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 note on the effect of within-strain sample sizes on QTL mapping in recombinant inbred strain studies

This note explores the effect of within-strain sample sizes on the correlations between a phenotype and a molecular-genetic marker in a battery of inbred strains. It is shown that the maximum correlation possible between a molecular marker and a behavioral or neuronal phenotype equals the additive-genetic correlation. How close the strain correlation will approach the additive-genetic correlation depends only on heritability and within-strain sample sizes. The equations derived can be used to optimize designs of studies attempting to localize Quantitative Trait Loci utilizing Recombinant Inbred Strains, provided information about the heritability of the character under study is available.     

ENVIRONMENT-DEPENDENCE OF QUANTITATIVE GENETIC PARAMETERS IN IMPATIENS PALLIDA

Population response to selection depends on the presence of additive genetic variance for traits under selection. When a population enters an alien environment, environment-induced changes in the expression of genetic variance may occur. These could have large effects on the response to selection. To investigate the environment-dependence of genetic variance, we conducted a reciprocal transplant experiment between two ecotypically differentiated populations of Impatiens pallida using the progeny of a standard mating design. The floodplain site was characterized by high water availability, moderate temperatures, and continuous dense stands of Impatiens. The hillside site was drier, with larger temperature extremes and supported only scattered patches of Impatiens with significantly lower seed production and earlier mortality. Estimates of heritability were low for each of the 13 traits measured in each population and site (range from 0–28%). Additive genetic variance for life-history traits tended to be larger than for morphological traits, but genetic variance in fitness was estimated to be not significantly different from zero in all cases. Significant heritability was detected in both populations for one trait (date of first cleistogamous flower) known to be closely related to fitness on the hillside. In general, heritability was reduced for populations when grown in the hillside site relative to the floodplain site, suggesting that stress acts to reduce the expression of genetic variance and the potential to respond to selection there. Consistent reductions in heritability associated with more stressful environments suggest that populations invading such sites may undergo little adaptive differentiation and be more prone to local extinction.     

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     

性状遗传力与QTL方差对标记辅助选择效果的影响

在采用动物模型标记辅助最佳线性无偏预测方法对个体育种值进行估计的基础上,模拟了在一个闭锁群体内连续对单个性状选择10个世代的情形,并系统地比较了性状遗传力和QTL方差对标记辅助选择所获得的遗传进展、QTL增效基因频率和群体近交系数变化的影响。结果表明：在对高遗传力和QTL方差较小的性状实施标记辅助选择时,可望获得更大的遗传进展;遗传力越高,QTL方差越大,则QTL增效基因频率的上升速度越快;遗传力较高时,群体近交系数上升的速度较为缓慢,而QTL方差对群体近交系数上升速度的影响则不甚明显。结合前人关于标记辅助选择相对效率的研究结果,可以认为：当选择性状的遗传力和QTL方差为中等水平时,标记辅助选择可望获得理想的效果。     

Heritability is not Evolvability

Short-term evolutionary potential depends on the additive genetic variance in the population. The additive variance is often measured as heritability, the fraction of the total phenotypic variance that is additive. Heritability is thus a common measure of evolutionary potential. An alternative is to measure evolutionary potential as expected proportional change under a unit strength of selection. This yields the mean-scaled additive variance as a measure of evolvability. Houle in Genetics 130:195–204, (1992) showed that these two ways of scaling additive variance are often inconsistent and can lead to different conclusions as to what traits are more evolvable. Here, we explore this relation in more detail through a literature review, and through theoretical arguments. We show that the correlation between heritability and evolvability is essentially zero, and we argue that this is likely due to inherent positive correlations between the additive variance and other components of phenotypic variance. This means that heritabilities are unsuitable as measures of evolutionary potential in natural populations. More generally we argue that scaling always involves non-trivial assumptions, and that a lack of awareness of these assumptions constitutes a systemic error in the field of evolutionary biology.     

Increases in the evolutionary potential of upper thermal limits under warmer temperatures in two rainforest Drosophila species

Tropical and subtropical species represent the majority of biodiversity. These species are predicted to lack the capacity to evolve higher thermal limits in response to selection imposed by climatic change. However, these assessments have relied on indirect estimates of adaptive capacity, using conditions that do not reflect environmental changes projected under climate change. Using a paternal half‐sib full‐sib breeding design, we estimated the additive genetic variance and narrow‐sense heritability for adult upper thermal limits in two rainforest‐restricted species of Drosophila reared under two thermal regimes, reflecting increases in seasonal temperature projected for the Wet Tropics of Australia and under standard laboratory conditions (constant 25°C). Estimates of additive genetic variation and narrow‐sense heritability for adult heat tolerance were significantly different from zero in both species under projected summer, but not winter or constant, thermal regimes. In contrast, significant broad‐sense genetic variation was apparent in all thermal regimes for egg‐to‐adult viability. Environment‐dependent changes in the expression of genetic variation for adult upper thermal limits suggest that predicting adaptive responses to climate change will be difficult. Estimating adaptive capacity under conditions that do not reflect future environmental conditions may provide limited insight into evolutionary responses to climate change.     

