval damage providing satisfactory results considering that larval emergence prediction was close to actual fruit damage observed in field. This information is very important considering that IPM programs rely on the use of biorational compounds, such as IGRs and bio‐toxins which are stage selective and often have a shorter residual activity than the preceding broad‐spectrum insecticides.     

The devil in the details: interactions between the branch-length prior and likelihood model affect node support and branch lengths in the phylogeny of the Psoraceae

In popular use of Bayesian phylogenetics, a default branch-length prior is almost universally applied without knowing how a different prior would have affected the outcome. We performed Bayesian and maximum likelihood (ML) inference of phylogeny based on empirical nucleotide sequence data from a family of lichenized ascomycetes, the Psoraceae, the morphological delimitation of which has been controversial. We specifically assessed the influence of the combination of Bayesian branch-length prior and likelihood model on the properties of the Markov chain Monte Carlo tree sample, including node support, branch lengths, and taxon stability. Data included two regions of the mitochondrial ribosomal RNA gene, the internal transcribed spacer region of the nuclear ribosomal RNA gene, and the protein-coding largest subunit of RNA polymerase II. Data partitioning was performed using Bayes' factors, whereas the best-fitting model of each partition was selected using the Bayesian information criterion (BIC). Given the data and model, short Bayesian branch-length priors generate higher numbers of strongly supported nodes as well as short and topologically similar trees sampled from parts of tree space that are largely unexplored by the ML bootstrap. Long branch-length priors generate fewer strongly supported nodes and longer and more dissimilar trees that are sampled mostly from inside the range of tree space sampled by the ML bootstrap. Priors near the ML distribution of branch lengths generate the best marginal likelihood and the highest frequency of "rogue" (unstable) taxa. The branch-length prior was shown to interact with the likelihood model. Trees inferred under complex partitioned models are more affected by the stretching effect of the branch-length prior. Fewer nodes are strongly supported under a complex model given the same branch-length prior. Irrespective of model, internal branches make up a larger proportion of total tree length under the shortest branch-length priors compared with longer priors. Relative effects on branch lengths caused by the branch-length prior can be problematic to downstream phylogenetic comparative methods making use of the branch lengths. Furthermore, given the same branch-length prior, trees are on average more dissimilar under a simple unpartitioned model compared with a more complex partitioned models. The distribution of ML branch lengths was shown to better fit a gamma or Pareto distribution than an exponential one. Model adequacy tests indicate that the best-fitting model selected by the BIC is insufficient for describing data patterns in 5 of 8 partitions. More general substitution models are required to explain the data in three of these partitions, one of which also requires nonstationarity. The two mitochondrial ribosomal RNA gene partitions need heterotachous models. We found no significant correlations between, on the one hand, the amount of ambiguous data or the smallest branch-length distance to another taxon and, on the other hand, the topological stability of individual taxa. Integrating over several exponentially distributed means under the best-fitting model, node support for the family Psoraceae, including Psora, Protoblastenia, and the Micarea sylvicola group, is approximately 0.96. Support for the genus Psora is distinctly lower, but we found no evidence to contradict the current classification.     

FastMG: a simple,fast, and accurate maximum likelihood procedure to estimate amino acid replacement rate matrices from large data sets

Background

Amino acid replacement rate matrices are a crucial component of many protein analysis systems such as sequence similarity search, sequence alignment, and phylogenetic inference. Ideally, the rate matrix reflects the mutational behavior of the actual data under study; however, estimating amino acid replacement rate matrices requires large protein alignments and is computationally expensive and complex. As a compromise, sub-optimal pre-calculated generic matrices are typically used for protein-based phylogeny. Sequence availability has now grown to a point where problem-specific rate matrices can often be calculated if the computational cost can be controlled.

Results

The most time consuming step in estimating rate matrices by maximum likelihood is building maximum likelihood phylogenetic trees from protein alignments. We propose a new procedure, called FastMG, to overcome this obstacle. The key innovation is the alignment-splitting algorithm that splits alignments with many sequences into non-overlapping sub-alignments prior to estimating amino acid replacement rates. Experiments with different large data sets showed that the FastMG procedure was an order of magnitude faster than without splitting. Importantly, there was no apparent loss in matrix quality if an appropriate splitting procedure is used.

Conclusions

FastMG is a simple, fast and accurate procedure to estimate amino acid replacement rate matrices from large data sets. It enables researchers to study the evolutionary relationships for specific groups of proteins or taxa with optimized, data-specific amino acid replacement rate matrices. The programs, data sets, and the new mammalian mitochondrial protein rate matrix are available at http://fastmg.codeplex.com.     

