The use of inverse sine transformations in the analysis of non-metric cranial data

In recent years osteologists have frequently used non-metric (dichotomous) cranial data to measure biological distance between skeletal samples of Homo sapiens. Applying methods used earlier by biologists, these workers begin by attempting to stabilize the variance of the measures used by transforming the observed trait frequencies using some type of inverse sine transformation. The frequently used Grewal-Smith transformation doesn't work well for small samples of the size often considered by osteologists. As a consequence the mean measure of divergence between populations determined by this method is strongly influenced by a bias which depends on sample size. This paper compares several transformations in terms of how close the actual variance of the transformed frequency corresponds to its nominal value. It is suggested that the traditional (Grewal-Smith) inverse sine transformation not be used, and several alternatives are considered.     

Cultural interaction and biological distance in postclassic period Mexico

Economic, political, and cultural relationships connected virtually every population throughout Mexico during Postclassic period (AD 900–1520). Much of what is known about population interaction in prehistoric Mexico is based on archaeological or ethnohistoric data. What is unclear, especially for the Postclassic period, is how these data correlate with biological population structure. We address this by assessing biological (phenotypic) distances among 28 samples based upon a comparison of dental morphology trait frequencies, which serve as a proxy for genetic variation, from 810 individuals. These distances were compared with models representing geographic and cultural relationships among the same groups. Results of Mantel and partial Mantel matrix correlation tests show that shared migration and trade are correlated with biological distances, but geographic distance is not. Trade and political interaction are also correlated with biological distance when combined in a single matrix. These results indicate that trade and political relationships affected population structure among Postclassic Mexican populations. We suggest that trade likely played a major role in shaping patterns of interaction between populations. This study also shows that the biological distance data support the migration histories described in ethnohistoric sources. Am J Phys Anthropol 157:121–133, 2015. © 2015 Wiley Periodicals, Inc.     

A Comparative Statistical Analysis of Genetic Distances. I - Estimation of Distances and of their Variances: Distribution of the Estimators

We present a Monte-Carlo simulation analysis of the statistical properties of absolute genetic distance and of Nei's minimum and standard genetic distances. The estimation of distances (bias) and of their variances is analysed as well as the distributions of distance and variance estimators, taking into account both gamete and locus samplings. Both of Nei's statistics are non-linear when distances are small and consequently the distributions of their estimators are extremely asymmetrical. It is difficult to find theoretical laws that fit such asymmetrical distributions. Absolute genetic distance is linear and its distributions are better fit by a normal distribution. When distances are medium or large, minimum distance and absolute distance distributions are close to a normal distribution, but those of the standard distance can never be considered as normal. For large distances the jack-knife estimator of the standard distance variance is bad; another standard distance estimator is suggested. Absolute distance, which has the best mathematical properties, is particularly interesting for small distances if the gamete sample size is large, even when the number of loci is small. When both distance and gamete sample size are small, this statistic is biased.     

An estimator for pairwise relatedness using molecular markers

I propose a new estimator for jointly estimating two-gene and four-gene coefficients of relatedness between individuals from an outbreeding population with data on codominant genetic markers and compare it, by Monte Carlo simulations, to previous ones in precision and accuracy for different distributions of population allele frequencies, numbers of alleles per locus, actual relationships, sample sizes, and proportions of relatives included in samples. In contrast to several previous estimators, the new estimator is well behaved and applies to any number of alleles per locus and any allele frequency distribution. The estimates for two- and four-gene coefficients of relatedness from the new estimator are unbiased irrespective of the sample size and have sampling variances decreasing consistently with an increasing number of alleles per locus to the minimum asymptotic values determined by the variation in identity-by-descent among loci per se, regardless of the actual relationship. The new estimator is also robust for small sample sizes and for unknown relatives being included in samples for estimating allele frequencies. Compared to previous estimators, the new one is generally advantageous, especially for highly polymorphic loci and/or small sample sizes.     

