Maximum Likelihood Analysis of Rare Binary Traits under Different Modes of Inheritance

Maximum likelihood methodology was applied to determine the mode of inheritance of rare binary traits with data structures typical for swine populations. The genetic models considered included a monogenic, a digenic, a polygenic, and three mixed polygenic and major gene models. The main emphasis was on the detection of major genes acting on a polygenic background. Deterministic algorithms were employed to integrate and maximize likelihoods. A simulation study was conducted to evaluate model selection and parameter estimation. Three designs were simulated that differed in the number of sires/number of dams within sires (10/10, 30/30, 100/30). Major gene effects of at least one SD of the liability were detected with satisfactory power under the mixed model of inheritance, except for the smallest design. Parameter estimates were empirically unbiased with acceptable standard errors, except for the smallest design, and allowed to distinguish clearly between the genetic models. Distributions of the likelihood ratio statistic were evaluated empirically, because asymptotic theory did not hold. For each simulation model, the Average Information Criterion was computed for all models of analysis. The model with the smallest value was chosen as the best model and was equal to the true model in almost every case studied.     

Mapping quantitative trait loci affecting fatness and breast muscle weight in meat-type chicken lines divergently selected on abdominal fatness

Quantitative trait loci (QTL) for abdominal fatness and breast muscle weight were investigated in a three-generation design performed by inter-crossing two experimental meat-type chicken lines that were divergently selected on abdominal fatness. A total of 585 F₂ male offspring from 5 F₁ sires and 38 F₁ dams were recorded at 8 weeks of age for live body, abdominal fat and breast muscle weights. One hundred-twenty nine microsatellite markers, evenly located throughout the genome and heterozygous for most of the F₁ sires, were used for genotyping the F₂ birds. In each sire family, those offspring exhibiting the most extreme values for each trait were genotyped. Multipoint QTL analyses using maximum likelihood methods were performed for abdominal fat and breast muscle weights, which were corrected for the effects of 8-week body weight, dam and hatching group. Isolated markers were assessed by analyses of variance. Two significant QTL were identified on chromosomes 1 and 5 with effects of about one within-family residual standard deviation. One breast muscle QTL was identified on GGA1 with an effect of 2.0 within-family residual standard deviation.     

An Approximate Model of Polygenic Inheritance

The finite polygenic model approximates polygenic inheritance by postulating that a quantitative trait is determined by n independent, additive loci. The 3(n) possible genotypes for each person in this model limit its applicability. CANNINGS, THOMPSON, and SKOLNICK suggested a simplified, nongenetic version of the model involving only 2n + 1 genotypes per person. This article shows that this hypergeometric polygenic model also approximates polygenic inheritance well. In particular, for noninbred pedigrees, trait means, variances, covariances, and marginal distributions match those of the ordinary finite polygenic model. Furthermore as n -> &, the trait values within a pedigree collectively tend toward multivariate normality. The implications of these results for likelihood evaluation under the polygenic threshold and mixed models of inheritance are discussed. Finally, a simple numerical example illustrates the application of the hypergeometric polygenic model to risk prediction under the polygenic threshold model.     

Estimating variance components and heritabilities in the wild: a case study using the ‘animal model’ approach

Using a genealogy containing over 1800 dams and nearly 400 sires (estimated by genetic paternity techniques), combined with maximum likelihood procedures and an ‘animal model’, we have estimated the heritabilities, genetic correlations and variance components of three morphometric traits in the Soay sheep (Ovis aries) on St Kilda, Scotland. This approach allows heritabilities to be estimated in natural populations that violate the assumptions of offspring–parent regression methods. Maternal (or paternal) effects can also be estimated under natural conditions. We demonstrate that all the traits, body weight, hind leg length and incisor arcade breadth, have low but significant heritabilities. Body weight, the trait that experiences the strongest selection, had the lowest heritability but the highest additive genetic coefficient of variation. An evolutionary response to selection is predicted. When maternal effects were not taken into consideration heritabilities were over‐estimated, although this effect was only significant in female offspring.     

