Genetic analysis of sexual dimorphism of body weight in broilers

Variation in sexual dimorphism (SD) is particularly marked in meat-type chickens. This paper investigates the genetic basis of SD in an important economic trait, i.e. body weight (BW) at 35 days of age, in broilers by applying quantitative genetic analysis. A large dataset comprising 203,323 BW records of a commercial line of broiler chicken was used. First, a bivariate approach was employed treating BW as a sex-specific trait. During this approach, seven bivariate models were applied and variances due to direct additive genetic, maternal genetic and maternal environmental effects were estimated via the restricted maximum likelihood method. The best-fitting model included direct additive genetic, maternal genetic and maternal environmental effects with a direct–maternal genetic covariance. Differences between male and female direct heritabilities were non-significant (0.28 vs. 0.29 for males and females, respectively), implying no need for sex-specific selection strategies. The direct–maternal genetic correlation was more strongly negative in males than in females (?0.72 vs. ?0.56), implying a more profound antagonism between direct additive and maternal genetic effects in this particular gender. The direct genetic correlation of BW between the two sexes was as high as 0.91, i.e. only slightly lower than unity. Second, variance components and genetic parameters of two measures of SD, i.e. the weight difference (Δ) and the weight ratio (R), between the genders were estimated. Direct heritabilities for both measures were significantly different to 0 but of low magnitude (0.04). Apart from the additive–maternal covariance, no other random effects were found to be of importance for Δ and R. The results of the present study suggest that only minimal selection responses due to the selection of Δ and/or R and a small capacity for amplifying or reducing the BW differences between the sexes are to be expected in this specific population. Furthermore, selection pressure on BW is expected to amplify SD.     

Effects of Ancestral X Irradiation Followed by Random Mating on Body Weight of Rats

Effects of nine generations of 450r per generation of ancestral spermatogonial X irradiation of inbred rats on body weight were examined. After six generations of random mating (avoiding inbreeding) following the termination of irradiation, descendants of irradiated males (R) were significantly lighter than their controls (C) at 3 and 6 weeks, but not at 10 weeks of age. However, differences in growth between R and C populations were small. Among-litter and within-litter variance estimates were generally larger in the R lines than in the C lines, suggesting that selection responses would be greater in R than in C lines. In conjunction with previous evidence—obtained during the irradiation phase of the experiment—this suggested that more rapid response to selection for 6-week body weight, in particular, might accrue in the R lines.     

Sexual dimorphism and direct and maternal genetic effects on body weight in mice

Summary Genetic and phenotypic parameters for three-, six- and eight-week body weight and for weight gain between three and six weeks of age were estimated from data collected over 14 generations in a randombred control population. Genetic parameters were also estimated for sexual dimorphism in body weight and gain. Heritability estimates were substantial for body weight at all ages and for body weight gain. Additive maternal variances were also large. Estimates of the covariance between direct and maternal genetic effects were negative and substantial for three- and six-week weights and gain. Also the covariance between maternal effects on weaning weight and direct genetic effects on six- and eight-week weights were negative. These results indicate a consistent antagonism between maternal and direct genetic effects in this population.The analysis of sexual dimorphism yielded estimates of 0.87±.09 and 0.71±.14 for the correlation between additive direct effects on males and females for six-week weight and body weight gain respectively. Corresponding heritability estimates were 0.07±.09 and 0.11±.09. Heritability estimates for sexual dimorphism in three- and eight-week weights were negative.Journal Paper No. 3687 of the North Carolina State University Agricultural Experiment Station. This investigation was supported in part by NIH Grant No. GM11546.     

Responses to Selection for Body Weight in Descendants of X-Irradiated Rats

The effectiveness of selection for high and low body weight at six weeks of age was studied in descendants of X-irradiated (R) and nonirradiated (C) inbred rats. There were two replicates of each of the direction of selection-irradiation treatments. In C lines, there were no consistent responses to selection, probably due to a low level of genetic variability. In R rats, selection was effective only for decreased body weight. The results of this experiment do not suggest the use of irradiation combined with selection as a means of enhancing responses to selection in animals.     

