Additive Genetic Values Research Articles

Analysis of Litter Size and Average Litter Weight in Pigs Using a Recursive Model

An analysis of litter size and average piglet weight at birth in Landrace and Yorkshire using a standard two-trait mixed model (SMM) and a recursive mixed model (RMM) is presented. The RMM establishes a one-way link from litter size to average piglet weight. It is shown that there is a one-to-one correspondence between the parameters of SMM and RMM and that they generate equivalent likelihoods. As parameterized in this work, the RMM tests for the presence of a recursive relationship between additive genetic values, permanent environmental effects, and specific environmental effects of litter size, on average piglet weight. The equivalent standard mixed model tests whether or not the covariance matrices of the random effects have a diagonal structure. In Landrace, posterior predictive model checking supports a model without any form of recursion or, alternatively, a SMM with diagonal covariance matrices of the three random effects. In Yorkshire, the same criterion favors a model with recursion at the level of specific environmental effects only, or, in terms of the SMM, the association between traits is shown to be exclusively due to an environmental (negative) correlation. It is argued that the choice between a SMM or a RMM should be guided by the availability of software, by ease of interpretation, or by the need to test a particular theory or hypothesis that may best be formulated under one parameterization and not the other.

Estimation of genetic parameters and prediction of breeding values for multivariate threshold and continuous data in a simulated horse population using Gibbs sampling and residual maximum likelihood

Simulated horse data were used to compare multivariate estimation of genetic parameters and prediction of breeding values (BV) for categorical, continuous and molecular genetic data using linear animal models via residual maximum likelihood (REML) and best linear unbiased prediction (BLUP) and mixed linear-threshold animal models via Gibbs sampling (GS). Simulation included additive genetic values, residuals and fixed effects for one continuous trait, liabilities of four binary traits, and quantitative trait locus (QTL) effects and genetic markers with different recombination rates and polymorphism information content for one of the liabilities. Analysed data sets differed in the number of animals with trait records and availability of genetic marker information. Consideration of genetic marker information in the model resulted in marked overestimation of the heritability of the QTL trait. If information on 10,000 or 5,000 animals was used, bias of heritabilities and additive genetic correlations was mostly smaller, correlation between true and predicted BV was always higher and identification of genetically superior and inferior animals was - with regard to the moderately heritable traits, in many cases - more reliable with GS than with REML/BLUP. If information on only 1,000 animals was used, neither GS nor REML/BLUP produced genetic parameter estimates with relative bias <or=25% and BV correlation >50% for all traits. Selection decisions for binary traits should rather be based on GS than on REML/BLUP breeding values.

Bayesian estimation of genetic parameters for multivariate threshold and continuous phenotypes and molecular genetic data in simulated horse populations using Gibbs sampling.

BackgroundRequirements for successful implementation of multivariate animal threshold models including phenotypic and genotypic information are not known yet. Here simulated horse data were used to investigate the properties of multivariate estimators of genetic parameters for categorical, continuous and molecular genetic data in the context of important radiological health traits using mixed linear-threshold animal models via Gibbs sampling. The simulated pedigree comprised 7 generations and 40000 animals per generation. Additive genetic values, residuals and fixed effects for one continuous trait and liabilities of four binary traits were simulated, resembling situations encountered in the Warmblood horse. Quantitative trait locus (QTL) effects and genetic marker information were simulated for one of the liabilities. Different scenarios with respect to recombination rate between genetic markers and QTL and polymorphism information content of genetic markers were studied. For each scenario ten replicates were sampled from the simulated population, and within each replicate six different datasets differing in number and distribution of animals with trait records and availability of genetic marker information were generated. (Co)Variance components were estimated using a Bayesian mixed linear-threshold animal model via Gibbs sampling. Residual variances were fixed to zero and a proper prior was used for the genetic covariance matrix.ResultsEffective sample sizes (ESS) and biases of genetic parameters differed significantly between datasets. Bias of heritability estimates was -6% to +6% for the continuous trait, -6% to +10% for the binary traits of moderate heritability, and -21% to +25% for the binary traits of low heritability. Additive genetic correlations were mostly underestimated between the continuous trait and binary traits of low heritability, under- or overestimated between the continuous trait and binary traits of moderate heritability, and overestimated between two binary traits. Use of trait information on two subsequent generations of animals increased ESS and reduced bias of parameter estimates more than mere increase of the number of informative animals from one generation. Consideration of genotype information as a fixed effect in the model resulted in overestimation of polygenic heritability of the QTL trait, but increased accuracy of estimated additive genetic correlations of the QTL trait.ConclusionCombined use of phenotype and genotype information on parents and offspring will help to identify agonistic and antagonistic genetic correlations between traits of interests, facilitating design of effective multiple trait selection schemes.

