The repeatability of fluctuating asymmetry: a revision and extension

Fluctuating asymmetry (FA) is an imperfect measure of the developmental stability of an individual. Estimates of the heritability of FA will underestimate the heritability of developmental stability; the extent of this bias can be estimated and corrected by estimating the repeatability of developmental stability. This note corrects an error in a previous derivation of this repeatability using the absolute value of the difference between sides as the measure of FA, and derives the repeatability of developmental stability for another common measure of FA, the variance among sides within an individual.     

Epistasis affecting litter size in mice

Litter size is an important reproductive trait as it makes a major contribution to fitness. Generally, traits closely related to fitness show low heritability perhaps because of the corrosive effects of directional natural selection on the additive genetic variance. Nonetheless, low heritability does not imply, necessarily, a complete absence of genetic variation because genetic interactions (epistasis and dominance) contribute to variation in traits displaying strong heterosis in crosses, such as litter size. In our study, we investigated the genetic architecture of litter size in 166 females from an F2 intercross of the SM/J and LG/J inbred mouse strains. Litter size had a low heritability (h2 = 12%) and a low repeatability (r = 33%). Using interval-mapping methods, we located two quantitative trait loci (QTL) affecting litter size at locations D7Mit21 + 0 cM and D12Mit6 + 8 cM, on chromosomes 7 and 12 respectively. These QTL accounted for 12.6% of the variance in litter size. In a two-way genome-wide epistasis scan we found eight QTL interacting epistatically involving chromosomes 2, 4, 5, 11, 14, 15 and 18. Taken together, the QTL and their interactions explain nearly 49% (39.5% adjusted multiple r2) of the phenotypic variation for litter size in this cross, an increase of 36% over the direct effects of the QTL. This indicates the importance of epistasis as a component of the genetic architecture of litter size and fitness in our intercross population.     

Characterization of OCA2 cDNA in different porcine breeds and analysis of its potential effect on skin pigmentation in a red Iberian strain

Although the function of the OCA2 gene product has not been totally clarified, variation in OCA2 has been associated with skin and hair pigmentation in human and mouse. However, its contribution to skin colour in domestic species has not been reported. In this study, cDNA and intron 9 sequences of the porcine OCA2 gene have been characterized in several pig populations. The cDNA sequence alignment of 20 animals from eight porcine populations allowed the identification of 10 single nucleotide polymorphisms (SNPs); five of the 10 SNPs were non-synonymous. The intron 9 sequence alignment of 12 animals belonging to four pig populations revealed four additional SNPs. Skin colour variation was analysed in a red strain of Iberian pigs with segregation of three SNPs forming two OCA2 intragenic haplotypes. Results from this study provide evidence of a suggestive dominant effect of haplotypes on colour intensity and indicate an important contribution of additive polygenic effects (h2 = 0.56 +/- 0.21) to the variance of this trait.     

An epistatic genetic basis for fluctuating asymmetry of tooth size and shape in mice

Although there typically is little additive genetic variation for fluctuating asymmetry (FA), or variation in nondirectional differences between left and right sides of bilateral characters, several investigators have hypothesized that FA may have an epistatic genetic basis. We tested this hypothesis by conducting a whole genome scan of FA of size and shape of the mandibular molars in house mice from an F2 intercross population generated from crossing the Large (LG/J) and Small (SM/J) inbred strains. Although no individual genes (QTLs=quantitative trait loci) on any of the 19 autosomes significantly affected FA for centroid size, and only two affected shape FA, a number of pairwise combinations of QTLs exhibited significant epistasis for FA in both molar size and shape. The QTLs involved in these interactions differed for FA in molar size versus FA in molar shape, but their epistatic contributions to the total variance was nearly the same (about 20%) for FA in both molar characters. It was noted that the genetic architecture of FA in the molar characters, consisting of little or no additive genetic variance but an abundance of epistatic genetic variance, is consistent with that of other typical fitness components such as litter size.     

