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Individuals of a specified pedigree relationship vary in the proportion of the genome they share identical by descent, i.e. in their realised or actual relationship. Predictions of the variance in realised relationship have previously been based solely on the proportion of the map length shared, which requires the implicit assumption that both recombination rate and genetic information are uniformly distributed along the genome. This ignores the possible existence of recombination hotspots, and fails to distinguish between coding and non-coding sequences. In this paper, we therefore quantify the effects of heterogeneity in recombination rate at broad and fine-scale levels on the variation in realised relationship. Variance is usually greater on a chromosome with a non-uniform recombination rate than on a chromosome with the same map length and uniform recombination rate, especially if recombination rates are higher towards chromosome ends. Reductions in variance can also be obtained, however, and the overall pattern of change is quite complex. In general, local (fine-scale) variation in recombination rate, e.g. hotspots, has a small influence on the variance in realised relationship. Differences in rates across longer regions and between chromosome ends can increase or decrease the variance in a realised relationship, depending on the genomic architecture.

Determination of degree of relationship traditionally has been undertaken using genotypic data on individual loci, typically assumed to be independent. With dense marker data as now available, it is possible to identify the regions of the genome shared identical by descent (ibd). This information can be used to determine pedigree relationship (R), e.g., cousins vs. second cousins, and also to distinguish pedigrees that have the same Wright’s relationship (R) such as half-sibs and uncle–nephew. We use simulation to investigate the accuracy with which pedigree relationship can be inferred from genome sharing for uniparental relatives (a common ancestor on only one side of their pedigree), specifically the number, position (whether at chromosome ends), and length of shared regions ibd on each chromosome. Moments of the distribution of the likelihood ratio (including its expectation, the Kullback-Leibler distance) for alternative relationships are estimated for model human genomes, with the ratio of the mean to the SD of the likelihood ratio providing a useful reference point. Two relationships differing in R can be readily distinguished provided at least one has high R, e.g., approximately 98.5% correct assignment of cousins and half-cousins, but only approximately 75% for second cousins once removed and third cousins. Two relationships with the same R can be distinguished only if R is high, e.g., half-sibs and uncle–nephew, with probability of correct assignment being approximately 5/6.

Anecdotal evidence points to genetic variation in resistance of cattle to infection with Mycobacterium bovis, the causative agent of bovine tuberculosis (BTB), and published experimental evidence in deer and cattle suggests significant genetic variation in resistance and reactivity to diagnostic tests. However, such genetic variation has not been properly quantified in the United Kingdom dairy cattle population; it is possible that it exists and may be a factor influencing the occurrence of BTB. Using models based on the outcome of the process of diagnosis (ultimate fate models) and on the outcome of a single stage of diagnosis (continuation ratio models, herd test-date models), this study shows that there is heritable variation in individual cow susceptibility to BTB, and that selection for milk yield is unlikely to have contributed to the current epidemic. Results demonstrate that genetics could play an important role in controlling BTB by reducing both the incidence and the severity of herd breakdowns.

We evaluate the extent to which changes in phenotypic variation among generations of populations kept in the same environment are due to changes in genetic (V(A)) or in environmental (V(E)) variance. Data were available on body weight of adult poultry on a total of 89186 birds (mainly females) from six generations of each of seven lines of layers. There was substantial heterogeneity of variation between generations, shown to be in both V(A) and V(E) components. Based on the Akaike information criterion (AIC), the best fit was with both components changing, and a better fit was obtained if V(A)/V(E) (i.e. heritability) or V(E), rather than V(A), was assumed constant. In analyses of quantitative genetic data spanning environmental groups, attention should be paid to whether and how the variance components change among groups before undertaking detailed variance partition that may be sensitive to such changes.

SummarySusceptibility to scrapie is known to be associated with polymorphisms at the prion protein (PrP) gene, and this association is the basis of current selective programmes implemented to control scrapie in many countries. However, these programmes might have unintended consequences for other traits that might be associated withPrPgenotype. The objective of this study was to investigate the relationship betweenPrPgenotype and coat colour characteristics in two UK native sheep breeds valued for their distinctive coat colour patterns. Coat colour pattern, darkness and spotting andPrPgenotype records were available for 11 674 Badgerfaced Welsh Mountain and 2338 Shetland sheep. The data were analysed with a log–linear model using maximum likelihood. Results showed a strong significant association ofPrPgenotype with coat colour pattern in Badgerfaced Welsh Mountain and Shetland sheep and with the presence of white spotting in Shetland sheep. Animals with the ARR/ARR genotype (the most scrapie resistant) had higher odds of having a light dorsum and a dark abdomen than the reverse pattern. The implication of these associations is that selection to increase resistance to scrapie based only onPrPgenotype could result in change in morphological diversity and affect other associated traits such as fitness.

