The genetic architecture of quantitative traits: lessons from Drosophila

Understanding the genetic architecture of quantitative traits begins with identifying the genes regulating these traits, mapping the subset of genetically varying quantitative trait loci (QTLs) in natural populations, and pinpointing the molecular polymorphisms defining QTL alleles. Studies in Drosophila have revealed large numbers of pleiotropic genes that interact epistatically to regulate quantitative traits, and large numbers of QTLs with sex-, environment- and genotype-specific effects. Multiple molecular polymorphisms in regulatory regions of candidate genes are often associated with variation for complex traits. These observations offer valuable lessons for understanding the genetic basis of variation for complex traits in other organisms, including humans.     

Bayesian robust analysis for genetic architecture of quantitative traits

MOTIVATION: In most quantitative trait locus (QTL) mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may affect the accuracy of QTL detection and lead to detection of spurious QTLs. To improve the robustness of QTL mapping methods, we replaced the normal distribution for residuals in multiple interacting QTL models with the normal/independent distributions that are a class of symmetric and long-tailed distributions and are able to accommodate residual outliers. Subsequently, we developed a Bayesian robust analysis strategy for dissecting genetic architecture of quantitative traits and for mapping genome-wide interacting QTLs in line crosses. RESULTS: Through computer simulations, we showed that our strategy had a similar power for QTL detection compared with traditional methods assuming normal-distributed traits, but had a substantially increased power for non-normal phenotypes. When this strategy was applied to a group of traits associated with physical/chemical characteristics and quality in rice, more main and epistatic QTLs were detected than traditional Bayesian model analyses under the normal assumption.     

SelSim: a program to simulate population genetic data with natural selection and recombination

SUMMARY: SelSim is a program for Monte Carlo simulation of DNA polymorphism data for a recombining region within which a single bi-allelic site has experienced natural selection. SelSim allows simulation from either a fully stochastic model of, or deterministic approximations to, natural selection within a coalescent framework. A number of different mutation models are available for simulating surrounding neutral variation. The package enables a detailed exploration of the effects of different models and strengths of selection on patterns of diversity. This provides a tool for the statistical analysis of both empirical data and methods designed to detect natural selection. AVAILABILITY: http://www.stats.ox.ac.uk/mathgen/software.html. SUPPLEMENTARY INFORMATION: http://www.stats.ox.ac.uk/mathgen/software.html.     

AQUASPLATCHE: a program to simulate genetic diversity in populations living in linear habitats

Classical models of structured populations do not apply well to species leaving in semilinear habitats such as freshwater fishes, since these habitats are intermediate between one‐dimensional and two‐dimensional stepping‐stone models. In order to investigate the genetic diversity of such populations, we have developed a new simulation program called aquasplatche . It starts by dividing a user‐defined vectorized network into segments of arbitrary length, each segment hosting a single deme. The program then proceeds by simulating the colonization of the environment from an arbitrary source, recording the evolution of the deme densities and the migration events between adjacent demes over time. This demographic history is then used to generate genetic data of population samples located in various segments of the network, using a backward coalescent framework. Different versions of aquasplatche are freely available on http://cmpg.unibe.ch/software/aquasplatche .     

The relation between the genetic architecture of quantitative traits and long-term genetic response

The genetic architecture of a quantitative trait refers to the number of genetic variants, allele frequencies, and effect sizes of variants that affect a trait and their mode of gene action. This study was conducted to investigate the effect of four shapes of allelic frequency distributions (constant, uniform, L-shaped and U-shaped) and different number of trait-affecting loci (50, 100, 200, 500) on allelic frequency changes, long term genetic response, and maintaining genetic variance. To this end, a population of 440 individuals composed of 40 males and 400 females as well as a genome of 200 cM consisting of two chromosomes and with a mutation rate of 2.5?×?10^?5 per locus was simulated. Selection of superior animals was done using best linear unbiased prediction (BLUP) with assumption of infinitesimal model. Selection intensity was constant over 30 generations of selection. The highest genetic progress obtained when the allelic frequency had L-shaped distribution and number of trait-affecting loci was high (500). Although quantitative genetic theories predict the extinction of genetic variance due to artificial selection in long time, our results showed that under L- and U-shapped allelic frequency distributions, the additive genetic variance is persistent after 30 generations of selection. Further, presence or absence of selection limit can be an indication of low (<50) or high (>100) number of trait-affecting loci, respectively. It was concluded that the genetic architecture of complex traits is an important subject which should be considered in studies concerning long-term response to selection.     

