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PubMed2006

Multilevel selection 1: Quantitative genetics of inheritance and response to selection.

Interaction among individuals is universal, both in animals and in plants, and substantially affects evolution of natural populations and responses to artificial selection in agriculture. Although quantitative genetics has successfully been applied to many traits, it does not provide a general theory accounting for interaction among individuals and selection acting on multiple levels. Consequently, current quantitative genetic theory fails to explain why some traits do not respond to selection among individuals, but respond greatly to selection among groups. Understanding the full impacts of heritable interactions on the outcomes of selection requires a quantitative genetic framework including all levels of selection and relatedness. Here we present such a framework and provide expressions for the response to selection. Results show that interaction among individuals may create substantial heritable variation, which is hidden to classical analyses. Selection acting on higher levels of organization captures this hidden variation and therefore always yields positive response, whereas individual selection may yield response in the opposite direction. Our work provides testable predictions of response to multilevel selection and reduces to classical theory in the absence of interaction. Statistical methodology provided elsewhere enables empirical application of our work to both natural and domestic populations.

Models, Genetic↗
PubMed2000

Estimating quantitative genetic parameters using sibships reconstructed from marker data.

Previous techniques for estimating quantitative genetic parameters, such as heritability in populations where exact relationships are unknown but are instead inferred from marker genotypes, have used data from individuals on a pairwise level only. At this level, families are weighted according to the number of pairs within which each family appears, hence by size rather than information content, and information from multiple relationships is lost. Estimates of parameters are therefore not the most efficient achievable. Here, Markov chain Monte Carlo techniques have been used to partition the population into complete sibships, including, if known, prior knowledge of the distribution of family sizes. These pedigrees have then been used with restricted maximum likelihood under an animal model to estimate quantitative genetic parameters. Simulations to compare the properties of parameter estimates with those of existing techniques indicate that the use of sibship reconstruction is superior to earlier methods, having lower mean square errors and showing nonsignificant downward bias. In addition, sibship reconstruction allows the estimation of population allele frequencies that account for the relationships within the sample, so prior knowledge of allele frequencies need not be assumed. Extensions to these techniques allow reconstruction of half sibships when some or all of the maternal genotypes are known.

Algorithms↗
PubMed2000

Characterizing the quantitative genetic contribution to rheumatoid arthritis using data from twins.

OBJECTIVE: Twin concordance data for rheumatoid arthritis (RA) on their own provide only limited insight into the relative genetic and environmental contribution to the disease. We applied quantitative genetic methods to assess the heritability of RA and to examine for evidence of differences in the genetic contribution according to sex, age, and clinical disease characteristics. METHODS: Data were analyzed from 2 previously published nationwide studies of twins with RA conducted in Finland and the United Kingdom. Heritability was assessed by variance components analysis. Differences in the genetic contribution by sex, age, age at disease onset, and clinical characteristics were examined by stratification. The power of the twin study design to detect these differences was examined through simulation. RESULTS: The heritability of RA was 65% (95% confidence interval [95% CI] 50-77) in the Finnish data and 53% (95% CI 40-65) in the UK data. There was no significant difference in the strength of the genetic contribution according to sex, age, age at onset, or disease severity subgroup. Both study designs had power to detect a contribution of at least 40% from the common family environment, and a difference in the genetic contribution of at least 50% between subgroups. CONCLUSION: Genetic factors have a substantial contribution to RA in the population, accounting for approximately 60% of the variation in liability to disease. Although tempered by power considerations, there is no evidence in these twin data that the overall genetic contribution to RA differs by sex, age, age at disease onset, and disease severity.

Adult↗
PubMedDate not supplied

The use of quantitative genetic methodology to gain insights into the origins of individual differences in later life.

There is great interest in the interindividual variability in aged populations. Knowledge of the etiology of these individual differences may lead to a more comprehensive understanding of aging. The purpose of this article is to discuss the use of quantitative genetic (or behavioral genetic) methodology to identify sources of individual variation in later life. These methods can provide insights into the proportion of environmental and genetic influences on behavior. Some of the basic procedures used in quantitative genetic analyses and their rationales are provided. In addition, the use of structural equation modeling to model genetic and environmental effects is discussed. Lastly, some of the special issues involved in quantitative genetic research on aged populations are discussed.

Aged↗
PubMed2003

Theory and practice in quantitative genetics.