Phenotypic and genetic parameters of biometrical and carcass traits from two pedigreed populations of an Atlantic salmon breeding program were estimated using restricted maximum likelihood. Each of the populations (broodstock and commercial sib test) comprised of the same 200 full-sib families. Heritability estimates for biometrical traits (sw1wt, sw2wt, harvwt, filletwt, harvlen, guttedwt, deheadwt, guts, head, and carcass) were low to high (0.12–0.53); estimates for fillet fat % and colour traits (hue, saturation, and intensity) were low to moderate (0.16–0.33). The heritabilities for yield traits (guttedwt%, deheadwt%, filletdeheadwt%, and fillet%) measured as a ratio of weights, were low (0.009–0.037), due to the two traits being a fixed proportion of each other. In the broodstock population significant sex (P Estimated genetic correlations (rG) between biometrical traits and fillet fat percentage were all positive and ranged from 0.34 to 0.82. Selection for increased harvest weight is expected to produce favourable changes in fillet weight (rG = 0.99) but unfavourable changes in fillet fat percentage (rG = 0.80). Favourable estimates of the genetic correlation between saturation (colour score) and biometrical traits were all positive (rG = 0.23–0.61).

Dairy farms vary a great deal in the feeding and management systems that are used. These differences affect the performance of the cows, and some genotypes may be affected more than others. If effects of such genotype-by-environment interactions (GxE) are large, then farmers must be made aware of them to make informed breeding decisions. To investigate GxE, a classification system for farm environments was developed based on national- and fine-level data from dairy herds across the United Kingdom. The national data included herd and yield characteristics and local weather information. The fine-level data included information on feeding and management systems on farms, and was obtained from survey results from 778 farms. A principal components analysis of the surveys identified 2 major dimensions characterizing the data. The first dimension explained 14.6% of the variation and was related to the level of production intensity. The second dimension explained 11.5% of the variation and was related to climate. Information on milk yield, herd characteristics, and climate was then extracted from national databases for the survey farms. A canonical correlation analysis was used to relate the survey data to the variables extracted from the national data set to determine the most relevant variables. The canonical correlation between the chosen sets of national data and survey variables was 0.62. This environmental classification was then used to determine how the farm environment affects the life span of dairy cows. The life span of the daughters of 1,000 sires was related to the type of farm environment. The daughters of a majority of sires showed a "plastic" response, with increased life span in less intensive farms. The daughters of a smaller number of sires showed a more generalized response, with life span being less affected by the environment. This GxE suggested that sires vary in the sensitivity of their daughters to different farm environments. This variation in response could allow breeding companies and farmers to match sires to particular farm environments.

SUMMARYThe development of the genetic control of nematode resistance in growing lambs is of biological interest, as well as being important in terms of designing practical strategies to breed for increased nematode resistance. The current paper demonstrates the use of random regression techniques for quantifying the development of the heritability of faecal egg count (Fec), the indicator of nematode resistance, in growing lambs and predicted inter-age genetic and phenotypic correlations for Fec. Fec data from 732 lambs, collected at 4-week intervals fromc. 8–24 weeks of age, were analysed using random regression techniques. Random effects fitted in the model included genetic, individual animal environmental, litter and residual random effects. Output (co)variance components were interpolated to weekly time points. Individual variance components showed complex patterns of change over time; however, the estimated heritability increased smoothly with age, from 0·10 to 0·38, and showed more stable time trends than were obtained from univariate analyses of Fec at individual time points. Inter-age correlations decreased as the time interval between measurements increased. Genetic correlations were always positive, with 0·6 of all possible inter-age correlations being greater than 0·80. Phenotypic correlations were lower, and decreased more quickly as the time interval between measurements increased. The results presented confirm biological understanding of the development of immunity to nematode infections in growing lambs. Additionally, they provide a tool to determine optimal sampling ages when assessing lambs' relative resistance to nematode infections.