Genetic aspects of aluminum tolerance in sorghum

To obtain crops tolerant to aluminum (Al) toxicity in acid soils, several methods have been used to screen different plant species and genotypes to this production constraint. Little is known about the effect of the method on genetic analyses and breeding method suggested. Three genetic studies were conducted to examine evaluation method on inheritance and gene action of sorghum [Sorghum bicolor (L.) Moench] to Al toxicity as measured by seedling dry matter production.Results of acid soil and solution culture studies indicated that tolerance to Al toxicity was inherited as a dominant character. Narrow-sense heritability estimates in the greenhouse acid-soil study were low for shoot and root dry matter production. Six of the same hybrids tested in solution culture produced high additive-genetic variance and had narrow-sense heritability estimates of 72% for shoot and 65% for root DM yields. Griffing's diallel analysis showed that seven of nine restorer lines had substantially higher specific than general combining ability variances for both root and shoot dry matter yields.Inconsistencies between the acid soil and solution culture techniques showed that different genetic responses to the treatments were being measured. The solution culture study indicated to the plant breeder that genes conditioning Al tolerance could be incorporated into pure lines while the greenhouse acid-soil study would predict that this would not be possible. The diallel study of plants grown in solution culture showed that developing both Al-tolerant varieties and hybrids would be possible depending upon Al-tolerant germplasm used. Acid-soil field studies of actual genetic gain for Al to lerance are needed.     

The value of gametoclonal variation in breeding for quantitative traits in flue-cured tobacco (Nicotiana tabacum L.)

Summary In tobacco (Nicotiana tabacum L.), anther-derived doubled haploid populations have been shown to exhibit large amounts of unexpected genetic variation and a severe depression in cured leaf yield when compared to conventionally inbred genotypes from comparable sources. A previous study had predicted that the yield depression observed in a doubled haploid population-derived from a near homozygous cultivar, NC95, might be overcome through a recurrent selection program. In the current study, progress from three cycles of full-sib family selection for improved yield in an anther-culture derived population of NC95 was measured, as well as the remaining genetic variation within the population. A design II experiment was conducted in the population following three cycles of selection. Results indicate that the NC95 yield level has been recovered in the third selection cycle population. Although most of the genetic variation in the population appears to be exhausted, the additive genetic variance among maternal half-sib families for yield is significant, and it appears that continued yield improvement can be made through recurrent selection. Significant additive-genetic variance for yield was found among maternal half-sib families but was essentially zero among the paternal half-sib families, suggesting that remaining genetic variation is not being transmitted through pollen. One possible explanation results from the phenomenon of DNA amplification that can occur during the anther culture process, and that may enable extraordinary recombinational events and reduce the viability of male gametes.     

Effects of data imbalance on estimation of heritability

Summary Effects of data imbalance on bias, sampling variance and mean square error of heritability estimated with variance components were examined using a random two-way nested classification. Four designs, ranging from zero imbalance (balanced data) to low, medium and high imbalance, were considered for each of four combinations of heritability (h²=0.2 and 0.4) and sample size (N=120 and 600). Observations were simulated for each design by drawing independent pseudo-random deviates from normal distributions with zero means, and variances determined by heritability. There were 100 replicates of each simulation; the same design matrix was used in all replications. Variance components were estimated by analysis of variance (Henderson's Method 1) and by maximum likelihood (ML). For the design and model used in this study, bias in heritability based on Method 1 and ML estimates of variance components was negligible. Effect of imbalance on variance of heritability was smaller for ML than for Method 1 estimation, and was smaller for heritability based on estimates of sire-plus-dam variance components than for heritability based on estimates of sire or dam variance components. Mean square error for heritability based on estimates of sire-plus-dam variance components appears to be less sensitive to data imbalance than heritability based on estimates of sire or dam variance components, especially when using Method 1 estimation. Estimation of heritability from sire-plus-dam components was insensitive to differences in data imbalance, especially for the larger sample size.Supported by grants from the Illinois Agricultural Experiment Station and the University of Illinois Research Board. Charles Smith, H. W. Norton and D. Gianola contributed valuable suggestions     

Why is there so much genetic variation for wing dimorphism?

