Genetic analysis of crossfostering data with sire and dam records

A method is presented for the analysis of data from crossfostering experiments in which parts of litters are reciprocally interchanged at birth. Observed variances and covariances of differently related individuals are expressed as functions of theoretical causal components of phenotypic variance (additive direct, dominance direct, additive maternal, dominance maternal, direct-maternal covariance, and environmental). Causal components are estimated by weighted least squares analysis of this system of equations, including a ridge-regression procedure to examine consequences of correlation between observed components. Ridge regression suggests that dominance direct genetic variance is generally underestimated, but that narrow-sense heritability estimates are reliable.     

Geometric estimates of heritability in biological shape

The recently developed geometric morphometrics methods represent an important contribution of statistics and geometry to the study of biological shapes. We propose simple protocols using shape distances that incorporate geometric techniques into linear quantitative genetic models that should provide insights into the contribution of genetics to shape variation in organisms. The geometric approaches use Procrustes distances in a curved shape space and distances in tangent spaces within and among families to estimate shape heritability. We illustrate the protocols with an example of wing shape variation in the honeybee, Apis mellifera. The heritability of overall shape variation was small, but some localized components depicting shape changes on distal wing regions showed medium to large heritabilities. The genetic variance-covariance matrix of the geometric shape variables was significantly correlated with the phenotypic shape variance-covariance matrix. A comparison of the results of geometric methods with the traditional multivariate analysis of interlandmark distances indicated that even with a larger dimensionality, the interlandmark distances were not as rich in shape information as the landmark coordinates. Quantitative genetics studies of shape should greatly benefit from the application of geometric methods.     

Testing marker-based estimates of heritability in the wild

Marker-based estimates of heritability are an attractive alternative to pedigree-based methods for estimating quantitative genetic parameters in field studies where it is difficult or impossible to determine relationships and pedigrees. Here I test the ability of the marker-based method to estimate heritability of a suite of traits in a wild population of bighorn sheep (Ovis canadensis) using marker data from 32 microsatellite loci. I compared marker-based estimates with estimates obtained using a pedigree and the animal model. Marker-based estimates of heritability were imprecise and downwardly biased. The high degree of uncertainty in marker-based estimates suggests that the method may be sufficient to detect the presence of genetic variance for highly heritable traits, but not sufficiently reliable to estimate genetic parameters.     

How meaningful are heritability estimates of liability?

It is commonly acknowledged that estimates of heritability from classical twin studies have many potential shortcomings. Despite this, in the post-GWAS era, these heritability estimates have come to be a continual source of interest and controversy. While the heritability estimates of a quantitative trait are subject to a number of biases, in this article we will argue that the standard statistical approach to estimating the heritability of a binary trait relies on some additional untestable assumptions which, if violated, can lead to badly biased estimates. The ACE liability threshold model assumes at its heart that each individual has an underlying liability or propensity to acquire the binary trait (e.g., disease), and that this unobservable liability is multivariate normally distributed. We investigated a number of different scenarios violating this assumption such as the existence of a single causal diallelic gene and the existence of a dichotomous exposure. For each scenario, we found that substantial asymptotic biases can occur, which no increase in sample size can remove. Asymptotic biases as much as four times larger than the true value were observed, and numerous cases also showed large negative biases. Additionally, regions of low bias occurred for specific parameter combinations. Using simulations, we also investigated the situation where all of the assumptions of the ACE liability model are met. We found that commonly used sample sizes can lead to biased heritability estimates. Thus, even if we are willing to accept the meaningfulness of the liability construct, heritability estimates under the ACE liability threshold model may not accurately reflect the heritability of this construct. The points made in this paper should be kept in mind when considering the meaningfulness of a reported heritability estimate for any specific disease.     

Chromatin and heritability: how epigenetic studies can complement genetic approaches

Despite the success in using genome-wide association studies to identify many loci associated with human disease, there are several gaps in understanding of how common genetic diseases are manifested. Epigenetic studies, which focus on DNA and chromatin modifications, have the potential to complement genetic approaches and provide more insight into mechanism, environmental effects and modes of inheritance, including the potential for non-DNA-based heritability. However, there are considerable challenges in designing and interpreting epigenetic studies associated with disease. Here, I review recent studies focused on individual variation in chromatin, and outline how epigenome-based studies can be used to complement genetic studies. In particular, I see more benefit to epigenetic studies being performed in the context of genetic studies, rather than as separate investigations.     