Avaliação genética de progênies de meio-irmãos de &lt;i&gt;Eucalyptus urophylla&lt;/i&gt; utilizando os procedimentos REML/BLUP e E(QM).

Realizou-se avaliação genética em cinco testes de progênies de meio-irmãos de Eucalyptus urophylla S. T. Blake procedentes da Indonésia, com o uso dos procedimentos REML/BLUP (máxima verossimilhaça restrita/melhor predição linear não-viesada) e pelo método dos quadrados mínimos E (QM). Os ensaios foram estabelecidos separadamente por procedência, sendo o delineamento experimental em blocos casualizados, com cinco repetições e parcelas lineares de seis plantas, no espaçamento 3,0 x 2,0 metros, em Guanhães, MG. Nos cinco testes avaliados aos 58 meses de idade, para a característica diâmetro à altura do peito (DAP), apresentaram valores dentro dos padrões da espécie, além de exibir variabilidade genética significativa, pelo teste F a 1% de probabilidade. Os coeficientes de variação genética aditiva apresentaram valores maiores no teste TP-71 originado de Wetar e no TP-68 originado de Alor, e nos outros testes apresentaram valores similares para a característica diâmetro à altura do peito (DAP). Os ganhos de seleção foram estimados na ordem de 12,8; 22,9; 9,5; 21,0 e 25,3% e tamanho efetivo populacional (Ne) na ordem de 60,2; 58,0; 131,8; 167,9 e 224,1 para ao testes TP-67, TP-68, TP-69, TP-70 e TP-71 respectivamente. O ganho de seleção no Pomar de Sementes Clonal (PSC) foi de 26,8 % com a seleção dos 21 indivíduos portadores dos maiores valores genéticos aditivos. Nos dois procedimentos, máxima verossimilhança restrita (REML) e esperança de quadrados mínimos E(QM), os valores dos parâmetros genéticos foram semelhantes, exceto entre familias, em que o procedimento REML proporcionou valores mais elevados com acurácia superior a 70% em todas as populações, mostrando-se como ferramenta apropriada para esse fim.

Multibreed analysis by splitting the breeding values

An equivalent model for multibreed variance covariance estimation is presented. It considers the additive case including or not the segregation variances. The model is based on splitting the additive genetic values in several independent parts depending on their genetic origin. For each part, it expresses the covariance between relatives as a partial numerator relationship matrix times the corresponding variance component. Estimation of fixed effects, random effects or variance components provided by the model are as simple as any model including several random factors. We present a small example describing the mixed model equations for genetic evaluations and two simulated examples to illustrate the Bayesian variance component estimation.

Random Regression Models for Male and Female Fertility Evaluation Using Longitudinal Binary Data

A longitudinal Bayesian threshold analysis of insemination outcomes was carried out using 2 random regression models with 3 (Model 1) and 5 (Model 2) parameters to model the additive genetic values at the liability scale. All insemination events of first-parity Holstein cows were used. The outcome of an insemination event was treated as a binary response of either a success (1) or a failure (0). Thus, all breeding information for a cow, including all service sires, was included, thereby allowing for a joint evaluation of male and female fertility. An edited data set of 369,353 insemination records from 210,373 first-lactation cows was used. On the liability scale, both models included the systematic effects of herd-year, month of insemination, technician, and regressions on age of service sire and milk yield during the first 100 d of lactation. The random effects in the model were the 3 or 5 random regression coefficients specific to each cow, the permanent effect of the cow, and the service sire effect. Using Model 1, the estimated heritability of an insemination outcome decreased from 0.035 at d 50 to 0.032 at d 140 and then increased continuously with DIM. The genetic correlations for insemination success at different time points ranged from 0.83 to 0.99, and their magnitude decreased with an increase in the interval between inseminations. A similar trend was observed for heritability and genetic correlations using Model 2. However, the average estimate of heritability was much higher (0.058) than those obtained using Model 1 or a repeatability model. In addition, the estimated genetic correlations followed the same trend as Model 1, but were lower and with a higher rate of decrease when the interval between inseminations increased. The posterior mean of service sire variance was 0.01 for both models, and permanent environmental variance was 0.05 and 0.02 for Models 1 and 2, respectively. Model comparison based on the Bayes factor indicated that Model 1 was more plausible, given the data.

