The phenotypic variance within plastic traits under migration-mutation-selection balance

How phenotypic variances of quantitative traits are influenced by the heterogeneity in environment is an important problem in evolutionary biology. In this study, both genetic and environmental variances in a plastic trait under migration-mutation-stabilizing selection are investigated. For this, a linear reaction norm is used to approximate the mapping from genotype to phenotype, and a population of clonal inheritance is assumed to live in a habitat consisting of many patches in which environmental conditions vary among patches and generations. The life cycle is assumed to be selection-reproduction-mutation-migration. Analysis shows that phenotypic plasticity is adaptive if correlations between the optimal phenotype and environment have become established in both space and/or time, and it is thus possible to maintain environmental variance (V(E)) in the plastic trait. Under the special situation of no mutation but maximum migration such that separate patches form an effective single-site habitat, the genotype that maximizes the geometric mean fitness will come to fixation and thus genetic variance (V(G)) cannot be maintained. With mutation and/or restricted migration, V(G) can be maintained and it increases with mutation rate but decreases with migration rate; whereas VE is little affected by them. Temporal variation in environmental quality increases V(G) while its spatial variance decreases V(G). Variation in environmental conditions may decrease the environmental variance in the plastic trait.     

月季F1代群体表型性状变异分析

以月季（Rosa spp.）品种‘云蒸霞蔚’和‘太阳城’正交获得的184株F₁代群体为研究对象,采用方差分析、变异系数、遗传分析、相关性分析对花部形态性状以及叶片形态性状进行测定分析。结果表明：该杂交群体表型变异丰富,变异系数在7.33%~68.08%,其中花瓣数量在群体中的变异程度最高;杂交后代各个性状上均发生分离变异,出现不同于亲本的表现型,且离散程度较高。表型性状的遗传特点与关联分析,为挖掘控制表型性状的优良基因及辅助选择育种提供参考。     

Quantitative genetics of ovariole number in Drosophila melanogaster. II. Mutational variation and genotype-environment interaction.

The rare alleles model of mutation-selection balance (MSB) hypothesis for the maintenance of genetic variation was evaluated for two quantitative traits, ovariole number and body size. Mutational variances (VM) for these traits, estimated from mutation accumulation lines, were 4.75 and 1.97 x 10(-4) times the environmental variance (VE), respectively. The mutation accumulation lines were studied in three environments to test for genotype x environment interaction (GEI) of new mutations; significant mutational GEI was found for both traits. Mutations for ovariole number have a quadratic relationship with competitive fitness, suggesting stabilizing selection for the trait; there is no significant correlation between mutations for body size and competitive fitness. Under MSB, the ratio of segregating genetic variance, VG, to mutational variance, VM, estimates the inverse of the selection coefficient against a heterozygote for a new mutation. Estimates of VG/VM for ovariole number and body size were both approximately 1.1 x 10(4). Thus, MSB can explain the level of variation, if mutations affecting these traits are under very weak selection, which is inconsistent with the empirical observation of stabilizing selection, or if the estimate of VM is biased downward by two orders of magnitude. GEI is a possible alternative explanation.     

Inheritance of human finger and palm dermatoglyphic characteristics]

The degree of genetic determination of 25 quantitative dermatoglyphic characteristics has been studied on family: twin material: 45 pairs of MZ and 75 single-sex DZ twins; and 53 single-sex "parent-child" pairs. Approximating formulae were used to estimate main components of phenotypic variance due to additive interaction of genetic factors, to non-linear effects (intralocus dominance) and to the effect of total-familiar and random environmental factors. All the finger dermatoglyphic characteristics studied had a high degree of genetic determination (G greater than 0,80), and for most of them the contribution into the large variance of intralocus dominance effects was comparable with that of additive gene interaction, included in the determination of these characters. There are some palm dermatoglyphic characteristics ("ad" distance "cd" comb counting, "bad", "adt" and "cda" angles), which degree of genetic determination is low (G less than 0,35). At least ten quantitative finger and palm dermatogliphic characteristics with a high degree of genetic determination can be used for special studies in frames of multidimentional genetical analysis, including determination of twin zygosity type. Earlier described "indices" (using twin data) of relative role of genetic and environment factors in the determination of populational variability of quantitative characters are considered. None of them is shown to be a reliable estimate of the coefficient of genetic character determination. The use of these indices in practical studies can result in wrong conclusions on the degree and the character of genetic determination of quantitative characters.     