Genetic parameters for growth traits of a Brazilian Bos taurus x Bos indicus beef composite

The genetic analysis of composite data is very complicated, mainly because it is necessary to adjust data to the effects of heterosis and breed complementarity, and because there is usually considerable confounding of these data with several other effects, such as contemporary group effects, breed composition of the animal and maternal breed composition, among others. Data on birth weight (n = 151,083), weaning weight adjusted to 205 days (n = 137,257), yearling weight adjusted to 390 days (n = 61,410), weight gain from weaning to yearling (n = 56,653), and scrotum circumference (n = 23,323) and muscle score (n = 54,770), both adjusted to 390 days, from Bos taurus x Bos indicus composite beef calves born from 1994 to 2003 were analyzed to estimate (co)variance components and genetic parameters of growth traits. The animals belonged to the Montana Tropical program. Estimation was made by three models that approach adjustment to heterozygosis in order to suggest the best model. The RM model included contemporary groups, class of age of dam, outcrossing percentages for direct and maternal effects, and direct and maternal additive genetic breed effects as covariates; the R model was the same as RM, but without additive maternal breed effects, and H was the same as RM, but not considering any additive breed effect. Both R2 values and consistency of genetic parameters indicate that the more complex model (RM), which considers maternal and individual additive genetic breed effect, produces the best estimates when compared to other models. The R model seems to overestimate (co)variance components. The magnitudes of direct and maternal heritability estimates, obtained in this study, would permit genetic improvement for weight and growth traits, as much by selection of direct genetic effects for weight and growth as for the improvement of maternal performance, but in different lineages. Therefore, the correlations between these effects were unfavorable.     

Combined genetic analysis of partial blast resistance in an upland rice population and recurrent selection for line and hybrid values

The CNA-IRAT 5 upland rice population has been improved for 4 years by recurrent selection for blast resistance in Brazil. In order to predict the efficiency of recurrent selection in different test systems and to compare the relative advantage of hybrids versus pure line breeding, a combined genetic analysis of partial blast resistance in the CNA-IRAT 5 population was undertaken. A three-level hierarchical design in inbreeding and a factorial design were derived from the base population. Partial blast resistance of lines and hybrids was evaluated in the greenhouse and in the field by inoculation with one virulent blast isolate. The means and genetic variances of the hybrids and lines were estimated. Genetic advance by recurrent selection was predicted from estimates of variance components. The inheritance of partial blast resistance was mainly additive but non-additive effects were detected at both levels of means and variances. Mean heterosis ranged from 4%–8% for lesion size and lesion density to 10–12% for leaf and panicle resistance. High dominance or homozygous dominance variances relative to additive variance and negative covariance between additive and homozygous dominance effects were estimated. A low frequency of favourable alleles for partial resistance would explain the observed organisation of genetic variability in the base population. Recurrent selection will efficiently improve partial blast resistance of the CNA-IRAT 5 population. Genetic advance for line or hybrid values was expected to be higher testing doubled haploid lines than S1 lines, or than general combining ability. Two components of partial resistance assessed in the greenhouse, lesion size and lesion density, could be used as indirect selection criteria to improve field resistance. On the whole, hybrid breeding for partial blast resistance appeared to be slightly more advantageous than pure line breeding.     

THE EVOLUTIONARY GENETICS OF MALE LIFE-HISTORY CHARACTERS IN DROSOPHILA MELANOGASTER

Alternative models of the maintenance of genetic variability, theories of life-history evolution, and theories of sexual selection and mate choice can be tested by measuring additive and nonadditive genetic variances of components of fitness. A quantitative genetic breeding design was used to produce estimates of genetic variances for male life-history traits in Drosophila melanogaster. Additive genetic covariances and correlations between traits were also estimated. Flies from a large, outbred, laboratory population were assayed for age-specific competitive mating ability, age-specific survivorship, body mass, and fertility. Variance-component analysis then allowed the decomposition of phenotypic variation into components associated with additive genetic, nonadditive genetic, and environmental variability. A comparison of dominance and additive components of genetic variation provides little support for an important role for balancing selection in maintaining genetic variance in this suite of traits. The results provide support for the mutation-accumulation theory, but not the antagonistic-pleiotropy theory of senescence. No evidence is found for the positive genetic correlations between mating success and offspring quality or quantity that are predicted by “good genes” models of sexual selection. Additive genetic coefficients of variation for life-history characters are larger than those for body weight. Finally, this set of male life-history characters exhibits a very low correspondence between estimates of genetic and phenotypic correlations.     

