Small-sample inference for the comparison of means of log-normal distributions

We propose a likelihood-based test for comparing the means of two or more log-normal distributions, with possibly unequal variances. A modification to the likelihood ratio test is needed when sample sizes are small. The performance of the proposed procedures is compared with the F-ratio test using Monte Carlo simulations.     

New Methods for Detecting Positive Selection at Single Amino Acid Sites

Inferring positive selection at single amino acid sites is of particular importance for studying evolutionary mechanisms of a protein. For this purpose, Suzuki and Gojobori (1999) developed a method (SG method) for comparing the rates of synonymous and nonsynonymous substitutions at each codon site in a protein-coding nucleotide sequence, using ancestral codons at interior nodes of the phylogenetic tree as inferred by the maximum parsimony method. In the SG method, however, selective neutrality of nucleotide substitutions cannot be tested at codon sites, where only termination codons are inferred at any interior node or the number of equally parsimonious inferences of ancestral codons at all interior nodes exceeds 10,000. Here I present a modified SG method which is free from these problems. Specifically, I use the distance-based Bayesian method for inferring the single most likely ancestral codon from 61 sense codons at each interior node. In the computer simulation and real data analysis, the modified SG method showed a higher overall efficiency of detecting positive selection than the original SG method, particularly at highly polymorphic codon sites. These results indicate that the modified SG method is useful for inferring positive selection at codon sites where neutrality cannot be tested by the original SG method. I also discuss that the p-distance is preferable to the number of synonymous substitutions for inferring the phylogenetic tree in the SG method, and present a maximum likelihood method for detecting positive selection at single amino acid sites, which produced reasonable results in the real data analysis.     

Evolution of host specificity in fleas: is it directional and irreversible?

Evolutionary trends in the evolution of host specificity have been the focus of much discussion but little rigorous empirical testing. On the one hand, specialization is often presumed to lead irreversibly into evolutionary dead ends and little diversification; this would mean that generalists might evolve into specialists, but not vice versa. On the other hand, low host specificity may limit the risk of extinction and provide more immediate fitness benefits to parasites, such that selection may favour evolution toward a generalist strategy. Here, we test for directionality in the evolution of host specificity using a large data set and phylogenetic information on 297 species of fleas parasitic on small mammals. The analyses determined whether host specificity, measured both as the number of host species exploited and their taxonomic diversity, was related to clade rank of the flea species, or the number of branching events between an extant species and the root of the phylogenetic tree (i.e., the total path length from the root of the tree to the species). Based on regression analyses, we found positive relationships between the number of host species used and clade rank across all 297 species, as well as within one (Hystrichopsyllidae) of four large families and one of seven large genera investigated separately; in addition, we found a positive relationship between the taxonomic diversity of host species used and clade rank in another of the seven genera. These results suggest a slight evolutionary trend of decreasing host specificity. Using a much more conservative likelihood ratio test, however, a random walk, or null model, of evolution could not be discarded in favour of the directional trends in all cases mentioned above. Still, these results suggest that host specificity may have tended to decrease in many flea lineages, a process that could have been driven by the benefits of exploiting a wide range of host species.     

Correlated evolution of fig size and color supports the dispersal syndromes hypothesis

The influence of seed dispersers on the evolution of fruit traits remains controversial, largely because most studies have failed to account for phylogeny and or have focused on conservative taxonomic levels. Under the hypothesis that fruit traits have evolved in response to different sets of selective pressures by disparate types of seed dispersers (the dispersal syndromes hypothesis), we test for two dispersal syndromes, defined as groups of fruit traits that appear together more often than expected by chance. (1) Bird syndrome fruits are brightly colored and small, because birds have acute color vision, and commonly swallow fruits whole. (2) Mammal syndrome fruits are dull-colored and larger on average than bird syndrome fruits, because mammals do not rely heavily on visual cues for finding fruits, and can eat fruits piecemeal. If, instead, phylogenetic inertia determines the co-occurrence of fruit size and color, we will observe that specific combinations of size and color evolved in a small number of ancestral species. We performed a comparative analysis of fruit traits for 64 species of Ficus (Moraceae), based on a phylogeny we constructed using nuclear ribosomal DNA. Using a concentrated changes test and assuming fruit color is an independent variable, we found that small-sized fruits evolve on branches with red and purple figs, as predicted by the dispersal syndromes hypothesis. When using diameter as the independent variable, results vary with the combination of algorithms used, which is discussed in detail. A likelihood ratio test confirms the pattern found with the concentrated changes test using color as the independent variable. These results support the dispersal syndromes hypothesis.     

A new meta-ANOVA approach for synthesizing information under signal-heterogeneity setting with application to nuclear magnetic resonance spectroscopic data

A new synthesizing statistical methodology is proposed to resolve issues of signal-heterogeneity in data sets collected through high-resolution ¹H nuclear magnetic resonance (NMR) spectroscopy. This signal-heterogeneity is typically caused by subjective operations for processing spectral profiles and measuring peak areas, non-homogeneous biological phases of experimental subjects, and variations of systems in multi-center. All these causes are likely to simultaneously impact signals of metabolic changes and their precision in a nonlinear fashion. As a combined effect, signal-heterogeneity chiefly manifests through non-homomorphic patterns of standardized treatment mean deviations spanning all experiments, and makes most remedial statistical models with linearity structure invalid. By avoiding a huge and very complex model, we develop a simple meta-ANOVA approach to synthesize many one-way-layout ANOVA analyses from individual experiments. A scale-invariant F-ratio statistic is taken as the summarizing sufficient statistic of a non-centrality parameter that supposedly captures the information about metabolic change from each experiment. Then a joint-likelihood function of a common non-centrality is constructed as the basis for maximum likelihood estimation and Chi-square likelihood ratio testing for statistical inference. We apply the meta-ANOVA to detect metabolic changes of three metabolites identified through pattern recognition on NMR spectral profiles obtained from muscle and liver tissues. We also detect effect differences among different treatments via meta-ANOVA multiple comparison.     