Wing dimorphism appears in general to be determined either by a single locus, 2 allele system in which brachyptery is dominant, or by the additive action of numerous loci. In the latter case studies indicate that the heritability is typically quite large. It is generally postulated that wing dimorphism is under strong selection: why then is genetic variation not eroded? In this paper I consider three possible explanations. First, genetic variation may not be exposed to selection because environmental heterogeneity effectively makes heritability zero. Because wing dimorphisms are known to evolve it seems unlikely that this is the primary factor. Second, directional selection on a threshold trait may push the population almost to monomorphism but erodes genetic variance at a very slow rate. This mechanism cannot preserve variation but makes it possible for other factors to more easily maintain variability. Finally, I demonstrate that in a heterogeneous environment spatio-temporal variation in fitness will itself maintain a genetic polymorphism for wing dimorphism.     

Basal metabolic rate can evolve independently of morphological and behavioural traits

Quantitative genetic analyses of basal metabolic rate (BMR) can inform us about the evolvability of the trait by providing estimates of heritability, and also of genetic correlations with other traits that may constrain the ability of BMR to respond to selection. Here, we studied a captive population of zebra finches (Taeniopygia guttata) in which selection lines for male courtship rate have been established. We measure BMR in these lines to see whether selection on male sexual activity would change BMR as a potentially correlated trait. We find that the genetic correlation between courtship rate and BMR is practically zero, indicating that the two traits can evolve independently of each other. Interestingly, we find that the heritability of BMR in our population (h²=0.45) is markedly higher than was previously reported for a captive zebra finch population from Norway. A comparison of the two studies shows that additive genetic variance in BMR has been largely depleted in the Norwegian population, especially the genetic variance in BMR that is independent of body mass. In our population, the slope of BMR increase with body mass differs not only between the sexes but also between the six selection lines, which we tentatively attribute to genetic drift and/or founder effects being strong in small populations. Our study therefore highlights two things. First, the evolvability of BMR may be less constrained by genetic correlations and lack of independent genetic variation than previously described. Second, genetic drift in small populations can rapidly lead to different evolvabilities across populations.     

Prediction of breeding values and selection responses with genetic heterogeneity of environmental variance

There is empirical evidence that genotypes differ not only in mean, but also in environmental variance of the traits they affect. Genetic heterogeneity of environmental variance may indicate genetic differences in environmental sensitivity. The aim of this study was to develop a general framework for prediction of breeding values and selection responses in mean and environmental variance with genetic heterogeneity of environmental variance. Both means and environmental variances were treated as heritable traits. Breeding values and selection responses were predicted with little bias using linear, quadratic, and cubic regression on individual phenotype or using linear regression on the mean and within-family variance of a group of relatives. A measure of heritability was proposed for environmental variance to standardize results in the literature and to facilitate comparisons to "conventional" traits. Genetic heterogeneity of environmental variance can be considered as a trait with a low heritability. Although a large amount of information is necessary to accurately estimate breeding values for environmental variance, response in environmental variance can be substantial, even with mass selection. The methods developed allow use of the well-known selection index framework to evaluate breeding strategies and effects of natural selection that simultaneously change the mean and the variance.     

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.     

Smaller gene networks permit longer persistence in fast-changing environments

The environments in which organisms live and reproduce are rarely static, and as the environment changes, populations must evolve so that phenotypes match the challenges presented. The quantitative traits that map to environmental variables are underlain by hundreds or thousands of interacting genes whose allele frequencies and epistatic relationships must change appropriately for adaptation to occur. Extending an earlier model in which individuals possess an ecologically-critical trait encoded by gene networks of 16 to 256 genes and random or scale-free topology, I test the hypothesis that smaller, scale-free networks permit longer persistence times in a constantly-changing environment. Genetic architecture interacting with the rate of environmental change accounts for 78% of the variance in trait heritability and 66% of the variance in population persistence times. When the rate of environmental change is high, the relationship between network size and heritability is apparent, with smaller and scale-free networks conferring a distinct advantage for persistence time. However, when the rate of environmental change is very slow, the relationship between network size and heritability disappears and populations persist the duration of the simulations, without regard to genetic architecture. These results provide a link between genes and population dynamics that may be tested as the -omics and bioinformatics fields mature, and as we are able to determine the genetic basis of ecologically-relevant quantitative traits.     