Survival analysis in two lines of rabbits selected for reproductive traits1

The objective of the study was to analyze the reproductive longevity of 2 selected lines of rabbits. The first one was the Prat line, a line selected in Spain on litter size at weaning, and raised in overlapping generations. The second one was a French line, the A1077 line, selected on litter size at birth and individual weight at 63 d of age, managed in batches, and artificially inseminated with discrete generations. Reproductive longevity was measured beginning at the first successful mating, assessed by a pregnancy diagnosis in the Prat line, and at the first kindling in the A1077 line. In the A1077 line, culling for infertility occurred after 3 unsuccessful artificial inseminations. The trait analyzed, defined as the doe length of productive life (LPL), was the time in days between date of the first positive pregnancy diagnosis and date of culling or death in the Prat line. In the A1077 line, the trait was the number of AI after the first kindling. Effects included in the model were year-season, litter size at birth, reproductive cycle or physiological status x cycle interaction, age at first mating, batch (only for the A1077 line), and additive genetic value of the animal as a random effect. Survival analyses were carried out with a Cox model for the Prat line and a discrete model for the A1077 line. The estimated heritability values for LPL were around 0.16 in the Prat and A1077 lines with a model including physiological status x cycle interaction effect. Removing this effect from the model led to an increase in estimated genetic variance with h2 = 0.24 and 0.19 in the Prat and A1077 lines, respectively. Including the traits LPL and number of AI from first fertile mating or AI in selection programs could increase reproductive longevity and decrease the replacement rate.

Genetic variation of farrowing kinetics traits and their relationships with litter size and perinatal mortality in French Large White sows

Genetic parameters of litter traits and their relationships with farrowing kinetics traits were estimated in a Large White population to examine the impact of selection for litter size on perinatal mortality and one of its main determinants, farrowing kinetics. Data were collected on 2,947 farrowings from 1,267 sows between 1996 and 2004. Litter traits included the number born in total (NBT), number born alive (NBA), and the number (NSB) and proportion (PSB) of stillborn piglets. Four farrowing kinetics traits were considered: farrowing duration (FD), birth interval (BI = FD/NBT), heterogeneity of birth intervals (SDNB = SD of the number of piglets born each one-half hour), and birth assistance (BA) during the farrowing process. Genetic parameters were estimated using restricted maximum likelihood methodology. All traits were analyzed using a mixed linear animal model including year x month and parity as fixed effects; the additive genetic value of each animal and the sow permanent environment were treated as random effects. To normalize their distribution, kinetics traits were Box-Cox-transformed. Low heritability estimates were obtained for litter size and mortality traits, which was in agreement with literature results (i.e., 0.10 +/- 0.02, 0.08 +/- 0.02, 0.19 +/- 0.02, and 0.14 +/- 0.02 for NBT, NBA, NSB, and PSB, respectively). Heritability values were also low for kinetics traits: 0.10 +/- 0.02, 0.08 +/- 0.02, 0.01 +/- 0.01, and 0.05 +/- 0.03 for FD, BI, SDNB, and BA, respectively. The genetic correlation between NBT and NBA was strongly positive (ra = 0.90). On both phenotypic and genetic scales, NBT was positively associated with stillbirth (ra = 0.45 +/- 0.11, rp = 0.38 for NSB; ra = 0.46 +/- 0.13, rp = 0.17 for PSB). Conversely, NBA had low correlations with SB and PSB. Number born in total was moderately correlated to FD (ra = 0.34 +/- 0.15) and BI (ra = -0.37 +/- 0.15). A stronger relationship was found between NBA and BI (ra = -0.49 +/- 0.13), whereas the relationship with FD was lower (ra = 0.16 +/- 0.17). Moreover, FD was strongly correlated with stillbirth (ra = 0.42 +/- 0.12 with NSB), whereas BI was nearly independent of stillbirth. Contrary to selection on NBT, selection on NBA appears to be a good way to limit the negative side effects on stillbirth. Moreover, selection on NBA would lead to a small increase in FD and a faster and more regular birth process than would be obtained by selecting on NBT.