Aims were to estimate the extent of genetic heterogeneity in environmental variance. Data comprised 99 535 records of 35-day body weights from broiler chickens reared in a controlled environment. Residual variance within dam families was estimated using ASREML, after fitting fixed effects such as genetic groups and hatches, for each of 377 genetically contemporary sires with a large number of progeny (> 100 males or females each). Residual variance was computed separately for male and female offspring, and after correction for sampling, strong evidence for heterogeneity was found, the standard deviation between sires in within variance amounting to 15–18% of its mean. Reanalysis using log-transformed data gave similar results, and elimination of 2–3% of outlier data reduced the heterogeneity but it was still over 10%. The correlation between estimates for males and females was low, however. The correlation between sire effects on progeny mean and residual variance for body weight was small and negative (-0.1). Using a data set bigger than any yet presented and on a trait measurable in both sexes, this study has shown evidence for heterogeneity in the residual variance, which could not be explained by segregation of major genes unless very few determined the trait.

Farrowing survival is usually analysed as a trait of the sow, but this precludes estimation of any direct genetic effects associated with individual piglets. In order to estimate these effects, which are particularly important for sire lines, it is necessary to fit an animal model. However this can be computationally very demanding. We show how direct and maternal genetic effects can be estimated with a simpler analysis based on the reduced animal model and we illustrate the method using farrowing survival information on 118 193 piglets in 10 314 litters. We achieve a 30% reduction in computing time and a 70% reduction in memory use, with no important loss of accuracy. This use of the reduced animal model is not only of interest for pig breeding but also for poultry and fish breeding where large full-sib families are performance tested.

Some dairy cattle breeders believe that dairy cows with high pin bones will have poorer fertility. The aim of this study was to examine this claim by investigating the relationships, both genetic and phenotypic, between fertility, rump angle, and other selected type traits in first-lactation Holstein-Friesians. Results showed an unfavorable genetic correlation (-0.16) between calving interval and rump angle, suggesting that animals with high pin bones would have a longer calving interval. However, no significant genetic or phenotypic correlation between days to first service and nonreturn rate and rump angle was observed. No evidence of a relationship, linear or quadratic, between any fertility trait and rump angle was found. Udder support and mammary system were unfavorably correlated to calving interval (0.25 and 0.14, respectively), suggesting that cows with more functional udders would have a longer calving interval. Legs and feet score was favorably correlated to nonreturn rate, suggesting that animals with good legs and feet would be less likely to return to service.

It is shown that maximum likelihood estimation of variance components from twin data can be parameterized in the framework of linear mixed models. Standard statistical packages can be used to analyze univariate or multivariate data for simple models such as the ACE and CE models. Furthermore, specialized variance component estimation software that can handle pedigree data and user-defined covariance structures can be used to analyze multivariate data for simple and complex models, including those where dominance and/or QTL effects are fitted. The linear mixed model framework is particularly useful for analyzing multiple traits in extended (twin) families with a large number of random effects.

International audience; Model selection is an essential issue in longitudinal data analysis since many different models have been proposed to fit the covariance structure. The likelihood criterion is commonly used and allows to compare the fit of alternative models. Its value does not reflect, however, the potential improvement that can still be reached in fitting the data unless a reference model with the actual covariance structure is available. The score test approach does not require the knowledge of a reference model, and the score statistic has a meaningful interpretation in itself as a goodness-of-fit measure. The aim of this paper was to show how the score statistic may be separated into the genetic and environmental parts, which is difficult with the likelihood criterion, and how it can be used to check parametric assumptions made on variance and correlation parameters. Selection of models for genetic analysis was applied to a dairy cattle example for milk production.