Recent advances in human quantitative-trait-locus mapping: comparison of methods for selected sibling pairs

During the past few years, there has been a great deal of new work on methods for mapping quantitative-trait loci by use of sibling pairs and sibships. There are several new methods based on linear regression, as well as several more that are based on score statistics. In theory, most of the new methods should be relatively robust to violations of distributional assumptions and to selected sampling, but, in practice, there has been little evaluation of how the methods perform on selected samples. We survey most of the new regression-based statistics and score statistics and propose a few minor variations on the score statistics. We use simulation to evaluate the type I error and the power of all of the statistics, considering (a) population samples of sibling pairs and (b) sibling pairs ascertained on the basis of at least one sibling with a trait value in the top 10% of the distribution. Most of the statistics have correct type I error for selected samples. The statistics proposed by Xu et al. and by Sham and Purcell are generally the most powerful, along with one of our score statistic variants. Even among the methods that are most powerful for "nice" data, some are more robust than others to non-Gaussian trait models and/or misspecified trait parameters.     

Dental morphology of early Holocene foragers of North India: Non-metric trait frequencies and biological affinities

The biological affinities of semi-nomadic, early to mid-Holocene foragers of the mid-Ganga Plain, North India are undetermined, yet understanding their place in the population history of South Asia is important. Non-metric tooth trait frequencies are reported for three broadly contemporary, bio-culturally similar, and geographically proximate samples, collectively known as Mesolithic Lake Culture (MLC). The Arizona State University – Dental Anthropology System was used to score 43 tooth-trait combinations (23 maxillary; 21 mandibular). Non-metric trait frequencies are used to determine biological affinities of MLC to a global sample of living populations and to prehistoric and living groups of South Asia.     

Determining Consistency of Spatial Dispersion of Nematodes in Small Plots

Nematode population densities in field plots were estimated by collecting samples consisting of 12 soil cores. Plots encompassed a variety of plant hosts and sampling dates, and provided data on the population densities of seven species of plant-parasitic nematodes. Three separate samples were collected per plot on each sampling date to obtain estimates of the mean and variance of numbers for each species. For each nematode species, these estimates were used to derive the Taylor''s Power Law regression over plots having identical hosts and sampling dates. For some nematode species, comparisons of regression equations among different sampling dates on the same host revealed similarities in values of a and b from Taylor''s Power Law. Parameters of Taylor''s Power Law relationships were used to develop sampling plans and to obtain estimates of sample precision. Precision estimates from specific and general sampling plans are illustrated for Belonolaimus longicaudatus.     

Full conjugate analysis of normal multiple traits with missing records using a generalized inverted Wishart distribution

A Markov chain Monte Carlo (MCMC) algorithm to sample an exchangeable covariance matrix, such as the one of the error terms (R₀) in a multiple trait animal model with missing records under normal-inverted Wishart priors is presented. The algorithm (FCG) is based on a conjugate form of the inverted Wishart density that avoids sampling the missing error terms. Normal prior densities are assumed for the ''fixed'' effects and breeding values, whereas the covariance matrices are assumed to follow inverted Wishart distributions. The inverted Wishart prior for the environmental covariance matrix is a product density of all patterns of missing data. The resulting MCMC scheme eliminates the correlation between the sampled missing residuals and the sampled R₀, which in turn has the effect of decreasing the total amount of samples needed to reach convergence. The use of the FCG algorithm in a multiple trait data set with an extreme pattern of missing records produced a dramatic reduction in the size of the autocorrelations among samples for all lags from 1 to 50, and this increased the effective sample size from 2.5 to 7 times and reduced the number of samples needed to attain convergence, when compared with the ''data augmentation'' algorithm.     

Sexual dimorphism in human cranial trait scores: Effects of population,age, and body size

Sex estimation from the skull is commonly performed by physical and forensic anthropologists using a five‐trait scoring system developed by Walker. Despite the popularity of this method, validation studies evaluating its accuracy across a variety of samples are lacking. Furthermore, it remains unclear what other intrinsic or extrinsic variables are related to the expression of these traits. In this study, cranial trait scores and postcranial measurements were collected from four diverse population groups (U.S. Whites, U.S. Blacks, medieval Nubians, and Arikara Native Americans) following Walker's protocols (total n = 499). Univariate and multivariate analyses were utilized to evaluate the accuracy of these traits in sex estimation, and to test for the effects of population, age, and body size on trait expressions. Results revealed significant effects of population on all trait scores. Sample‐specific correct sex classification rates ranged from 74% to 94%, with an overall accuracy of 85% for the pooled sample. Classification performance varied among the traits (best for glabella and mastoid scores and worst for nuchal scores). Furthermore, correlations between traits were weak or nonsignificant, suggesting that different factors may influence individual traits. Some traits displayed correlations with age and/or postcranial size that were significant but weak, and within‐population analyses did not reveal any consistent relationships between these traits across all groups. These results indicate that neither age nor body size plays a large role in trait expression, and thus does not need to be incorporated into sex estimation methods. Am J Phys Anthropol 154:259–269, 2014. © 2014 Wiley Periodicals, Inc.     