Multilocus analysis of variation using a large empirical data set: phenylpropanoid pathway genes in Arabidopsis thaliana

Detecting the signature of adaptation on nucleotide variation is often difficult in species that like Arabidopsis thaliana might have a complex demographic history. Recent re-sequencing surveys in this species provided genome-wide information that would mainly reflect its demographic history. We have used a large empirical data set (LED) as well as multilocus coalescent simulations to analyse sequence variation at loci involved in the phenylpropanoid pathway of this species. We surveyed and examined DNA sequence variation at nine of these loci (about 19.7 kb) in 23 accessions of A. thaliana and one accession of its closely related species Arabidopsis lyrata . Nucleotide variation was lower at nonsynonymous sites than at silent sites in all loci, indicating generalized functional constraint at the protein level. No association between variation and position in the metabolic pathway was detected. When the data were contrasted against the standard neutral model, significant deviations for silent variation were detected with Tajima's D , Fu's F_S and Fay and Wu's H multilocus test statistics. These deviations were in the same direction than in previous large-scale multilocus analyses, suggesting a genome-wide effect. When the nine-locus data set was contrasted against the large empirical data set, the level (Watterson's θ) and pattern of variation (Tajima's D ) detected in these loci did not deviate either at the single-locus or multilocus level from the corresponding empirical distributions. These results would support an important role of the demographic history of A. thaliana in shaping nucleotide variation at the nine studied phenylpropanoid loci. The potential and limitations of the empirical distribution approach are discussed.     

Estimating amino acid substitution models: a comparison of Dayhoff's estimator, the resolvent approach and a maximum likelihood method.

Evolution of proteins is generally modeled as a Markov process acting on each site of the sequence. Replacement frequencies need to be estimated based on sequence alignments. Here we compare three approaches: First, the original method by Dayhoff, Schwartz, and Orcutt (1978) Atlas Protein Seq. Struc. 5:345-352, secondly, the resolvent method (RV) by Müller and Vingron (2000) J. Comput. Biol. 7(6):761-776, and finally a maximum likelihood approach (ML) developed in this paper. We evaluate the methods using a highly divergent and inhomogeneous set of sequence alignments as an input to the estimation procedure. ML is the method of choice for small sets of input data. Although the RV method is computationally much less demanding it performs only slightly worse than ML. Therefore, it is perfectly appropriate for large-scale applications.     

Marijuana: effects on pulse rate, subjective estimates of intoxication and multiple measures of memory

Twelve experienced marijuana users received marijuana cigarettes containing 10 mg Δ⁹-THC or placebo in two experimental sessions each separated by a one week interval. The effects of both treatments on pulse rate, subjective estimates of intoxication, multiple measures of memory including free, serial and delayed recall, final free recall, and recognition memory were assessed. Pulse rate and subjective ratings were elevated significantly following intoxication with active marijuana in comparison to placebo. Each of the three types of recall were significantly reduced following intoxication with marijuana but no differential effects of drug on recall condition were noted. Intrusion errors were elevated on the final free recall test following intoxication but recognition memory was unaffected.     

The effects of temporal variation in predation risk on anti-predator behaviour: an empirical test using marine snails.

Foraging animals must often balance the conflicting demands of finding food and avoiding predators. Temporal variation in predation risk is expected to influence how animals allocate time to these behaviours. Counterintuitively, the proportion of time spent foraging during both high- and low-risk periods should increase with increasing time exposed to high risk. We tested this prediction using intertidal marine snails (Littorina spp.) that were exposed to temporal variation in perceived predation risk from crabs (Cancer productus and Cancer magister). Our results were consistent with those predicted for high-risk, but not low-risk, periods. During high-risk periods, a greater number of snails foraged (versus those that left the water or remained in their shells) as time at high perceived risk increased. For low-risk periods, there was no relationship between the number of snails foraging and time at high risk. This might be due to snails in all treatments foraging maximally in the low-risk periods. As a consequence, the difference in the number of snails foraging between high- and low-risk periods decreased with increasing time subject to high risk. These results indicate that the commonly used protocol of exposing foragers to a single pulse of heightened risk might tend to overestimate their typical investment in anti-predator behaviour.     