Longitudinal analyses of correlated response efficiencies of fillet traits in Nile tilapia

Recent studies with Nile tilapia have shown divergent results regarding the possibility of selecting on morphometric measurements to promote indirect genetic gains in fillet yield (FY). The use of indirect selection for fillet traits is important as these traits are only measurable after harvesting. Random regression models are a powerful tool in association studies to identify the best time point to measure and select animals. Random regression models can also be applied in a multiple trait approach to analyze indirect response to selection, which would avoid the need to sacrifice candidate fish. Therefore, the aim of this study was to investigate the genetic relationships between several body measurements, weight and fillet traits throughout the growth period and to evaluate the possibility of indirect selection for fillet traits in Nile tilapia. Data were collected from 2042 fish and was divided into two subsets. The first subset was used to estimate genetic parameters, including the permanent environmental effect for BW and body measurements (8758 records for each body measurement, as each fish was individually weighed and measured a maximum of six times). The second subset (2042 records for each trait) was used to estimate genetic correlations and heritabilities, which enabled the calculation of correlated response efficiencies between body measurements and the fillet traits. Heritability estimates across ages ranged from 0.05 to 0.5 for height, 0.02 to 0.48 for corrected length (CL), 0.05 to 0.68 for width, 0.08 to 0.57 for fillet weight (FW) and 0.12 to 0.42 for FY. All genetic correlation estimates between body measurements and FW were positive and strong (0.64 to 0.98). The estimates of genetic correlation between body measurements and FY were positive (except for CL at some ages), but weak to moderate (−0.08 to 0.68). These estimates resulted in strong and favorable correlated response efficiencies for FW and positive, but moderate for FY. These results indicate the possibility of achieving indirect genetic gains for FW and by selecting for morphometric traits, but low efficiency for FY when compared with direct selection.     

Direct genetic and postnatal maternal genetic effects on body composition in mice selected for body weight.

Line crossfostering techniques were used to study differences among selected and control lines of mice in direct genetic and postnatal maternal genetic influences on preweaning (day 12) body weight and composition. The lines were selected for high (H6) and low (L6) 6-week body weight and the control line (C2) was maintained by random selection. There were positive correlated responses to selection in both direct genetic and postnatal maternal genetic effects on body weight and weights of all body components (P less than 0.01) except for water and ash weight in H6. The correlated responses in postnatal maternal genetic effects were of the same order of magnitude as those in direct genetic effects. Correlated responses were greater in L6 than in H6. Correlated responses in direct genetic effects were positive (P less than 0.01) for water percent in H6 and ether extract percent in L6, and negative (P less than 0.01) for water percent and lean percent in L6. Correlated responses in postnatal maternal genetic effects were positive for ether extract percent and negative for water percent (P less than 0.01). Correlated responses were far greater in L6 than in H6 and were greater for postnatal maternal genetic effects than for direct genetic effects. Analyses of covariance results indicated line differences in the relative growth rates of the body components.     