Pattern‐oriented modelling of population genetic structure

Although several statistical approaches can be used to describe patterns of genetic variation and infer stochastic differentiation, selective responses, or interruptions of gene flow due to physical or environmental barriers, it is worthwhile to note that similar processes, controlled by several parameters in theoretical models, frequently give rise to similar patterns. Here, we develop a Pattern‐Oriented Modelling (POM) approach that allows us to determine how a complex set of parameters potentially driving empirical genetic differentiation among populations generate alternative scenarios that can be fitted to observed data. We generated 10 000 random combinations of parameters related to population size, gene flow and response to gradients (both driven by dispersal and selection) in a spatially explicit model, and analysed simulated patterns with F_ST statistics and mean correlograms using Moran's I spatial autocorrelation coefficients. These statistics were compared with observed patterns for a tree species endemic to the Brazilian Cerrado. For a best match with observed F_ST (equal to 0.182), the important parameters driving simulated scenario are mainly related to population structure, including low population size with closed populations (low N_m), strong distance decay of gene flow, in addition to a strong effect of the initial variance of allele frequencies. These scenarios present a low autocorrelation of allele frequencies. Best matching of correlograms, on the other hand, appears in simulations with a large population size, high N_m and low population differentiation and F_ST (as well as more gene flow). Thus, targeting the two statistics (correlograms and F_ST) shows that best matches with empirical data with two distinct sets of parameters in the simulations, because observed patterns involve both a relatively high F_ST and significant autocorrelation. This conflict can be resolved by assuming that initial variance in allele frequencies can be interpreted as reflecting deep‐time historical variation and evolutionary dynamics of allele frequencies, creating a relatively high level of population differentiation, whereas current patterns in gene flow creates spatial autocorrelation. This make sense in terms of the previous knowledge on population differentiation in D. alata, especially if patterns are explained by a combination of isolation‐by‐distance and allelic surfing due to range expansion after the last glacial maximum. This reveals the potential for more complex applications of POM in population genetics. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 113 , 1152–1161.     

Statistics for Nonparametric Linkage Analysis of X-Linked Traits in General Pedigrees

We have compared the power of several allele-sharing statistics for "nonparametric" linkage analysis of X-linked traits in nuclear families and extended pedigrees. Our rationale was that, although several of these statistics have been implemented in popular software packages, there has been no formal evaluation of their relative power. Here, we evaluate the relative performance of five test statistics, including two new test statistics. We considered sibships of sizes two through four, four different extended pedigrees, 15 different genetic models (12 single-locus models and 3 two-locus models), and varying recombination fractions between the marker and the trait locus. We analytically estimated the sample sizes required for 80% power at a significance level of.001 and also used simulation methods to estimate power for a sample size of 10 families. We tried to identify statistics whose power was robust over a wide variety of models, with the idea that such statistics would be particularly useful for detection of X-linked loci associated with complex traits. We found that a commonly used statistic, S(all), generally performed well under various conditions and had close to the optimal sample sizes in most cases but that there were certain cases in which it performed quite poorly. Our two new statistics did not perform any better than those already in the literature. We also note that, under dominant and additive models, regardless of the statistic used, pedigrees with all-female siblings have very little power to detect X-linked loci.     