Improving estimates of genetic maps: a maximum likelihood approach

As a result of previous large, multipoint linkage studies there is a substantial amount of existing marker data. Due to the increased sample size, genetic maps estimated from these data could be more accurate than publicly available maps. However, current methods for map estimation are restricted to data sets containing pedigrees with a small number of individuals, or cannot make full use of marker data that are observed at several loci on members of large, extended pedigrees. In this article, a maximum likelihood (ML) method for map estimation that can make full use of the marker data in a large, multipoint linkage study is described. The method is applied to replicate sets of simulated marker data involving seven linked loci, and pedigree structures based on the real multipoint linkage study of Abkevich et al. (2003, American Journal of Human Genetics 73, 1271-1281). The variance of the ML estimate is accurately estimated, and tests of both simple and composite null hypotheses are performed. An efficient procedure for combining map estimates over data sets is also suggested.     

Comparing likelihood and Bayesian coalescent estimation of population parameters

We have developed a Bayesian version of our likelihood-based Markov chain Monte Carlo genealogy sampler LAMARC and compared the two versions for estimation of theta = 4N(e)mu, exponential growth rate, and recombination rate. We used simulated DNA data to assess accuracy of means and support or credibility intervals. In all cases the two methods had very similar results. Some parameter combinations led to overly narrow support or credibility intervals, excluding the truth more often than the desired percentage, for both methods. However, the Bayesian approach rejected the generative parameter values significantly less often than the likelihood approach, both in cases where the level of rejection was normal and in cases where it was too high.     

Are heritability estimates generalizable? Lack of evidence from cross-sample correlations

The majority of research indicates that estimates of heritability are not generalizable beyond the specific sample on which they have been calculated. This research has been limited, however, in its scope. The present set of investigations center upon an examination of previously reported heritability estimates for the scales of the Minnesota Multiphasic Personality Inventory (MMPI). The first investigation correlates the estimates for eight samples derived from a variety of published studies. The second investigated correlates the DZ twin pair and MZ twin pair intraclass correlations from four of the first investigation's samples. The third investigation correlates the estimates from one study in which the same sample was tested twice over a period of less than five years. It is concluded that no evidence is available for the generalizability of these estimates of MMPI scale heritability either across samples or even across time with the same sample.     

Interpreting estimates of heritability – A note on the twin decomposition

While most outcomes may in part be genetically mediated, quantifying genetic heritability is a different matter. To explore data on twins and decompose the variation is a classical method to determine whether variation in outcomes, e.g. IQ or schooling, originate from genetic endowments or environmental factors. Despite some criticism, the model is still widely used. The critique is generally related to how estimates of heritability may encompass environmental mediation. This aspect is sometimes left implicit by authors even though its relevance for the interpretation is potentially profound. This short note is an appeal for clarity from authors when interpreting the magnitude of heritability estimates. It is demonstrated how disregarding existing theoretical contributions can easily lead to unnecessary misinterpretations and/or controversies. The key arguments are relevant also for estimates based on data of adopted children or from modern molecular genetics research.     

Application of jackknife procedures to inter-experiment comparisons of parameter estimates for the Michaelis-Menten equation.

The jackknife procedure is introduced as a means of making comparisons among Michaelis-Menten parameter estimates for six different experimental conditions. In addition to providing a solution to the general inter-experimental comparison problem, the jackknife procedure will provide valid parameter estimates even when some of the assumptions usually required for statistical analysis are violated, e.g., the random errors are not normally distributed and the variances are not homogeneous. Other recent variations of the jackknife have also been introduced and briefly investigated: (i) the linear jackknife, which is more efficient computationally, and (ii) the weighted jackknife, which reduces the influence of design points (substrate concentrations) that have an excessive influence on the precision of parameter estimates.     

Environmental stability and heritability estimates for grain yield and test weight in triticale

Hexaploid triticale has many advantages over both parental species for both grain and forage production in certain environments. Additional information on environmental stability and heritability would be desirable to develop appropriate selection strategies in the production of superior widely-adapted cultivars. The grain yield of 22 diverse genotypes grown at four ecologically-distinct geographical locations [Quincy, FL, USA (approximate geographical coordinates (AGC) = 30 degreesN 84 degreesW, approximate elevation (AE) = 58 m), Plains, GA, USA (AGC = 32 degreesN 84 degreesW, AE = 76 m), Bozeman, MT USA (AGC = 45 degreesN 111 degreesW, AE = 1458 m), and Aberdeen, ID, USA (AGC = 42 degreesN 112 degreesW, AE = 1360 m)] was measured in two years with winter and spring planting dates only at Bozeman and Aberdeen. Test weight (grain weight in a given volume) was determined for two years at Bozeman and Aberdeen at both planting dates and one year at Quincy. Stability analyses indicated that significant (P < 0.01) variation in means, regression coefficients, and deviation mean squares of the genotypes were present for both characters. Realized heritability (h2) estimates were as follows: grain yield ranged from -0.02 to 0.80 with a mean of 0.57; test weight ranged from 0.63 to 1.05 with a mean of 0.93. The results indicated that substantial genetic variation is present and selection for widely-adapted cultivars would be effective for both characters especially test weight.     