A new obesity-prone,glucose-intolerant rat strain (F.DIO)

Previous breeding for the diet-induced obese (DIO) trait from outbred Sprague-Dawley rats produced a substrain with selection characteristics suggesting a polygenic mode of inheritance. To assess this issue further, selectively bred DIO male rats were crossed with obesity-resistant inbred Fischer F344 dams. Male offspring were crossed twice more against female F344 dams. The resultant N3 (F.DIO) rats were then inbred three more times. On low-fat chow, 10-wk-old male and female DIO rats weighed 86 and 59% more than respective F344 rats. By the N3 (F.DIO) generation, they were only 12 and 10% heavier, respectively. After three additional inbreeding cycles, chow-fed F.DIO males had an exaggerated insulin response to oral glucose compared with F344 rats. After 3 wk on a 31% fat (high-energy) diet, male N3 F.DIO rats gained 16-20% more carcass and adipose weight with 98% higher plasma leptin levels, whereas F.DIO females gained 36-54% more carcass and adipose weight with 130% higher leptin levels than comparable F344 rats. After three inbreeding cycles, F.DIO males still gained more weight on high-energy diet and developed a threefold greater insulin response to oral glucose than F344 males. Preservation of the DIO and glucose intolerance traits through successive backcrosses and inbreeding cycles to produce the F.DIO strain lends further support to the idea that they inherited in a polygenic fashion.     

SEXUAL SELECTION IN AMERICAN TOADS: A TEST OF A GOOD-GENES HYPOTHESIS

Adaptive mate choice in species lacking male resource control and/or paternal care might be maintained by selection because preferred males sire genetically superior offspring. For such a process to occur, some male phenotypic trait(s) must both reliably indicate male genetic quality and influence the pattern of mate choice by females. In American toads, Bufo americanus, male body length has been documented to influence female mating patterns: females usually mate with males that are larger than average. However, the relationship between male size and male genetic quality is unknown. We conducted a controlled breeding experiment using 48 sires and 19 dams to determine if larger males sire offspring with superior larval performance characteristics (greater survival to metamorphosis, larger mass at metamorphosis, and earlier metamorphosis). We also aged each sire to test the hypothesis that older males are, on average, genetically superior to younger males. We crossed each female with three sires representing three body size categories (mean and 1 SD ± mean snout-ischium length). Hatchlings (500 from each cross) were reared to metamorphosis in seminatural ponds in the field. Metamorph weight (log transformed) and age at metamorphosis showed significant heritability and were genetically correlated with each other. Hence, sires differed in genetic quality. However, none of the three measures of offspring performance was correlated with sire body size or age. Thus, we obtained no support for the prediction that sire body size or age is related to genetic quality.     

Linkage Analysis with an Alternative Formulation for the Mixed Model of Inheritance: The Finite Polygenic Mixed Model

This paper presents an extension of the finite polygenic mixed model of FERNANDO et al. (1994) to linkage analysis. The finite polygenic mixed model, extended for linkage analysis, leads to a likelihood that can be calculated using efficient algorithms developed for oligogenic models. For comparison, linkage analysis of 5 simulated 4021-member pedigrees was performed using the usual mixed model of inheritance, approximated by HASSTEDT (1982), and the finite polygenic mixed model extended for linkage analysis presented here. Maximum likelihood estimates of the finite polygenic mixed model could be inferred to be closer to the simulated values in these pedigrees.     

Shifting patterns in genetic control at the embryo-alevin boundary in brook charr