Inheritance of an oviposition behavior by an egg parasitoid

A quantitative genetic study revealed genetic and environmental sources of variance in percentage parasitism of European corn borer egg masses and secondary sex ratios by Trichogramma nubilale. Full and half-sib groups of T. nubilale were obtained from a nested mating design, which permitted the partitioning of the variance of T. nubilale parasitism of European corn borer egg masses into additive genetic variance, maternal/dominant variance and environmental variance. A mother-daughter regression of the percentage of an egg mass parasitized allowed a determination of the direction of a potential response to selection in the event of maternal effects. No or very little additive genetic effects were associated with the percentage of eggs within a mass parasitized and secondary sex ratios, but a significant amount of the variance for both traits had a maternal and/or dominant genetic source. The relationship between mothers and daughters in egg mass parasitism was positive, and 55.4% of the progeny of a given mother had behaviors that resemble their mother. Most of the variance had an environmental and/or unknown genetic source implying potentially high phenotypic plasticity associated with all these traits. The presence of maternal effects and phenotypic plasticity could have multiple and complex effects on progeny characters and potential responses to selection.     

Phenotypic, maximum genetic, and special environmental variability in prehistoric human populations

The phenotypic variance (V(P)) may be divided into the genetic variance (V(G)), the general environmental variance (V(Eg)), and the special environmental variance (V(Es)). The latter is estimated through repeatability calculation (b). This value is considered the upper limit of heritability and represents maximum genetic variance proportion (V(Gm) = V(G) + V(Eg)) in relation to V(P) (b = (V(G) + V(Eg))/V(P)). This process allows an improved determination of biological relationships among groups from estimators maximizing the genetic information of quantitative characters. Two hundred and thirty-seven individuals inhabiting the northern coast of Chile for 4,000 years were taken as a sample. Measurement was made of six metric characters at both sides of the cranium. Special environmental values (es) were obtained by regression. The difference between these values and the phenotypic values (p) consists in the genetic values plus the general environmental values (g + eg). A mean b value of 0.83 indicated that V(Es) represents 17% of V(P). The results showed: 1) high stability of the maximum genetic variance in time and space, 2) high correlation between the biological relationships model, the phenotypic model, and the maximum genetic model, and 3) random distribution of the nongenetic variation, as expected from the quantitative genetics theory. These results support the use of phenotypic data for the interpretation of the evolution history of prehistoric populations.     

Contribution of genetic and environmental factors in the phenotypic variability of major indices of child development at different stages of postnatal ontogenesis

Main indices of physical development of monozygotic and dizygotic twins were investigated during 13 years period. Using the coefficients of the within-pair correlation of characters studied an attempt was made to estimate the correlative contribution of genetic and environmental determinants to formation of phenotypic variance of height, weight and chest circumference from birth up to 13 years old. The indices of composing components obtained suggest that underlying formation of phenotypic variance of each of the characters analysed are the mechanisms reflecting qualitative, quantitative and time peculiarities of functioning of polygenic systems involved in determination of characters studied and peculiarities of their interaction with environmental factors.     