Comparison of year-of-exam- and age-matched estimates of heritability in the Framingham Heart Study data

Several different approaches can be used to examine generational and temporal trends in family studies. The measurement of offspring and parents can be made over a short period of time with parents and offspring having quite different ages, or measurements can be made at the same ages but with decades between parent and offspring measures. A third approach, used in the Framingham Heart Study, has repeated examinations across a broad range of age and time, and provides a unique opportunity to compare these approaches. Parents and offspring were matched both on (year of exam) and on age. Heritability estimates for systolic blood pressure, body mass index, height, weight, cholesterol, and glucose were obtained by regressing offspring on midparent values with and without adjustment for age. Higher estimates of heritability were obtained for age-matched than for year-of-exam-matched data for all traits considered. For most traits, estimates of the heritability of the change over time (slope) of the trait were near zero. These results suggest that the optimal design to identify genetic effects in traits with large age-related effects may be to measure parents and offspring at similar ages and not to rely on age-adjustment or longitudinal measures to account for these temporal effects.     

Testicular size at weaning in tropically-adapted beef bulls as influenced by breed of sire and dam

This study was conducted to evaluate testicular size at weaning for bulls representing diverse tropically-adapted genotypes. Calves from 2 locations were weighed and castrated at weaning. In one herd, calves were born to Brahman dams and Angus, Tuli, and Brahman sires. Body weights and paired testes weights were heavier (P < 0.01) for Angus x Brahman (AB) genotype than for Tuli x Brahman (TB) and purebred Brahman (BB) genotype calves. The testes:body weight ratio was greater (P < 0.01) for AB than for TB and BB calves. In a second herd, calves were born to Angus cows and Brahman, Tuli, and Senepol sires. Means were similar between Brahman- (BA), Tuli-(TA), and Senepol-sired (SA) calves for body weight and testes:body weight ratio. Paired testes weight was heavier (P < 0.05) for SA than BA calves. Across locations, paired testes weights were heavier (P < 0.01) for TA than TB calves but their body weights were similar. Within-herd deviations were greater (P < 0.01) for AB than BA calves for paired testes weight and testes:body weight ratio. The correlation between the proportion of Bos indicus genetic contribution and testes:body weight ratio was significantly negative. Tropically-adapted calves differed in testicular size at weaning due to breed of sire and dam effects.     

Branch length estimation and divergence dating: estimates of error in Bayesian and maximum likelihood frameworks

Background  

Estimates of divergence dates between species improve our understanding of processes ranging from nucleotide substitution to speciation. Such estimates are frequently based on molecular genetic differences between species; therefore, they rely on accurate estimates of the number of such differences (i.e. substitutions per site, measured as branch length on phylogenies). We used simulations to determine the effects of dataset size, branch length heterogeneity, branch depth, and analytical framework on branch length estimation across a range of branch lengths. We then reanalyzed an empirical dataset for plethodontid salamanders to determine how inaccurate branch length estimation can affect estimates of divergence dates.     

MLEP: an R package for exploring the maximum likelihood estimates of penetrance parameters

ABSTRACT: BACKGROUND: Linkage analysis is a useful tool for detecting genetic variants that regulate a trait of interest, especially genes associated with a given disease. Although penetrance parameters play an important role in determining gene location, they are assigned arbitrary values according to the researcher's intuition or as estimated by the maximum likelihood principle. Several methods exist by which to evaluate the maximum likelihood estimates of penetrance, although not all of these are supported by software packages and some are biased by marker genotype information, even when disease development is due solely to the genotype of a single allele. FINDINGS: Programs for exploring the maximum likelihood estimates of penetrance parameters were developed using the R statistical programming language supplemented by external C functions. The software returns a vector of polynomial coefficients of penetrance parameters, representing the likelihood of pedigree data. From the likelihood polynomial supplied by the proposed method, the likelihood value and its gradient can be precisely computed. To reduce the effect of the supplied dataset on the likelihood function, feasible parameter constraints can be introduced into maximum likelihood estimates, thus enabling flexible exploration of the penetrance estimates. An auxiliary program generates a perspective plot allowing visual validation of the model's convergence. The functions are collectively available as the MLEP R package. CONCLUSIONS: Linkage analysis using penetrance parameters estimated by the MLEP package enables feasible localization of a disease locus. This is shown through a simulation study and by demonstrating how the package is used to explore maximum likelihood estimates. Although the input dataset tends to bias the likelihood estimates, the method yields accurate results superior to the analysis using intuitive penetrance values for disease with low allele frequencies. MLEP is part of the Comprehensive R Archive Network and is freely available at http://cran.r-project.org/web/packages/MLEP/index.html.