Mitochondrial lineages reveal intense gene flow between Iberian wild boars and South Iberian pig breeds

The phylogeography of wild boars (WB) and domestic pigs (Sus scrofa) has contributed important insights into where and when domestication occurred. The geographic distribution of two core haplotypes (E1a and E1c) of the main European phylogenetic clade suggests that Central Europe was an early domestication centre, although the complexity of the pattern does not exclude the possibility that multiple domestication events occurred in different regions. To investigate the relationships among WB and domestic pig breeds in Iberia, a fragment of the mitochondrial DNA control region from a large sample (n = 409) of WB and local pig breeds was co‐analysed with published sequences from other European populations. The Iberian sample revealed a high frequency of a sub‐cluster (E1c) of the European haplogroup E1 in 77% of total Iberian samples, 96% of WB, 90% of Alentejano (Portugal) and 87% of Iberian breed pigs (Spain; Black Hairy, Black Hairless and Red varieties). Low genetic distance (F’_ST = 0.105) was observed between Alentejano (Portugal) and Iberian breed pigs (Spain). Alentejano and Iberian breed pigs showed low genetic distances to both Iberian and Central European WB (average F’_ST = 0.345 and 0.215, respectively). This pattern suggests that early pig husbandry in the Iberian Peninsula did not solely rely on imported Central European stock, but also included the recruitment of local WB.     

Unexpected high polymorphism at the FABP4 gene unveils a complex history for pig populations

Fatty acid bing protein 4 (FABP4) plays a key role in fat regulation in mammals and is a strong positional candidate gene for the FAT1 quantitative trait locus located on porcine chromosome 4. DNA resequencing of the FABP4 gene region in 23 pigs from 10 breeds and wild boar revealed 134 variants in 6.4 kb, representing a silent nucleotide diversity of piS=0.01, much higher than reported so far in animal domestic species. Moreover, this diversity was highly structured. Also strikingly, the FABP4 phylogenetic tree did not show any geographical or breed origin clustering, with distant breeds sharing similar haplotypes and some of the most heterozygous samples pertaining to highly inbred animals like Iberian Guadyerbas (inbreeding coefficient approximately 0.3) or British Tamworth. In contrast, the cytochrome b (mtDNA) phylogenetic tree was coherent with geographical origin. The estimated age of the most recent common ancestor for the most divergent Iberian or Tamworth haplotypes was much older than domestication. An additional panel of 100 pigs from 8 different breeds and wild boar from Spain, Tunisia, Sardinia, and Japan was genotyped for seven selected single nucleotide polymorphisms and shows that high variability at the porcine FABP4 is the rule rather than the exception. Pig populations, even highly inbred, can maintain high levels of variability for surprisingly long periods of time.     

Exploring alternative models for sex-linked quantitative trait loci in outbred populations: application to an iberian x landrace pig intercross

We present a very flexible method that allows us to analyze X-linked quantitative trait loci (QTL) in crosses between outbred lines. The dosage compensation phenomenon is modeled explicitly in an identity-by-descent approach. A variety of models can be fitted, ranging from considering alternative fixed alleles within the founder breeds to a model where the only genetic variation is within breeds, as well as mixed models. Different genetic variances within each founder breed can be estimated. We illustrate the method with data from an F(2) cross between Iberian x Landrace pigs for intramuscular fat content and meat color component a*. The Iberian allele exhibited a strong overdominant effect for intramuscular fat in females. There was also limited evidence of one or more regions affecting color component a*. The analysis suggested that the QTL alleles were fixed in the Iberian founders, whereas there was some evidence of segregation in Landrace for the QTL affecting a* color component.     

