A quantitative genetics model for viability selection

Viability selection will change gene frequencies of loci controlling fitness. Consequently, the frequencies of marker loci linked to the viability loci will also change. In genetic mapping, the change of marker allelic frequencies is reflected by the departure from Mendelian segregation ratio. The non-Mendelian segregation of markers has been used to map viability loci along the genome. However, current methods have not been able to detect the amount of selection (s) and the degree of dominance (h) simultaneously. We developed a method to detect both s and h using an F2 mating design under the classical fitness model. We also developed a quantitative genetics model for viability selection by proposing a continuous liability controlling the viability of individuals. With the liability model, mapping viability loci has been formulated as mapping quantitative trait loci. As a result, nongenetic systematic environmental effects can be easily incorporated into the model and subsequently separated from the genetic effects of the viability loci. The quantitative genetic model has been verified with a series of Monte Carlo simulation experiments.     

Quantitative Trait Loci Differentiating the Outbreeding Mimulus Guttatus from the Inbreeding M. Platycalyx

Theoretical predictions about the evolution of selfing depend on the genetic architecture of loci controlling selfing (monogenic vs. polygenic determination, large vs. small effect of alleles, dominance vs. recessiveness), and studies of such architecture are lacking. We inferred the genetic basis of mating system differences between the outbreeding Mimulus guttatus and the inbreeding M. platycalyx by quantitative trait locus (QTL) mapping using random amplified polymorphic DNA and isozyme markers. One to three QTL were detected for each of five mating system characters, and each QTL explained 7.6-28.6% of the phenotypic variance. Taken together, QTL accounted for up to 38% of the variation in mating system characters, and a large proportion of variation was unaccounted for. Inferred QTL often affected more than one trait, contributing to the genetic correlation between those traits. These results are consistent with the hypothesis that quantitative variation in plant mating system characters is primarily controlled by loci with small effect.     

The genetic architecture of resistance to virus infection in Drosophila

Variation in susceptibility to infection has a substantial genetic component in natural populations, and it has been argued that selection by pathogens may result in it having a simpler genetic architecture than many other quantitative traits. This is important as models of host–pathogen co‐evolution typically assume resistance is controlled by a small number of genes. Using the Drosophila melanogaster multiparent advanced intercross, we investigated the genetic architecture of resistance to two naturally occurring viruses, the sigma virus and DCV (Drosophila C virus). We found extensive genetic variation in resistance to both viruses. For DCV resistance, this variation is largely caused by two major‐effect loci. Sigma virus resistance involves more genes – we mapped five loci, and together these explained less than half the genetic variance. Nonetheless, several of these had a large effect on resistance. Models of co‐evolution typically assume strong epistatic interactions between polymorphisms controlling resistance, but we were only able to detect one locus that altered the effect of the main effect loci we had mapped. Most of the loci we mapped were probably at an intermediate frequency in natural populations. Overall, our results are consistent with major‐effect genes commonly affecting susceptibility to infectious diseases, with DCV resistance being a near‐Mendelian trait.     

MULTIPLE EQUILIBRIA AND MAINTENANCE OF ADDITIVE GENETIC VARIANCE IN A MODEL OF PLEIOTROPY

We describe a multilocus model that incorporates pleiotropic stabilizing selection on a large number of characters. We find many different stable equilibria with different levels of polymorphism and additive genetic variability. The results lend support to Wright's concept of a complex adaptive surface with many peaks of different heights. The model assumes that alleles contribute additively to the characters. We analyze the multilocus model by first considering a two-locus model. The two-locus model depends critically on having loci of different effect and on having the optimum phenotype not be that of a completely heterozygous individual. The effects of different loci need to differ only by less than a factor of two. For the multilocus, multicharacter model, we assume that completely heterozygous individuals do not have the optimum phenotype. By restricting attention to a two-allele model, we also assume that there are no alleles that can affect all characters in all possible combinations of directions.     