Effets génétiques et non génétiques sur le poids de toison des ovins des races Boujaâd et Sardi

L’analyse a porté sur 1 937 et 2 005 poids de toison des ovins, respectivement des races Boujaâd et Sardi. Les données ont été collectées durant huit ans, de 1994 à 2001, dans le domaine expérimental Déroua à l’Inra. L’âge à la tonte, l’année de tonte et le sexe de l’animal ont eu des effets significatifs sur le poids de toison des ovins des deux races. Les animaux âgés de moins de 18 mois et de sexe mâle ont montré les performances les plus élevées. La répétabilité et l’héritabilité du poids de toison ont été estimées par la méthode Reml appliquée à un modèle animal. Les répétabilités estimées du poids de la toison ont été de 0,46 et 0,57 respectivement pour les ovins des races Boujaâd et Sardi, et les héritabilités ont été respectivement de 0,27 et 0,40. La régression de la valeur génétique additive de chaque animal pour le poids de toison, estimée par la méthode Blup appliquée à un modèle animal en son année de naissance a montré un progrès génétique annuel de 32 g/an pour la race Boujaâd et de 68 g/an pour la race Sardi. Il a été conclu que la sélection serait très efficace pour l’amélioration du poids de toison des ovins des races Boujaâd et Sardi

Estimates of genetic parameters and prediction of additive genetic values in Pinus kesya progenies

The objeetive ofthis study was to seleet Pinus kesya prog enies by lhe estimation of g enetic p arameters using lhe method of restricted maximum likelihood (Remi) and prediction of additive genetic values by the best linear unbiased prediction (Blup ). The Pinus kesya progeny tesl was installed in randomized b/oeks. which consist ed of 30 progenies and three replications. Tlze twenty-year-old trees were evaluated for lhe traits diameter at breast heiglit (DBH), height (HT) and st em form (FOR). The DBH, HT and FOR means \Vere, respectively, 21.89 em, 21.89111 and 1.56 and their respective mean herit ability estimares of progenies were 0.58, 0.39 and 0.66. DBH presented the highest coefficient of additive genetic variation (17.89%). Tlze selection ofthe 80 best t rees whicli belon ged 1021 progenies provided a gain 0/,9.62%for FOR witli a mean of 3.81 trees selected per prog eny, an effective population si:e 0/,30.86 and g enetic diverg ence ofO.37.

Genetic relationship between milk score and litter weight for Targhee, Columbia, Rambouillet, and Polypay sheep1

This study was conducted to evaluate the relationship between milk score (MS) and litter weight at 70 d (LW) for four sheep breeds in the United States. Milk score is a subjective measure of milk production used to assess milk production of range ewes when milk yield cannot be quantitatively determined. Variance components for MS and LW were estimated for each of Targhee, Columbia, Rambouillet, and Polypay breeds. Data collected from 1990 through 2000 at the U.S. Sheep Exp. Stn. in Dubois, ID, were analyzed with an animal model using REML. There were 13,900 records of MS and LW for 5,807 ewes. Records were grouped according to parity as first, second, and greater (mature), and all records (lifetime). Estimates of heritability for MS were in the range of 0.05 to 0.18 for first, 0.01 to 0.27 for second, 0.05 to 0.10 for mature, and 0.08 to 0.13 for all lifetime parity groups. Estimates of genetic correlation between MS at first and second parities ranged from 0.74 to 1.00. Similarly, mature MS was highly correlated genetically with MS at first (0.83 to 1.00) and at second (0.60 to 1.00) parities, suggesting that additive genetic value for milking ability at maturity could be evaluated as early as at first parity. Heritability estimates for LW ranged from 0.00 to 0.18 over all breeds and parity groupings. The genetic correlation between LW at first and second parity groups ranged from 0.43 to 1.00. Estimates of genetic correlation between LW at first or second parity with mature LW were mostly high and positive, except for Targhee (-0.10) and Polypay (0.14) at first parity. Litter weight for mature ewes could be improved by selection at first or second parity. Estimates of genetic correlation at first parity between MS and LW were high (1.00) for Rambouillet and Polypay, and near zero for Columbia and Targhee. At second parity, estimates of genetic correlation between MS and LW were positive and moderate for Rambouillet and Polypay but more variable for Columbia and Targhee. Estimates of genetic correlation between MS and LW were mostly positive and may be favorable with smaller estimates of standard errors using all lifetime records rather than first or second parity records. Although estimates are variable, the average of the estimates of the genetic correlation suggests that LW can be improved by selecting ewes for favorable MS.