With the rapid advances in molecular biology, the near completion of the human genome, the development of appropriate statistical genetic methods and the availability of the necessary computing power, the identification of quantitative trait loci has now become a realistic prospect for quantitative geneticists. We briefly describe the theoretical biometrical foundations underlying quantitative genetics. These theoretical underpinnings are translated into mathematical equations that allow the assessment of the contribution of observed (using DNA samples) and unobserved (using known genetic relationships) genetic variation to population variance in quantitative traits. Several statistical models for quantitative genetic analyses are described, such as models for the classical twin design, multivariate and longitudinal genetic analyses, extended twin analyses, and linkage and association analyses. For each, we show how the theoretical biometrical model can be translated into algebraic equations that may be used to generate scripts for statistical genetic software packages, such as Mx, Lisrel, SOLAR, or MERLIN. For using the former program a web-library (available from http://www.psy.vu.nl/mxbib) has been developed of freely available scripts that can be used to conduct all genetic analyses described in this paper.

Genetic Linkage↗
PubMed1998

The molecular basis of quantitative genetic variation in central and secondary metabolism in Arabidopsis.

To find the genes controlling quantitative variation, we need model systems where functional information on physiology, development, and gene regulation can guide evolutionary inferences. We mapped quantitative trait loci (QTLs) influencing quantitative levels of enzyme activity in primary and secondary metabolism in Arabidopsis. All 10 enzymes showed highly significant quantitative genetic variation. Strong positive genetic correlations were found among activity levels of 5 glycolytic enzymes, PGI, PGM, GPD, FBP, and G6P, suggesting that enzymes with closely related metabolic functions are coregulated. Significant QTLs were found influencing activity of most enzymes. Some enzyme activity QTLs mapped very close to known enzyme-encoding loci (e.g., hexokinase, PGI, and PGM). A hexokinase QTL is attributable to cis-acting regulatory variation at the AtHXK1 locus or a closely linked regulatory locus, rather than polypeptide sequence differences. We also found a QTL on chromosome IV that may be a joint regulator of GPD, PGI, and G6P activity. In addition, a QTL affecting PGM activity maps within 700 kb of the PGM-encoding locus. This QTL is predicted to alter starch biosynthesis by 3.4%, corresponding with theoretical models, suggesting that QTLs reflect pleiotropic effects of mutant alleles.

Analysis of Variance↗
PubMed1997

Simple sequence repeats as a source of quantitative genetic variation.

Most traits in biological populations appear to be under stabilizing selection, which acts to eliminate quantitative genetic variation. Yet, virtually all measured traits in biological populations continue to show significant quantitative genetic variation. The paradox can be resolved by postulating the existence of an abundant, though unspecified, source of mutations that has quantitative effects on phenotype, but does not reduce fitness. Does such a source actually exist? We propose that it does, in the form of repeat-number variation in SSRs (simple sequence repeats, of which the triplet repeats of human neurodegenerative diseases are a special case). Viewing SSRs as a major source of quantitative mutation has broad implications for understanding molecular processes of evolutionary adaptation, including the evolutionary control of the mutation process itself.

Animals↗
PubMed2006

Data depth, data completeness, and their influence on quantitative genetic estimation in two contrasting bird populations.

Evolutionary biologists increasingly use pedigree-based quantitative genetic methods to address questions about the evolutionary dynamics of traits in wild populations. In many cases, phenotypic data may have been collected only for recent parts of the study. How does this influence the performance of the models used to analyse these data? Here we explore how data depth (number of years) and completeness (number of observations) influence estimates of genetic variance and covariance within the context of an existing pedigree. Using long-term data from the great tit Parus major and the mute swan Cygnus olor, species with different life-histories, we examined the effect of manipulating the amount of data included on quantitative genetic parameter estimates. Manipulating data depth and completeness had little influence on estimated genetic variances, heritabilities, or genetic correlations, but (as expected) did influence confidence in these estimates. Estimated breeding values in the great tit were not influenced by data depth but were in the mute swan, probably because of differences in pedigree structure. Our analyses suggest the 'rule of thumb' that data from 3 years and a minimum of 100 individuals per year are needed to estimate genetic parameters with acceptable confidence, and that using pedigree data is worthwhile, even if phenotypes are only available toward the tips of the pedigree.

Animals↗
PubMed2006

The quantitative genetic basis of polyandry in the parasitoid wasp, Nasonia vitripennis.

Understanding the evolution of female multiple mating (polyandry) is crucial for understanding sexual selection and sexual conflict. Despite this interest, little is known about its genetic basis or whether genetics influences the evolutionary origin or maintenance of polyandry. Here, we explore the quantitative genetic basis of polyandry in the parasitoid wasp Nasonia vitripennis, a species in which female re-mating has been observed to evolve in the laboratory. We performed a quantitative genetic experiment on a recently collected population of wasps. We found low heritabilities of female polyandry (re-mating frequency after 18 h), low heritability of courtship duration and a slightly higher heritability of copulation duration. However, the coefficients of additive genetic variance for these traits were all reasonably large (CV(A)>7.0). We also found considerable dam effects for all traits after controlling for common environment, suggesting either dominance or maternal effects. Our work adds to the evidence that nonadditive genetic effects may influence the evolution of mating behaviour in Nasonia vitripennis, and the evolution of polyandry more generally.