籼型黑米粒形性状的遗传效应及其与矿质元素含量的遗传相关性

采用禾谷类作物种子数量性状的遗传模型,分析了灿型黑米稻品种双列杂交F1和F2种子的粒重,粒长,粒宽和粒长／粒宽等粒形性状的遗传效应及其与米粒中矿质元素Fe,Zn,Mn和P含量的遗传相关性,结果表明：4种粒形性状同时受制于种子直接遗传效应,母体效应和细胞质作用影响,其中种子直接遗传效应比母体效应和细胞质效应的作用更大,且种子直接遗传效应以加性效应占主导,粒重,粒宽和粒长／粒宽的种子直接遗传率较高,杂种早代单粒选择效果较好,粒长的种子直接遗传率和母体遗传率均属中等,较高世代的杂种进行单株选择和单粒选择均有一定效果,4种粒形性状与其米粒中矿质元素Fe,Zn,Mn和P含量表现较强的种子直接加性相关,直接显性相关,细胞质相关,母体加性相关和母体显性相关,在特种稻育种实践中,可以通过粒形性的间接选择,达到改良其矿质元素含量等营养品质性状的目标。     

Analysis of cytoplasmic and maternal effects. II. Genetic models for triploid endosperms

Genetic models for quantitative traits of triploid endosperms are proposed for the analysis of direct gene effects, cytoplasmic effects, and maternal gene effects. The maternal effect is partitioned into maternal additive and dominance components. In the full genetic model, the direct effect is partitioned into direct additive and dominance components and high-order dominance component, which are the cumulative effects of three-allele interactions. If the high-order dominance effects are of no importance, a reduced genetic model can be used. Monte Carlo simulations were conducted in this study for demonstrating unbiasedness of estimated variance and covariance components from the MINQUE (0/1) procedure, which is a minimum norm quadratic unbiased estimation (MINQUE) method setting 0 for all the prior covariances and 1 for all the prior variances. Robustness of estimating variance and covariance components for the genetic models was tested by simulations. Both full and reduced genetic models are shown to be robust for estimating variance and covariance components under several situations of no specific effects. Efficiency of predicting random genetic effects for the genetic models by the MINQUE (0/1) procedure was compared with the best linear unbiased prediction (BLUP). A worked example is given to illustrate the use of the reduced genetic model for kernel growth characteristics in corn (Zea mays L.).     

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.     

Breeding for Biomass Yield in Switchgrass Using Surrogate Measures of Yield

Development of switchgrass (Panicum virgatum L.) as a dedicated biomass crop for conversion to energy requires substantial increases in biomass yield. Most efforts to breed for increased biomass yield are based on some form of indirect selection. The objective of this paper is to evaluate and compare the expected efficiency of several indirect measures of breeding value for improving sward-plot biomass yield of switchgrass. Sward-plot biomass yield, row-plot biomass, and spaced-plant biomass were measured on 144 half-sib families or their maternal parents from the WS4U-C2 breeding population of upland switchgrass. Heading date was also scored on row plots and anthesis date was scored on spaced plants. Use of any of these indirect selection criteria was expected to be less efficient than direct selection for biomass yield measured on sward plots, when expressed as genetic gain per year. Combining any of these indirect selection criteria with half-sib family selection for biomass yield resulted in increases in efficiency of 14 to 36%, but this could only be achieved at a very large cost of measuring phenotype on literally thousands of plants that would eventually have no chance of being selected because they were derived from inferior families. Genomic prediction methods offered the best solution to increase breeding efficiency by reducing average cycle time, increasing selection intensity, and placing selection pressure on all additive genetic variance within the population. Use of genomic selection methods is expected to double or triple genetic gains over field-based half-sib family selection.     

Estimates of genetic variance in an F2 maize population

Maize (Zea mays L.) breeders have used several genetic-statistical models to study the inheritance of quantitative traits. These models provide information on the importance of additive, dominance, and epistatic genetic variance for a quantitative trait. Estimates of genetic variances are useful in understanding heterosis and determining the response to selection. The objectives of this study were to estimate additive and dominance genetic variances and the average level of dominance for an F2 population derived from the B73 x Mo17 hybrid and use weighted least squares to determine the importance of digenic epistatic variances relative to additive and dominance variances. Genetic variances were estimated using Design III and weighted least squares analyses. Both analyses determined that dominance variance was more important than additive variance for grain yield. For other traits, additive genetic variance was more important than dominance variance. The average level of dominance suggests either overdominant gene effects were present for grain yield or pseudo-overdominance because of linkage disequilibrium in the F2 population. Epistatic variances generally were not significantly different from zero and therefore were relatively less important than additive and dominance variances. For several traits estimates of additive by additive epistatic variance decreased estimates of additive genetic variance, but generally the decrease in additive genetic variance was not significant.     