Genetic trends in the performance and reproductive traits of pigs

The selection and evaluation of breeds and purebred lines to be used as the parental stock is an important step for the success of any animal breeding program. In this study, the feed:gain ratio, backfat thickness corrected for 100 kg, age to 100 kg, average daily gain, and age of sow at first farrowing were used to evaluate the genetic trends for direct and maternal additive genetic values in Large White pigs. The total number of piglets born or born alive and the litter weight at birth were used as indicators of the genetic trends for the direct additive values. The genetic trends were calculated by regression of the average predicted genetic values per year for each trait versus the offspring's year of birth (for performance traits) or versus the dam year of birth (for reproduction traits). The genetic trend estimates for direct effects showed that selection decisions made during the breeding program effectively improved the performance traits. However, for reproductive traits, the regression estimates showed no definite trend. The genetic trends for the maternal effects were generally positive but of low magnitude.

Selection of Pinus caribaea var. bahamensis progenies based on the predicted genetic value

Pinus caribaea var. bahamensis progenies were selected by mixed models using the estimate of the genetic parameters by REML for the prediction of additive genetic values by BLUP. The experimental design was a 11 x 11 partially balanced square lattice containing 119 progenies and two commercial controls. After 13 years, the diameter at breast height (DBH), height and volume were evaluated. The progenies presented good mean performance (18.83 m, 20.80 cm and 0.462 m 3 tree -1 ), and heritability estimates of 0.12, 0.20 and 0.21 for height, DBH and volume, respectively. The trait with greatest variability was the volume w ith a genetic variation coefficient of 22.60% while the genetic variation for height was lower (3.73%). A genetic gain of 14.5% was obtained for DBH with a selection of 250 trees from 56 progenies, with a mean of 4.46 trees selected per progeny and an effecti ve population size of 72.

Evidence for Genetic Control of Adult Weight Plasticity in the Snail Helix aspersa

Phenotypic plasticity and canalization are important topics in quantitative genetics and evolution. Both concepts are related to environmental sensitivity. The latter can be modeled using a model with genetically structured environmental variance. This work reports the results of a genetic analysis of adult weight in the snail Helix aspersa. Several models of heterogeneous variance are fitted using a Bayesian, MCMC approach. Exploratory analyses using posterior predictive model checking and model comparisons based on the deviance information criterion favor a model postulating a genetically structured heterogeneous environmental variance. Our analysis provides a strong indication of a positive genetic correlation between additive genetic values affecting the mean and those affecting environmental variation of adult body weight. The possibility of manipulating environmental variance by selection is illustrated numerically using estimates of parameters derived from the snail data set.

A method of computing restricted best linear unbiased prediction of breeding values for some animals in a population.

Restricted BLUP (R-BLUP) is derived by imposing restrictions directly within a multiple-trait mixed model. As a result, the R-BLUP procedure requires the solution of high-order simultaneous equations. If restrictions are imposed on breeding values for only some animals in a population, calculations become more complex. A new procedure for computing the R-BLUP of breeding values was derived when constraints were imposed on the additive genetic values of only some animals in a population. Rules for including records when proportional constraints are imposed were developed based on the traits that are recorded for an animal. The technique was better than the previous method in both memory requirement and central processing unit time.

Partitioning variances of growth in ultrasound longissimus muscle area measures in Angus bulls and heifers.

