An improved statistical method for detecting heterotachy in nucleotide sequences

The principle of heterotachy states that the substitution rate of sites in a gene can change through time. In this article, we propose a powerful statistical test to detect sites that evolve according to the process of heterotachy. We apply this test to an alignment of 1289 eukaryotic rRNA molecules to 1) determine how widespread the phenomenon of heterotachy is in ribosomal RNA, 2) to test whether these heterotachous sites are nonrandomly distributed, that is, linked to secondary structure features of ribosomal RNA, and 3) to determine the impact of heterotachous sites on the bootstrap support of monophyletic groupings. Our study revealed that with 21 monophyletic taxa, approximately two-thirds of the sites in the considered set of sequences is heterotachous. Although the detected heterotachous sites do not appear bound to specific structural features of the small subunit rRNA, their presence is shown to have a large beneficial influence on the bootstrap support of monophyletic groups. Using extensive testing, we show that this may not be due to heterotachy itself but merely due to the increased substitution rate at the detected heterotachous sites.     

Estimating index of population trend by re-sampling techniques (jackknife and bootstrap) and its application to the life table study of rice leaf roller, Cnaphalocrocis medinalis (Lepidoptera: Pyralidae)

Taking a published natural population life table of rice leaf roller, Cnaphalocrocis medinalis (Lepidoptera: Pyralidae), as an example, we estimated the population trend index, I, via re‐sampling methods (jackknife and bootstrap), determined its statistical properties and illustrated the application of these methods in determining the control effectiveness of bio‐agents and chemical insecticides. Depending on the simulation outputs, the smoothed distribution pattern of the estimates of I by delete‐1 jackknife is visually distinguishable from the normal density, but the smoothed pattern produced by delete‐d jackknife, and logarithm‐transformed smoothed patterns produced by both empirical and parametric bootstraps, matched well the corresponding normal density. Thus, the estimates of I produced by delete‐1 jackknife were not used to determine the suppressive effect of wasps and insecticides. The 95% percent confidence intervals or the narrowest 95 percentiles and Z‐test criterion were employed to compare the effectiveness of Trichogramma japonicum Ashmead and insecticides (powder, 1.5% mevinphos + 3% alpha‐hexachloro cyclohexane) against the rice leaf roller based on the estimates of I produced by delete‐d jackknife and bootstrap techniques. At α= 0.05 level, there were statistical differences between wasp treatment and control, and between wasp and insecticide treatments, if the normality is ensured, or by the narrowest 95 percentiles. However, there is still no difference between insecticide treatment and control. By Z‐test criterion, wasp treatment is better than control and insecticide treatment with P‐value < 0.01. Insecticide treatment is similar to control with P‐value > 0.2 indicating that 95% confidence intervals procedure is more conservative. Although similar conclusions may be drawn by re‐sampling techniques, such as the delta method, about the suppressive effect of trichogramma and insecticides, the normality of the estimates can be checked and guaranteed, and the correlation among sequential life stages of rice leaf roller is also considered in the estimation. Judged by the P‐values from Z‐test, the delta method is more conservative.     

Covarion structure in plastid genome evolution: a new statistical test

Covarion models of molecular evolution allow the rate of evolution of a site to vary through time. There are few simple and effective tests for covarion evolution, and consequently, little is known about the presence of covarion processes in molecular evolution. We describe two new tests for covarion evolution and demonstrate with simulations that they perform well under a wide range of conditions. A survey of covarion evolution in sequenced plastid genomes found evidence of covarion drift in at least 26 out of 57 genes. Covarion evolution is most evident in first and second codon positions of the plastid genes, and there is no evidence of covarion evolution in third codon positions. Therefore, the significant covarion tests are likely due to changes in the selective constraints of amino acids. The frequency of covarion evolution within the plastid genome suggests that covarion processes of evolution were important in generating the observed patterns of sequence variation among plastid genomes.     