Effect of parasitic sex-ratio distorters on host gene frequencies in a mainland-island context

It was previously argued that infection by parasitic sex-ratio distorters can enhance both random genetic drift and genetic influx from outside the population. However, these two enhancement effects have been studied independently. Here, we study the equilibrium frequencies of alleles (neutral and selected) in a mainland-island scenario where both genetic drift and genetic influx are enhanced due to infection by a cytoplasmic feminizing element. Interestingly, our model reveals that at neutral loci, the two effects almost exactly cancel each other out, such that infection has only a very minor effect on the equilibrium frequency distributions of alleles. At selected loci, in contrast, the two effects are unbalanced and infection has conspicuous effects. Despite the cryptic effects of infection at neutral loci, we demonstrate that temporally spaced data can be used to evaluate the effect of infection on genetic drift and that on gene flow separately.     

Quantitative trait locus analysis for rice panicle and grain characteristics

 The development of molecular genetic maps has accelerated the identification and mapping of genomic regions controlling quantitative characters, referred to as quantitative trait loci or QTLs. A molecular map derived from an F₂ population of a tropical japonica×indica cross (Labelle/Black Gora) consisted of 116 restriction fragment length polymorphism (RFLP) markers. Composite interval mapping was used to identify the QTLs controlling six panicle and grain characteristics. Two QTLs were identified for panicle size at LOD>3.0, with one on chromosome 3 accounting for 16% of the phenotypic variation. Four loci controlling spikelet fertility accounted for 23% of the phenotypic variation. Seven, four, three and two QTLs were detected for grain length, breadth, shape and weight, respectively, with the most prominent QTLs being on chromosomes 3, 4, and 7. Grain shape, measured as the ratio of length to breadth, was mostly controlled by loci on chromosomes 3 and 7 that coincided with the most important QTLs identified for length and breadth, respectively. A model including three loci accounted for 45% of the phenotypic variation for this trait. The identification of economically important QTLs will be useful in breeding for improved grain characteristics. Received: 18 July 1997 / Accepted: 9 December 1997     

A quantitative genetics and ecological model system: understanding the aliphatic glucosinolate biosynthetic network via QTLs

Plants’ sessile nature has led them to develop chemical defenses, secondary metabolites, to directly cope with environmental changes rather than escape to more favorable sites. The diversity and fluctuation in biological stresses faced by a plant have generated extraordinary genetic diversity controlling the synthesis and regulation of secondary metabolites that is only now being explored. The glucosinolate secondary metabolites, amino acid derived thioglucosides specific to the order Capparales, is a model system for understanding the molecular basis of complex quantitative traits and their potential ecological role. This review focuses on the extensive progress being made towards understanding the complete molecular basis underlying the glucosinolate genetic diversity at both biosynthetic and regulatory loci. This has identified a highly interactive genetic network whereby biosynthetic loci have additional functions as regulatory loci and laid the foundation for glucosinolates to be a model system for understanding quantitative traits in a broader context.     

Pleiotropic quantitative trait loci contribute to population divergence in traits associated with life-history variation in Mimulus guttatus

Evolutionary biologists seek to understand the genetic basis for multivariate phenotypic divergence. We constructed an F2 mapping population (N = 539) between two distinct populations of Mimulus guttatus. We measured 20 floral, vegetative, and life-history characters on parents and F1 and F2 hybrids in a common garden experiment. We employed multitrait composite interval mapping to determine the number, effect, and degree of pleiotropy in quantitative trait loci (QTL) affecting divergence in floral, vegetative, and life-history characters. We detected 16 QTL affecting floral traits; 7 affecting vegetative traits; and 5 affecting selected floral, vegetative, and life-history traits. Floral and vegetative traits are clearly polygenic. We detected a few major QTL, with all remaining QTL of small effect. Most detected QTL are pleiotropic, implying that the evolutionary shift between these annual and perennial populations is constrained. We also compared the genetic architecture controlling floral trait divergence both within (our intraspecific study) and between species, on the basis of a previously published analysis of M. guttatus and M. nasutus. Eleven of our 16 floral QTL map to approximately the same location in the interspecific map based on shared, collinear markers, implying that there may be a shared genetic basis for floral divergence within and among species of Mimulus.     