Comparison of properties of tests for assessing tumor clonality

SUMMARY: In a recent article Begg et al. (2007, Biometrics 63, 522-530) proposed a statistical test to determine whether or not a diagnosed second primary tumor is biologically independent of the original primary tumor, by comparing patterns of allelic losses at candidate genetic loci. The proposed concordant mutations test is a conditional test, an adaptation of Fisher's exact test, that requires no knowledge of the marginal mutation probabilities. The test was shown to have generally good properties, but is susceptible to anticonservative bias if there is wide variation in mutation probabilities between loci, or if the individual mutation probabilities of the parental alleles for individual patients differ substantially from each other. In this article, a likelihood ratio test is derived in an effort to address these validity issues. This test requires prespecification of the marginal mutation probabilities at each locus, parameters for which some information will typically be available in the literature. In simulations this test is shown to be valid, but to be considerably less efficient than the concordant mutations test for sample sizes (numbers of informative loci) typical of this problem. Much of the efficiency deficit can be recovered, however, by restricting the allelic imbalance parameter estimate to a prespecified range, assuming that this parameter is in the prespecified range.     

Conditional properties of unconditional parametric bootstrap procedures for inference in exponential families

Higher-order inference about a scalar parameter in the presenceof nuisance parameters can be achieved by bootstrapping, incircumstances where the parameter of interest is a componentof the canonical parameter in a full exponential family. Theoptimal test, which is approximated, is a conditional one basedon conditioning on the sufficient statistic for the nuisanceparameter. A bootstrap procedure that ignores the conditioningis shown to have desirable conditional properties in providingthird-order relative accuracy in approximation of p-values associatedwith the optimal test, in both continuous and discrete models.The bootstrap approach is equivalent to third-order analyticalapproaches, and is demonstrated in a number of examples to givevery accurate approximations even for very small sample sizes.     

Testing for group effect in a 2 x k heteroscedastic ANOVA model

It is natural to want to relax the assumption of homoscedasticity and Gaussian error in ANOVA models. For a two-way ANOVA model with 2 x k cells, one can derive tests of main effect for the factor with two levels (referred to as group) without assuming homoscedasticity or Gaussian error. Empirical likelihood can be used to derive testing procedures. An approximate empirical likelihood ratio test (AELRT) is derived for the test of group main effect. To approximate the distributions of the test statistics under the null hypothesis, simulation from the approximate empirical maximum likelihood estimate (AEMLE) restricted by the null hypothesis is used. The homoscedastic ANOVA F -test and a Box-type approximation to the distribution of the heteroscedastic ANOVA F -test are compared to the AELRT in level and power. The AELRT procedure is shown by simulation to have appropriate type I error control (although possibly conservative) when the distribution of the test statistics are approximated by simulation from the constrained AEMLE. The methodology is motivated and illustrated by an analysis of folate levels in the blood among two alcohol intake groups while accounting for gender.     

Evolutionary modelling of feed forward loops in gene regulatory networks

Feed forward loops (FFLs) are gene regulatory network motifs. They exist in different types, defined by the signs of the effects of genes in the motif on one another. We examine 36 feed forward loops in Escherichia coli, using evolutionary simulations to predict the forms of FFL expected to evolve to generate the pattern of expression of the output gene. These predictions are tested using likelihood ratios, comparing likelihoods of the observed FFL structures with their likelihoods under null models. The very high likelihood ratios generated, of over 10(11), suggest that evolutionary simulation is a valuable component in the explanation of FFL structure.     

The Effect of Branch Length Variation on the Selection of Models of Molecular Evolution

Models of sequence evolution play an important role in molecular evolutionary studies. The use of inappropriate models of evolution may bias the results of the analysis and lead to erroneous conclusions. Several procedures for selecting the best-fit model of evolution for the data at hand have been proposed, like the likelihood ratio test (LRT) and the Akaike (AIC) and Bayesian (BIC) information criteria. The relative performance of these model-selecting algorithms has not yet been studied under a range of different model trees. In this study, the influence of branch length variation upon model selection is characterized. This is done by simulating sequence alignments under a known model of nucleotide substitution, and recording how often this true model is recovered by different model-fitting strategies. Results of this study agree with previous simulations and suggest that model selection is reasonably accurate. However, different model selection methods showed distinct levels of accuracy. Some LRT approaches showed better performance than the AIC or BIC information criteria. Within the LRTs, model selection is affected by the complexity of the initial model selected for the comparisons, and only slightly by the order in which different parameters are added to the model. A specific hierarchy of LRTs, which starts from a simple model of evolution, performed overall better than other possible LRT hierarchies, or than the AIC or BIC. Received: 2 October 2000 / Accepted: 4 January 2001