Range limits in spatially explicit models of quantitative traits

In an influential paper, Kirkpatrick and Barton (Am Nat 150:1–23 1997) presented a system of diffusive partial differential equations modeling the joint evolution of population density and the mean of a quantitative trait when the trait optimum varies over a continuous spatial domain. We present a stability theorem for steady states of a simplified version of the system, originally studied in Kirkpatrick and Barton (Am Nat 150:1–23 1997). We also present a derivation of the system.     

Functional mapping - how to map and study the genetic architecture of dynamic complex traits

The development of any organism is a complex dynamic process that is controlled by a network of genes as well as by environmental factors. Traditional mapping approaches for analysing phenotypic data measured at a single time point are too simple to reveal the genetic control of developmental processes. A general statistical mapping framework, called functional mapping, has been proposed to characterize, in a single step, the quantitative trait loci (QTLs) or nucleotides (QTNs) that underlie a complex dynamic trait. Functional mapping estimates mathematical parameters that describe the developmental mechanisms of trait formation and expression for each QTL or QTN. The approach provides a useful quantitative and testable framework for assessing the interplay between gene actions or interactions and developmental changes.     

SASQuant: a SAS software program to estimate genetic effects and heritabilities of quantitative traits in populations consisting of 6 related generations

Plant breeders are interested in the analysis of phenotypic data to measure genetic effects and heritability of quantitative traits and predict gain from selection. Measurement of phenotypic values of 6 related generations (parents, F(1), F(2), and backcrosses) allows for the simultaneous analysis of both Mendelian and quantitative traits. In 1997, Liu et al. released a SAS software based program (SASGENE) for the analysis of inheritance and linkage of qualitative traits. We have developed a new program (SASQuant) that estimates gene effects (Hayman's model), genetic variances, heritability, predicted gain from selection (Wright's and Warner's models), and number of effective factors (Wright's, Mather's, and Lande's models). SASQuant makes use of traditional genetic models and allows for their easy application to complex data sets. SASQuant is freely available and is intended for scientists studying quantitative traits in plant populations.     

ForSim: a tool for exploring the genetic architecture of complex traits with controlled truth

Many important problems in biology involve complex traits affected by multiple coding or regulatory parts of the genome. How well the underlying genetic architecture can be inferred by statistical methods such as mapping and association studies are active research areas. ForSim is a flexible forward evolutionary simulation tool for exploring the consequences of evolution by phenotype, whereby demographic, chance, behavioral and selective effects mold genetic architecture. Simulation is useful for exploring these issues as well as the choice of study design inferential methods. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Neutral additive genetic variance in a metapopulation

For neutral, additive quantitative characters, the amount of additive genetic variance within and among populations is predictable from Wright's FST, the effective population size and the mutational variance. The structure of quantitative genetic variance in a subdivided metapopulation can be predicted from results from coalescent theory, thereby allowing single-locus results to predict quantitative genetic processes. The expected total amount of additive genetic variance in a metapopulation of diploid individual is given by 2Ne sigma m2 (1 + FST), where FST is Wright's among-population fixation index, Ne is the eigenvalue effective size of the metapopulation, and sigma m2 is the mutational variance. The expected additive genetic variance within populations is given by 2Ne sigma e2(1-FST), and the variance among demes is given by 4FSTNe sigma m2. These results are general with respect to the types of population structure involved. Furthermore, the dimensionless measure of the quantitative genetic variance among populations, QST, is shown to be generally equal to FST for the neutral additive model. Thus, for all population structures, a value of QST greater than FST for neutral loci is evidence for spatially divergent evolution by natural selection.     