Maternal inputs to offspring early in development are initially high but the process of development suggests that ontogenetic shifts in the importance of maternal genetic variation relative to other sources should occur. We investigated additive genetic variance and covariance for direct (animal), sire, and maternal effects on embryonic length (EL), yolk sac volume (YSV), and alevin (after yolk sac resorption) length (AL) for 460 embryonic and 460 alevin brook charr (Salvelinus fontinalis) in 23 half-sib families (12 sires, 23 dams). There were no additive genetic effects of sires or individual animals on their own phenotype using sire-dam and maternal-animal models for YSV or EL (h(a)2 < 0.05). However, at the alevin stage we detected low but significant heritability for AL (h(a)2 = 0.14 +/- 0.11). Conversely, maternal genetic effects were high for both embryonic traits (h(EL)2 = 0.61 +/- 0.05; h(YSU)2 = 0.57 +/- 0.06) but faded rapidly for postresorption length (h(AL)2 = 0.18 +/- 0.04). Maternal effects in the sire-dam model corresponded highly with those in the animal-dam model. We did not detect significant genetic covariance between progeny and dams for preresorption traits or between sires and dams for any trait. However, following resorption of the yolk sac, the genetic value of dams for AL was negatively correlated with that of individual progeny (r(m,a) = -0.38 +/- 0.13), suggesting trade-offs and/or stabilizing selection between maternal and animal genetic trait value. This finding was supported by models of dam fecundity on offspring length and dam weight in phenotypic space. Heritability estimates using simple regression of embryo phenotype on adult parental phenotype produced upwardly biased estimates of genetic variance (h2 > 1.0). We propose that development through the embryo-alevin boundary may be a major point in salmonids for ontogenetic changes in the genetic architecture of embryo size from maternal genetic effects to those of the individual organism, and that maternal-offspring conflicts in resource allocation related to size may be partially indicated by negative genetic covariance.     

The finite polygenic mixed model: An alternative formulation for the mixed model of inheritance

This paper presents a mixed model of inheritance with a finite number of polygenic loci. This model leads to a likelihood that can be calculated using efficient algorithms developed for oligogenic models. For comparison, likelihood profiles were obtained for the finite polygenic mixed model, the usual mixed model, with exact and approximate calculations, and for a class D regressive model. The profiles for the finite polygenic mixed model were closest to the profiles for the usual mixed model with exact calculations.     

Evidence that an imprinted gene on the X chromosome increases ovulation rate in sheep

Ovulation rate records from 1311 female progeny of 50 Coopworth rams were used to study the inheritance of ovulation rate in a screened high prolificacy sheep flock. Breeding values (BV) for ovulation rate for 33 sires used within the screened flock and ovulation rate deviations for a further 17 sires progeny tested in commercial flocks suggest that a major gene (WOODLANDS: gene) for ovulation rate with a non-Mendelian inheritance pattern is segregating in a family line. Rams assigned as carriers of the putative gene did not produce carrier sons (zero of three), and this coupled with the observation that daughters of carrier rams had ovulation rates of 0. 39 (standard error of difference [SED] = 0.06) higher than contemporaries without a significant increase in the variance of log ovulation rate strongly suggests that the gene is on the X chromosome. The evidence suggests that the gene is also maternally imprinted because ovulation rate data indicate that it is expressed where females inherit a paternal allele but is silenced when inherited on a maternal allele. Maternal granddaughters of carrier rams had mean ovulation rates that were only 0.02 (SED = 0.06) higher than noncarrier ewes from the same flock. Furthermore, carrier dams expressing the gene (paternal allele) had 24 sons, none of which had female offspring that expressed the gene, whereas carrier dams not expressing the gene (maternal allele) had 7 out of 17 sons that had female progeny expressing the gene. There is no evidence of the infertility that occurs in homozygous ewes carrying the X-linked Inverdale gene. Collectively, these results suggest the existence of a novel gene for prolificacy located on the X chromosome that is maternally imprinted. The WOODLANDS: gene was only expressed upon paternal inheritance from carrier males that were the progeny of nonexpressing carrier dams. The gene was not expressed in ewes that received it from either carrier dams (expressing or nonexpressing) or from carrier males that were the progeny of expressing carrier dams.     

Behavioral syndromes influence mating systems: floater pairs of a lizard have heavier offspring

