A class of permutation tests for stratified survival data

We propose a class of permutation tests for stratified survival data. The tests are derived using the framework of Fay and Shih (1998, Journal of the American Statistical Association 93, 387-396), which creates tests by permuting scores based on a functional of estimated distribution functions. Here the estimated distribution function for each possibly right-, left-, or interval-censored observation is based on a shrinkage estimator similar to the nonparametric empirical estimator of Ghosh, Lahiri, and Tiwari (1989, Communications in Statistics--Theory and Methods 18, 121-146), and permutation is carried out within strata. The proposed test with a weighted Mann-Whitney functional is similar to the permutation form of the stratified log-rank test when there is a large strata effect or the sample size in each stratum is large and is similar to the permutation form of the ordinary log-rank test when there is little strata effect. Thus, the proposed test unifies the advantages of both the stratified and ordinary log-rank tests. By changing the functional, we may obtain a stratified Prentice-Wilcoxon test or a difference in means test with similar unifying properties. We show through simulations the advantage of the proposed test over existing tests for uncensored and right-censored data.     

Two-part permutation tests for DNA methylation and microarray data

Background  

One important application of microarray experiments is to identify differentially expressed genes. Often, small and negative expression levels were clipped-off to be equal to an arbitrarily chosen cutoff value before a statistical test is carried out. Then, there are two types of data: truncated values and original observations. The truncated values are not just another point on the continuum of possible values and, therefore, it is appropriate to combine two statistical tests in a two-part model rather than using standard statistical methods. A similar situation occurs when DNA methylation data are investigated. In that case, there are null values (undetectable methylation) and observed positive values. For these data, we propose a two-part permutation test.     

Vicariance and dispersal effects on phylogeographic structure and speciation in a widespread estuarine invertebrate

Vicariance and dispersal can strongly influence population genetic structure and allopatric speciation, but their importance in the origin of marine biodiversity is unresolved. In transitional estuarine environments, habitat discreteness and dispersal barriers could enhance divergence and provide insight to evolutionary mechanisms underlying marine and freshwater biodiversity. We examined this by assessing phylogeographic structure in the widespread amphipod Gammarus tigrinus across 13 estuaries spanning its northwest Atlantic range from Quebec to Florida. Mitochondrial cytochrome c oxidase I and nuclear internal transcribed spacer 1 phylogenies supported deep genetic structure consistent with Pliocene separation and cryptic northern and southern species. This break occurred across the Virginian-Carolinian coastal biogeographic zone, where an oceanographic discontinuity may restrict gene flow. Ten estuarine populations of the northern species occurred in four distinct clades, supportive of Pleistocene separation. Glaciation effects on genetic structure of estuarine populations are largely unknown, but analysis of molecular variance (AMOVA) supported a phylogeographic break among clades in formerly glaciated versus nonglaciated areas across Cape Cod, Massachusetts. This finding was concordant with patterns in other coastal species, though there was no significant relationship between latitude and genetic diversity. This supports Pleistocene vicariance events and divergence of clades in different northern glacial refugia. AMOVA results and private haplotypes in most populations support an allopatric distribution across estuaries. Clade mixture zones are consistent with historical colonization and human-mediated transfer. An isolation-by-distance model of divergence was detected after we excluded a suspected invasive haplotype in the St. Lawrence estuary. The occurrence of cryptic species and divergent population structure support limited dispersal, dispersed habitat distribution, and historical factors as important determinants of estuarine speciation and diversification.     

Model-derived dispersal pathways from multiple source populations explain variability of invertebrate larval supply

Background

Predicting the spatial and temporal patterns of marine larval dispersal and supply is a challenging task due to the small size of the larvae and the variability of oceanographic processes. Addressing this problem requires the use of novel approaches capable of capturing the inherent variability in the mechanisms involved.

Methodology/Principal Findings

In this study we test whether dispersal and connectivity patterns generated from a bio-physical model of larval dispersal of the crab Carcinus maenas, along the west coast of the Iberian Peninsula, can predict the highly variable daily pattern of wind-driven larval supply to an estuary observed during the peak reproductive season (March–June) in 2006 and 2007. Cross-correlations between observed and predicted supply were significant (p<0.05) and strong, ranging from 0.34 to 0.81 at time lags of −6 to +5 d. Importantly, the model correctly predicted observed cross-shelf distributions (Pearson r = 0.82, p<0.001, and r = 0.79, p<0.01, in 2006 and 2007) and indicated that all supply events were comprised of larvae that had been retained within the inner shelf; larvae transported to the outer shelf and beyond never recruited. Estimated average dispersal distances ranged from 57 to 198 km and were only marginally affected by mortality.