Experimental investigation of branch flow ratio, angle, and Reynolds number effects on the pressure and flow fields in arterial branch models

An experimental investigation was carried out to acquire an understanding of local pressure changes and flow along the main lumen of arterial branch models similar to the femoral artery of man with three different branch angles (30, 60, and 90 deg) and side branch to the main lumen diameter ratio of 0.4. Effects of branch to main lumen flow rate ratios and physiological Reynolds numbers were found to be significant on the local pressure changes, while that of branch angle was also found to be important. The flow visualization study revealed that the flow separated in the main lumen near the branch junction when the pressure rise coefficient along the main lumen was above a critical value (i.e., 0.35 - 0.46), which was observed to be a function of the Reynolds number. The critical value of the branch to main lumen flow rate ratio was found to be about 0.38 - 0.44 also depending on the Reynolds number. Time averaged pressure distributions for pulsatile flow were similar in trend to steady flow values although they differed somewhat in detail in the main lumen in the branch region.     

Evidence of seasonal variation in longitudinal growth of height in a sample of boys from Stuttgart Carlsschule, 1771-1793, using combined principal component analysis and maximum likelihood principle

Recent progress in modelling individual growth has been achieved by combining the principal component analysis and the maximum likelihood principle. This combination models growth even in incomplete sets of data and in data obtained at irregular intervals. We re-analysed late 18th century longitudinal growth of German boys from the boarding school Carlsschule in Stuttgart. The boys aged 6-23 years, were measured at irregular 3-12 monthly intervals during the period 1771-1793. At the age of 18 years, mean height was 1652 mm, but height variation was large. The shortest boy reached 1474 mm, the tallest 1826 mm. Measured height closely paralleled modelled height, with mean difference of 4 mm, SD 7 mm. Seasonal height variation was found. Low growth rates occurred in spring and high growth rates in summer and autumn. The present study demonstrates that combining the principal component analysis and the maximum likelihood principle enables growth modelling in historic height data also.     

Testing for genetic evidence of population expansion and contraction: an empirical analysis of microsatellite DNA variation using a hierarchical Bayesian model

The role of past climatic change in shaping the distributions of tropical rain forest vertebrates is central to long-standing hypotheses about the legacy of the Quaternary ice ages. One approach to testing such hypotheses is to use genetic data to infer the demographic history of codistributed species. Population genetic theory that relates the structure of allelic genealogies to historical changes in effective population size can be used to detect a past history of demographic expansion or contraction. The fruit bats Cynopterus sphinx and C. brachyotis (Chiroptera: Pteropodidae) exhibit markedly different distribution patterns across the Indomalayan region and therefore represent an exemplary species pair to use for such tests. The purpose of this study was to test alternative hypotheses about historical patterns of demographic expansion and contraction in C. sphinx and C. brachyotis using a coalescent-based analysis of microsatellite variation. Specifically, we used a hierarchical Bayesian model based on Markov chain Monte Carlo simulations to estimate the posterior distribution of genealogical and demographic parameters. The results revealed strong evidence for population contraction in both species. Evidence for a population contraction in C. brachyotis was expected on the basis of biogeographic considerations. However, similar evidence for population contraction in C. sphinx does not support the hypothesis that this species underwent a pronounced range expansion during the late Quaternary. Genetic evidence for population decline may reflect the consequences of habitat destruction on a more recent time scale.     

Estimation of disease prevalence, true positive rate, and false positive rate of two screening tests when disease verification is applied on only screen-positives: a hierarchical model using multi-center data

Objectives: A model is proposed to estimate and compare cervical cancer screening test properties for third world populations when only subjects with a positive screen receive the gold standard test. Two fallible screening tests are compared, VIA and VILI. Methods: We extend the model of Berry et al. [1] to the multi-site case in order to pool information across sites and form better estimates for prevalences of cervical cancer, the true positive rates (TPRs), and false positive rates (FPRs). For 10 centers in five African countries and India involving more than 52,000 women, Bayesian methods were applied when gold standard results for subjects who screened negative on both tests were treated as missing. The Bayesian methods employed suitably correct for the missing screen negative subjects. The study included gold standard verification for all cases, making it possible to validate model-based estimation of accuracy using only outcomes of women with positive VIA or VILI result (ignoring verification of double negative screening test results) with the observed full data outcomes. Results: Across the sites, estimates for the sensitivity of VIA ranged from 0.792 to 0.917 while for VILI sensitivities ranged from 0.929 to 0.977. False positive estimates ranged from 0.056 to 0.256 for VIA and 0.085 to 0.269 for VILI. The pooled estimates for the TPR of VIA and VILI are 0.871 and 0.968, respectively, compared to the full data values of 0.816 and 0.918. Similarly, the pooled estimates for the FPR of VIA and VILI are 0.134 and 0.146, respectively, compared to the full data values of 0.144 and 0.146. Globally, we found VILI had a statistically significant higher sensitivity but no statistical difference for the false positive rates could be determined. Conclusion: Hierarchical Bayesian methods provide a straight forward approach to estimate screening test properties, prevalences, and to perform comparisons for screening studies where screen negative subjects do not receive the gold standard test. The hierarchical model with random effects used to analyze the sites simultaneously resulted in improved estimates compared to the single-site analyses with improved TPR estimates and nearly identical FPR estimates to the full data outcomes. Furthermore, higher TPRs but similar FPRs were observed for VILI compared to VIA.     