Genetic parameters and direct,maternal and heterosis effects on litter size in a diallel cross among three commercial varieties of Iberian pig

The Iberian pig is one of the pig breeds that has the highest meat quality. Traditionally, producers have bred one of the available varieties, exclusively, and have not used crosses between them, which has contrasted sharply with other populations of commercial pigs for which crossbreeding has been a standard procedure. The objective of this study was to perform an experiment under full diallel design among three contemporary commercial varieties of Iberian pig and estimate the additive genetic variation and the crossbreeding effects (direct, maternal and heterosis) for prolificacy. The data set comprised 18 193 records for total number born and number born alive from 3800 sows of three varieties of the Iberian breed (Retinto, Torbiscal and Entrepelado) and their reciprocal crosses (Retinto × Torbiscal, Torbiscal × Retinto, Retinto × Entrepelado, Entrepelado × Retinto, Torbiscal × Entrepelado and Entrepelado × Torbiscal), and a pedigree of 4609 individuals. The analysis was based on a multiple population repeatability model, and we developed a model comparison test that indicated the presence of direct line, maternal and heterosis effects. The results indicated the superiorities of the direct line effect of the Retinto and the maternal effect of the Entrepelado populations. All of the potential crosses produced significant heterosis, and additive genetic variation was higher in the Entrepelado than it was in the other two populations. The recommended cross for the highest yield in prolificacy is a Retinto father and an Entrepelado mother to generate a hybrid commercial sow.     

Mitochondrial DNA sequence variation and phylogenetic relationships among Iberian pigs and other domestic and wild pig populations

Nucleotide sequences of mitochondrial DNA (mtDNA) cytochrome B gene (1140 bp) and control region (707 bp) were used to determine the phylogenetic relationships among 51 pig samples representing ancient and current varieties of Iberian pigs (26), Spanish wild boars (seven) and other domestic pigs (18) of cosmopolitan (Duroc, Large White, Landrace, Pietrain and Meishan) and local (Spotted Black Jabugo, Basque and Mangalitza) breeds. A neighbour-joining tree constructed from pairwise distances provide evidence of the European origin of both Iberian pigs and Spanish wild boars. The introgression of Asian mtDNA haplotypes in the genetic pool of the Iberian breed seems unlikely. Four estimates of sequence divergence between European and Asian clades were calculated from the two main domains of the D-loop region and the synonymous and nonsynonymous nucleotide substitutions in the cytochrome B gene. The time since the divergence of pig ancestors was estimated at about 600,000 years before present.     

The quantitative genetics of fluctuating asymmetry: a comparison of two models

The genetic basis of fluctuating asymmetry (FA), a measure of random deviations from perfect bilateral symmetry, has been the subject of much recent work. In this paper we compare two perspectives on the quantitative genetic analysis of FA and directional asymmetry (DA). We call these two approaches the character-state model and the environmental responsiveness model. In the former approach, the right and left sides are viewed as separate traits whose genetic coupling is manifested by the genetic correlation. This model leads to the relationship, h2(DA) = h2[(1-rA)/(1-rp)), where h2 is the heritability of each component trait (assumed to be the same), rA and rp are the genetic and phenotypic correlations between traits, respectively. Simulation shows that, under this model, the heritability of FA is considerably less than that of DA, except when heritabilities are very close to zero. The environmental responsiveness model permits genetic variance in FA even when the genetic correlation between traits is + 1. Simulation shows that under this model the heritability of FA can be uncoupled from that of DA. The additive and nonadditive components of the component (right and left) traits, their DA and FA values are estimated using a diallel cross of seven inbred lines of the sand cricket, Gryllus firmus. Four leg measurements were made and both the individual DA and FA values and the compound measures DASUM and CFA estimated. The heritabilities of the compound measures are slightly larger than the individual estimates. Dominance variance is observed in the individual traits but predicted to be an even smaller component of the phenotypic variance than the additive genetic variance. The estimated values confirm this, although a previous study has demonstrated that dominance variance is present. Because the heritabilities of FA are generally larger than those of DA, which never exceed 0.02, the environmental responsiveness model is more consistent with the data than the character-state model. A review of other data suggests that both sources of variation might be found in some species.     