Conclusions/Significance

The high degree of predicted demographic connectivity over relatively large geographic scales is consistent with the lack of genetic structuring in C. maenas along the Iberian Peninsula. These findings indicate that the dynamic nature of larval dispersal can be captured by mechanistic biophysical models, which can be used to provide meaningful predictions of the patterns and causes of fine-scale variability in larval supply to marine populations.     

Using weighted permutation scores to detect differential gene expression with microarray data

A class of nonparametric statistical methods, including a nonparametric empirical Bayes (EB) method, the Significance Analysis of Microarrays (SAM) and the mixture model method (MMM) have been proposed to detect differential gene expression for replicated microarray experiments. They all depend on constructing a test statistic, for example, a t-statistic, and then using permutation to draw inferences. However, due to special features of microarray data, using standard permutation scores may not estimate the null distribution of the test statistic well, leading to possibly too conservative inferences. We propose a new method of constructing weighted permutation scores to overcome the problem: posterior probabilities of having no differential expression from the EB method are used as weights for genes to better estimate the null distribution of the test statistic. We also propose a weighted method to estimate the false discovery rate (FDR) using the posterior probabilities. Using simulated data and real data for time-course microarray experiments, we show the improved performance of the proposed methods when implemented in MMM, EB and SAM.     

Data-dependent permutation techniques for the analysis of ecological data

Two distribution-free permutation techniques are described for the analysis of ecological data. These methods are completely data dependent and provide analyses for the commonly-encountered completely-randomized and randomized-block designs in a multivariate framework. Euclidean distance forms the basis of both techniques, providing consistency with the observed distribution of data in many ecological studies.Abbreviations MRPP= Multiresponse permutation procedure - MRBP= Ibid, randomized block analog     

Improving animal phylogenies with genomic data

Since the first animal genomes were completely sequenced ten years ago, evolutionary biologists have attempted to use the encoded information to reconstruct different aspects of the earliest stages of animal evolution. One of the most important uses of genome sequences is to understand relationships between animal phyla. Despite the wealth of data available, ranging from primary sequence data to gene and genome structures, our lack of understanding of the modes of evolution of genomic characters means that using these data is fraught with potential difficulties, leading to errors in phylogeny reconstruction. Improved understanding of how different character types evolve, the use of this knowledge to develop more accurate models of evolution, and denser taxonomic sampling, are now minimizing the sources of error. The wealth of genomic data now being produced promises that a well-resolved tree of the animal phyla will be available in the near future.     

Foundations of gregariousness: a dispersal polymorphism among the planktonic larvae of a marine invertebrate

Theory predicts that selection should favor genotypes that can vary their tendency to disperse in habitats that are spatially or temporally variable or those that remain near their carrying capacity. Although many marine habitats appear to fit these criteria, confirmed examples of dispersal polymorphism among marine invertebrates are exceedingly rare. Competent larvae of the gregarious tubeworm, Hydroides dianthus, settle specifically in response to living conspecific worms, but a small proportion of each spawn settle nonspecifically on uninhabited substrata concurrently with their gregarious siblings. Here, using a parental half-sib analysis, we show that the proportion of a spawn settling in response to uninhabited biofilm is highly heritable. When estimated as a continuous trait based on a one-way ANOVA, heritability is estimated to be 0.83 +/- 0.31. When founder production was analyzed as a threshold trait, heritability was estimated to be 0.68 +/- 0.10 based on the breeding design experiment and 0.65 +/- 0.09 based on the artificial selection experiments. Realized heritability based on the selection experiments was considerably lower, however (0.17 per generation and 0.02 cumulative). Artificial selection was ineffectual at sequentially increasing the proportion of founder larvae among inbred family lines, but after three generations of selection, the proportion of larvae settling in response to biofilm was significantly higher among inbred lines than among the field-collected parents. The obligate planktonic larval stage common among so many marine invertebrates is thought to preclude the evolution of dispersal polymorphisms in these animals. Theoretical expectations of variable dispersal may instead be realized through individual behavioral differences resulting in differential transport or settlement preference, but this possibility remains largely unexplored among marine invertebrates.