The heritability of fitness: some single gene models

Summary Because directional selection exhausts additive-genetic variance, it is frequently claimed that the heritability of fitness should be very close to zero. However, mutation-selection balance generates a certain amount of additive-genetic variance, so that even parent-offspring measures of heritability may be greater than zero at equilibrium. Intra-generation heritability may also be non-zero, providing the potentials for genetic change following environmental change.     

孙女设计中标记密度对QTL定位精确性的影响

采用蒙特卡罗方法分析了在孙女设计中不同的嫩体结构、性状遗传力、ＱＴＬ效应大小和ＱＴＬ在染色体上的位置中个因素不同水平组合下４种标记密度（标记间隔５ｃＭ,１０ｃＭ,２０ｃＭ、５０ｃＭ对ＱＴＬ定位精确性（以均方误ＭＳＥ为衡量指标）的影响,并从经济学角度探讨了应用于标记辅助选（ＭＡＳ）的ＱＴＬ定位的最佳标记密度。结果表明,一般说来,在各因素水平都较低时,ＭＳＥ随标记密度加大而下降的相对幅度也较 小,反之     

基于选择基因型对数量性状进行关联分析

数量性状的遗传分析可以通过＂选择基因型＂的方式完成。本文提出了一个利用极端样本来对数量性状位点（QTL）进行关联分析的统计量T。统计量T比较上极端群体样本中具有纯合子标记的性状值差异。通过计算机模拟考察了无关联情形时T的分布和Ⅰ型错误率,结果表明,在各种样本选择策略下,T的分布近似于χ^2-分布,Ⅰ型错误率接近设定的显著性水平。同时,考察了各种遗传模型下不同遗传率,不同样本大小,及不同样本选择阈值对T的统计功效的影响,结果表明,T的功效随着标记和QTL间连锁不平衡程度的增强及遗传率和样本大小的增大而增大,当样本选择阈值更严格时,功效也越大。     

THE HERITABLE BASIS OF VARIATION IN LARVAL DEVELOPMENTAL PATTERNS WITHIN POPULATIONS OF THE WOOD FROG (RANA SYLVATICA)

This study compares the heritable basis of variation in larval developmental patterns of mountain and lowland populations of the wood frog, Rana sylvatica. Additive genetic variances, heritabilities, and genetic correlations for larval developmental time and size at metamorphosis are estimated from half-sib and full-sib crosses. Considerable additive-genetic variances and high heritabilities are revealed for developmental time in both the mountain and the lowland population. There was a high level of additive-genetic variance and high heritability for body size at metamorphosis in the mountain population, but these were very low in the lowland population. The genetic correlations between developmental rate and larval body size are negative for the mountain population and near zero for the lowland population. It is argued that the differences in genetic structure between these two populations reflect differences in the selective regimes of their respective environments.     

A multi-marker test based on family data in genome-wide association study

Background

Requirements for successful implementation of multivariate animal threshold models including phenotypic and genotypic information are not known yet. Here simulated horse data were used to investigate the properties of multivariate estimators of genetic parameters for categorical, continuous and molecular genetic data in the context of important radiological health traits using mixed linear-threshold animal models via Gibbs sampling. The simulated pedigree comprised 7 generations and 40000 animals per generation. Additive genetic values, residuals and fixed effects for one continuous trait and liabilities of four binary traits were simulated, resembling situations encountered in the Warmblood horse. Quantitative trait locus (QTL) effects and genetic marker information were simulated for one of the liabilities. Different scenarios with respect to recombination rate between genetic markers and QTL and polymorphism information content of genetic markers were studied. For each scenario ten replicates were sampled from the simulated population, and within each replicate six different datasets differing in number and distribution of animals with trait records and availability of genetic marker information were generated. (Co)Variance components were estimated using a Bayesian mixed linear-threshold animal model via Gibbs sampling. Residual variances were fixed to zero and a proper prior was used for the genetic covariance matrix.

