Squamate richness in the Brazilian Cerrado and its environmental–climatic associations

We investigate patterns of species richness of squamates (lizards, snakes, and amphisbaenians) in the Brazilian Cerrado, identifying areas of particularly high richness, and testing predictions of large‐scale richness hypotheses by analysing the relationship between species richness and environmental climatic variables. We used point localities from museum collections to produce maps of the predicted distributions for 237 Cerrado squamate species, using niche‐modelling techniques. We superimposed distributions of all species on a composite map, depicting richness across the ecosystem. Then, we performed a multiple regression analysis using eigenvector‐based spatial filtering (Principal Coordinate of Neighbour Matrices) to assess environmental–climatic variables that are best predictors of species richness. We found that the environmental–climatic and spatial filters multiple regression model explained 78% of the variation in Cerrado squamate richness (r² = 0.78; F = 32.66; P < 0.01). Best predictors of species richness were: annual precipitation, precipitation seasonality, altitude, net primary productivity, and precipitation during the driest quarter. A model selection approach revealed that several mechanisms related to the different diversity hypothesis might work together to explain richness variation in the Cerrado. Areas of higher species richness in Cerrado were located mainly in the south‐west, north, extreme east, and scattered areas in the north‐west portions of the biome. Partitioning of energy among species, habitat differentiation, and tolerance to variable environments may be the primary ecological factors determining variation in squamate richness across the Cerrado. High richness areas in northern Cerrado, predicted by our models, are still poorly sampled, and biological surveys are warranted in that region. The south‐western region of the Cerrado exhibits high species richness and is also undergoing high levels of deforestation. Therefore, maintenance of existing reserves, establishment of ecological corridors among reserves, and creation of new reserves are urgently needed to ensure conservation of species in these areas.     

Nonparametric scanning tests of homogeneity for hierarchical models with continuous covariates

In many applications of hierarchical models, there is often interest in evaluating the inherent heterogeneity in view of observed data. When the underlying hypothesis involves parameters resting on the boundary of their support space such as variances and mixture proportions, it is a usual practice to entertain testing procedures that rely on common heterogeneity assumptions. Such procedures, albeit omnibus for general alternatives, may entail a substantial loss of power for specific alternatives such as heterogeneity varying with covariates. We introduce a novel and flexible approach that uses covariate information to improve the power to detect heterogeneity, without imposing unnecessary restrictions. With continuous covariates, the approach does not impose a regression model relating heterogeneity parameters to covariates or rely on arbitrary discretizations. Instead, a scanning approach requiring continuous dichotomizations of the covariates is proposed. Empirical processes resulting from these dichotomizations are then used to construct the test statistics, with limiting null distributions shown to be functionals of tight random processes. We illustrate our proposals and results on a popular class of two-component mixture models, followed by simulation studies and applications to two real datasets in cancer and caries research.     

Average weighted nucleotide diversity is more precise than pixy in estimating the true value of π from sequence sets containing missing data

Nucleotide diversity remains an important statistic in population genetic/genomic studies. Although recent advances in massive sequencing make generating sequence data sets cheaper and faster, currently used technologies often introduce substantial amounts of missing nucleotides in their output. A novel method of estimating π from data sets containing missing data – pixy - has also recently been proposed. In this study, the pixy estimator, π_pixy, was compared to average weighted nucleotide diversity, π_W. The estimators were tested both on sequences simulated in fastsimcoal and real sequence sets. Both sets were modified by random insertion of missing nucleotides. Weighted nucleotide diversity performed better in all pairwise comparisons. It was characterized by a smaller error and a narrower distribution of the results. π_pixy tends to overestimate the nucleotide diversity when both the proportion of missing data and the level of variation is low. Of the two estimators, only π_W estimated the true nucleotide diversity in a part of the simulations. A simple formula for estimating π_W allows for easy integration of the estimator in packages such as pixy, which would allow obtaining more precise estimates of nucleotide diversity either in a sliding window or for discrete genomic regions.     

Spatial patterns of plant association in grazed and ungrazed shrublands in the semi‐arid Karoo,South Africa

Abstract. The investigation of vegetation pattern and plant association by spatial statistics has become increasingly popular among plant ecologists. Recently, Individual‐centered analysis (ICA) has been introduced as a new tool for analysis of multi‐species co‐occurrence patterns. We tested this new technique by applying it to spatial data from grazed and ungrazed shrub communities in the semi‐arid Great Karoo, South Africa. There were substantial but complex and scale‐dependent differences in pattern between grazed and ungrazed vegetation. Unpalatable species that increase in abundance in grazed vegetation possibly play a key role in the change of vegetation pattern. At small scales we found indications of aggregation (< 30 cm) at the ungrazed, but of repulsion (30 – 40 cm) at the grazed site. An additional non‐random pattern at 60 – 170 cm at the grazed site was probably due to the clumped distributions of some species on broader scales. We show that the interpretability of ICA results is improved when the actual observed and expected frequencies of species combinations are added to the program output. The main strength of ICA is that it has the potential to detect association patterns that involve more than two species.     