Random regression models have been advocated for the analysis of test day records in dairy cattle. The effectiveness of a random regression analysis depends on the function used to model the data. To investigate functions suitable for the analysis of daily milk yield, test day milk yields of 7860 first lactation Holstein Friesian cows were analysed using random regression models involving three types of curves. Each analysis fitted the same curve to model overall trends through a fixed regression and random deviations due to animals. Curves included orthogonal polynomials, fitted to order 3 (quadratic), 4 (cubic) and 5 (quartic), respectively, a three-parameter parametric curve and a five-parameter parametric curve. Sets of random regression coefficients were fitted to model both animals’ genetic effects and permanent environmental effects. Temporary measurement errors were assumed independently but heterogeneously distributed, and assigned to one of 12 classes. Results showed that the measurement error variances were generally lowest around peak lactation, and higher at the beginning and end of lactation. Parametric curves yielded the highest likelihoods, but produced negative genetic associations between yield in early lactation and later lactation yields, while positive genetic correlations across the entire lactation were estimated with all models involving orthogonal polynomials. The fit of models using orthogonal polynomials to model test day yield was improved by including higher order fixed regressions.

In dairy cattle type classification schemes, heifers are condition scored (CS) only once during their first lactation. Although genetic analysis of condition-score changes is not possible using an animal model, the data can be analysed as repeated observations on the sire.CS records for 100 078 Holstein Friesian heifers, the progeny of 797 sires, were available. Sires differed in the shape of the regression of mean daughter CS on stage of lactation at both the phenotypic and genetic level. Genetic analysis was carried out using a random regression model (RRM) which can account for differences between sires in the shape of the CS curves. CS curves for individual sires were modelled using a cubic polynomial.Heritability estimates for CS at each stage of lactation generally increased through the lactation from 0·20 in stage 2 (days in milk 31 to 60) to 0·28 in later lactation stages. Genetic correlations between CS at different stages were generally high (0·80), with the exception of correlations with stage 1 (days in milk 1 to 30) which decreased to 0·63 with stages 6 and 7, suggesting that CS at stage 1 is under different biological control from CS at other stages of the lactation. Using RRM, sire estimated breeding values (EBVs) for CS at each stage of the lactation were estimated. Sire rankings on EBV at each stage were seen to change through early, mid and later lactation stages.

Summary Topex, an index of topographic exposure, has been an important component of regression models that predict site windiness. However, field-based topex can overestimate the shelter of distant hills and does not discriminate between hilltop and plateau sites. By using digital terrain models, it has become possible to calculate alternative formulations of topex with limits to the distance within which the skyline is sought, and with declinations (negative values) permitted. These alternatives have been tested using a dataset of tatter flags in upland Britain. A series of multiple regressions was performed with explanatory variables grid, elevation and modified topex, expressed as total topex and as sinusoidal terms to represent aspect and valley shape and direction. A distance limit of 0.5 km proved superior to thresholds of 0.25, 0.75, 1.0, 2.0, 3.0 and 10.0 km, and to field topex. Each term except aspect showed a peak in variance ratio at the 0.5 km distance. Although the coefficients varied little between regressions, the topex component of estimated exposure for hilltop sites can vary substantially with the choice of threshold. The use of a distance threshold can lead to improved estimates for these sites. There was no overall improvement in prediction of site windiness when compared with a previous regression and recalculation of the windiness index of upland Britain currently used in prediction of windthrow and in ecological site classification is not obviously required. However, the use of a distance limit would be worth while in future studies using topographic indices because of the apparent improvement in site discrimination and because distance-limited topex may be more easily calculated.

The mating system among 45 maternal clones in a Sitka spruce seed orchard was studied by isozyme electrophoresis of 6 polymorphic loci (GOT2, PGI1, PGI2, PGM1, PGM2 and GDH2) in embryos and endosperms of germinating seeds. Single locus estimates of outcrossing rate ranged from 0.973 to 1.000. The multilocus estimate of outcrossing rate was 0.981.