Variation in correlated behaviors or behavioral syndromes couldhave interesting effects on mating systems, especially if thevariation in syndrome exists in both sexes. Both males and femalesof the lizard Eulamprus heatwolei display two behavioral typesof a behavioral syndrome, defined by correlations between territorial,exploratory, and predator avoidance behaviors. We tested howthis variation in behavioral syndrome influences reproductivesuccess, pairing patterns, and offspring weight. We used spatialbehavior and residency in the field to identify territorialand floater individuals. Females were relocated to the laboratoryto give birth, and all offspring, dams, and potential sireswere genotyped to determine offspring paternity. During fieldsurveys, 164 lizards were caught of which 27.5% were territorialand the rest were floaters. Paternity was assigned to 66% ofthe 104 offspring produced by 33 dams. Territorial sires fathereda greater proportion of the offspring of territorial dams thanfloater sires. Larger territorial males were more likely tosire the entire clutch or share paternity with fewer additionalsires than smaller territorial males. Floater sire size, however,did not influence the number of fathers per litter. Floaterfemales produced heavier offspring than their territorial counterparts,and offspring fathered by floaters were heavier than maternalhalf-sibs fathered by territorial males. We speculate that differencesin offspring weight may be the result of differences in yolkprovisioning by females and parent genetic compatibility.     

The Use of Mixture Models to Detect Effects of Major Genes on Quantitative Characters in a Plant Breeding Experiment

An analysis based on Elston's model of mixed major locus and polygenic inheritance is extended to include populations of progeny testing such as F(3), B(1s) and B(2s) families derived from F(2) and backcrosses in a cross between two inbred lines. Genetic hypotheses that can be validly tested by the likelihood ratio method in the analysis of a breeding experiment include homogeneity of variances due to environment and/or polygenes with transformable scale effect by Box-Cox power function, random and independent segregation of major genes, invariance of the effects of major genes with population types and additive and dominant models for polygenes. Testing hypotheses in the order suggested here can lead to a gradual simplification of the models and increases the feasibility of the subsequent analysis, but caution must be paid to the possible bias in parameter estimation and hypotheses tests. The procedure is applied to a set of data on plant height of rice with the effects of dwarf genes in crosses among three varieties. Two recessive dwarf genes are shown to be nonallelic and unlinked. One dwarf gene is shown to reduce plant height about 36-56 cm, and another 52-61 cm. The effect of polygenes, estimated as the standard deviation among possible inbred lines derived from these crosses, is about 11.7 cm. Interactions between the dwarf genes and the polygenic background are found, especially for one of the two genes. Both the polygenic effects and the interactions are much smaller than the effects of the major dwarf genes.     

Genetic analysis of a red tilapia (<Emphasis Type="Italic">Oreochromis</Emphasis> spp.) population undergoing three generations of selection for increased body weight at harvest

Quantitative genetic analysis was performed on 10,919 data records collected over three generations from the selection programme for increased body weight at harvest in red tilapia (Oreochromis spp.). They were offspring of 224 sires and 226 dams (50 sires and 60 dams per generation, on average). Linear mixed models were used to analyse body traits (weight, length, width and depth), whereas threshold generalised models assuming probit distribution were employed to examine genetic inheritance of survival rate, sexual maturity and body colour. The estimates of heritability for traits studied (body weight, standard length, body width, body depth, body colour, early sexual maturation and survival) across statistical models were moderate to high (0.13–0.45). Genetic correlations among body traits and survival were high and positive (0.68–0.96). Body length and width exhibited negative genetic correlations with body colour (? 0.47 to ? 0.25). Sexual maturity was genetically correlated positively with measurements of body traits (weight and length). Direct and correlated genetic responses to selection were measured as estimated breeding values in each generation and expressed in genetic standard deviation units (σ_G). The cumulative improvement achieved for harvest body weight was 1.72 σ_G after three generations or 12.5% per generation when the gain was expressed as a percentage of the base population. Selection for improved body weight also resulted in correlated increase in other body traits (length, width and depth) and survival rate (ranging from 0.25 to 0.81 genetic standard deviation units). Avoidance of black spot parent matings also improved the overall red colour of the selected population. It is concluded that the selective breeding programme for red tilapia has succeeded in achieving significant genetic improvement for a range of commercially important traits in this species, and the large genetic variation in body colour and survival also shows that there are prospects for future improvement of these traits in this population of red tilapia.     