Results

Effective sample sizes (ESS) and biases of genetic parameters differed significantly between datasets. Bias of heritability estimates was -6% to +6% for the continuous trait, -6% to +10% for the binary traits of moderate heritability, and -21% to +25% for the binary traits of low heritability. Additive genetic correlations were mostly underestimated between the continuous trait and binary traits of low heritability, under- or overestimated between the continuous trait and binary traits of moderate heritability, and overestimated between two binary traits. Use of trait information on two subsequent generations of animals increased ESS and reduced bias of parameter estimates more than mere increase of the number of informative animals from one generation. Consideration of genotype information as a fixed effect in the model resulted in overestimation of polygenic heritability of the QTL trait, but increased accuracy of estimated additive genetic correlations of the QTL trait.

Conclusion

Combined use of phenotype and genotype information on parents and offspring will help to identify agonistic and antagonistic genetic correlations between traits of interests, facilitating design of effective multiple trait selection schemes.     

Laboratory Estimates of Heritabilities and Genetic Correlations in Nature

A lower bound on heritability in a natural environment can be determined from the regression of offspring raised in the laboratory on parents raised in nature. An estimate of additive genetic variance in the laboratory is also required. The estimated lower bounds on heritabilities can sometimes be used to demonstrate a significant genetic correlation between two traits in nature, if their genetic and phenotypic correlations in nature have the same sign, and if sample sizes are large, and heritabilities and phenotypic and genetic correlations are high.     

Geographical range size heritability: what do neutral models with different modes of speciation predict?

Aim Phylogenetic conservatism or heritability of the geographical range sizes of species (i.e. the tendency for closely related species to share similar range sizes) has been predicted to occur because of the strong phylogenetic conservatism of niche traits. However, the extent of such heritability in range size is disputed and the role of biology in shaping this attribute remains unclear. Here, we investigate the level of heritability of geographical range sizes that is generated from neutral models assuming no biological differences between species. Methods We used three different neutral models, which differ in their speciation mode, to simulate the life‐history of 250,000 individuals in a square lattice of 50 × 50 cells. These individuals can speciate, reproduce, migrate and die in the metacommunity according to stochastic events. We ran each model for 3000 steps and recorded the range size of each species at each step. The heritability of geographical range size was assessed using an asymmetry coefficient between range sizes of sister species and using the coefficient of correlation between the range sizes of ancestors and their descendants. Results Our results demonstrated the ability of neutral models to mimic some important observed patterns in the heritability of geographical range size. Consistently, sister species exhibited higher asymmetry in range sizes than expected by chance, and correlations between the range sizes of ancestor–descendant species pairs, although often weak, were almost invariably positive. Main conclusions Our findings suggest that, even without any biological trait differences, statistically significant heritability in the geographical range sizes of species can be found. This heritability is weaker than that observed in some empirical studies, but suggests that even here a substantial component of heritability may not necessarily be associated with niche conservatism. We also conclude that both present‐day and fossil data sets may provide similar information on the heritability of the geographical range sizes of species, while the omission of rare species will tend to overestimate this heritability.     

Genomic BLUP Decoded: A Look into the Black Box of Genomic Prediction

Genomic best linear unbiased prediction (BLUP) is a statistical method that uses relationships between individuals calculated from single-nucleotide polymorphisms (SNPs) to capture relationships at quantitative trait loci (QTL). We show that genomic BLUP exploits not only linkage disequilibrium (LD) and additive-genetic relationships, but also cosegregation to capture relationships at QTL. Simulations were used to study the contributions of those types of information to accuracy of genomic estimated breeding values (GEBVs), their persistence over generations without retraining, and their effect on the correlation of GEBVs within families. We show that accuracy of GEBVs based on additive-genetic relationships can decline with increasing training data size and speculate that modeling polygenic effects via pedigree relationships jointly with genomic breeding values using Bayesian methods may prevent that decline. Cosegregation information from half sibs contributes little to accuracy of GEBVs in current dairy cattle breeding schemes but from full sibs it contributes considerably to accuracy within family in corn breeding. Cosegregation information also declines with increasing training data size, and its persistence over generations is lower than that of LD, suggesting the need to model LD and cosegregation explicitly. The correlation between GEBVs within families depends largely on additive-genetic relationship information, which is determined by the effective number of SNPs and training data size. As genomic BLUP cannot capture short-range LD information well, we recommend Bayesian methods with t-distributed priors.     