Moose body mass variation revisited: disentangling effects of environmental conditions and genetics

Large-scale geographical variation in phenotypic traits within species is often correlated to local environmental conditions and population density. Such phenotypic variation has recently been shown to also be influenced by genetic structuring of populations. In ungulates, large-scale geographical variation in phenotypic traits, such as body mass, has been related to environmental conditions and population density, but little is known about the genetic influences. Research on the genetic structure of moose suggests two distinct genetic lineages in Norway, structured along a north-south gradient. This corresponds with many environmental gradients, thus genetic structuring provides an additional factor affecting geographical phenotypic variation in Norwegian moose. We investigated if genetic structure explained geographical variation in body mass in Norwegian moose while accounting for environmental conditions, age and sex, and if it captured some of the variance in body mass that previously was attributed to environmental factors. Genetic structuring of moose was the most important variable in explaining the geographic variation in body mass within age and sex classes. Several environmental variables also had strong explanatory power, related to habitat diversity, environmental seasonality and winter harshness. The results suggest that environmental conditions, landscape characteristics, and genetic structure should be evaluated together when explaining large-scale patterns in phenotypic characters or life history traits. However, to better understand the role of genetic and environmental effects on phenotypic traits in moose, an extended individual-based study of variation in fitness-related characters is needed, preferably in an area of convergence between different genetic lineages.     

Inclusive heritability: combining genetic and non‐genetic information to study animal behavior and culture

Phenotypic variance results from variation in biological information possessed by individuals. Quantitative geneticists often strive to partition out all environmental variance to measure heritability. Behavioral biologists and ecologists however, require methods to integrate genetic and environmental components of inherited phenotypic variance in order to estimate the evolutionary potential of traits, which encompasses any form of information that is inherited. To help develop this integration, we build on the tools of quantitative genetics and offer the concept of ‘inclusive heritability’ which identifies and unifies the various mechanisms of information transmission across generations. A controversial component of non‐genetic information is animal culture, which is the part of phenotypic variance inherited through social learning. Culture has the unique property of being transmitted horizontally and obliquely, as well as vertically. Accounting for cultural variation would allow us to examine a broader range of evolutionary mechanisms. Culture may, for instance, produce behavioral isolating mechanisms leading to speciation. To advance the study of animal culture, we offer a definition of culture that is rooted in quantitative genetics. We also offer four testable criteria to determine whether a trait is culturally inherited. These criteria may constitute a conceptual tool to study animal culture. We briefly discuss methods to partition out cultural variance. Several authors have recently called for ‘modernizing the modern synthesis’ by including non‐genetic factors such as epigenetics and phenotypic plasticity in order to more fully explain phenotypic evolution. Here, we further propose to broaden the concept of inheritance by incorporating the cultural component of behavior. Applying the concept of inclusive heritability may advance the integration of multiple forms of inheritance into the study of evolution.     

Genotype-Phenotype Maps Maximizing Evolvability: Modularity Revisited

The mechanisms translating genetic to phenotypic variation determine the distribution of heritable phenotypic variance available to selection. Pleiotropy is an aspect of this structure that limits independent variation of characters. Modularization of pleiotropy has been suggested to promote evolvability by restricting genetic covariance among unrelated characters and reducing constraints due to correlated response. However, modularity may also reduce total genetic variation of characters. We study the properties of genotype-phenotype maps that maximize average conditional evolvability, measured as the amount of unconstrained genetic variation in random directions of phenotypic space. In general, maximal evolvability occurs by maximizing genetic variance and minimizing genetic covariance. This does not necessarily require modularity, only patterns of pleiotropy that cancel on average. The detailed structure of the most evolvable genotype-phenotype maps depends on the distribution of molecular variance. When molecular variance is determined by mutation-selection equilibrium either highly pleiotropic or highly modular genotype-phenotype maps can be optimal, depending on the mutation rate and the relative strengths of stabilizing selection on the characters.     

Estimating the heritability of hair colour and eye colour

In the present study the colours of hair and eyes are regarded as quantitative genetic characters. The genetic and environmental components of the total variance of the characters are determined by analysis of correlation between parents and children as well as full sibs. An analysis of correlation coefficients makes it possible to further examine whether autosomal dominance or X-linked factors play a role in the inheritance.     