A comprehensive analysis of QTL for abdominal fat and breast muscle weights on chicken chromosome 5 using a multivariate approach

Quantitative trait loci (QTL) influencing the weight of abdominal fat (AF) and of breast muscle (BM) were detected on chicken chromosome 5 (GGA5) using two successive F₂ crosses between two divergently selected 'Fat' and 'Lean' INRA broiler lines. Based on these results, the aim of the present study was to identify the number, location and effects of these putative QTL by performing multitrait and multi-QTL analyses of the whole available data set. Data concerned 1186 F₂ offspring produced by 10 F₁ sires and 85 F₁ dams. AF and BM traits were measured on F₂ animals at slaughter, at 8 (first cross) or 9 (second cross) weeks of age. The F₀, F₁ and F₂ birds were genotyped for 11 microsatellite markers evenly spaced along GGA5. Before QTL detection, phenotypes were adjusted for the fixed effects of sex, F₂ design, hatching group within the design, and for body weight as a covariable. Univariate analyses confirmed the QTL segregation for AF and BM on GGA5 in male offspring, but not in female offspring. Analyses of male offspring data using multitrait and linked-QTL models led us to conclude the presence of two QTL on the distal part of GGA5, each controlling one trait. Linked QTL models were applied after correction of phenotypic values for the effects of these distal QTL. Several QTL for AF and BM were then discovered in the central region of GGA5, splitting one large QTL region for AF into several distinct QTL. Neither the 'Fat' nor the 'Lean' line appeared to be fixed for any QTL genotype. These results have important implications for prospective fine mapping studies and for the identification of underlying genes and causal mutations.     

Power analysis of QTL detection in half-sib families using selective DNA pooling

Individual loci of economic importance (QTL) can be detected by comparing the inheritance of a trait and the inheritance of loci with alleles readily identifiable by laboratory methods (genetic markers). Data on allele segregation at the individual level are costly and alternatives have been proposed that make use of allele frequencies among progeny, rather than individual genotypes. Among the factors that may affect the power of the set up, the most important are those intrinsic to the QTL: the additive effect of the QTL, and its dominance, and distance between markers and QTL. Other factors are relative to the choice of animals and markers, such as the frequency of the QTL and marker alleles among dams and sires. Data collection may affect the detection power through the size of half-sib families, selection rate within families, and the technical error incurred when estimating genetic frequencies. We present results for a sensitivity analysis for QTL detection using pools of DNA from selected half-sibs. Simulations showed that conclusive detection may be achieved with families of at least 500 half-sibs if sires are chosen on the criteria that most of their marker alleles are either both missing, or one is fixed, among dams.     

Determining the mode of inheritance of pesticide resistance with backcross experiments

The most widely used method for evaluating the mode of inheritance of pesticide resistance is based on bioassays of individuals from a backcross between F1 (hybrid of resistant and susceptible strains) and parental resistant or susceptible strains. Monte Carlo simulations of the standard backcross method showed that the probability of incorrectly rejecting the null hypothesis of monogenic inheritance (Type I error) was generally more than double the conventional value of P = 0.05. Conversely, the null hypothesis of monogenic inheritance was likely to be accepted in a relatively large proportion of cases in which resistance is controlled by two or more loci. Expected differences in mortality of backcross offspring between monogenic and additive polygenic models approached zero as dose approached extremely low values, extremely high values, and the LD50 of the backcross generation. Thus, the effectiveness of the backcross method depended strongly on dose. The power of the standard backcross method to correctly reject the null hypothesis of monogenic inheritance increased as number of loci, slope of parental dose-mortality lines, magnitude of resistance, and sample size increased. Guidelines for improving the design and interpretation of backcross experiments are presented.     

Influence of the dam and sire on size at birth and subsequent growth, milk production and fertility in dairy heifers