The quantitative LOD score: test statistic and sample size for exclusion and linkage of quantitative traits in human sibships.

We present a test statistic, the quantitative LOD (QLOD) score, for the testing of both linkage and exclusion of quantitative-trait loci in randomly selected human sibships. As with the traditional LOD score, the boundary values of 3, for linkage, and -2, for exclusion, can be used for the QLOD score. We investigated the sample sizes required for inferring exclusion and linkage, for various combinations of linked genetic variance, total heritability, recombination distance, and sibship size, using fixed-size sampling. The sample sizes required for both linkage and exclusion were not qualitatively different and depended on the percentage of variance being linked or excluded and on the total genetic variance. Information regarding linkage and exclusion in sibships larger than size 2 increased as approximately all possible pairs n(n-1)/2 up to sibships of size 6. Increasing the recombination (theta) distance between the marker and the trait loci reduced empirically the power for both linkage and exclusion, as a function of approximately (1-2theta)4.     

Inheritance of height and maturity in crosses between pearl millet landraces and inbred Tift 85DB

Summary Over 300 landraces of pearl millet were collected in Burkina Faso and grown at the Coastal Plain Experiment Station in Tifton/GA. At Tifton, these landraces are predominantly tall and late-maturing. The photoperiod requirements of these landraces hinder evaluation of their performance in the field and their use in breeding programs. A conversion program has been initiated to transfer genes for dwarf stature and early flowering into the tall, late-maturing landraces. The inbred Tift 85DB is being used as a donor of genes for the dwarf and early characteristics, and was crossed to nine randomly selected landraces from Burkina Faso. The parents, F₁, F₂, and backcrosses to each parent were grown in the field and evaluated for plant height at anthesis and time in days from planting to anthesis. In general, plant height of F₁s was taller than the tallest parent, and in all crosses the maturity of F₁s was intermediate between the parents. Numbers of loci conferring height varied among crosses, ranging from 0 to 9.6, and averaged 1.6. Estimated numbers of loci conferring maturity ranged from 0 to 12.8 and averaged 3.4. Broad-sense heritability estimates for height and maturity averaged 60.2 and 65.7%, respectively. Corresponding narrow-sense estimates averaged 23.8 and 48.2%. Joint scaling tests revealed that additive-genetic effects were highly significant for both traits, but dominance and epistatic-genetic effects contributed to the inheritance of each trait in some crosses. The low gene numbers, high heritability estimates, and preponderance of additive-genetic effects suggest that selection for these traits should be effective.     

ESTIMATING GENETIC CORRELATIONS FROM MEASUREMENTS OF FIELD-CAUGHT WATERSTRIDERS

Abstract Lynch (1999) proposed a method for estimation of genetic correlations from phenotypic measurements of individuals for which no pedigree information is available. This method assumes that shared environmental effects do not contribute to the similarity of relatives, and it is expected to perform best when sample sizes are large, many individuals in the sample are paired with close relatives, and heritability of the traits is high. We tested the practicality of this method for field biologists by using it to estimate genetic correlations from measurements of field‐caught waterstriders {Aquarius remigis). Results for sample sizes of less than 100 pairs were often unstable or undefined, and even with more than 500 pairs only half of those correlations that had been found to be significant in standard laboratory experiments were statistically significant in this study. Statistically removing the influence of environmental effects (shared between relatives) weakened the estimates, possibly by removing some of the genetic similarity between relatives. However, the method did generate statistically significant estimates for some genetic correlations. Lynch (1999) anticipated the problems found, and proposed another method that uses estimates of relatedness between members of pairs (from molecular marker data) to improve the estimates of genetic correlations, but that approach has yet to be tested in the field.     