Inheritance of nesting behaviour across natural environmental variation in a turtle with temperature-dependent sex determination

Nesting behaviour is critical for reproductive success in oviparous organisms with no parental care. In organisms where sex is determined by incubation temperature, nesting behaviour may be a prime target of selection in response to unbalanced sex ratios. To produce an evolutionary change in response to sex-ratio selection, components of nesting behaviour must be heritable. We estimated the field heritability of two key components of nesting behaviour in a population of painted turtles (Chrysemys picta) with temperature-dependent sex determination by applying the ‘animal model’ to a pedigree reconstructed from genotype data. We obtained estimates of low to non-detectable heritability using repeated records across all environments. We then determined environment-specific heritability by grouping records with similar temperatures for the winter preceding the nesting season, a variable known to be highly associated with our two traits of interest, nest vegetation cover and Julian date of nesting. The heritability estimates of nest vegetation cover and Julian date of nesting were qualitatively highest and significant, or nearly so, after hot winters. Additive genetic variance for these traits was not detectable after cold winters. Our analysis suggests that the potential for evolutionary change of nesting behaviour may be dependent on the thermal conditions of the preceding winter, a season that is predicted to be especially subject to climate change.     

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.     

Is there a trade-off between egg weight and clutch size in wild Lesser Snow Geese (Anser c. caerulescens)?

Previous studies of arctic nesting geese suggest that laying is limited by the size of a female's body reserves and that larger eggs contain more nutrients. These observations imply a life-history trade-off between egg size and clutch size which may give rise to a negative genetic correlation between the two characters. We estimated the genetic correlation between egg weight and clutch size using measurements from mothers and their daughters in a wild population of Lesser Snow Geese Anser caerulescens caerulescens. Between 65 and 80 % of the variance in egg weight is attributable to differences between individuals, and heritability of egg weight is about 60 %. In contrast, 10–20 % of the variance in clutch size is attributable to differences between individuals, and heritability of clutch size is about 15 %. The genetic correlation coefficient between egg weight and clutch size ranges from 0.09 to 0.32 and does not differ significantly from zero. We discuss the possible reasons for the lack of the expected negative genetic correlation.     

Assumptions and Properties of Limiting Pathway Models for Analysis of Epistasis in Complex Traits

For most complex traits, results from genome-wide association studies show that the proportion of the phenotypic variance attributable to the additive effects of individual SNPs, that is, the heritability explained by the SNPs, is substantially less than the estimate of heritability obtained by standard methods using correlations between relatives. This difference has been called the “missing heritability”. One explanation is that heritability estimates from family (including twin) studies are biased upwards. Zuk et al. revisited overestimation of narrow sense heritability from twin studies as a result of confounding with non-additive genetic variance. They propose a limiting pathway (LP) model that generates significant epistatic variation and its simple parametrization provides a convenient way to explore implications of epistasis. They conclude that over-estimation of narrow sense heritability from family data (‘phantom heritability’) may explain an important proportion of missing heritability. We show that for highly heritable quantitative traits large phantom heritability estimates from twin studies are possible only if a large contribution of common environment is assumed. The LP model is underpinned by strong assumptions that are unlikely to hold, including that all contributing pathways have the same mean and variance and are uncorrelated. Here, we relax the assumptions that underlie the LP model to be more biologically plausible. Together with theoretical, empirical, and pragmatic arguments we conclude that in outbred populations the contribution of additive genetic variance is likely to be much more important than the contribution of non-additive variance.     

Genetic Control of Glycolysis in Human Erythrocytes

We have studied heritability of the concentration of each glycolytic intermediate and adenine nucleotide in the cytosol of human erythrocytes obtained from a random sample of apparently healthy young individuals. Preliminary to analysis of heritability, each trait was statistically described and the effects attributable to variation in measured concomitants were removed by regression. Heritability was estimated using the family-set method. This method removes covariances between the index case, sibling and first cousin, due to those environmental determinants of the phenotypic values that are shared with a matched, unrelated control member of the family set. It also removes covariances due to environments that are shared by siblings and first cousins. Heritability was estimated by employing the fact that the variance of differences between first cousins minus the variance of differences between full siblings estimates three-fourths of the additive genetic variance. The heritability estimates for G6P†, F6P, ATP and some other metabolite concentrations are high and significantly greater than zero. The heritabilities of G6P and F6P are likely attributable to genetic variation in the in vivo activity of HK and/or PFK, because the concentrations of these metabolites are tightly controlled by the two regulatory enzymes. Statistically significant heritability estimates for HK and PFK mass action ratios strongly suggest genes are responsible for a portion of the quantitative variation in these enzyme activities. Since HK and PFK regulate glycolysis and the production of ATP, genetic variation in their activities might be causally related to the heritability of ATP concentration.