Maximum likelihood inference and bootstrap methods for plant organ growth via multi-phase kinetic models and their application to maize

* BACKGROUND AND AIMS: Fitting the parameters of models of plant organ growth is a means to investigate how environmental conditions affect plant architecture. The aim of this article is to evaluate some non-linear methods for fitting the parameters of multi-phase models of the kinetics of extension of plant organs such as laminae, sheaths and internodes. * METHODS: A set of computational procedures was developed allowing parameter-fitting of multi-phase models, using the maximum likelihood criterion, in which phases are identified with reference to ontogenic processes. Two bootstrap methods were compared to assess the precision of the estimates of fitted parameters, and of functions of these parameters such as the final leaf length, and the duration and rate of the rapid extension phase. Methods were applied to an experimental dataset, representing the kinetics of laminae, sheaths and internodes along the maize shoot, for two contrasting densities. * KEY RESULTS: A set of multi-phase models was proposed to describe the extension of laminae, sheaths and internodes along the shoot. The distinguishable phases differed between laminae, sheaths and internodes. For sheaths and laminae, but not for internodes, the same model could be fitted to all phytomers along the shoot. The variation of parameters along the shoot and between density treatments, as well as derived functions such as the durations of the phases of extension, are presented for laminae. It was the duration of the fast extension period, rather than its rate, which determined the difference in final length between treatments. * CONCLUSIONS: Such methods permit a large degree of objectivity and facilitate the analysis of such rather complicated but co-ordinated datasets. The work also illustrates some natural limitations of maximum likelihood methods, and viable ways of overcoming them by including a priori knowledge in the model fitting method are discussed.     

Historical biogeography of the livebearing fish genus Poeciliopsis (Poeciliidae: Cyprinodontiformes)

To assess the historical biogeography of freshwater topminnows in the genus Poeciliopsis, we examined sequence variation in two mitochondrial genes, cytochrome b (1140 bp) and NADH subunit 2 (1047 bp). This widespread fish genus is distributed from Arizona to western Colombia, and nearly half of its 21 named species have distributions that border on the geologically active Trans-Mexican Volcanic Belt (TMVB), a region that defines the uplifted plateau (Mesa Central) of Mexico. We used the parametric bootstrap method to test the hypothesis that a single vicariant event associated with the TMVB was responsible for divergence of taxa found to the north and south of this boundary. Because the single-event hypothesis was rejected as highly unlikely, we hypothesize that at least two geological events were responsible for divergence of these species. The first (8-16 million years ago) separated ancestral populations that were distributed across the present TMVB region. A second event (2.8-6.4 million years ago) was associated with northward dispersal and subsequent vicariance of two independent southern lineages across the TMVB. The geological history of this tectonically and volcanically active region is discussed and systematic implications for the genus are outlined.     

Enzyme function less conserved than anticipated

The level of sequence similarity that implies similarity in protein structure is well established. Recently, many groups proposed thresholds for similarity in sequence implying similarity in enzymatic function. All previous results suggest the strong conservation of enzymatic function above levels of 50% pairwise sequence identity. Here, I argue that all groups substantially overestimated the conservation of enzyme function because their data sets were either too biased, or too small. An unbiased analysis suggested that less than 30% of the pair fragments above 50% sequence identity have entirely identical EC numbers. Another surprising finding was that even BLAST E-values below 10(-50) did not suffice to automatically transfer enzyme function without errors. As expected, most misclassifications originated from similarities in relatively short regions and/or from transferring annotations for different domains. Both problems cannot be corrected easily by adjusting the thresholds for automatic transfer of genome annotations. A score relating sequence identity to alignment length (distance from HSSP-threshold) outperformed statistical BLAST scores for high sequence similarity. In particular, the distance score allowed error-free transfer of enzyme function for the 10% most similar enzyme pairs. The results illustrated how difficult it is to assess the conservation of protein function and to guarantee error-free genome annotations, in general: sets with millions of pair comparisons might not suffice to arrive at statistically significant conclusions. In practice, the revised detailed estimates for the sequence conservation of enzyme function may provide important benchmarks for everyday sequence analysis and for more cautious automatic genome annotations.     