Evolution of the environmental component of the phenotypic variance: stabilizing selection in changing environments and the cost of homogeneity

Quantitative traits show abundant genetic, environmental, and phenotypic variance, yet if they are subject to stabilizing selection for an optimal phenotype, both the genetic and environmental components are expected to decline. The mechanisms that determine the level and maintenance of phenotypic variance are not yet fully understood. While there has been extensive study of mechanisms maintaining genetic variability, it has generally been assumed that environmental variance is not dependent on the genotype and therefore not subject to change. However, accumulating data suggest that the environmental variance is under some degree of genetic control. In this study, it is assumed accordingly that both the genotypic value (i.e., mean phenotypic value) and the variance of phenotypic value given genotypic value depend on the genotype. Two models are investigated as potentially able to explain the protected maintenance of environmental variance of quantitative traits under stabilizing selection. One is varying environment among generations, such that both the optimal phenotype and the strength of the stabilizing selection vary between generations. The other is the cost of homogeneity, which is based on an assumption of an engineering cost of minimizing variability in development. It is shown that a small homogeneity cost is enough to maintain the observed levels of environmental variance, whereas a large amount of temporal variation in the optimal phenotype and the strength of selection would be necessary.     

Genetic,phenotypic, and environmental correlations in black medic,Medicago lupulina L., grown in three different environments

We have investigated the relationship between phenotypic and genetic correlations among a large number of quantitative traits (36) in three different environments in order to determine their degree of disparity and whether phenotypic correlations could be substituted for their genetic counterparts whatever the environment. We also studied the influence of the environment on genetic and phenotypic correlations. Twenty accessions (full-sib families) ofMedicago luPulina were grown in three environments. In two of these two levels of environmental stress were generated by harvesting plants at flowering and by growing plants in competition with barley, respectively. A third environment, with no treatment, was used as a control with no stress. Average values of pod and shoot weight indicate that competition induces the highest level of stress. The genetic and phenotypic correlations among the 36 traits were compared. Significant phenotypic correlations were obtained easily, while there was no genetic variation for 1 or the 2 characters being correlated. The large positive correlation between the genetic and phenotypic correlation matrices indicated a good proportionality between genetic and phenotypic correlations matrices but not their similarity. In a given environment, when only those traits with a significant genetic variance were taken into account, there were still differences between genetic and phenotypic correlations, even when levels of significance for phenotypic correlations were lowered. Consequently, it is dangerous to substitute phenotypic correlations for genetic correlations. The number of traits that showed genetic variability increased with increasing environmental stress, consequently the number of significant genetic correlations also increased with increasing environmental stress. In contrast, the number of significant phenotypic correlations was not influnced by the environment. The structures of both phenotypic and genetic matrices, however, depended on the environment, and not in the same way for both matrices.     

Inheritance of finger pattern types in MZ and DZ twins

Digital patterns of a sample on twins were analyzed to estimate the resemblance between monozygotic (MZ) and dizygotic (DZ) twins and to evaluate the mode of inheritance by the use of maximum likelihood based variance decomposition analysis. MZ twin resemblance of finger pattern types appears to be more pronounced than in DZ twins, which suggests the presence of genetic factors in the forming of fingertip patterns. The most parsimonious model shows twin resemblance in count of all three basic finger patterns on 10 fingers. It has significant dominant genetic variance component across all fingers. In the general model, the dominant genetic variance component proportion is similar for all fingertips (about 60%) and the sibling environmental variance is significantly nonzero, but the proportion between additive and dominant variance components was different. Application of genetic model fitting technique of segregation analyses clearly shows mode of inheritance. A dominant genetic variance component or a specific genetic system modifies the phenotypic expression of the fingertip patterns. The present study provided evidence of strong genetic component in finger pattern types and seems more informative compared to the earlier traditional method of correlation analysis.     