Eventing competitions in Great Britain (GB) comprise three disciplines, each split into four grades, yielding 12 discipline-grade traits. As there is a demand for tools to estimate (co)variance matrices with a large number of traits, the aim of this work was to investigate different methods to produce large (co)variance matrices using GB eventing data. Data from 1999 to 2008 were used and penalty points were converted to normal scores. A sire model was utilised to estimate fixed effects of gender, age and class, and random effects of sire, horse and rider. Three methods were used to estimate (co)variance matrices. Method 1 used a method based on Gibbs sampling and data augmentation and imputation. Methods 2a and 2b combined sub-matrices from bivariate analyses; one took samples from a multivariate Normal distribution defined by the covariance matrix from each bivariate analysis, then analysed these data in a 12-trait multivariate analysis; the other replaced negative eigenvalues in the matrix with positive values to obtain a positive definite (co)variance matrix. A formal comparison of models could not be conducted; however, estimates from all methods, particularly Methods 2a/2b, were in reasonable agreement. The computational requirements of Method 1 were much less compared with Methods 2a or 2b. Method 2a heritability estimates were as follows: for dressage 7.2% to 9.0%, for show jumping 8.9% to 16.2% and for cross-country 1.3% to 1.4%. Method 1 heritability estimates were higher for the advanced grades, particularly for dressage (17.1%) and show jumping (22.6%). Irrespective of the model, genetic correlations between grades, for dressage and show jumping, were positive, high and significant, ranging from 0.59 to 0.99 for Method 2a and 0.78 to 0.95 for Method 1. For cross-country, using Method 2a, genetic correlations were only significant between novice and pre-novice (0.75); however, using Method 1 estimates were all significant and low to moderate (0.36 to 0.70). Between-discipline correlations were all low and of mixed sign. All methods produced positive definite 12 × 12 (co)variance matrices, suitable for the prediction of breeding values. Method 1 benefits from much reduced computational requirements, and by performing a true multivariate analysis.

Genetic parameters for mean and for environmental variation in egg weight, body weight, age at first egg, and egg production were estimated in eight layer lines. The data were recorded from years 1999-2007, with on average of 6500 birds per line. An iterative mean-variance REML method was applied with a sire-plus-dam model for mean, a sire model for variance, and a fixed effect of hatch within generation for both mean and variance. The estimated heritability of environmental variation averaged about 5% for body weight, 3% for egg weight, and 11% for age at first egg, but was inconsistent among the lines for egg production (0-15%). Correlations between means and variances were slightly positive for body weight, egg weight, and age at first egg; and strongly negative for egg production. Age at first egg had the highest heritability of environmental variation; and favourable correlations with egg production and with variation in other production traits indicate that reducing variation in this trait may have potential benefits for the breeding industry.

Background Here, we jointly summarise scientific evidence for genetic variation in resistance to infection with Mycobacterium bovis, the primary agent of bovine tuberculosis (TB), provided by two recent and separate studies of Holstein-Friesian dairy cow populations in Great Britain (GB) and Ireland. Methods The studies quantified genetic variation within archived data from field and abattoir surveillance control programmes within each country. These data included results from the single intradermal comparative tuberculin test (SICTT), abattoir inspection for TB lesions and laboratory confirmation of disease status. Threshold animal models were used to estimate variance components for responsiveness to the SICTT and abattoir confirmed M. bovis infection. The link functions between the observed 0/1 scale and the liability scale were the complementary log-log in the GB, and logit link function in the Irish population. Results and discussion The estimated heritability of susceptibility to TB, as judged by responsiveness to the SICTT, was 0.16 (0.012) and 0.14 (0.025) in the GB and Irish populations, respectively. For abattoir or laboratory confirmation of infection, estimates were 0.18 (0.044) and 0.18 (0.041) from the GB and the Irish populations, respectively. Conclusions Estimates were all significantly different from zero and indicate that exploitable variation exists among GB and Irish Holstein Friesian dairy cows for resistance to TB. Epidemiological analysis suggests that factors such as variation in exposure or imperfect sensitivity and specificity would have resulted in underestimation of the true values.

The first objective of this study on broiler breeders was to investigate the genetic basis of variability in hatchability over age using a longitudinal model. Weekly percentage hatch of fertile and hatch of set eggs were available for 23,250 dams mated to 3,106 sires of the same age between the 28th and 54th week of life. Hatch of set was very highly correlated with fertility and showed a similar pattern through lay. There was a genetic contribution of the dam but not the sire to hatch of fertile; its heritability was about 6% from peak lay onward but lower earlier. The second objective was to investigate the relationship between hatchability and internal and external egg quality traits measured at 48 wk of age. These traits, specific gravity, weight loss, egg weight, and Haugh units, had moderate to high heritabilities, 0.53, 0.38, 0.65, and 0.38, respectively. Parameters of the genetic trend in weekly hatchability (mean and persistency) were significantly correlated with these egg quality traits, suggesting that in a bulk mating situation in which individual recording of hatchability is not possible, these quality traits could provide some indication on the trend in flock hatchability.