Linking extinction-colonization dynamics to genetic structure in a salamander metapopulation

Theory predicts that founder effects have a primary role in determining metapopulation genetic structure. However, ecological factors that affect extinction-colonization dynamics may also create spatial variation in the strength of genetic drift and migration. We tested the hypothesis that ecological factors underlying extinction-colonization dynamics influenced the genetic structure of a tiger salamander (Ambystoma tigrinum) metapopulation. We used empirical data on metapopulation dynamics to make a priori predictions about the effects of population age and ecological factors on genetic diversity and divergence among 41 populations. Metapopulation dynamics of A. tigrinum depended on wetland area, connectivity and presence of predatory fish. We found that newly colonized populations were more genetically differentiated than established populations, suggesting that founder effects influenced genetic structure. However, ecological drivers of metapopulation dynamics were more important than age in predicting genetic structure. Consistent with demographic predictions from metapopulation theory, genetic diversity and divergence depended on wetland area and connectivity. Divergence was greatest in small, isolated wetlands where genetic diversity was low. Our results show that ecological factors underlying metapopulation dynamics can be key determinants of spatial genetic structure, and that habitat area and isolation may mediate the contributions of drift and migration to divergence and evolution in local populations.     

Short-term population differences in the genetic architecture of life history traits related to sexuality in an aphid species

One of the most important factors that determine the evolutionary trajectory of a suite of traits in a population is the structure of the genetic variance-covariance matrix (G). We studied the cyclically parthenogenetic aphid Rhopalosiphum padi, whose populations exhibit two types of reproductive lineages respectively specialized in sexuality (that is, cyclically parthenogenetic lineages) and in asexuality (that is, obligate parthenogenetic lineages). We compared the quantitative genetics of life histories in these two lineage types. Our results suggest that both, the elements and the whole structure of the resulting G matrices differ in the very short term, between lineage types. This would involve the evolution toward different evolutionary optima in the same population, depending on whether sexual or asexual lineages predominate. Since sexual and asexual lineages vary seasonally in their abundance, a fluctuating selective regime has been proposed for this species, which would contribute to the maintenance of the reproductive polymorphism that these populations exhibit.     

Modular genetic architecture of floral morphology in Nicotiana: quantitative genetic and comparative phenotypic approaches to floral integration

Animal‐pollinated flowers are complex structures that may require a precise configuration of floral organs for proper function. As such, they represent an excellent system with which we can examine the role of phenotypic integration and modularity in morphological evolution. We use complementary quantitative genetic and comparative phenotypic approaches to examine correlations among floral characters in Nicotiana alata, N. forgetiana and their artificial fourth‐generation hybrids. Flowers of both species share basic patterns of genetic and phenotypic correlations characterized by at least two integrated character suites that are relatively independent of each other and are not disrupted by four generations of recombination in hybrids. We conclude that these integrated character suites represent phenotypic modules that are the product of a modular genetic architecture. Intrafloral modularity may have been critical for rapid specialization of these species to different pollinators.     

Multifactorial genetic models for quantitative traits in humans.

Quantitative traits measured in human families can be analyzed to partition the total population variance into genetic and environmental components, or to elucidate the genetic mechanism involved. We review the estimation of variance components directly from human pedigree data, or in the form of path coefficients from correlations between pairs of relatives. To elucidate genetic mechanisms, a mixed model that allows for segregation at a major locus, a polygenic effect and a sibling environmental correlation is described for nuclear families. In each case appropriate likelihoods are derived as a basis, using numerical maximum likelihood methods, for parameter estimation and hypothesis testing. A general model is then described that allows for several familial sources of environmental variation, assortative mating, and both major gene and polygenic effects; and an algorithm for calculating the likelihood of a pedigree under this model is indicated. Finally, some of the remaining problems in this area of biometric analysis are pointed out.     