Directional and Fluctuating Asymmetry in Sexual and Asexual Otiorhynchus alpicola Populations

This study concerns the contribution of directional asymmetry (DA) and fluctuating asymmetry (FA) as a characterization of variation in six sexual (diploid) and two asexual (triploid and tetraploid) populations of the weevil Otiorhynchus alpicola. It is shown that DA in sexual populations is about 1 % of the mean length of each of the seven bilateral traits and the average contribution of DA to trait variation is even lower in asexual populations (about 0.85 in triploids and 0.65 in tetraploids forms). The average contribution of FA to the total phenotypic variance is about 23 %, 12 % and 19 % in diploid, triploid and tetraploid populations, respectively. Since FA is generally regarded as a measure of developmental stability, our data indicate that triploid forms of O. alpicola are developmentally more stable than diploid and tetraploid forms. The relationship between the level of ploidy and FA is discussed.     

Temperature and genotypic effects on life history and fluctuating asymmetry in a field strain of Culex pipiens

Fluctuating asymmetry (FA) has been proposed as a tool to measure levels of stress experienced by populations of organisms during development. To be of value as a bio-marker to highlight conditions at particular sites, it is important that variation in FA is due to environmental (eg pollution) variation and not genetic variation among populations and families, in other words heritability for FA should be very close to zero. A full-sib design was set up in which families of Culex pipiens mosquitoes collected from the field were reared at three different developmental temperatures. The effects of temperature and family on developmental rate, egg to adult survival and four wing morphological measures were assessed. There was both a temperature and a family effect on development rate and survival. Temperature affected all four wing traits, but an influence of family was only evident in two of the wing traits. Two separate measures of FA for each of the wing traits were obtained. The mean estimates of FA were mainly around 1% of the value of the character measured. There was evidence of an increase in FA with increase in temperature stress. Heritability was estimated for the wing traits and wing trait FA's using restricted estimation maximum likelihood. The estimates of heritability for the wing traits were small and, individually, did not differ significantly from zero. There was also no evidence of heritable genetic variation for any of the wing trait FA's. The results are discussed in relation to other studies where FA heritabilities have been estimated and in relation to the use of FA as an indicator of environmental stress.     

THE ASSOCIATION BETWEEN FLUCTUATING ASYMMETRY,TRAIT VARIABILITY,TRAIT HERITABILITY,AND STRESS: A MULTIPLY REPLICATED EXPERIMENT ON COMBINED STRESSES IN DROSOPHILA MELANOGASTER

A number of hypotheses have been proposed about the association between developmental stability phenotypic variability, heritability, and environmental stress. Stress is often considered to increase both the asymmetry and phenotypic variability of bilateral traits, although this may depend on trait heritability. Empirical studies of such associations often yield inconsistent results. This may reflect the diversity of traits and conditions used or a low repeatability of any associations. To test for repeatable associations between these variables, multiply replicated experiments were undertaken on Drosophila melanogaster using a combination stress at the egg, larval and adult stages of reduced protein, ethanol in the medium, and a cold shock. Both metric and meristic traits were measured and levels of heritable variation for each trait estimated by maximum likelihood and parent-offspring regression over three generations. Trait means were reduced by stress, whereas among-individual variation increased Fluctuating asymmetry (FA) was increased by stress in some cases, but few comparisons were significant. Only one trait orbital bristle, showed consistent increases in FA. Changes in trait means, trait phenotypic variability, and developmental stability as a result of stress were not correlated. Extreme phenotypes tended to have higher levels of FA but only the results for orbital bristles were significant. All traits had low to intermediate heritabilities except orbital bristle, which showed no heritable variation. Only traits with low heritability and high levels of phenotypic variability may show consistent increases in FA under stress. Overall, the independence of phenotypic variability, plasticity, and the developmental stability of traits extend to changes in these measures under stressful conditions.     

