Choice of column scores for testing independence in ordered 2 X K contingency tables

The numerous statistical methods for testing no association between a binary response (rows) and K ordered categories (columns) group naturally into two classes: those that require preassigned numerical column scores and those that do not. An example of the former would be a logistic regression analysis, and of the latter would be a Wilcoxon rank-sum test. In this paper we demonstrate that the perceived advantage of not preassigning scores is illusory. We do this by presenting an example from our consulting experience in which the midrank scores used by the rank tests that do not require preassigned scores are clearly inappropriate. Our recommendations are to assign reasonable column scores whenever possible, and to consider equally spaced scores when the choice is not apparent. Midranks as scores should always be examined for their appropriateness before a rank test is applied.     

Drawbacks to Integer Scoring for Ordered Categorical Data

Linear rank tests are widely used when testing for independence against stochastic order in a 2 x J contingency table with two treatments and J ordered outcome levels. For this purpose, numerical scores are assigned, possibly by default, to the J outcome levels. When the choice of scores is not apparent, integer (equally spaced) scores are often assigned. We show that this practice generally leads to unnecessarily conservative tests. The use of slightly perturbed scores will result in a less conservative and uniformly more powerful test.     

Community heritability measures the evolutionary consequences of indirect genetic effects on community structure

The evolutionary analysis of community organization is considered a major frontier in biology. Nevertheless, current explanations for community structure exclude the effects of genes and selection at levels above the individual. Here, we demonstrate a genetic basis for community structure, arising from the fitness consequences of genetic interactions among species (i.e., interspecific indirect genetic effects or IIGEs). Using simulated and natural communities of arthropods inhabiting North American cottonwoods (Populus), we show that when species comprising ecological communities are summarized using a multivariate statistical method, nonmetric multidimensional scaling (NMDS), the resulting univariate scores can be analyzed using standard techniques for estimating the heritability of quantitative traits. Our estimates of the broad-sense heritability of arthropod communities on known genotypes of cottonwood trees in common gardens explained 56-63% of the total variation in community phenotype. To justify and help interpret our empirical approach, we modeled synthetic communities in which the number, intensity, and fitness consequences of the genetic interactions among species comprising the community were explicitly known. Results from the model suggest that our empirical estimates of broad-sense community heritability arise from heritable variation in a host tree trait and the fitness consequences of IGEs that extend from tree trait to arthropods. When arthropod traits are heritable, interspecific IGEs cause species interactions to change, and community evolution occurs. Our results have implications for establishing the genetic foundations of communities and ecosystems.     

The Heritability of Difference Scores when Environments are Correlated

The statistical analysis of difference scores (contrasts) is a fundamental problem in all learning, feeding, and training experiments and tests, and in longitudinal studies of growth and development. Outgoing from the analogy between the mathematical models of classical psychological test theory and quantitative genetics, as well as between the parameters reliability and heritability of these models, the present paper derives the formulas of the heritability of difference scores in general cases where it is not assumed that environmental deviations on distinct tests and measurements are uncorrelated. Contrary to the assertion, made by FELDMAN and LEWONTIN , heritabilities in the broad sense can be used as ideal weighting factors in long-range personnel index selection. Longitudinal studies of twins and the cotwin method are powerful experimental designs to estimate heritabilities of differences.     

An Effective Method to Identify Heritable Components from Multivariate Phenotypes

Multivariate phenotypes may be characterized collectively by a variety of low level traits, such as in the diagnosis of a disease that relies on multiple disease indicators. Such multivariate phenotypes are often used in genetic association studies. If highly heritable components of a multivariate phenotype can be identified, it can maximize the likelihood of finding genetic associations. Existing methods for phenotype refinement perform unsupervised cluster analysis on low-level traits and hence do not assess heritability. Existing heritable component analytics either cannot utilize general pedigrees or have to estimate the entire covariance matrix of low-level traits from limited samples, which leads to inaccurate estimates and is often computationally prohibitive. It is also difficult for these methods to exclude fixed effects from other covariates such as age, sex and race, in order to identify truly heritable components. We propose to search for a combination of low-level traits and directly maximize the heritability of this combined trait. A quadratic optimization problem is thus derived where the objective function is formulated by decomposing the traditional maximum likelihood method for estimating the heritability of a quantitative trait. The proposed approach can generate linearly-combined traits of high heritability that has been corrected for the fixed effects of covariates. The effectiveness of the proposed approach is demonstrated in simulations and by a case study of cocaine dependence. Our approach was computationally efficient and derived traits of higher heritability than those by other methods. Additional association analysis with the derived cocaine-use trait identified genetic markers that were replicated in an independent sample, further confirming the utility and advantage of the proposed approach.     