Efficient Bayesian Sample Size Calculation for Designing a Clinical Trial with Multi‐Cluster Outcome Data

Health care utilization and outcome studies call for hierarchical approaches. The objectives were to predict major complications following percutaneous coronary interventions by health providers, and to compare Bayesian and non‐Bayesian sample size calculation methods. The hierarchical data structure consisted of: (1) Strata: PGY4, PGY7, and physician assistant as providers with varied experiences; (2) Clusters: k_s providers per stratum; (3) Individuals: n_s patients reviewed by each provider. The main outcome event illustrated was mortality modeled by a Bayesian beta‐binomial model. Pilot information and assumptions were utilized to elicit beta prior distributions. Sample size calculations were based on the approximated average length, fixed at 1%, of 95% posterior intervals of the mean event rate parameter. Necessary sample sizes by both non‐Bayesian and Bayesian methods were compared. We demonstrated that the developed Bayesian methods can be efficient and may require fewer subjects to satisfy the same length criterion.     

The Mystery of Two Straight Lines in Bacterial Genome Statistics

In special coordinates (codon position-specific nucleotide frequencies), bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial genomes available in Genbank in April 2007, belong to these lines with high accuracy. The main challenge now is to explain the observed high accuracy. The new phenomenon of complementary symmetry for codon position-specific nucleotide frequencies is observed. The results of analysis of several codon usage models are presented. We demonstrate that the mean-field approximation, which is also known as context-free, or complete independence model, or Segre variety, can serve as a reasonable approximation to the real codon usage. The first two principal components of codon usage correlate strongly with genomic G+C content and the optimal growth temperature, respectively. The variation of codon usage along the third component is related to the curvature of the mean-field approximation. First three eigenvalues in codon usage PCA explain 59.1%, 7.8% and 4.7% of variation. The eubacterial and archaeal genomes codon usage is clearly distributed along two third order curves with genomic G+C content as a parameter.     

An unexpected influence of widely used significance thresholds on the distribution of reported P-values

We consider the problematic relationship between publication success and statistical significance in the light of analyses in which we examine the distribution of published probability (P) values across the statistical 'significance' range, below the 5% probability threshold. P-values are often judged according to whether they lie beneath traditionally accepted thresholds (< 0.05, < 0.01, < 0.001, < 0.0001); we examine how these thresholds influence the distribution of reported absolute P-values in published scientific papers, the majority in biological sciences. We collected published P-values from three leading journals, and summarized their distribution using the frequencies falling across and within these four threshold values between 0.05 and 0. These published frequencies were then fitted to three complementary null models which allowed us to predict the expected proportions of P-values in the top and bottom half of each inter-threshold interval (i.e. those lying below, as opposed to above, each P-value threshold). Statistical comparison of these predicted proportions, against those actually observed, provides the first empirical evidence for a remarkable excess of probability values being cited on, or just below, each threshold relative to the smoothed theoretical distributions. The pattern is consistent across thresholds and journals, and for whichever theoretical approach used to generate our expected proportions. We discuss this novel finding and its implications for solving the problems of publication bias and selective reporting in evolutionary biology.     

Reconstructing community relationships: the impact of sampling error, ordination approach, and gradient length

Effectively summarizing complex community relationships is an important feature in studies such as biodiversity, global change, and invasion ecology. The reliability of such community summaries depends on the degree of sampling variability that is present in the data, the structure of the data, and the choice of ordination method, but the relative importance of these factors is not understood. We compared the validity of results from different ordination methods by applying five levels of sampling error to a simulated coenoplane model at two gradient lengths using two types of data (abundance and presence–absence). The multivariate methods we compared were correspondence analysis (CA), detrended correspondence analysis (DCA), non-metric multidimensional scaling (NMDS), principal component analysis (PCA) and principal coordinates analysis (PCoA). Our results showed CA and PCA using presence–absence data were the most successful methods regardless of sampling error and gradient length, closely followed by the other methods using presence–absence data. With abundance data, PCA and CA were the most successful approaches with the short and long gradients, respectively. Approaches based on PCoA and NMDS using abundance data did not perform well regardless of the choice of distance measure used in the analysis. Both of these methods, along with the PCA using abundance data, were strongly affected by the longer gradient, leading to more distorted results.