A Two-Locus Forensic Match Probability for Subdivided Populations

A two-locus match probability is presented that incorporates the effects of within-subpopulation inbreeding (consanguinity) in addition to population subdivision. The usual practice of calculating multi-locus match probabilities as the product of single-locus probabilities assumes independence between loci. There are a number of population genetics phenomena that can violate this assumption: in addition to consanguinity, which increases homozygosity at all loci simultaneously, gametic disequilibrium will introduce dependence into DNA profiles. However, in forensics the latter problem is usually addressed in part by the careful choice of unlinked loci. Hence, as is conventional, we assume gametic equilibrium here, and focus instead on between-locus dependence due to consanguinity. The resulting match probability formulae are an extension of existing methods in the literature, and are shown to be more conservative than these methods in the case of double homozygote matches. For two-locus profiles involving one or more heterozygous genotypes, results are similar to, or smaller than, the existing approaches. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dispersal ability of marked,irradiated olive fruit flies [Bactrocera oleae (Rossi) (Diptera: Tephritidae)] in arid regions

The dispersal of marked, irradiated olive fruit flies originating from a hybrid laboratory strain was studied in an olive groove located in the arid regions of southern Israel. Release–recapture experiments (eight in total) were conducted throughout a period of 5 months (July–December 2008). In each experiment, ca. 5000 flies were released. Recapture of flies was conducted using a grid of 30 yellow sticky traps set in expanding semicircles from the centre of release. Service of traps was conducted 3 and 15 days after the release. Fly quality and adult food type (only sucrose and protein + sucrose) before release was also investigated. Results point at an average dispersal distance of marked, irradiated olive flies of ca. 50 m. Pre‐release adult diet did not affect dispersal ability. Fly recovery averaged ca. 3.5% during summer and ca. 1.5% during autumn. Most of the recovery concentrated during the first 3 days after releases, suggesting low survival of the released flies afterwards. As inferred from circular statistics, direction of dispersal was non‐random with a significant directionality to the north‐west. Results are discussed in view of environmental temperatures and wind direction.     

The effect of intraspecific sample size on type I and type II error rates in comparative studies

Comparative studies have increased greatly in number in recent years due to advances in statistical and phylogenetic methodologies. For these studies, a trade-off often exists between the number of species that can be included in any given study and the number of individuals examined per species. Here, we describe a simple simulation study examining the effect of intraspecific sample size on statistical error in comparative studies. We find that ignoring measurement error has no effect on type I error of nonphylogenetic analyses, but can lead to increased type I error under some circumstances when using independent contrasts. We suggest using ANOVA to evaluate the relative amounts of within- and between-species variation when considering a phylogenetic comparative study. If within-species variance is particularly large and intraspecific sample sizes small, then either larger sample sizes or comparative methods that account for measurement error are necessary.     

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.