Group differences in the heritability of items and test scores

It is important to understand potential sources of group differences in the heritability of intelligence test scores. On the basis of a basic item response model we argue that heritabilities which are based on dichotomous item scores normally do not generalize from one sample to the next. If groups differ in mean ability, the functioning of items at different ability levels may result in group differences in the heritability of items, even when these items function equivalently across groups and the heritability of the underlying ability is equal across groups. We illustrate this graphically, by computer simulation, and by focusing on several problems associated with a recent study by Rushton et al. who argued that the heritability estimates of items of Raven''s Progressive Matrices test in North-American twin samples generalized to other population groups, and hence that the population group differences on this test of general mental ability (or intelligence) had a substantial genetic component. Our results show that item heritabilities are strongly dependent on the group on which the heritabilities were based. Rushton et al.''s results were artefactual and do not speak to the nature of population group differences in intelligence test performance.     

Genomic Selection Using Low-Density Marker Panels

Genomic selection (GS) using high-density single-nucleotide polymorphisms (SNPs) is promising to improve response to selection in populations that are under artificial selection. High-density SNP genotyping of all selection candidates each generation, however, may not be cost effective. Smaller panels with SNPs that show strong associations with phenotype can be used, but this may require separate SNPs for each trait and each population. As an alternative, we propose to use a panel of evenly spaced low-density SNPs across the genome to estimate genome-assisted breeding values of selection candidates in pedigreed populations. The principle of this approach is to utilize cosegregation information from low-density SNPs to track effects of high-density SNP alleles within families. Simulations were used to analyze the loss of accuracy of estimated breeding values from using evenly spaced and selected SNP panels compared to using all high-density SNPs in a Bayesian analysis. Forward stepwise selection and a Bayesian approach were used to select SNPs. Loss of accuracy was nearly independent of the number of simulated quantitative trait loci (QTL) with evenly spaced SNPs, but increased with number of QTL for the selected SNP panels. Loss of accuracy with evenly spaced SNPs increased steadily over generations but was constant when the smaller number individuals that are selected for breeding each generation were also genotyped using the high-density SNP panel. With equal numbers of low-density SNPs, panels with SNPs selected on the basis of the Bayesian approach had the smallest loss in accuracy for a single trait, but a panel with evenly spaced SNPs at 10 cM was only slightly worse, whereas a panel with SNPs selected by forward stepwise selection was inferior. Panels with evenly spaced SNPs can, however, be used across traits and populations and their performance is independent of the number of QTL affecting the trait and of the methods used to estimate effects in the training data and are, therefore, preferred for broad applications in pedigreed populations under artificial selection.     

Using two palpable measurements improves the subject-specific femoral modeling

Subject-specific musculoskeletal models are essential to biomedical research and clinical applications, such as customized joint replacement, computer-aided surgical planning, gait analysis and automated segmentation. Generating these models from CT or magnetic resonance imaging (MRI) is time and resource intensive, requiring special skills. Therefore, in many studies individual bone models are approximated by scaling a generic template. Thus, the primary goal of this study was to determine a set of clinically available parameters (palpable measures and demographic data) that could improve the prediction of femoral dimensions, as compared to predicting these variables using uniform scaling based on palpable length. Similar to previous non-homogenous anthropometric scaling methods, the non-homogenous scaling method proposed in this study improved the prediction over uniform scaling of five key femoral measures. Homogenous scaling forces all dimensions of an object to be scaled equally, whereas non-homogenous scaling allows the dimensions to be scaled independently. The largest improvement was in femoral depth, where the coefficient of determination (r²) improved from 0.22 (homogenous) to 0.60 (non-homogeneous). In general, the major advantage of this non-homogenous scaling method is its ability to support the accurate and rapid generation of subject-specific femoral models since all parameters can be collected clinically, without imaging or invasive methods.     

Parametric and Nonparametric Analyses of Repeated Ordinal Categorical Data

We compare two models for the analysis of repeated ordinal categorical data: the classical parametric model for means of scores assigned to the categories of the response variable and a nonparametric model based on relative effects derived from the marginal distribution functions of the response. An example in the field of Dentistry is used to illustrate and to compare the models. We also consider a simulation study to evaluate the type‐I error rates and the power of tests under both models in a balanced design setup. The simulation results suggest that both approaches behave similarly for equally spaced scores but may perform differently otherwise. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Disease and Polygenic Architecture: Avoid Trio Design and Appropriately Account for Unscreened Control Subjects for Common Disease