Genetic selection has resulted in larger cows with high milk production potential but a tendency for poor fertility. In multiparous cows fetal development competes for nutrients with concurrent milk production. This study tested the hypotheses that (a) maternal age and milk yield during pregnancy alter calf birth size and (b) birth weight influences subsequent productivity and fertility. Concurrently born Holstein-Friesian heifers (n=65) with multiparous dams and three sires were monitored from birth to the end of their first lactation to assess effects of birth weight on growth, milk production and fertility. Calves were analyzed as three subgroups: low (L), average (A) and high (H) birth weight (BW) calves (n=21-22 per group). LBW calves were born 10 kg lighter than HBW calves and remained significantly lighter throughout the study. They were generally smaller in other measured indices (length, height, girth, ponderal index) between birth and 9 months and were more likely to have older dams (lactations 3-6) with higher peak yields (>42 kg/day). Milk production parameters were indistinguishable between the 3 birthweight groups and metabolic parameters (IGF-I, insulin, glucose) measured around first calving were unaffected. HBW offspring were more likely to have persistent corpora lutea following their first calving and other fertility parameters also tended to be worse. Sire influenced gestation length but not birth size. Sire heritability estimates showed that weight, IGF-I and insulin concentrations after first calving and fertility in the first lactation were all heritable. The results support the hypothesis that high milk production in the dam may predispose to birth of a smaller calf. Smaller birth size did not, however, have any subsequent adverse effects on productivity or fertility in the first lactation and sire was more influential at this stage.     

Bayesian segregation analysis of milk flow in Swiss dairy cattle using Gibbs sampling

Segregation analyses with Gibbs sampling were applied to investigate the mode of inheritance and to estimate the genetic parameters of milk flow of Swiss dairy cattle. The data consisted of 204 397, 655 989 and 40 242 lactation records of milk flow in Brown Swiss, Simmental and Holstein cattle, respectively (4 to 22 years). Separate genetic analyses of first and multiple lactations were carried out for each breed. The results show that genetic parameters especially polygenic variance and heritability of milk flow in the first lactation were very similar under both mixed inheritance (polygenes + major gene) and polygenic models. Segregation analyses yielded very low major gene variances which favour the polygenic determinism of milk flow. Heritabilities and repeatabilities of milk flow in both Brown Swiss and Simmental were high (0.44 to 0.48 and 0.54 to 0.59, respectively). The heritability of milk flow based on scores of milking ability in Holstein was intermediate (0.25). Variance components and heritabilities in the first lactation were slightly larger than those estimates for multiple lactations. The results suggest that milk flow (the quantity of milk per minute of milking) is a relevant measurement to characterise the cows milking ability which is a good candidate trait to be evaluated for a possible inclusion in the selection objectives in dairy cattle.     

Male sand crickets trade-off flight capability for reproductive potential

In this paper, we test the hypothesis that male sand crickets, Gryllus firmus, experience a trade-off between flight capability and reproductive potential expressed as reduced testis weight in flight-capable morphs. We used a half-sib design with 130 sires, three dams per sire and an average of 5.66 males per dam family, for a total of 2206 F1 offspring. Traits measured were head width, somatic dry weight, testis weight, wing morph (micropterous/macropterous), weight of the dorso-longitudinal flight muscles (DLM) and the functional status of these muscles. Heritabilities of all traits were significant and ranged from 0.14 to 0.43. All traits were positively correlated with body size, but removal of this covariance revealed a highly significant trade-off, both phenotypically and genetically, between testes size and flight capability as measured by wing morph, DLM size or DLM status. The possible implications of this for morph-specific reproductive tactics are discussed.     

Genetic variability in milking speed of dairy goats

The present investigation deals with the genetic variability of milking speed, measured as the volume of milk collected during the first minute of milking (MD1), and its association with dairy traits. Data originated from 2589 lactations of 1421 Alpine goats, sired by 93 bucks, measured between 1985 and 1997 at the Moissac Goat Experimental Station (Lozère, France). Two genetic analyses were carried out. Firstly, a polygenic model was used to estimate genetic and phenotypic parameters among milking speed and dairy traits using a multiple-trait animal model. Secondly, segregation analysis was used to test the hypothesis of mixed model inheritance (polygenes + major gene) for MF1. Heritability and repeatability of MF1 under the polygenic model were high (0.65 and 0.82, respectively). Estimated genetic and phenotypic correlations between milking speed and dairy traits were low, positive for yields and negative for contents. Segregation analysis yielded a highly significant likelihood ratio, confirming the segregation of a major gene with two alleles with partial dominance. The difference between the mean values of the two homozygotes was around 2.3 phenotypic standard deviation units of the trait. The major gene explained more than 60% of the estimated total genetic variance. The estimate of the 'residual' heritability, after taking into account the effect of the major locus, was 0.30.