Genetic variability of body weight in two goose strains under long-term selection

Body weight is one of the most important traits in any genetic improvement program in geese for at least 2 reasons. First, measurements of the trait are very easy. Second, body weight is correlated with a number of other meat performance traits. However, the genetic background of body weight shows considerable complexity. Three genetic models (with direct, maternal genetic and permanent maternal environmental effects) were employed in this study. Records of 3076 individuals of maternal strain W11 and 2656 individuals of paternal strain W33 over 6 consecutive generations, kept in the pedigree farm of Ko?uda Wielka, were analysed. Body weight (in kilograms) was measured in weeks 8 (BW8) and 11 (BW11). The inbreeding levels in both populations were relatively low (0.14% and 0.02% for W11 and W33, respectively), therefore these effects were not included in the linear models to estimate genetic parameters. Three fixed effects (hatch period, sex and year) were included in each linear model. Two criteria (AIC, BIC) were used to check the goodness of fit of the models. The computations were performed by WOMBAT software. In general, the genetic parameter estimates varied across the traits, models and strains studied. Direct additive heritability estimates ranged from 0.0001 (for BW11 of W33) to 0.55 (for BW11 of W33). Maternal and total heritabilities were also variable. Estimates of ratios of direct-maternal effect covariance in phenotypic variance were both positive and negative, but they were negligible, whereas ratios of the permanent environmental maternal variance to phenotypic variance were close to zero. Both of the applied criteria of model adequacy indicate that the model with maternal genetic and environmental effects should be considered as optimal. Genetic trends were close to zero. It seems that they were influenced by long-term selection. Similar tendencies have been observed for phenotypic trends, as well.     

Genetics of Mandible Form in the Mouse

The underlying determination of phenotypic variability and covariability is described for 14 traits that define the morphological size and shape of the mature mouse mandible. Variability is partitioned into components due to direct additive and dominance genetic effects, indirect maternal additive genetic effects, genetic covariance between direct additive and indirect maternal additive effects and common and residual environmental effects. Multivariate analyses of the dimensionality of genetic variability indicate several complex and independent genetic components underlie the morphological form of the mandible. The multidimensional nature of the genetic components suggests a complex picture with regard to the consequences of selection on mandibular form.     

Estimates of direct and indirect effects for early juvenile survival in captive populations maintained for conservation purposes: the case of Cuvier's gazelle

Together with the avoidance of any negative impact of inbreeding, preservation of genetic variability for life‐history traits that could undergo future selective pressure is a major issue in endangered species management programmes. However, most of these programmes ignore that, apart from the direct action of genes on such traits, parents, as contributors of offspring environment, can influence offspring performance through indirect parental effects (when parental genotype and phenotype exerts environmental influences on offspring phenotype independently of additive genetic effects). Using quantitative genetic models, we estimated the additive genetic variance for juvenile survival in a population of the endangered Cuvier's gazelle kept in captivity since 1975. The dataset analyzed included performance recording for 700 calves and a total pedigree of 740 individuals. Results indicated that in this population juvenile survival harbors significant additive genetic variance. The estimates of heritability obtained were in general moderate (0.115–0.457) and not affected by the inclusion of inbreeding in the models. Maternal genetic contribution to juvenile survival seems to be of major importance in this gazelle's population as well. Indirect genetic and indirect environmental effects assigned to mothers (i.e., maternal genetic and maternal permanent environmental effects) roughly explain a quarter of the total variance estimated for the trait analyzed. These findings have major evolutionary consequences for the species as show that offspring phenotypes can evolve strictly through changes in the environment provided by mothers. They are also relevant for the captive breeding programme of the species. To take into account, the contribution that mothers have on offspring phenotype through indirect genetic effects when designing pairing strategies might serve to identify those females with better ability to recruit, and, additionally, to predict reliable responses to selection in the captive population.     