Genome-wide association studies (GWASs) are an optimal design for discovery of disease risk loci for diseases whose underlying genetic architecture includes many common causal loci of small effect (a polygenic architecture). We consider two designs that deserve careful consideration if the true underlying genetic architecture of the trait is polygenic: parent-offspring trios and unscreened control subjects. We assess these designs in terms of quantification of the total contribution of genome-wide genetic markers to disease risk (SNP heritability) and power to detect an associated risk allele. First, we show that trio designs should be avoided when: (1) the disease has a lifetime risk > 1%; (2) trio probands are ascertained from families with more than one affected sibling under which scenario the SNP heritability can drop by more than 50% and power can drop as much as from 0.9 to 0.15 for a sample of 20,000 subjects; or (3) assortative mating occurs (spouse correlation of the underlying liability to the disorder), which decreases the SNP heritability but not the power to detect a single locus in the trio design. Some studies use unscreened rather than screened control subjects because these can be easier to collect; we show that the estimated SNP heritability should then be scaled by dividing by (1 − K × u)² for disorders with population prevalence K and proportion of unscreened control subjects u. When omitting to scale appropriately, the SNP heritability of, for example, major depressive disorder (K = 0.15) would be underestimated by 28% when none of the control subjects are screened.     

Perspectives of genomics for genetic conservation of livestock

Genomics provides new opportunities for conservation genetics. Conservation genetics in livestock is based on estimating diversity by pedigree relatedness and managing diversity by choosing those animals that maximize genetic diversity. Animals can be chosen as parents for the next generation, as donors of material to a gene bank, or as breeds for targeting conservation efforts. Genomics provides opportunities to estimate diversity for specific parts of the genome, such as neutral and adaptive diversity and genetic diversity underlying specific traits. This enables us to choose candidates for conservation based on specific genetic diversity (e.g. diversity of traits or adaptive diversity) or to monitor the loss of diversity without conservation. In wild animals direct genetic management, by choosing candidates for conservation as in livestock, is generally not practiced. With dense marker maps opportunities exist for monitoring relatedness and genetic diversity in wild populations, thus enabling a more active management of diversity.     

Heritability of specific language impairment depends on diagnostic criteria

Heritability estimates for specific language impairment (SLI) have been inconsistent. Four twin studies reported heritability of 0.5 or more, but a recent report from the Twins Early Development Study found negligible genetic influence in 4-year-olds. We considered whether the method of ascertainment influenced results and found substantially higher heritability if SLI was defined in terms of referral to speech and language pathology services than if defined by language test scores. Further analysis showed that presence of speech difficulties played a major role in determining whether a child had contact with services. Childhood language disorders that are identified by population screening are likely to have a different phenotype and different etiology from clinically referred cases. Genetic studies are more likely to find high heritability if they focus on cases who have speech difficulties and who have been referred for intervention.     

Heritability and phenotypic variation of canine hip dysplasia radiographic traits in a cohort of Australian German shepherd dogs

Canine Hip Dysplasia (CHD) is a common, painful and debilitating orthopaedic disorder of dogs with a partly genetic, multifactorial aetiology. Worldwide, potential breeding dogs are evaluated for CHD using radiographically based screening schemes such as the nine ordinally-scored British Veterinary Association Hip Traits (BVAHTs). The effectiveness of selective breeding based on screening results requires that a significant proportion of the phenotypic variation is caused by the presence of favourable alleles segregating in the population. This proportion, heritability, was measured in a cohort of 13,124 Australian German Shepherd Dogs born between 1976 and 2005, displaying phenotypic variation for BVAHTs, using ordinal, linear and binary mixed models fitted by a Restricted Maximum Likelihood method. Heritability estimates for the nine BVAHTs ranged from 0.14-0.24 (ordinal models), 0.14-0.25 (linear models) and 0.12-0.40 (binary models). Heritability for the summed BVAHT phenotype was 0.30 ± 0.02. The presence of heritable variation demonstrates that selection based on BVAHTs has the potential to improve BVAHT scores in the population. Assuming a genetic correlation between BVAHT scores and CHD-related pain and dysfunction, the welfare of Australian German Shepherds can be improved by continuing to consider BVAHT scores in the selection of breeding dogs, but that as heritability values are only moderate in magnitude the accuracy, and effectiveness, of selection could be improved by the use of Estimated Breeding Values in preference to solely phenotype based selection of breeding animals.     

SNP-based heritability estimation using a Bayesian approach

Heritability is a central element in quantitative genetics. New molecular markers to assess genetic variance and heritability are continually under development. The availability of molecular single nucleotide polymorphism (SNP) markers can be applied for estimation of variance components and heritability on population, where relationship information is unknown. In this study, we evaluated the capabilities of two Bayesian genomic models to estimate heritability in simulated populations. The populations comprised different family structures of either no or a limited number of relatives, a single quantitative trait, and with one of two densities of SNP markers. All individuals were both genotyped and phenotyped. Results illustrated that the two models were capable of estimating heritability, when true heritability was 0.15 or higher and populations had a sample size of 400 or higher. For heritabilities of 0.05, all models had difficulties in estimating the true heritability. The two Bayesian models were compared with a restricted maximum likelihood (REML) approach using a genomic relationship matrix. The comparison showed that the Bayesian approaches performed equally well as the REML approach. Differences in family structure were in general not found to influence the estimation of the heritability. For the sample sizes used in this study, a 10-fold increase of SNP density did not improve precision estimates compared with set-ups with a less dense distribution of SNPs. The methods used in this study showed that it was possible to estimate heritabilities on the basis of SNPs in animals with direct measurements. This conclusion is valuable in cases when quantitative traits are either difficult or expensive to measure.     