Animals↗
PubMed2003

Quantitative genetic tests of recent senescence theory: age-specific mortality and male fertility in Drosophila melanogaster.

Quantitative genetic models of aging predict that additive genetic variance for fitness components should increase with age. However, recent studies have found that at very late ages, the genetic variance components decline. This decline may be due to an age-related drop in reproductive effort. If genetic variance in reproductive effort affects the genetic variance in mortality, the decline in reproductive effort at late ages should lead to a decrease in the genetic variance in mortality. To test this, we carried out a large-scale quantitative genetic analysis of age-specific mortality and fertility in virgin male Drosophila melanogaster. As in earlier studies, we found that the additive variance for age-specific mortality and fertility declined at late ages. Also, recent theoretical developments provide new predictions to distinguish between the mutation accumulation (MA) and antagonistic pleiotropy (AP) models of senescence. The deleterious effects of inbreeding are expected to increase with age under MA, but not under AP. This prediction was supported for both age-specific mortality and male fertility. Under AP, the ratio of dominance to additive variance is expected to decline with age. This predicition, too, was supported by the data analyzed here. Taken together, these analyses provide support for both the models playing a role in the aging process. We argue that the time has come to move beyond a simple comparison of these genetic models, and to think more deeply about the evolutionary causes and consequences of senescence.

Age Factors↗
PubMed2004

Quantitative genetics of sexually dimorphic traits and capture of genetic variance by a sexually-selected condition-dependent ornament in red junglefowl (Gallus gallus).

We studied the quantitative genetics of sexually selected traits in a captive population of red junglefowl (Gallus gallus L.) using a multi-generational 'animal model' approach. We found significant heritability of mass, tarsus length (both strongly sexually dimorphic), residual mass, and male comb (a fleshy head ornament) length. Residual mass has a genetic correlation between the sexes smaller than unity and so could show partially independent responses to selection in the two sexes. In males, tarsus length and mass were not genetically correlated, and this produced a negative genetic correlation between tarsus length and residual mass. The male red junglefowl's comb, an ornament influencing female choice, is highly condition dependent. We show that expression of this ornament is heritable, however, and shows strong genetic correlation with a condition index, residual mass. Because residual mass is partly influenced by various aspects of condition, it appears that comb size has 'captured' genetic variability in condition.

Analysis of Variance↗
PubMed2025

A single-locus quantitative genetic model incorporating DNA methylation.

We describe a single-locus quantitative genetic model that incorporates effects due to DNA methylation. Extending Fisher's decomposition of the genotypic value, we distinguish two quantities to predict an individual's phenotypic or genetic values: the "basic genetic value" and the "expressed genetic value". We show how these quantities relate to the concept of breeding value and derive their corresponding formulas, along with those for phenotypic variance and covariance between relatives. The resulting parameters are influenced by several factors, including the population distribution of DNA methylation levels, the functional relationship between methylation and phenotype, the magnitudes of genetic and methylation effects, and allele frequencies. We show that under the conditions modeled, the presence of DNA methylation does not bias estimated breeding values.

DNA Methylation↗
PubMed1995

Estimation of quantitative genetic parameters under non-normal models.

In traditional quantitative genetics, the relationship between the observed value of a quantitative trait in a set of families and its genetic and environmental contributions can be described as a linear additive relationship. Generally, it is assumed that the genetic and environmental effects are independent and normally distributed. Consequently, the quantitative trait also has a normal distribution. However, there are some situations where the phenotype does not follow the normal distribution. To deal with this problem the author suggests the families of distributions that belong to the Johnson Translation System (JTS). As an example, two dependent quantitative traits, weight and height, are investigated assuming that they have a lognormal and normal distribution, respectively. Computational methods for estimating the genotypic variances and covariances are presented.

Finland↗
PubMed2002

Hierarchical and factorial mating designs for quantitative genetic analysis in tetrasomic potato.

Plant breeders need to quantify additive and non-additive components of genetic variance in order to determine appropriate selection methods to improve quantitative characteristics. Hierarchical and factorial mating designs (also known as North Carolina mating designs I and II, respectively) allow one to determine these variance components. The relative advantages of these two designs in the quantitative genetics of tuber yield in tetrasomic potato were investigated. Likewise, the number of female parents to include in design I was also investigated. Data were collected from two independent experiments at two contrasting Peruvian locations: La Molina in the dry coast and San Ramon in the humid mid-altitude. In the first experiment, although design I gave a negative digenic variance (sigma(2)(D)), this design provided almost the same estimate of narrow-sense heritability (h(2)) for tuber yield as that obtained in design II (0.291 and 0.260, respectively). Therefore, design I appears to be appropriate for quantitative genetics research in tetrasomic potato, a crop in which some clones are male sterile. The easy handling of crosses (distinct random females included in the crossing scheme) is another advantage of design I relative to design II. In the second experiment, 12 males were crossed with either two or four females following a design-I mating scheme. The additive genetic variance (sigma(2)(A)) was zero (or negative) when two females per male were included but was positive with four females. These results suggest that two females per male may not be enough for design I in tetrasomic potato. Four females per male are preferable to determine sigma(2)(A) in design I for this tetrasomic crop.

