Testing hypotheses about ecological specialization using phylogenetic trees

It is often assumed that ecological specialization represents an evolutionary "dead-end" that limits further evolution. Maximum-likelihood (ML) analyses on phylogenies for 15 groups of phytophagous insects revealed that high transition rates both to and from specialization occurred, but that the mean ratio of rates was significantly biased toward a higher rate to specialization. Here we explore the consequences of the fact that transition rates inferred by ML are affected not only by the distribution, but also by the frequency, of character states. Higher rates to the more common state were inferred in the analyses of Nosil (2002), in similar studies published since 2002, and in a small set of simulations. Thus, the ratio of the rate toward versus away from specialization was strongly, positively correlated with the proportion of specialist species at the tips of the phylogeny and whether transitions away from specialization occur remains unclear. Here we reexamine these data using methods that do not rely on directly comparing transition rates. Maximum-likelihood analyses show that models with no transitions in one direction (e.g., irreversible evolution as predicted by the "specialist as dead end" framework) are usually strongly rejected, independent of the proportion of specialists at the tips. Ancestral state reconstruction revealed two instances where generalists were unambiguously derived from specialists. Transition rates would need to biased 100-fold and 5000-fold toward specialization to reconstruct a history where these shifts from specialization toward generalization do not occur. The general conclusions of Nosil (2002) appear to hold; transitions in either direction likely occur such that specialization does not always limit further evolution. Most generally, inferences regarding character evolution can be strengthened by comparing models of character change and examining ancestor states, rather than only comparing parameter values.     

Testing for Poisson Zero Inflation in Disease Mapping

When analyzing mortality data due to rare diseases in small areas, it is common to find several health zones with no mortality cases. In these circumstances, the classical homogeneous model based on the Poisson distribution used to estimate the relative risks within each area may encounter lack of fit due to a disproportionately large frequency of zeros. To cope with these zeros, the zero inflated Poisson model can be used. In this paper, we propose a test for detecting zero inflation in the context of disease mapping which is based on bootstrap techniques. The test is illustrated using male mortality data due to brain cancer in Navarra, Spain. In addition, comparisons with other tests for Poisson zero inflation such as the score test and the likelihood ratio test are carried out in terms of empirical power and size using the brain cancer scenario. The proposed bootstrap test has good power and size and works well when detecting the excess of zeros in small area data sets. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation‐based evaluation of the performance of the F test in a linear multilevel model setting with sparseness at the level of the primary unit

In a linear multilevel model, significance of all fixed effects can be determined using F tests under maximum likelihood (ML) or restricted maximum likelihood (REML). In this paper, we demonstrate that in the presence of primary unit sparseness, the performance of the F test under both REML and ML is rather poor. Using simulations based on the structure of a data example on ceftriaxone consumption in hospitalized children, we studied variability, type I error rate and power in scenarios with a varying number of secondary units within the primary units. In general, the variability in the estimates for the effect of the primary unit decreased as the number of secondary units increased. In the presence of singletons (i.e., only one secondary unit within a primary unit), REML consistently outperformed ML, although even under REML the performance of the F test was found inadequate. When modeling the primary unit as a random effect, the power was lower while the type I error rate was unstable. The options of dropping, regrouping, or splitting the singletons could solve either the problem of a high type I error rate or a low power, while worsening the other. The permutation test appeared to be a valid alternative as it outperformed the F test, especially under REML. We conclude that in the presence of singletons, one should be careful in using the F test to determine the significance of the fixed effects, and propose the permutation test (under REML) as an alternative.     

Testing for equal rates of cladogenesis in diverse taxa

Taxa differ widely in numbers of species, which may be due either to chance alone or to factors that cause differences in speciation and extinction rates between taxa. To test whether an observed distribution of species over taxa differs from the distribution expected from chance alone, one must take into account that neither speciation nor extinction rates are known. This paper introduces a way to estimate speciation and extinction probabilities from the distribution of extant species over families and to test whether the observed distribution is different from expected. Application of this procedure to the distributions of bird, hexapod, primate, and angiosperm species over taxa provides statistical evidence of differences in rates of cladogenesis between taxa.     

A likelihood-based approach to estimating and testing for isolation by distance

Simple regression of genetic similarities between pairs of populations on their corresponding geographic distances is frequently used to detect the presence of isolation by distance (IBD). However, these pairwise values are obviously not independent and there is no parametric procedure for estimating and testing for the IBD intercepts and slopes based on standard regression theory. Nonparametric tests, such as the Mantel test, and resampling techniques, such as bootstrapping, have been exploited with limited success. Here, I describe a likelihood-based analysis to allow for simultaneously detecting patterns of correlated residuals and estimating and testing for the presence of IBD. It is shown, through the analysis of two molecular datasets in pine species, that different covariance structures of the residuals exist. More over, the likelihood ratio tests under these covariance structures are less sensitive to the presence of IBD than the Mantel test and the simple regression analysis but more sensitive than the bootstrap and jackknife samples over independent populations or population pairs. Because the likelihood analysis directly models and accounts for nonindependence of residuals, it should legitimately detect the presence of IBD, thereby allowing for accurate inferences about evolutionary and demographic processes influencing the extent and patterns of IBD.     