Genetic parameters for milkability from the first three lactations in Fleckvieh cows

Test-day records for average flow rate (AFR) from the routine dairy recording from Bavarian Fleckvieh cows were analysed. Two data sets with observations on approximately 20 000 cows each were sampled from the total data set. For the estimation of variance parameters, a two-step approach was applied. In a first step multiple-trait restricted maximum likelihood (REML) analyses were carried out. For each of the first three lactations, six time periods with up to 33 days were defined. An algorithm for iterative summing of expanded part matrices was applied in order to combine the estimates. In a second step covariance functions (CF) for additive-genetic variances and non-genetic animal variances were derived using second-order Legendre polynomials plus an exponential term. Estimates of test-day heritability for AFR ranged from 0.21 to 0.40, and were largest in lactation 1. For lactations 1 and 3, heritabilities decreased considerably towards the end of lactation. Genetic correlation estimates within lactation decreased as the distance between days in milk (DIM) increased. Genetic correlations between corresponding DIM in the three lactations were generally large, ranging from 0.80 to 0.99. The largest estimates were found between DIM from lactations 2 and 3. Results from this study suggest that including AFR data from second and third lactations in genetic evaluation systems could the improve accuracy of genetic selection.     

Methodological Considerations in Estimation of Phenotype Heritability Using Genome-Wide SNP Data,Illustrated by an Analysis of the Heritability of Height in a Large Sample of African Ancestry Adults

Height has an extremely polygenic pattern of inheritance. Genome-wide association studies (GWAS) have revealed hundreds of common variants that are associated with human height at genome-wide levels of significance. However, only a small fraction of phenotypic variation can be explained by the aggregate of these common variants. In a large study of African-American men and women (n = 14,419), we genotyped and analyzed 966,578 autosomal SNPs across the entire genome using a linear mixed model variance components approach implemented in the program GCTA (Yang et al Nat Genet 2010), and estimated an additive heritability of 44.7% (se: 3.7%) for this phenotype in a sample of evidently unrelated individuals. While this estimated value is similar to that given by Yang et al in their analyses, we remain concerned about two related issues: (1) whether in the complete absence of hidden relatedness, variance components methods have adequate power to estimate heritability when a very large number of SNPs are used in the analysis; and (2) whether estimation of heritability may be biased, in real studies, by low levels of residual hidden relatedness. We addressed the first question in a semi-analytic fashion by directly simulating the distribution of the score statistic for a test of zero heritability with and without low levels of relatedness. The second question was addressed by a very careful comparison of the behavior of estimated heritability for both observed (self-reported) height and simulated phenotypes compared to imputation R² as a function of the number of SNPs used in the analysis. These simulations help to address the important question about whether today''s GWAS SNPs will remain useful for imputing causal variants that are discovered using very large sample sizes in future studies of height, or whether the causal variants themselves will need to be genotyped de novo in order to build a prediction model that ultimately captures a large fraction of the variability of height, and by implication other complex phenotypes. Our overall conclusions are that when study sizes are quite large (5,000 or so) the additive heritability estimate for height is not apparently biased upwards using the linear mixed model; however there is evidence in our simulation that a very large number of causal variants (many thousands) each with very small effect on phenotypic variance will need to be discovered to fill the gap between the heritability explained by known versus unknown causal variants. We conclude that today''s GWAS data will remain useful in the future for causal variant prediction, but that finding the causal variants that need to be predicted may be extremely laborious.     

Power and Effective Study Size in Heritability Studies

Correlation between study units in quantitative genetics studies often makes it difficult to compare important inferential aspects of studies. Describing the relatedness between study units is critical to capture features of pedigree studies involving heritability, including power and precision of heritability estimates. Blangero et al. (Adv Genet 81:1–31, 2012) showed that in pedigree studies the power to detect heritability is a function of the true heritability and the eigenvalues of the kinship matrix. We extend this to a more general setting which allows statements about expected precision of heritability estimates. Using two different Taylor series approximations, we summarize the relatedness in a study design by one or two parameters. These relatedness summary parameters (RSPs) are functions of the eigenvalues or log-eigenvalues of the kinship matrix. Using the RSPs based on the log-eigenvalues, we accurately approximate the expectation of the likelihood ratio test and expected confidence interval widths. We define an effective sample size of a target study as one which has the equivalent power and precision to a reference design. Using unrelated sibpairs as the reference design provides very accurate assessments of power. RSPs and effective sample sizes provide new tools for comparing studies and communicating information about relatedness in heritability studies.     