Exploring the effects of gene dosage on mandible shape in mice as a model for studying the genetic basis of natural variation

Mandible shape in the mouse is a complex trait that is influenced by many genetic factors. However, little is known about the action of single genes on adult mandible shape so far, since most developmentally relevant genes are already required during embryogenesis, i.e., knockouts lead to embryonic death or severe deformations, before the mandible is fully formed. We employ here a geometric morphometric approach to identify subtle phenotypic differences caused by dosage effects of candidate genes. We use mouse strains with specific gene modifications (knockouts and knockins) to compare heterozygous animals with controls from the same stock, which is expected to be equivalent to a change of gene expression of the respective locus. Such differences in expression level are also likely to occur as part of the natural variation. We focus on Bmp pathway genes (Bmp4, its antagonist Noggin, and combinations of Bmp5-7 genotypes), but include also two other developmental control genes suspected to affect mandible development in some way (Egfr and Irf6). In addition, we study the effects of Hoxd13, as well as an extracellular matrix constituent (Col2a1). We find that subtle but significant shape differences are caused by differences in gene dosage of several of these genes. The changes seen for Bmp4 and Noggin are partially compatible with the action of these genes known from birds and fish. We find significant shape changes also for Hoxd13, although this gene has so far only been implicated in skeletal patterning processes of the limbs. Comparing the effect sizes of gene dosage changes to the variation found in natural populations of mice as well as quantitative trait loci (QTL) effects on mandible shape, we find that the effect sizes caused by gene dosage changes are at the lower end of the spectrum of natural variation, but larger than the average additive effects found in QTL studies. We conclude that studying gene dosage effects have the potential to provide new insights into aspects of craniofacial development, variation, and evolution.     

Landscape influences on dispersal behaviour: a theoretical model and empirical test using the fire salamander,Salamandra infraimmaculata

When populations reside within a heterogeneous landscape, isolation by distance may not be a good predictor of genetic divergence if dispersal behaviour and therefore gene flow depend on landscape features. Commonly used approaches linking landscape features to gene flow include the least cost path (LCP), random walk (RW), and isolation by resistance (IBR) models. However, none of these models is likely to be the most appropriate for all species and in all environments. We compared the performance of LCP, RW and IBR models of dispersal with the aid of simulations conducted on artificially generated landscapes. We also applied each model to empirical data on the landscape genetics of the endangered fire salamander, Salamandra infraimmaculata, in northern Israel, where conservation planning requires an understanding of the dispersal corridors. Our simulations demonstrate that wide dispersal corridors of the low-cost environment facilitate dispersal in the IBR model, but inhibit dispersal in the RW model. In our empirical study, IBR explained the genetic divergence better than the LCP and RW models (partial Mantel correlation 0.413 for IBR, compared to 0.212 for LCP, and 0.340 for RW). Overall dispersal cost in salamanders was also well predicted by landscape feature slope steepness (76 %), and elevation (24 %). We conclude that fire salamander dispersal is well characterised by IBR predictions. Together with our simulation findings, these results indicate that wide dispersal corridors facilitate, rather than hinder, salamander dispersal. Comparison of genetic data to dispersal model outputs can be a useful technique in inferring dispersal behaviour from population genetic data.     

Detecting the effects of diversity on measures of ecosystem function: experimental design, null models and empirical observations

Here we present a novel experimental approach to examine the relationship between diversity and ecosystem function. We develop four null predictive models, with which to differentiate between the 'sampling effect'– the chance inclusion of a highly productive species, and 'species complementarity'– the complementary use of resources by species that differ in their niche or resource use. We investigate the effects of manipulating species and functional richness on ecosystem function in a marine benthic system and using empirical data from our own experiments we illustrate the application of these models.