Genetic parameters for litter size in sheep: natural versus hormone-induced oestrus

The litter size in Suffolk and Texel-sheep was analysed using REML and Bayesian methods. Litters born after hormonal induced oestrus and after natural oestrus were treated as different traits in order to estimate the genetic correlation between the traits. Explanatory variables were the age of the ewe at lambing, period of lambing, a year*flock-effect, a permanent environmental effect associated with the ewe, and the additive genetic effect. The heritability estimates for litter size ranged from 0.06 to 0.13 using REML in bi-variate linear models. Transformation of the estimates to the underlying scale resulted in heritability estimates from 0.12 to 0.17. Posterior means of the heritability of litter size in the Bayesian approach with bi-variate threshold models varied from 0.05 to 0.18. REML estimates of the genetic correlations between the two types of litter size ranged from 0.57 to 0.64 in the Suffolk and from 0.75 to 0.81 in the Texel. The posterior means of the genetic correlation (Bayesian analysis) were 0.40 and 0.44 for the Suffolk and 0.56 and 0.75 for the Texel in the sire and animal model respectively. A bivariate threshold model seems appropriate for the genetic evaluation of prolificacy in the breeds concerned.     

Genetic mapping of developmental instability: design, model and algorithm

Developmental instability or noise, defined as the phenotypic imprecision of an organism in the face of internal or external stochastic disturbances, has been thought to play an important role in shaping evolutionary processes and patterns. The genetic studies of developmental instability have been based on fluctuating asymmetry (FA) that measures random differences between the left and the right sides of bilateral traits. In this article, we frame an experimental design characterized by a spatial autocorrelation structure for determining the genetic control of developmental instability for those traits that cannot be bilaterally measured. This design allows the residual environmental variance of a quantitative trait to be dissolved into two components due to permanent and random environmental factors. The degree of developmental instability is quantified by the relative proportion of the random residual variance to the total residual variance. We formulate a mixture model to estimate and test the genetic effects of quantitative trait loci (QTL) on the developmental instability of the trait. The genetic parameters including the QTL position, the QTL effects, and spatial autocorrelations are estimated by implementing the EM algorithm within the mixture model framework. Simulation studies were performed to investigate the statistical behavior of the model. A live example for poplar trees was used to map the QTL that control root length growth and its developmental instability from cuttings in water culture.     

The contribution of social effects to heritable variation in finishing traits of domestic pigs (Sus scrofa)

Social interactions among individuals are ubiquitous both in animals and in plants, and in natural as well as domestic populations. These interactions affect both the direction and the magnitude of responses to selection and are a key factor in evolutionary success of species and in the design of breeding schemes in agriculture. At present, however, very little is known of the contribution of social effects to heritable variance in trait values. Here we present estimates of the direct and social genetic variance in growth rate, feed intake, back fat thickness, and muscle depth in a population of 14,032 domestic pigs with known pedigree. Results show that social effects contribute the vast majority of heritable variance in growth rate and feed intake in this population. Total heritable variance expressed relative to phenotypic variance was 71% for growth rate and 70% for feed intake. These values clearly exceed the usual range of heritability for those traits. Back fat thickness and muscle depth showed no heritable variance due to social effects. Our results suggest that genetic improvement in agriculture can be substantially advanced by redirecting breeding schemes, so as to capture heritable variance due to social effects.     

Individual differences in developmental precision and fluctuating asymmetry: a model and its implications

In many studies, fluctuating asymmetry (FA) has been used as a measure of individual differences in developmental imprecision. A model of how variation in developmental imprecision is associated with variation in asymmetry is described and applied to important issues about FA. If individual differences in developmental imprecision exist, asymmetry due to developmental error should be leptokurtically distributed. Moreover, the greater the magnitude of individual differences, the greater the leptokurtosis. Asymmetry purportedly due to developmental error in a variety of species is indeed leptokurtically distributed. The level of leptokurtosis suggests that the CV in individual differences in underlying developmental imprecision is generally 20–25, consistent with it being a fitness trait. In addition, data suggest that: (1) the individual differences that underlie the developmental imprecision of different traits are largely shared across traits and not trait-specific; (2) the heritability of these individual differences may average between 35 and 55%, despite small heritabilities of individual trait FAs; and (3) correlations between FA and fitness traits or components suggest high correlations between underlying variation in developmental precision and fitness in many species. Theoretical implications are discussed.     