On the heritability of geographic range sizes

Within taxonomic groups, most species are restricted in their geographic range sizes, with only a few being widespread. The possibility that species-level selection on range sizes contributes to the characteristic form of such species-range size distributions has previously been raised. This would require that closely related species have similar range sizes, an indication of "heritability" of range sizes at the species level. Support for this view came from a positive correlation between the range sizes of closely related pairs of fossil mollusc species. We extend this analysis by considering the relationship between the geographic range sizes of 103 pairs of contemporary avian sister species. Range sizes in these sister species show no evidence of being more similar to each other than expected by chance. A reassessment of the mollusc data also suggests that the high correlation was probably overestimated because of the skewed nature of range size data. The fact that sister species tend to have similar life histories and ecologies suggests that any relationship between range sizes and biology is likely to be complicated and will be influenced by historical factors, such as mode of speciation and postspeciation range size transformations.     

Spatial overlap enhances geographic range size conservatism

Phylogenetic conservatism or heritability of the geographic range sizes of species has been predicted to occur because of the phylogenetic conservatism of niche traits. However, evidence for range size conservatism is mixed, and even when statistically significant is often rather weak and of questionable biological importance. Here, we test the prediction that such conservatism will be more strongly expressed when the amount of spatial overlap between sister species increases. We used the global distributions of 1136 avian species (>10% of extant members of this Class), and tested the conservatism of geographic range sizes using the coefficients of correlation between values for pairs of sister species. We used a null model to test whether the range sizes of sister species were more similar to one another than expected by chance. We found that sister species showed a significant positive relationship between their geographic range sizes whatever the degree of spatial overlap. However, as predicted, the level of conservatism increases with the level of range overlap between sister species. More precisely, the strong increase in the coefficient of correlation between sister species' range sizes when we add species with some range overlap to the pool of pairs without any such overlap indicates an important threshold effect. These results suggest that niche conservatism is more likely to lead to marked heritability of the range sizes of species when similar niche traits are expressed under more similar environmental conditions. These results have significant implications because they suggest 1) that previous analyses of conservatism of range sizes have been confounded by the level of spatial overlap, and 2) that closely related species experiencing similar conditions may tend to expand or restrict their geographic ranges in parallel when faced with climate change.     

Mapping quantitative trait loci by genotyping haploid tissues.

Mapping strategies based on a half- or full-sib family design have been developed to map quantitative trait loci (QTL) for outcrossing species. However, these strategies are dependent on controlled crosses where marker-allelic frequency and linkage disequilibrium between the marker and QTL may limit their application. In this article, a maximum-likelihood method is developed to map QTL segregating in an open-pollinated progeny population using dominant markers derived from haploid tissues from single meiotic events. Results from the haploid-based mapping strategy are not influenced by the allelic frequencies of markers and their linkage disequilibria with QTL, because the probabilities of QTL genotypes conditional on marker genotypes of haploid tissues are independent of these population parameters. Parameter estimation and hypothesis testing are implemented via expectation/conditional maximization algorithm. Parameters estimated include the additive effect, the dominant effect, the population mean, the chromosomal location of the QTL in the interval, and the residual variance within the QTL genotypes, plus two population parameters, outcrossing rate and QTL-allelic frequency. Simulation experiments show that the accuracy and power of parameter estimates are affected by the magnitude of QTL effects, heritability levels of a trait, and sample sizes used. The application and limitation of the method are discussed.     