Questions of khoesan continuity: Dental affinities among the indigenous holocene peoples of South Africa

The present report follows up on the findings of previous research, including recent bioarchaeological study of well‐dated Khoesan skeletal remains, that posits long term biological continuity among the indigenous peoples of South Africa after the Pleistocene. The Arizona State University Dental Anthropology System was used to record key crown, root, and intraoral osseous nonmetric traits in six early‐through‐late Holocene samples from the Cape coasts. Based on these data, phenetic affinities and an identification of traits most important in driving intersample variation were determined using principal components analysis and the mean measure of divergence distance statistic. To expand biological affinity comparisons into more recent times, and thus preliminarily assess the dental impact of disproportionate non‐Khoesan gene flow into local peoples, dental data from historic Khoekhoe and San were also included. Results from the prehistoric comparisons are supportive of population continuity, though a sample from Matjes River Rockshelter exhibits slight phenetic distance from other early samples. This and some insignificant regional divergence among these coastal samples may be related to environmental and cultural factors that drove low‐level reproductive isolation. Finally, a close affinity of historic San to all samples, and a significant difference of Khoekhoe from most early samples is reflective of documented population history following immigration of Bantu‐speakers and, later, Europeans into South Africa. Am J Phys Anthropol 155:33–44, 2014. © 2014 Wiley Periodicals, Inc.     

TESTING FOR PHYLOGENETIC SIGNAL IN BIOLOGICAL TRAITS: THE UBIQUITY OF CROSS‐PRODUCT STATISTICS

To evaluate rates of evolution, to establish tests of correlation between two traits, or to investigate to what degree the phylogeny of a species assemblage is predictive of a trait value so‐called tests for phylogenetic signal are used. Being based on different approaches, these tests are generally thought to possess quite different statistical performances. In this article, we show that the Blomberg et al. K and K*, the Abouheif index, the Moran's I, and the Mantel correlation are all based on a cross‐product statistic, and are thus all related to each other when they are associated to a permutation test of phylogenetic signal. What changes is only the way phylogenetic and trait similarities (or dissimilarities) among the tips of a phylogeny are computed. The definitions of the phylogenetic and trait‐based (dis)similarities among tips thus determines the performance of the tests. We shortly discuss the biological and statistical consequences (in terms of power and type I error of the tests) of the observed relatedness among the statistics that allow tests for phylogenetic signal. Blomberg et al. K* statistic appears as one on the most efficient approaches to test for phylogenetic signal. When branch lengths are not available or not accurate, Abouheif's C_mean statistic is a powerful alternative to K*.     

Genotypic diversity: estimation and prediction in samples

We show that a commonly used statistic of genotypic diversity can be used to reflect one form of deviation from panmixia, viz. clonal reproduction, by comparing observed and predicted sample statistics. The characteristics of the statistic, in particular its relationship with population genotypic diversity, are formalised and a method of predicting the genotypic diversity of a sample drawn from a panmictic population using allelic frequencies and sample size is developed. The sensitivity of some possible tests of significance of the deviation from panmictic expectations is examined using computer simulations. Goodness-of-fit tests are robust but produce an unacceptably high level of type II error. With means and variances calculated either from Monte Carlo simulations or from distributional and series approximations, t-tests perform better than goodness-of-fit tests. Under simulation, both forms of t-test exhibit acceptable rates of type I error. Rates of type II are usually large when allele frequencies are severely skewed although the latter test performs the better in those conditions.     

Properties of Statistical Tests of Neutrality for DNA Polymorphism Data

A class of statistical tests based on molecular polymorphism data is studied to determine size and power properties. The class includes TAJIMA''s D statistic as well as the D* and F* tests proposed by FU and LI. A new method of constructing critical values for these tests is described. Simulations indicate that TAJIMA''s test is generally most powerful against the alternative hypotheses of selective sweep, population bottleneck, and population subdivision, among tests within this class. However, even TAJIMA''s test can detect a selective sweep or bottleneck only if it has occurred within a specific interval of time in the recent past or population subdivision only when it has persisted for a very long time. For greatest power against the particular alternatives studied here, it is better to sequence more alleles than more sites.     