Journal Article↗
PubMed1984

A quantitative genetic model of two-policy games between relatives.

Equations are derived for the change per generation of the population mean of the probability that an individual adopts a policy 1 as opposed to a policy 2 in a behavioral interaction between two diploid individuals of the same generation in which two policies are possible. The probability is assumed to be a quantitative genetic trait determined by many additively acting genes of small effects and an independent environmental component. Equations are derived for the case that interactions occur at random between all members of the population and also for the case that interactions occur between relatives of the same average degree of relatedness. It is assumed that each group of relatives and the number of such groups is sufficiently large. For a quantitative genetic trait with the additional assumption of unlinked loci the latter equation can be heuristically derived from the first by substituting the corresponding inclusive fitness effects. When per locus selection coefficients are small and linkage equilibrium holds, the average degree of relatedness can be equated approximately with Wright's coefficient of relationship. Thus, the quantitative genetic model provides a genetic basis for the inclusive fitness approach toward games between relatives. By contrast, in a monogenic system with major gene effects we obtain substantially different results which contradict those obtained by the inclusive fitness approach in game theory. Applications are made to the hawk-dove game, and the simple and iterated forms of the prisoner's dilemma.

Altruism↗
PubMed1990

Multipoint analysis of human quantitative genetic variation.

A unique method of partitioning human quantitative genetic variation into effects due to specific chromosomal regions is presented. This method is based on estimating the proportion of genetic material, R, shared identical by descent (IBD) by sibling pairs in a specified chromosomal region, on the basis of their marker genotypes at a set of marker loci spanning the region. The mean and variance of the distribution of R conditional on IBD status and recombination pattern between two marker loci are derived as a function of the distance between the two loci. The distribution of the estimates of R is exemplified using data on 22 loci on chromosome 7. A method of using the estimated R values and observed values of a quantitative trait in a set of sibships to estimate the proportion of total genetic variance explained by loci in the region of interest is presented. Monte Carlo simulation techniques are used to show that this method is more powerful than existing methods of quantitative linkage analysis based on sib pairs. It is also shown through simulation studies that the proposed method is sensitive to genetic variation arising from both a single locus of large effect as well as from several loosely linked loci of moderate phenotypic effect.

Chromosomes, Human, Pair 7↗
PubMed1993

Mutation models and quantitative genetic variation.

Analyses of evolution and maintenance of quantitative genetic variation depend on the mutation models assumed. Currently two polygenic mutation models have been used in theoretical analyses. One is the random walk mutation model and the other is the house-of-cards mutation model. Although in the short term the two models give similar results for the evolution of neutral genetic variation within and between populations, the predictions of the changes of the variation are qualitatively different in the long term. In this paper a more general mutation model, called the regression mutation model, is proposed to bridge the gap of the two models. The model regards the regression coefficient, gamma, of the effect of an allele after mutation on the effect of the allele before mutation as a parameter. When gamma = 1 or 0, the model becomes the random walk model or the house-of-cards model, respectively. The additive genetic variances within and between populations are formulated for this mutation model, and some insights are gained by looking at the changes of the genetic variances as gamma changes. The effects of gamma on the statistical test of selection for quantitative characters during macroevolution are also discussed. The results suggest that the random walk mutation model should not be interpreted as a null hypothesis of neutrality for testing against alternative hypotheses of selection during macroevolution because it can potentially allocate too much variation for the change of population means under neutrality.

Biological Evolution↗
PubMed2005

Up hill, down dale: quantitative genetics of curvaceous traits.

'Repeated' measurements for a trait and individual, taken along some continuous scale such as time, can be thought of as representing points on a curve, where both means and covariances along the trajectory can change, gradually and continually. Such traits are commonly referred to as 'function-valued' (FV) traits. This review shows that standard quantitative genetic concepts extend readily to FV traits, with individual statistics, such as estimated breeding values and selection response, replaced by corresponding curves, modelled by respective functions. Covariance functions are introduced as the FV equivalent to matrices of covariances. Considering the class of functions represented by a regression on the continuous covariable, FV traits can be analysed within the linear mixed model framework commonly employed in quantitative genetics, giving rise to the so-called random regression model. Estimation of covariance functions, either indirectly from estimated covariances or directly from the data using restricted maximum likelihood or Bayesian analysis, is considered. It is shown that direct estimation of the leading principal components of covariance functions is feasible and advantageous. Extensions to multi-dimensional analyses are discussed.

Analysis of Variance↗