Climatic and temporal effects on the expression of secondary sexual characters: genetic and environmental components

Despite great interest in sexual selection, relatively little is known in detail about the genetic and environmental determinants of secondary sexual characters in natural populations. Such information is important for determining the way in which populations may respond to sexual selection. We report analyses of genetic and large-scale environmental components of phenotypic variation of two secondary sexual plumage characters (forehead and wing patch size) in the collared flycatcher Ficedula albicollis over a 22-year period. We found significant heritability for both characters but little genetic covariance between the two. We found a positive association between forehead patch size and a large-scale climatic index, the North Atlantic Oscillation (NAO) index, but not for wing patch. This pattern was observed in both cross-sectional and longitudinal data suggesting that the population response to NAO index can be explained as the result of phenotypic plasticity. Heritability of forehead patch size for old males, calculated under favorable conditions (NAO index > or = median), was greater than that under unfavorable conditions (NAO index < median). These changes occurred because there were opposing changes in additive genetic variance (VA) and residual variance (VR) under favorable and unfavorable conditions, with VA increasing and VR decreasing in good environments. However, no such effect was detected for young birds, or for wing patch size in either age class. In addition to these environmental effects on both phenotypic and genetic variances, we found evidence for a significant decrease of forehead patch size over time in older birds. This change appears to be caused by a change in the sign of viability selection on forehead patch size, which is associated with a decline in the breeding value of multiple breeders. Our data thus reveal complex patterns of environmental influence on the expression of secondary sexual characters, which may have important implications for understanding selection and evolution of these characters.     

Consanguineous marriages in Italy: A Note

Abstract

A general multifactorial model is given for the inheritance of traits that exhibit a sexual dimorphism. The model allows for polygenic inheritance, cultural transmission, phenotypic assortative mating, and a common environment of rearing. Several cultural mechanisms are described for which transmission from parent to offspring is sex‐dependent and for which many different patterns of sex‐specific correlations can result. A special case of the general model is described in which phenotypic differences between males and females are due only to differences in nontransmissible environmental factors and/or genetic factors that do not contribute to variability within a sex. Application of these models to human spatial visualizing ability, using data reported by others, gives an estimate of 45 per cent for the proportion of the variance that is accounted for by transmissible factors. Neither an X‐linked hypothesis nor a sex‐specific cultural mechanism is required to explain the transmission of spatial ability.     

A POPULATION GENETIC THEORY OF CANALIZATION

Canalization is the suppression of phenotypic variation. Depending on the causes of phenotypic variation, one speaks either of genetic or environmental canalization. Genetic canalization describes insensitivity of a character to mutations, and the insensitivity to environmental factors is called environmental canalization. Genetic canalization is of interest because it influences the availability of heritable phenotypic variation to natural selection, and is thus potentially important in determining the pattern of phenotypic evolution. In this paper a number of population genetic models are considered of a quantitative character under stabilizing selection. The main purpose of this study is to define the population genetic conditions and constraints for the evolution of canalization. Environmental canalization is modeled as genotype specific environmental variance. It is shown that stabilizing selection favors genes that decrease environmental variance of quantitative characters. However, the theoretical limit of zero environmental variance has never been observed. Of the many ways to explain this fact, two are addressed by our model. It is shown that a “canalization limit” is reached if canalizing effects of mutations are correlated with direct effects on the same character. This canalization limit is predicted to be independent of the strength of stabilizing selection, which is inconsistent with recent experimental data (Sterns et al. 1995). The second model assumes that the canalizing genes have deleterious pleiotropic effects. If these deleterious effects are of the same magnitude as all the other mutations affecting fitness very strong stabilizing selection is required to allow the evolution of environmental canalization. Genetic canalization is modeled as an influence on the average effect of mutations at a locus of other genes. It is found that the selection for genetic canalization critically depends on the amount of genetic variation present in the population. The more genetic variation, the stronger the selection for canalizing effects. All factors that increase genetic variation favor the evolution of genetic canalization (large population size, high mutation rate, large number of genes). If genetic variation is maintained by mutation-selection balance, strong stabilizing selection can inhibit the evolution of genetic canalization. Strong stabilizing selection eliminates genetic variation to a level where selection for canalization does not work anymore. It is predicted that the most important characters (in terms of fitness) are not necessarily the most canalized ones, if they are under very strong stabilizing selection (k > 0.2V_e). The rate of decrease of mutational variance V_m is found to be less than 10% of the initial V_m. From this result it is concluded that characters with typical mutational variances of about 10^–3 V_e are in a metastable state where further evolution of genetic canalization is too slow to be of importance at a microevolutionary time scale. The implications for the explanation of macroevolutionary patterns are discussed.     