An Alternative Nonlinear Genetic Model

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ADAPTIVE RADIATION AND GENETIC DIFFERENTIATION IN HAWAIIAN BIDENS

The genus Bidens (Asteraceae) has undergone extensive adaptive radiation on the Hawaiian Islands. The 19 species and eight subspecies endemic to Hawaii exhibit much more morphological and ecological differentiation than the continental members of the genus. However, the Hawaiian taxa have the same chromosome number and retain the capacity to interbreed in all possible combinations. Twenty-two populations of 15 Hawaiian taxa and four populations of American taxa were compared at 21 loci controlling eight enzyme systems. Populations of Hawaiian taxa are highly polymorphic. However, little genetic differentiation has occurred among taxa in spite of the high levels of genetic variability. Genetic identities calculated for pairs of populations show that populations of the same taxon are genetically more similar than are populations belonging to different taxa, but all values are high. The level of genetic differentiation that has occurred among the species of Hawaiian Bidens is comparable to the level of genetic differences found among populations within single continental plant species. Moreover, there is no correlation between the isozyme data and morphological data. No groups of taxa are evident in the genetic data, although morphological groups exist. Genetic differentiation at isozyme loci has not occurred at the same rate as the acquisition of presumably adaptive morphological and ecological characters in Hawaiian Bidens. Adaptive radiation may be limited to a few genes controlling morphological and ecological characters.     

Allelic interaction at seed-shattering loci in the genetic backgrounds of wild and cultivated rice species

It is known that the common cultivated rice (Oryza sativa) was domesticated from Asian wild rice, O. rufipogon. Among the morphological differences between them, loss of seed shattering is one of the striking characters specific for the cultivated forms. In order to understand the genetic control on shattering habit, QTL analysis was carried out using BC(2)F(1) backcross population between O. sativa cv. Nipponbare (a recurrent parent) and O. rufipogon acc. W630 (a donor parent). As a result, two strong QTLs were detected on chromosomes 1 and 4, and they were found to be identical to the two major seed-shattering loci, qSH1 and sh4, respectively. The allelic interaction at these loci was further examined using two sets of backcross populations having reciprocal genetic backgrounds, cultivated and wild. In the genetic background of cultivated rice, the wild qSH1 allele has stronger effect on seed shattering than that of sh4. In addition, the wild alleles at both qSH1 and sh4 loci showed semi-dominant effects. On the other hand, in the genetic background of wild rice, non-shattering effects of Nipponbare alleles at both loci were examined to inspect rice domestication from a viewpoint of seed shattering. It was serendipitous that the backcross plants individually having Nipponbare homozygous alleles at either shattering locus (qSH1 or sh4) shed all the seeds. This fact strongly indicates that the non-shattering behavior was not obtained by a single mutation in the genetic background of wild rice. Probably, some other minor genes are still associated with the formation or activation of abscission layer, which enhance the seed shattering.     

Contribution of maternal effect QTL to genetic architecture of early growth in mice