The objective of the study was to estimate variance components, heritability, and repeatability of ultrasound longissimus muscle area (ULMA) measures. Data included 4,653 serial ULMA measures from 882 purebred Angus bulls and heifers. Animals were born over a 4-yr period from 1998 to 2001. Each year, bulls and heifers were ultrasonically scanned four to eight times, with a 4- to 6-wk interval between scans. Initially, data were subdivided by scan session across years and were analyzed in a multitrait model (MTM). Data pooled across years and scan session were then analyzed using random regression models (RRM) to estimate trends in genetic parameter estimates. Additive direct genetic variance increased with advancing scan session ranging from 8.67 cm4 at the first scan (mean age = 35 wk) to a maximum of 19.48 cm4 at the sixth scan (mean age = 56 wk). Heritability of ULMA increased from 0.35 at first scan to a maximum of 0.48 at the fourth scan (mean age = 50 wk). Additive direct genetic variance and heritability values at about 1 yr of age (fifth scan) were 18.24 cm4 and 0.45, respectively. Estimates from RRM also showed an increase in sigma(a)2 and h2 with age. Trends in sigma(pe)2 estimates, although tending to fluctuate, also increased with age. Additive direct genetic variance at 1 yr of age ranged from 15.8 cm4 to 17.0 cm4 for the different models. Heritability of yearling ULMA measures ranged from 0.40 to 0.42 and repeatabilities ranged from 0.80 to 0.84. For the range of ages used in the current study, both MTM and RRM showed close to maximum heritability values at around 1 yr of age. Therefore, phenotypic differences in yearling ULMA between Angus cattle are better indicators of genetic differences than earlier measurements. Angus breeders could, therefore, use ULMA measures made at around 1 yr of age to select next generation parents.

Normal linear models with genetically structured residual variance heterogeneity: a case study

Normal mixed models with different levels of heterogeneity in the residual variance are fitted to pig litter size data. Exploratory analysis and model assessment is based on examination of various posterior predictive distributions. Comparisons based on Bayes factors and related criteria favour models with a genetically structured residual variance heterogeneity. There is, moreover, strong evidence of a negative correlation between the additive genetic values affecting litter size and those affecting residual variance. The models are also compared according to the purposes for which they might be used, such as prediction of 'future' data, inference about response to selection and ranking candidates for selection. A brief discussion is given of some implications for selection of the genetically structured residual variance model.

Prediction error variance and expected response to selection, when selection is based on the best predictor - for Gaussian and threshold characters, traits following a Poisson mixed model and survival traits.

In this paper, we consider selection based on the best predictor of animal additive genetic values in Gaussian linear mixed models, threshold models, Poisson mixed models, and log normal frailty models for survival data (including models with time-dependent covariates with associated fixed or random effects). In the different models, expressions are given (when these can be found – otherwise unbiased estimates are given) for prediction error variance, accuracy of selection and expected response to selection on the additive genetic scale and on the observed scale. The expressions given for non Gaussian traits are generalisations of the well-known formulas for Gaussian traits – and reflect, for Poisson mixed models and frailty models for survival data, the hierarchal structure of the models. In general the ratio of the additive genetic variance to the total variance in the Gaussian part of the model (heritability on the normally distributed level of the model) or a generalised version of heritability plays a central role in these formulas.

Prediction error variance and expected response to selection, when selection is based on the best predictor - for Gaussian and threshold characters, traits following a Poisson mixed model and survival traits

In this paper, we consider selection based on the best predictor of animal additive genetic values in Gaussian linear mixed models, threshold models, Poisson mixed models, and log normal frailty models for survival data (including models with time-dependent covariates with associated fixed or random effects). In the different models, expressions are given (when these can be found – otherwise unbiased estimates are given) for prediction error variance, accuracy of selection and expected response to selection on the additive genetic scale and on the observed scale. The expressions given for non Gaussian traits are generalisations of the well-known formulas for Gaussian traits – and reflect, for Poisson mixed models and frailty models for survival data, the hierarchal structure of the models. In general the ratio of the additive genetic variance to the total variance in the Gaussian part of the model (heritability on the normally distributed level of the model) or a generalised version of heritability plays a central role in these formulas.

The genetic variance for multiple linked quantitative trait loci conditional on marker information in a crossed population

In the prediction of genetic values and quantitative trait loci (QTLs) mapping via the mixed model method incorporating marker information in animal populations, it is important to model the genetic variance for individuals with an arbitrary pedigree structure. In this study, for a crossed population originated from different genetic groups such as breeds or outbred strains, the variance of additive genetic values for multiple linked QTLs that are contained in a chromosome segment, especially the segregation variance, is investigated assuming the use of marker data. The variance for a finite number of QTLs in one chromosomal segment is first examined for the crossed population with the general pedigree. Then, applying the concept of the expectation of identity-by-descent proportion, an approximation to the mean of the conditional probabilities for the linked QTLs over all loci is obtained, and using it an expression for the variance in the case of an infinite number of linked QTLs marked by flanking markers is derived. It appears that the approach presented can be useful in the segment mapping using, and in the genetic evaluation of, crosses with general pedigrees in the population of concern. The calculation of the segregation variance through the current approach is illustrated numerically, using a small data-set.