Technical note: Quantification of neurocranial shape variation using the shortest paths connecting pairs of anatomical landmarks

Three‐dimensional geometric morphometric techniques have been widely used in quantitative comparisons of craniofacial morphology in humans and nonhuman primates. However, few anatomical landmarks can actually be defined on the neurocranium. In this study, an alternative method is proposed for defining semi‐landmarks on neurocranial surfaces for use in detailed analysis of cranial shape. Specifically, midsagittal, nuchal, and temporal lines were approximated using Bezier curves and equally spaced points along each of the curves were defined as semi‐landmarks. The shortest paths connecting pairs of anatomical landmarks as well as semi‐landmarks were then calculated in order to represent the surface morphology between landmarks using equally spaced points along the paths. To evaluate the efficacy of this method, the previously outlined technique was used in morphological analysis of sexual dimorphism in modern Japanese crania. The study sample comprised 22 specimens that were used to generate 110 anatomical semi‐landmarks, which were used in geometric morphometric analysis. Although variations due to sexual dimorphism in human crania are very small, differences could be identified using the proposed landmark placement, which demonstrated the efficacy of the proposed method. Am J Phys Anthropol 151:658–666, 2013. © 2013 Wiley Periodicals, Inc.     

The power of interval mapping of quantitative trait loci, using selected sib pairs.

The interval-mapping procedure of Fulker and Cardon for analysis of a quantitative-trait loci (QTL) is extended for application to selected samples of sib pairs. Phenotypic selection of sib pairs, which is known to yield striking increases in power when a single marker is used, provides further increases in power when the interval-mapping approach is used. The greatest benefits of the combined approach are apparent with coarse maps, where QTLs of relatively modest (15%-20%) heritability can be detected with widely spaced markers (40-60 cM apart) in reasonably sized sibling samples. Useful information concerning QTL location is afforded by interval mapping in both selected and unselected samples.     

Maternal and genetic factors determine early life telomere length

In a broad range of species—including humans—it has been demonstrated that telomere length declines throughout life and that it may be involved in cell and organismal senescence. This potential link to ageing and thus to fitness has triggered recent interest in understanding how variation in telomere length is inherited and maintained. However, previous studies suffer from two main drawbacks that limit the possibility of understanding the relative importance of genetic, parental and environmental influences on telomere length variation. These studies have been based on (i) telomere lengths measured at different time points in different individuals, despite the fact that telomere length changes over life, and (ii) parent–offspring regression techniques, which do not enable differentiation between genetic and parental components of inheritance. To overcome these drawbacks, in our study of a songbird, the great reed warbler, we have analysed telomere length measured early in life in both parents and offspring and applied statistical models (so-called ‘animal models'') that are based on long-term pedigree data. Our results showed a significant heritability of telomere length on the maternal but not on the paternal side, and that the mother''s age was positively correlated with their offspring''s telomere length. Furthermore, the pedigree-based analyses revealed a significant heritability and an equally large maternal effect. Our study demonstrates strong maternal influence on telomere length and future studies now need to elucidate possible underlying factors, including which types of maternal effects are involved.     

Range size heritability in Carnivora is driven by geographic constraints

Range size heritability refers to an intriguing pattern where closely related species occupy geographic ranges of similar extent. Its existence may indicate selection on traits emergent only at the species level, with interesting consequences for evolutionary processes. We explore whether range size heritability may be attributable to the fact that range size is largely driven by the size of geographic domains (i.e., continents, biomes, areas given by species' climatic tolerance) that tend to be similar in phylogenetically related species. Using a well-resolved phylogeny of Carnivora, we show that range sizes are indeed constrained by geographic domains and that the phylogenetic signal in range sizes diminishes if the domain sizes are accounted for. Moreover, more detailed delimitation of species' geographic domain leads to a weaker signal in range size heritability, indicating the importance of definition of the null model against which the pattern is tested. Our findings do not reject the hypothesis of range size heritability but rather unravel its underlying mechanisms. Additional analyses imply that evolutionary conservatism in niche breadth delimits the species' geographic domain, which in turn shapes the species' range size. Range size heritability patterns thus emerge as a consequence of this interplay between evolutionary and geographic constraints.