Competition can maintain genetic but not environmental variance in the presence of stabilizing selection

A population in which there is stabilizing selection acting on quantitative traits toward an intermediate optimum becomes monomorphic in the absence of mutation. Further, genotypes that show least environmental variation are also favored, such that selection is likely to reduce both genetic and environmental components of phenotypic variance. In contrast, intraspecific competition for resources is more severe between phenotypically similar individuals, such that those deviating from prevailing phenotypes have a selective advantage. It has been shown previously that polymorphism and phenotypic variance can be maintained if competition between individuals is "effectively" stronger than stabilizing selection. Environmental variance is generally observed in quantitative traits, so mechanisms to explain its maintenance are sought, but the impact of competition on its magnitude has not previously been studied. Here we assume that a quantitative trait is subject to selection for an optimal value and to selection due to competition. Further, we assume that both the mean and variance of the phenotypic value depend on genotype, such that both may be affected by selection. Theoretical analysis and numerical simulations reveal that environmental variance can be maintained only when the genetic variance (in mean phenotypic value) is constrained to a very low level. Environmental variance will be replaced entirely by genotypic variance if a range of genotypes that vary widely in mean phenotype are present or become so by mutation. The distribution of mean phenotypic values is discrete when competition is strong relative to stabilizing selection; but more genotypes segregate and the distribution can approach continuity as competition becomes extremely strong. If the magnitude of the environmental variance is not under genetic control, there is a complementary relationship between the levels of environmental and genetic variance such that the level of phenotypic variance is little affected.     

On the quantitative genetics of mixture characters

Finite mixture models are helpful for uncovering heterogeneity due to hidden structure. Quantitative genetics issues of continuous characters having a finite mixture of Gaussian components as statistical distribution are explored in this article. The partition of variance in a mixture, the covariance between relatives under the supposition of an additive genetic model, and the offspring-parent regression are derived. Formulas for assessing the effect of mass selection operating on a mixture are given. Expressions for the genetic and phenotypic correlations between mixture and Gaussian traits and between two mixture traits are presented. It is found that, if there is heterogeneity in a population at the genetic or environmental level, then genetic parameters based on theory treating distributions as homogeneous can lead to misleading interpretations. Some peculiarities of mixture characters are: heritability depends on the mean values of the component distributions, the offspring-parent regression is nonlinear, and genetic or phenotypic correlations cannot be interpreted devoid of the mixture proportions and of the parameters of the distributions mixed.     

Estimation of the heritability of hair and eye color

In the present study the colours of hair are regarded as quantitative genetic characters. The genetic and environmental components of the total variance of the characters are determined by analysis of correlation between parents and children as well as full sibs. An analysis of correlation coefficients makes it possible to further examine whether autosomal dominance or X-linked factors play a role in the inheritance. The correlations between the parents make the genetical analysis more complicated as they raise the correlation coefficients between relatives. The estimates of heritability are 0.61 (hair-colour) and 0.80 (eye-colour). These estimates may serve as preliminary values of orientation. Only further studies will show whether the relative large part of the variance caused by the environment can be confirmed. Dominance may play a small role in the case of hair colour, while it seems to be absent in eye-colour. There are no sufficient indications of X-linked factors for both characters.