The evolutionary potential of developmental instability

Whether or not developmental instability (DI) has evolutionary potential is subject to much debate. Generally, studies fail to detect significant heritability for fluctuating asymmetry (FA), a trait assumed to reflect DI. In addition, between‐trait correlations in FA are low, suggesting that DI is trait‐ rather than individual‐specific. Among the various attempts to explain these patterns, the overall weak correlation between FA and DI at the individual level has received most attention. Presently, the concept of hypothetical repeatability (R) of individual FA allows us to correct for this weak relationship, transforming patterns of FA into unbiased patterns of DI. By applying R to data presented in the literature, we show that heritability of DI remains lower than predicted but between‐trait correlations in DI substantially increase after transformation. We further provide evidence that DI changes from a trait‐ to an individual‐specific property with higher values of R. As increasing hypothetical repeatability might co‐occur with increased environmental or genetic stress, we discuss the potential implications of our results for the study of evolution of stress resistance. From this we conclude that there is an urgent need for studies that compare the evolutionary potential of developmental instability under a variety of stress conditions.     

Response to selection for litter size in Danish Landrace pigs: a Bayesian analysis

A replicated selection experiment aimed at increasing litter size (total number of pigs born per litter) in Danish Landrace pigs was conducted from 1984 to 1991. The experiment included two selection and two control lines. In each generation, 30 and 14 first litters were produced in selection and control lines, respectively, and dams produced two litters. Each replicate, consisting of one selection and one control line, was founded from 60 families chosen randomly from the population at large. Family selection was practiced, and the criterion was the predicted breeding value for litter size computed using a repeatability animal model, and taking into account all available information. The data consisted of 947 records from 523 dams (424 dams had two litters) representing five cycles of selection of increased litter size. Data were analyzed from a Bayesian perspective, based on marginal posterior distributions of genetic parameters of interest. Marginalization was achieved using Gibbs sampling, with a single chain length of 1 205 000. After discarding the first 5 000 iterations, a sample was drawn every ten iterations, so 120 000 samples in total were saved. Densities were estimated and plotted, and summary statistics were computed from the estimated densities. The posterior means (± standard error) of heritability and repeatability were 0.22 ± 0.06 and 0.32 ± 0.05, respectively. These point estimates of genetic parameters were within the range of literature values, although on the high side. The posterior mean (± standard error) of genetic response to selection, defined as the difference between the mean breeding values of the selected lines and that of the base population, was 1.37 ± 0.43 pigs after five cycles of selection. The regression (through the origin) of breeding values in the selected lines on generation was 0.25 ± 0.08 pigs. Several informative priors constructed from information obtained with field data in this population were used to examine their influence on inferences. The priors were influential because of the relatively small scale of the experiment. An analysis excluding data from one of the control lines gave smaller genetic variance and heritability, and a smaller response to selection. However, it appears that selection for litter size is effective, but that the true rate of response is probably smaller than data from this experiment suggest.     

Lack of response to selection for lower fluctuating asymmetry of mutant eyespots in the butterfly Bicyclus anynana

Fluctuating asymmetry (FA) is claimed both to provide a means of evaluating developmental stability, and to reflect an individual's quality or the stress experienced during development. FA refers to the nondirectional variation between left and right sides, whereas directional asymmetry (DA) refers to a significant directional variation between the sides. We studied four eyespots on the dorsal forewing of the tropical butterfly, Bicyclus anynana. Two of the eyespots were specified by a mutant allele, Spotty, that was fixed in the stock. These eyespots showed higher FA than the two flanking, wild-type eyespots, although they are all formed by the same developmental pathway. We applied artificial selection for lower FA of the novel eyespots in an attempt to increase their developmental stability. There was significant variation present in individual FA in our study. However, this did not change as a result of the artificial selection. Most of the variation in FA can be accounted for by individual differences in developmental stability rather than by the applied selection or by environmental variation. Thus, it was not possible to produce any increased developmental stability of the novel eyespots by selecting for low FA. The estimates of realized heritability for both FA and DA of each eyespot were not significantly different from zero. The results suggest that FA provides little, if any, potential for exploring the mechanistic basis of developmental stability.