Existing approaches to characterizing quantitative trait loci (QTL) utilize a paradigm explicitly focused on the direct effects of genes, where phenotypic variation among individuals is mapped onto genetic variation of those individuals. For many characters, however, the genotype of the mother via its maternal effect accounts for a considerable portion of the genetically based variation in progeny phenotypes. Thus the focus on direct effect QTL may result in an insufficient or misleading characterization of genetic architecture due to the omission of the potentially important source of genetic variance contributed by maternal effects. We analyze the relative contribution of direct and maternal effect (ME) QTL to early growth in mice using a three-generation intercross of the Small (SM/J) and Large (LG/J) inbred mouse lineages. Using interval mapping and composite interval mapping, direct effect (DE) QTL for early growth (change in body mass during the interval from week 1 to 2) were detected in the F(2) generation of the intercross (n = 510), where no maternal genetic effect variance is present (all individuals are progeny of genetically identical F(1) mothers). ME QTL were detected by treating the phenotypes of cross-fostered F(3) pups as a characteristic of their nurse-dam (n = 168 dams with cross-fostered progeny). Five DE QTL, significant at a chromosome wide level (alpha = 0.05), were detected, with two significant at a genome wide level. FourME QTL significant at the chromosome wide level were detected, with three significant at the genome wide level. A model containing only DE QTL accounted for 11.8% of phenotypic variance, while a model containing only ME QTL accounted for 31.5% of the among litter variance in growth. There was no evidence for pleiotropy of DE and ME loci since there was no overlap between loci detected in these two analyses. Epistasis between all pairs of loci was analyzed for both DEs and MEs. Ten pairs of loci showed significant epistasis for MEs (alpha = 0.05 corrected for multiple comparisons) while four pairs showed significant epistasis for DEs on early growth.     

Mutational variability of enzyme loci in unstable Drosophila melanogaster strains

Biochemical analysis of a number of related unstable Drosophila melanogaster strains was carried out. These strains have been shown to undergo mutational transformations caused by insertion/excision of transposable elements (Gerasimova, 1985). Activity and mobility variants of alpha-GPDH, ADH, SOD, G6PD, 6PGD and EST-6 were analysed. Two loci controlling SOD and 6PGD proved to be invariable, the loci alpha-Gpdh and Est-6 causing reduced activity of their products in the initial strain ctMR2. The direct and reversed transformations analogous to the mutational passages of morphological characters were traced in two loci controlling ADH and G6PD. The data obtained are discussed in terms of up-to-date views on the functional role of transposable elements, in relation to the genetic stability of the strains studied, under the multiple transpositions of mobile elements.     

Relationship between the Reproductive Capability of a Subdivided Population and Its Genetic Structure: Computer Simulation,the Simplest Multilocus Model

An original computer model, simulating joint genetic and demographic dynamics of subdivided populations, is proposed. The model accounts for the reverse effect of the genetic structure on the reproductive capability of a population, which is based on a postulated limited set of biallelic loci, controlling variation in an adaptive quantitative trait. The model allows to simulate spreading of the population, originating from a single small colony, resulting in establishment of involves genetic and demographic equilibrium (a normal population-genetic process) and reorganization of the genetic structure of the subdivided population under anthropogenic pressure, associated with a decrease in its reproductive capability (an adverse population-genetic process).     

COMPARISON OF NON‐GAUSSIAN QUANTITATIVE GENETIC MODELS FOR MIGRATION AND STABILIZING SELECTION

The balance between stabilizing selection and migration of maladapted individuals has formerly been modeled using a variety of quantitative genetic models of increasing complexity, including models based on a constant expressed genetic variance and models based on normality. The infinitesimal model can accommodate nonnormality and a nonconstant genetic variance as a result of linkage disequilibrium. It can be seen as a parsimonious one‐parameter model that approximates the underlying genetic details well when a large number of loci are involved. Here, the performance of this model is compared to several more realistic explicit multilocus models, with either two, several or a large number of alleles per locus with unequal effect sizes. Predictions for the deviation of the population mean from the optimum are highly similar across the different models, so that the non‐Gaussian infinitesimal model forms a good approximation. It does, however, generally estimate a higher genetic variance than the multilocus models, with the difference decreasing with an increasing number of loci. The difference between multilocus models depends more strongly on the effective number of loci, accounting for relative contributions of loci to the variance, than on the number of alleles per locus.     