Parametric and semiparametric approaches to testing for seasonal trend in serial count data

We present two tests for seasonal trend in monthly incidence data. The first approach uses a penalized likelihood to choose the number of harmonic terms to include in a parametric harmonic model (which includes time trends and autogression as well as seasonal harmonic terms) and then tests for seasonality using a parametric bootstrap test. The second approach uses a semiparametric regression model to test for seasonal trend. In the semiparametric model, the seasonal pattern is modeled nonparametrically, parametric terms are included for autoregressive effects and a linear time trend, and a parametric bootstrap test is used to test for seasonality. For both procedures, a null distribution is generated under a null Poisson model with time trends and autoregression parameters.We apply the methods to skin melanoma incidence rates collected by the surveillance, epidemiology, and end results (SEER) program of the National Cancer Institute, and perform simulation studies to evaluate the type I error rate and power for the two procedures. These simulations suggest that both procedures are alpha-level procedures. In addition, the harmonic model/bootstrap test had similar or larger power than the semiparametric model/bootstrap test for a wide range of alternatives, and the harmonic model/bootstrap test is much easier to implement. Thus, we recommend the harmonic model/bootstrap test for the analysis of seasonal incidence data.     

When Being “Most Likely” Is Not Enough: Examining the Performance of Three Uses of the Parametric Bootstrap in Phylogenetics

Abstract I show that three parametric-bootstrap (PB) applications that have been proposed for phylogenetic analysis, can be misleading as currently implemented. First, I show that simulating a topology estimated from preliminary data in order to determine the sequence length that should allow the best tree obtained from more extensive data to be correct with a desired probability, delivers an accurate estimate of this length only in topological situations in which most preliminary trees are expected to be both correct and statistically significant, i.e. when no further analysis would be needed. Otherwise, one obtains strong underestimates of the length or similarly biased values for incorrect trees. Second, I show that PB-based topology tests that use as null hypothesis the most likely tree congruent with a pre-specified topological relationship alternative to the unconstrained most likely tree, and simulate this tree for P value estimation, produce excessive type I error (from 50% to 600% and higher) when they are applied to null data generated by star-shaped or dichotomous four-taxon topologies. Simulating the most likely star topology for P value estimation results instead in correct type-I-error production even when the null data are generated by a dichotomous topology. This is a strong indication that the star topology is the correct default null hypothesis for phylogenies. Third, I show that PB-estimated confidence intervals (CIs) for the length of a tree branch are generally accurate, although in some situations they can be strongly over- or under-estimated relative to the “true” CI. Attempts to identify a biased CI through a further round of simulations were unsuccessful. Tracing the origin and propagation of parameter estimate error through the CI estimation exercise, showed that the sparseness of site-patterns which are crucial to the estimation of pivotal parameters, can allow homoplasy to bias these estimates and ultimately the PB-based CI estimation. Concluding, I stress that statistical techniques that simulate models estimated from limited data need to be carefully calibrated, and I defend the point that pattern-sparseness assessment will be the next frontier in the statistical analysis of phylogenies, an effort that will require taking advantage of the merits of black-box maximum-likelihood approaches and of insights from intuitive, site-pattern-oriented approaches like parsimony.     

Convergence and coevolution in a mutualism: evidence from a molecular phylogeny of Ficus

Abstract.— The interaction between Ficus (Moraceae) and their pollinating wasps (Chalcidoidea: Agaonidae; more than 700 species-specific couples) is one of the most specialized mutualisms found in nature. Both partners of this interaction show extensive variation in their respective biology. Here we investigate Ficus life-history trait evolution and fig/fig wasp coadaptation in the context of a well-resolved molecular phylogeny. Mapping out variations in Ficus life-history traits on an independently derived phylogeny constructed from ribosomal DNA sequences (external and internal transcribed spacer) reveals several parallel transitions in Ficus growth habit and breeding system. Convergent trait evolution might explain the discrepancies between morphological analyses and our molecular reconstruction of the genus. Morphological characters probably correlate with growth habit and breeding system and could therefore be subject to convergent evolution. Furthermore, we reconstruct the evolution of Ficus inflorescence characters that are considered adaptations to the pollinators. Our phylogeny reveals convergences in ostiole shape, stigma morphology, and stamen:ovule ratio. Statistical tests taking into account the phylogenetic relationship of the species show that transitions in ostiole shape are correlated with variation in wasp pollinator head shape, and evolutionary changes in stigma morphology and stamen:ovule ratio correlate with changes in the pollination behavior of the associated wasp. These correlations provide evidence for reciprocal adaptations of morphological characters between these mutualistic partners that have interacted over a long evolutionary time. In light of previous ecological studies on mutualism, we discuss the adaptive significance of these correlations and what they can tell us about the coevolutionary process occurring between figs and their pollinators.