QTLNetwork: mapping and visualizing genetic architecture of complex traits in experimental populations

SUMMARY: QTLNetwork is a software package for mapping and visualizing the genetic architecture underlying complex traits for experimental populations derived from a cross between two inbred lines. It can simultaneously map quantitative trait loci (QTL) with individual effects, epistasis and QTL-environment interaction. Currently, it is able to handle data from F(2), backcross, recombinant inbred lines and double-haploid populations, as well as populations from specific mating designs (immortalized F(2) and BC(n)F(n) populations). The Windows version of QTLNetwork was developed with a graphical user interface. Alternatively, the command-line versions have the facility to be run in other prevalent operating systems, such as Linux, Unix and MacOS. AVAILABILITY: http://ibi.zju.edu.cn/software/qtlnetwork.     

Spatially structured genetic variation in a broadcast spawning bivalve: quantitative vs. molecular traits

Understanding the origin, maintenance and significance of phenotypic variation is one of the central issues in evolutionary biology. An ongoing discussion focuses on the relative roles of isolation and selection as being at the heart of genetically based spatial variation. We address this issue in a representative of a taxon group in which isolation is unlikely: a marine broadcast spawning invertebrate. During the free-swimming larval phase, dispersal is potentially very large. For such taxa, small-scale population genetic structuring in neutral molecular markers tends to be limited, conform expectations. Small-scale differentiation of selective traits is expected to be hindered by the putatively high gene flow. We determined the geographical distribution of molecular markers and of variation in a shell shape measure, globosity, for the bivalve Macoma balthica (L.) in the western Dutch Wadden Sea and adjacent North Sea in three subsequent years, and found that shells of this clam are more globose in the Wadden Sea. By rearing clams in a common garden in the laboratory starting from the gamete phase, we show that the ecotypes are genetically different; heritability is estimated at 23%. The proportion of total genetic variation that is between sites is much larger for the morphological additive genetic variation (QST = 0.416) than for allozyme (FST = 0.000-0.022) and mitochondrial DNA cytochrome-c-oxidase-1 sequence variation (phiST = 0.017). Divergent selection must be involved and intraspecific spatial genetic differentiation in marine broadcast spawners is apparently not constrained by low levels of isolation.     

Generalizing Levins metapopulation model in explicit space: models of intermediate complexity

A recent study [Harding and McNamara, 2002. A unifying framework for metapopulation dynamics. Am. Nat. 160, 173-185] presented a unifying framework for the classic Levins metapopulation model by incorporating several realistic biological processes, such as the Allee effect, the Rescue effect and the Anti-rescue effect, via appropriate modifications of the two basic functions of colonization and extinction rates. Here we embed these model extensions on a spatially explicit framework. We consider population dynamics on a regular grid, each site of which represents a patch that is either occupied or empty, and with spatial coupling by neighborhood dispersal. While broad qualitative similarities exist between the spatially explicit models and their spatially implicit (mean-field) counterparts, there are also important differences that result from the details of local processes. Because of localized dispersal, spatial correlation develops among the dynamics of neighboring populations that decays with distance between patches. The extent of this correlation at equilibrium differs among the metapopulation types, depending on which processes prevail in the colonization and extinction dynamics. These differences among dynamical processes become manifest in the spatial pattern and distribution of “clusters” of occupied patches. Moreover, metapopulation dynamics along a smooth gradient of habitat availability show significant differences in the spatial pattern at the range limit. The relevance of these results to the dynamics of disease spread in metapopulations is discussed.     

Hetero: a program to simulate the evolution of DNA on a four-taxon tree

We present a computer program to simulate the evolution of a nucleotide sequence on a phylogenetic tree with four tips. The program, Hetero, allows users to assign lineage-specific differences in the rate matrices used to describe the evolutionary process. It has a simple user interface and output, making it equally useful in the teaching and research of phylogenetics.