WHAT DO WE KNOW ABOUT THE HERITABILITY OF DEVELOPMENTAL INSTABILITY? ANSWERS FROM A BAYESIAN MODEL

In spite of over half a century of research, little is known about the genetic basis of developmental instability (DI). The estimation of the heritability of DI is seriously hampered by the fact that fluctuating asymmetry-FA, that is, the observable outcome of DI-only poorly reflects DI. This results in an underestimation of the heritability of DI. Current methods transforming heritabilities in FA into those of DI fail to take all sources of variation into account and yield incorrect confidence bands that are usually based on unrealistic assumptions. Therefore, a Bayesian latent variable model is developed and explored. Simulations show that with sample sizes currently applied in empirical studies, extremely wide posterior distributions are obtained and data do not allow to distinguish between high (0.5) and low (0.1) heritabilities of DI at all. Even sample sizes of 5000 result in very wide posteriors in many cases. Furthermore, for smaller samples (250 and 1250), up to 70% of the estimates of the heritability of DI were below the mean expected value because of the high skewness of its distribution. Knowing that in only one study, sample sizes were above 5000, there is a need for larger studies to evaluate the evolutionary potential of DI. Designs with relatively low numbers of sires (1-2% of total number of offspring) appear most efficient. Because such high sample sizes are hard to obtain for many study organisms, more insights are required about how data from different traits can be combined in a single analysis. In addition, new designs and methods, such as QTL analyses and micro-array techniques, should be applied to gain a better understanding of the genetic basis of DI.     

More on the efficiency of marker-assisted selection

 Computer simulations were used to study the efficiency of marker-assisted selection (MAS) based on an index combining the phenotypic value and the molecular score of individuals. The molecular score is computed from the effects attributed to markers by multiple regression of phenotype on marker genotype. The results show that in the first generation the ratio RE of the expected efficiency of MAS over the expected efficiency of purely phenotypic selection generally increases when considering: (1) larger population sizes, (2) lower heritability values of the trait, and (3) a higher type-I error risk of the regression. This is consistent with previously published results. However, at low heritabilities our results point out that response to MAS is more variable than response to phenotypic selection. Hence, when the difference of genetic gains is considered instead of their ratio, RE, the heritability values corresponding to maximal advantage of using MAS rather than phenotypic selection are still low, but higher than predicted based on RE. The study over several successive generations of the rate of fixation of QTLs shows that the higher efficiency of MAS on QTLs with large effects in early generations is balanced by a higher rate of fixation of unfavourable alleles at QTLs with small effects in later generations. This explains why MAS may become less efficient than phenotypic selection in the long term. MAS efficiency therefore depends on the genetic determinism of the trait. Finally, we investigate a modified MAS method involving an alternation of selection on markers with and without phenotypic evaluation. Our results indicate that such a selection method could at low cost, provide an important increase in the genetic gain per unit of time in practical breeding programs. Received: 11 July 1997 / Accepted: 4 August 1997     

Genetic analysis of ecologically relevant morphological variability in Plantago lanceolata L.

Summary Morphological variability was studied in two populations of Plantago lanceolata using diallel analysis. In each population, reciprocal crosses between all possible pairs of ten plants were made. In the greenhouse, six members of each family were grown and many characters were measured. Using the model of Cockerham and Weir, the contributions of the different genetic variance components were calculated. From earlier papers it was postulated in advance to what extent and by which effect the characters in both populations were genetically determined. The populations had been differentiated for life history and morphological characters, and varied also in the relative contribution of genetic components to variability. In the Merrevliet (Me) population, where strong biotic selection was assumed, low levels of additive-genetic variability were present and the relative dominance appeared to be high. The contrasting population, Westduinen (Wd), which is abiotically controlled and shows strong environmental variability, possessed higher levels of additive-genetic variability and lower levels of relative dominance. It is possible that differential natural selection has diminished additive-genetic variability to different extents in both populations: plasticity and environmental heterogeneity prevented the loss of additive-genetic variability in Wd, whereas in the stable population, Me, natural selection had the opportunity of not only changing the means of the characters but also of diminishing additive-genetic variability to a great extent.Grassland Species Research Group Publication No. 146