Higher order inference for the consensus mean in inter-laboratory studies

In inter-laboratory studies, a fundamental problem of interest is inference concerning the consensus mean, when the measurements are made by several laboratories which may exhibit different within-laboratory variances, apart from the between laboratory variability. A heteroscedastic one-way random model is very often used to model this scenario. Under such a model, a modified signed log-likelihood ratio procedure is developed for the interval estimation of the common mean. Furthermore, simulation results are presented to show the accuracy of the proposed confidence interval, especially for small samples. The results are illustrated using an example on the determination of selenium in non-fat milk powder by combining the results of four methods. Here, the sample size is small, and the confidence limits for the common mean obtained by different methods produce very different results. The confidence interval based on the modified signed log-likelihood ratio procedure appears to be quite satisfactory.     

Testing fundamental evolutionary hypotheses

Sober and Steel (J. Theor. Biol. 218, 395-408) give important limits on the use of current models with sequence data for studying ancient aspects of evolution; but they go too far in suggesting that several fundamental aspects of evolutionary theory cannot be tested in a normal scientific manner. To the contrary, we show examples of how some alternatives to the theory of descent can be formulated in such a way that they lead to predictions that can be evaluated (and rejected). The critical factor is a logical formulation of the alternatives, even though not all possible alternatives can be tested simultaneously. Similarly, some of the limits using DNA sequence data can be overcome by other types of sequence derived characters. The uniqueness (or not) of the origin of life, though still difficult, is similarly amenable to the testing of alternative hypotheses.     

Testing hypotheses in order

In certain circumstances, one wishes to test one hypothesisonly if certain other hypotheses have been rejected. This orderingof hypotheses simplifies the task of controlling the probabilityof rejecting any true hypothesis. In an example from an observationalstudy, a treated group is shown to be further from both of twocontrol groups than the two control groups are from each other.     

A standardized reanalysis of molecular phylogenetic hypotheses of Gobioidei

Gobioidei is a suborder of perciform fishes with about 2000 species distributed worldwide. Despite the evolutionary and ecological importance of gobioids, their phylogenetic inter- and intrarelationships are still poorly understood. Only a few studies (either morphological or molecular) have tackled the phylogeny of Gobioidei as a whole. Of these, only six studies thus far have addressed gobioid intrarelationships based on molecular data (each using different taxon sampling, genes, outgroups and method of phylogenetic inference), yielding contrasting results regarding the phylogenetic relationships among major lineages. In this study, we have reanalysed data from four of these molecular phylogenetic studies of Gobioidei under standardization criteria (same outgroup and methods of phylogenetic inference) in order to assess the robustness of their results, as well as to identify which parts of the gobioid tree are least resolved. Results from all datasets reanalysed in this study are generally similar to those of the respective original studies, and suggest broad patterns of phylogenetic relationships among gobioid lineages. However, there are numerous topological discrepancies among the four studies, support is low for many phylogenetic relationships and topology tests are unable to reject the vast majority of alternative topologies tested. The concatenation of datasets yields a relatively robust phylogeny of major lineages of Gobioidei, but there are some issues of overlap and missing data, which are ameliorated with the inclusion of additional homologous sequences from GenBank that increase dataset completeness. Because both monophyly of major gobioid groups and phylogenetic relationships among them cannot be fully resolved, it is clear that further phylogenetic research is needed, and this should be accompanied by a major taxonomic revision of the Gobioidei. Nevertheless, even with the relatively unstable nature of the available molecular phylogenies, there are some monophyletic units that can be identified, and a basic structure of the gobioid tree appears evident.     

Testing threshold and hormesis in a random effects dose-response model applied to developmental toxicity data

Here we describe a random effects threshold dose-response model for clustered binary-response data from developmental toxicity studies. For our model we assume that a hormetic effect occurs in addition to a threshold effect. Therefore, the dose-response curve is based on two components: relationships below the threshold (hormetic u-shaped model) and those above the threshold (logistic model). In the absence of hormesis and threshold effects, the estimation procedure is straightforward. We introduce score tests that are derived from a random effects hormetic-threshold dose-response model. The model and tests are applied to clustered binary data from developmental toxicity studies of animals to test for hormesis and threshold effects. We also compare the score test and likelihood ratio test to test for hormesis and threshold effects in a simulated study.     

Group Testing Regression Models with Fixed and Random Effects

Summary Group testing, where subjects are tested in pools rather than individually, has a long history of successful application in infectious disease screening. In this article, we develop group testing regression models to include covariate effects that are best regarded as random. We present approaches to fit mixed effects models using maximum likelihood, investigate likelihood ratio and score tests for variance components, and evaluate small sample performance using simulation. We illustrate our methods using chlamydia and gonorrhea data collected by the state of Nebraska as part of the Infertility Prevention Project.