Powerful allele sharing statistics for nonparametric linkage analysis

Nonparametric linkage analysis is widely used to map susceptibility genes for complex diseases. This paper introduces six nonparametric statistics for measuring marker allele sharing among the affected members of a pedigree. We compare the power of these new statistics and three previous statistics to detect linkage with Mendelian diseases having recessive, additive, and dominant modes of inheritance. The nine statistics represent all possible combinations of three different IBD scoring functions and three different schemes for sampling genes among affecteds. Our results strongly suggest that the statistic T(rec)(blocks) is best for recessive traits, while the two statistics T(kin)(pairs) and T(all)(kin) vie for best for an additive trait. The best statistic for a dominant trait is less clear. The statistics T(kin)(pairs) and T(all)(kin) are equally promising for small sibships, but in extended pedigrees the statistics T(dom)(blocks) and T(dom)(pairs) appear best. For a complex trait, we advocate computing several of these statistics.     

Properties of different selection signature statistics and a new strategy for combining them

Identifying signatures of recent or ongoing selection is of high relevance in livestock population genomics. From a statistical perspective, determining a proper testing procedure and combining various test statistics is challenging. On the basis of extensive simulations in this study, we discuss the statistical properties of eight different established selection signature statistics. In the considered scenario, we show that a reasonable power to detect selection signatures is achieved with high marker density (>1 SNP/kb) as obtained from sequencing, while rather small sample sizes (~15 diploid individuals) appear to be sufficient. Most selection signature statistics such as composite likelihood ratio and cross population extended haplotype homozogysity have the highest power when fixation of the selected allele is reached, while integrated haplotype score has the highest power when selection is ongoing. We suggest a novel strategy, called de-correlated composite of multiple signals (DCMS) to combine different statistics for detecting selection signatures while accounting for the correlation between the different selection signature statistics. When examined with simulated data, DCMS consistently has a higher power than most of the single statistics and shows a reliable positional resolution. We illustrate the new statistic to the established selective sweep around the lactase gene in human HapMap data providing further evidence of the reliability of this new statistic. Then, we apply it to scan selection signatures in two chicken samples with diverse skin color. Our analysis suggests that a set of well-known genes such as BCO2, MC1R, ASIP and TYR were involved in the divergent selection for this trait.     

Sample Size Determination for Designing a Strata-Matched Case-Control Study to Detect Multiple Risk Factors

Investigations of sample size for planning case-control studies have usually been limited to detecting a single factor. In this paper, we investigate sample size for multiple risk factors in strata-matched case-control studies. We construct an omnibus statistic for testing M different risk factors based on the jointly sufficient statistics of parameters associated with the risk factors. The statistic is non-iterative, and it reduces to the Cochran statistic when M = 1. The asymptotic power function of the test is a non-central chi-square with M degrees of freedom and the sample size required for a specific power can be obtained by the inverse relationship. We find that the equal sample allocation is optimum. A Monte Carlo experiment demonstrates that an approximate formula for calculating sample size is satisfactory in typical epidemiologic studies. An approximate sample size obtained using Bonferroni's method for multiple comparisons is much larger than that obtained using the omnibus test. Approximate sample size formulas investigated in this paper using the omnibus test, as well as the individual tests, can be useful in designing case-control studies for detecting multiple risk factors.     

Genomic prediction in CIMMYT maize and wheat breeding programs

Genomic selection (GS) has been implemented in animal and plant species, and is regarded as a useful tool for accelerating genetic gains. Varying levels of genomic prediction accuracy have been obtained in plants, depending on the prediction problem assessed and on several other factors, such as trait heritability, the relationship between the individuals to be predicted and those used to train the models for prediction, number of markers, sample size and genotype × environment interaction (GE). The main objective of this article is to describe the results of genomic prediction in International Maize and Wheat Improvement Center''s (CIMMYT''s) maize and wheat breeding programs, from the initial assessment of the predictive ability of different models using pedigree and marker information to the present, when methods for implementing GS in practical global maize and wheat breeding programs are being studied and investigated. Results show that pedigree (population structure) accounts for a sizeable proportion of the prediction accuracy when a global population is the prediction problem to be assessed. However, when the prediction uses unrelated populations to train the prediction equations, prediction accuracy becomes negligible. When genomic prediction includes modeling GE, an increase in prediction accuracy can be achieved by borrowing information from correlated environments. Several questions on how to incorporate GS into CIMMYT''s maize and wheat programs remain unanswered and subject to further investigation, for example, prediction within and between related bi-parental crosses. Further research on the quantification of breeding value components for GS in plant breeding populations is required.