Estimation of genetic parameters and variance components for growth traits in Romosinuano cattle in the Colombian humid tropics

(Co)variance components and genetic parameters were estimated for body weights of a Romosinuano herd located in Sinú Valley, Cordoba, Colombia. Restricted maximum likelihood methods were used with a univariate animal model for birth weight, weaning weight (270 days), 16-month weight (480 days), weaning daily gain, and post-weaning daily gain. Models included random animal direct and maternal genetic effects, maternal permanent environmental effect (c2), and sex-year-month of birth and age of dam, as fixed effects. Estimates of direct effect for birth weight, weaning weight, 480-day weight, weaning daily gain, and post-weaning daily gain were: 0.25 +/- 0.0001, 0.34 +/- 0.063, 0.33 +/- 0.066, 0.32 +/- 0.062, and 0.17 +/- 0.052, respectively. Estimates of direct maternal genetic effects were low and ranged from 0.06 +/- 0.003 for birth weight to 0.20 +/- 0.054 for weaning daily gain. The genetic correlations between direct and maternal genetic effects were negative and low for 480-day weight (-0.05 +/- 0.219) and showed values of -0.37 +/- 0.007, -0.34 +/- 0.133, -0.33 +/- 0.135, and -0.38 +/- 0.232 for birth, weaning weight, weaning, and post-weaning daily gain, respectively. Permanent environmental maternal effects were not significant; the highest values were found for weaning weight, and weaning daily gain (0.086 +/- 0.031 and 0.078 +/- 0.031, respectively). We conclude that direct and maternal effects should be included in a selection program for all of these traits, and also that selection of weaning weights would be the most productive way to improve performance in Romosinuano cattle.     

Long-Term Selection Response for 12-Day Litter Weight in Mice

Long-term selection for increased 12-day litter weight in two replicate lines (W₂, W₃) of mice resulted in an apparent selection limit at about 17 generations. Quadratic polynomial and exponential models were fitted to the data in order to estimate the plateaued response and half-life of the selection process. Using the polynomial results, the half-life estimates were 4.5 and 8.6 generations for W₂ and W₃, respectively. The plateaued responses were 5.1 and 5.8 g which, when expressed in phenotypic standard deviation units, became 1.1 and 1.3. The exponential model provides similar estimates. A negative association between 12-day litter weight and fitness was not considered to be an adequate explanation for the plateau since there was no decrease in fertility of the selected lines. Evidence that exhaustion of genetic variability was not the cause of the plateau came from the immediate response to reverse selection. It was proposed that the plateau may be due to a negative genetic correlation between direct and maternal genetic effects, which would be expected to occur after many generations of selection. There were positive correlated responses in both replicates for adult body weight, which was in agreement with the positive genetic correlation between preweaning and postweaning body weight. The expected positive correlated response for number born was realized in only one of the replicates.     

Quantitative Genetics of Transgenic Mice: Components of Phenotypic Variation in Body Weights and Weight Gains

Transgenic mice possessing an ovine growth hormone gene were used to study the effects of elevated growth hormone on quantitative genetic variation. Males hemizygous for the transgene were mated to wild-type females to produce half- and full-sib families in which approximately half the progeny were transgenic and half were wild type. Analyses of body weights at 3-10 weeks, and weight gains from 3 to 6, and 6 to 10 weeks produced estimates of the proportion of total variance due to additive genetic effects (h(2)) and common litter effects (c(2)), and the genetic correlation between transgenic and wild-type expression of each trait. At 10 weeks, body weight of transgenics exceeded that of wild types by 26 and 49% in males and females, respectively. Estimated genetic variances in the transgenic group were significantly greater than zero for body weights at most ages and for both measurements of gain. Common litter effects accounted for a similar proportion of variation in the wild-type and transgenic groups. Additive genetic correlations between wild-type and transgenic expression of body weights tended to decline with age, indicating that a partially different array of genes may have begun to affect body weight in the transgenic group.