Relationship between the reproductive capability of a subdivided population and its genetic structure: computer simulation, the simplest multilocus model

An original computer model, simulating joint genetic and demographic dynamics of subdivided populations, is proposed. The model accounts for the reverse effect of the genetic structure on the reproductive capability of a population, which is based on a postulated limited set of biallelic loci, controlling variation in an adaptive quantitative trait. The model allows to simulate spreading of the population, originating from a single small colony, which involves genetic and demographic equilibrium (a normal population-genetic process) and reorganization of the genetic structure of the subdivided population upon anthropogenic pressure, associated with a decrease in its reproductive capability (an adverse population-genetic process).     

Quantitative trait loci analysis of nitrogen use efficiency in Arabidopsis

Improving plant nitrogen (N) use efficiency or controlling soil N requires a better knowledge of the regulation of plant N metabolism. This could be achieved using Arabidopsis as a model genetic system, taking advantage of the natural variation available among ecotypes. Here, we describe an extensive study of N metabolism variation in the Bay-0 x Shahdara recombinant inbred line population, using quantitative trait locus (QTL) mapping. We mapped QTL for traits such as shoot growth, total N, nitrate, and free-amino acid contents, measured in two contrasting N environments (contrasting nitrate availability in the soil), in controlled conditions. Genetic variation and transgression were observed for all traits, and most of the genetic variation was identified through QTL and QTL x QTL epistatic interactions. The 48 significant QTL represent at least 18 loci that are polymorphic between parents; some may correspond to known genes from the N metabolic pathway, but others represent new genes controlling or interacting with N physiology. The correlations between traits are dissected through QTL colocalizations: The identification of the individual factors contributing to the regulation of different traits sheds new light on the relations among these characters. We also point out that the regulation of our traits is mostly specific to the N environment (N availability). Finally, we describe four interesting loci at which positional cloning is feasible.     

Quantitative trait locus analysis of leaf dissection in tomato using Lycopersicon pennellii segmental introgression lines

Leaves are one of the most conspicuous and important organs of all seed plants. A fundamental source of morphological diversity in leaves is the degree to which the leaf is dissected by lobes and leaflets. We used publicly available segmental introgression lines to describe the quantitative trait loci (QTL) controlling the difference in leaf dissection seen between two tomato species, Lycopersicon esculentum and L. pennellii. We define eight morphological characteristics that comprise the mature tomato leaf and describe loci that affect each of these characters. We found 30 QTL that contribute one or more of these characters. Of these 30 QTL, 22 primarily affect leaf dissection and 8 primarily affect leaf size. On the basis of which characters are affected, four classes of loci emerge that affect leaf dissection. The majority of the QTL produce phenotypes intermediate to the two parent lines, while 5 QTL result in transgression with drastically increased dissection relative to both parent lines.     

INHERITANCE OF MERISTIC VARIATION AND THE EVOLUTION OF DEVELOPMENTAL STABILITY IN RAINBOW TROUT

We found relatively high heritabilities in the narrow sense for seven of eight meristic characters in a population of rainbow trout using regression of mean progeny values on mid-parent values. In sharp contrast, there is no statistically significant additive genetic variance controlling developmental stability, as measured by fluctuating asymmetry (h² = 0.02). However, there is a significant correlation between the average heterozygosity of each family at isozyme loci and the average number of asymmetric traits per individual. We have previously reported a strong correlation between heterozygosity at protein loci and decreased fluctuating asymmetry in this and other salmonid populations. Thus, there is little or no additive, but substantial dominance, genetic variation affecting fluctuating asymmetry. This suggests that there has been directional selection for increased developmental stability.     

Population structure and quantitative characters

A migration matrix model is used to investigate the behavior of neutral polygenic characters in subdivided populations. It is shown that gametic disequilibrium has a large effect on the variance among groups but none at all on its expectation. The variance of among-group variance is substantial and does not depend on the number of loci contributing to variance in the character. It is just as large for polygenic characters as for single loci with the same additive variance. This implies that one polygenic character contains exactly as much information about population relationships as one single-locus marker. The theory is compared with observed differentiation of dermatoglyphic and anthropometric characters among Bougainville islanders.