We evaluate the extent to which changes in phenotypic variation among generations of populations kept in the same environment are due to changes in genetic (V(A)) or in environmental (V(E)) variance. Data were available on body weight of adult poultry on a total of 89186 birds (mainly females) from six generations of each of seven lines of layers. There was substantial heterogeneity of variation between generations, shown to be in both V(A) and V(E) components. Based on the Akaike information criterion (AIC), the best fit was with both components changing, and a better fit was obtained if V(A)/V(E) (i.e. heritability) or V(E), rather than V(A), was assumed constant. In analyses of quantitative genetic data spanning environmental groups, attention should be paid to whether and how the variance components change among groups before undertaking detailed variance partition that may be sensitive to such changes.

The soil water regime was monitored at a forested experimental site in Cumbria, UK. Over an 83-week period following the clearfelling of 35-year-old Sitka spruce, soil water level measurements were related to total weekly rainfall in drainage treatment plots (10, 20 and 40 m ditch spacing) in three replicate blocks. Analysis showed a block × treatment interaction which might be related to soil differences between blocks. Significantly deeper soil water levels were measured in the most intensively drained plots of the two gently sloping blocks on a peaty gley soil. Drainage intensity had no effect on soil water level in the third block situated on a surface-water gley soil on a steep slope.

Background The fertility of a chicken's egg is a trait which depends on both the hen that lays the egg and on her mate. It is also known that fertility of an individual changes over the laying period. Methods Longitudinal models including both random genetic and permanent environmental effects of both the female and her male mate were used to model the proportion of fertile eggs in a pedigree broiler population over the ages 29-54 weeks. Results Both the male and the female contribute to variation in fertility. Estimates of heritability of weekly records were typically 7% for female and 10% for male contributions to fertility. Repeatability estimates ranged from 24 to 33%, respectively. The estimated genetic variance remained almost constant for both sexes over the laying period and the genetic correlations between different ages were close to 1.0. The permanent environment components increased substantially towards the end of the analyzed period, and correlations between permanent environment effects at different ages declined with increasing age difference The heritability of mean fertility over the whole laying period was estimated at 13% for females and 17% for males. A small positive correlation between genetic effects for male and female fertility was found. Conclusion Opportunities to improve fertility in broiler stocks by selection on both sexes exist and should have an impact throughout the laying period.

The aim of the study was to estimate genetic variance in residual variation of BW and body conformation scores of 34-d-old male and female broiler chickens. The data set included performance records of 52,349 female and 49,001 male birds. Two models were used: an iterative mean-variance restricted maximum likelihood sire plus dam model and a Bayesian sire plus dam model, in each case with heterogeneity in residual variances across sire families. They gave similar results. Estimates of heritability for BW in females and males were, respectively, 0.25 and 0.21, and for conformation score were 0.24 and 0.15, and genetic correlations for the same trait between sexes were high. Estimates of genetic correlations between means and variances were positive for both sexes and both traits. Estimates of the heritability of residual variation were low, between 0.023 and 0.038 for both traits, but genetic CV were substantial (between 0.25 and 0.40), indicating the possibility of improving uniformity of BW and conformation by means of selection.

There is currently considerable interest in genetic analysis of quantitative traits such as blood pressure and body mass index. Despite the fact that these traits change throughout life they are commonly analyzed only at a single time point. The genetic basis of such traits can be better understood by collecting and effectively analyzing longitudinal data. Analyses of these data are complicated by the need to incorporate information from complex pedigree structures and genetic markers. We propose conducting longitudinal quantitative trait locus (QTL) analyses on such data sets by using a flexible random regression estimation technique. The relationship between genetic effects at different ages is efficiently modeled using covariance functions (CFs). Using simulated data we show that the change in genetic effects over time can be well characterized using CFs and that including parameters to model the change in effect with age can provide substantial increases in power to detect QTL compared with repeated measure or univariate techniques. The asymptotic distributions of the methods used are investigated and methods for overcoming the practical difficulties in fitting CFs are discussed. The CF-based techniques should allow efficient multivariate analyses of many data sets in human and natural population genetics.

This paper gives a short review of the development of genetic parameter estimation over the last 40 years. This shows the development of more statistically and computationally efficient methods that allow the fitting of more biologically appropriate models. Methods have evolved from direct methods based on covariances between relatives to methods based on individual animal models. Maximum-likelihood methods have a natural interpretation in terms of best linear unbiased predictors. Improvements in iterative schemes to give estimates are discussed. As an example, a recent estimation of genetic parameters for a British population of dairy cattle is discussed. The development makes a connection to relevant work by Bill Hill.

Background The PAX6 protein is a highly conserved transcriptional regulator that is important for normal ocular and neural development. In humans, heterozygous mutations of the PAX6 gene cause aniridia (absence of the iris) and related developmental eye diseases. PAX6 mutations are archived in the Human PAX6 Allelic Variant Database, which currently contains 309 records, 286 of which are mutations in patients with eye malformations. Results We examined the records in the Human PAX6 Allelic Variant Database and documented the frequency of different mutation types, the phenotypes associated with different mutation types, the contribution of CpG transitions to the PAX6 mutation spectrum, and the distribution of chain-terminating mutations in the open reading frame. Mutations that introduce a premature termination codon into the open reading frame are predominantly associated with aniridia; in contrast, non-aniridia phenotypes are typically associated with missense mutations. Four CpG dinucleotides in exons 8, 9, 10 and 11 are major mutation hotspots, and transitions at these CpG's account for over half of all nonsense mutations in the database. Truncating mutations are distributed throughout the PAX6 coding region, except for the last half of exon 12 and the coding part of exon 13, where they are completely absent. The absence of truncating mutations in the 3' part of the coding region is statistically significant and is consistent with the idea that nonsense-mediated decay acts on PAX6 mutant alleles. Conclusion The PAX6 Allelic Variant Database is a valuable resource for studying genotype-phenotype correlations. The consistent association of truncating mutations with the aniridia phenotype, and the distribution of truncating mutations in the PAX6 open reading frame, suggests that nonsense-mediated decay acts on PAX6 mutant alleles.

The Framingham Heart Study offspring cohort, a complex data set with irregularly spaced longitudinal phenotype data, was made available as part of Genetic Analysis Workshop 13. To allow an analysis of all of the data simultaneously, a mixed-model- based random-regression (RR) approach was used. The RR accounted for the variation in genetic effects (including marker-specific quantitative trait locus (QTL) effects) across time by fitting polynomials of age. The use of a mixed model allowed both fixed (such as sex) and random (such as familial environment) effects to be accounted for appropriately. Using this method we performed a QTL analysis of all of the available adult phenotype data (26,106 phenotypic records). In addition to RR, conventional univariate variance component techniques were applied. The traits of interest were BMI, HDLC, total cholesterol, and height. The longitudinal method allowed the characterization of the change in QTL effects with aging. A QTL affecting BMI was shown to act mainly at early ages.

The hypothesis that polymorphisms at two candidate genes that code for angiotensin-converting-enzyme (ACE) and methylenetetrahydrofolate reductase (MTHFR) are associated with normal cognitive ageing was tested using a sample (n ¼ 536) of healthy 80-year-old people who were born in 1921 and whose cognitive ability at age 11 was measured in the Scottish Mental Survey 1932. Cognitive ability at age 11 and age 80 was assessed using the Moray House Test. Cognitive ageing was defined as the change in IQ from age 11 to 80. There was no significant association between the tested ACE and MTHFR polymorphisms and IQ score at age 11, IQ at age 80, and IQ change (all P . 0:05). The ACE genotypes deviated significantly from Hardy ‐ Weinberg equilibrium proportions (P ¼ 0:02), which could indicate that this gene is under selection. Polymorphisms at the two studied genes are unlikely to be risk factors for normal cognitive ageing. q 2003 Elsevier Science Ireland Ltd. All rights reserved.

Several studies with test-day models for the lactation curve show heterogeneity of residual variance over time. The most common approach is to divide the lactation length into subclasses, assuming homogeneity within these classes and heterogeneity between them. The main drawbacks of this approach are that it can lead to many parameters being estimated and that classes have to be arbitrarily defined, whereas the residual variance changes continuously over time. A methodology that overcomes these drawbacks is proposed here. A structural model on the residual variance is assumed in which the covariates are parametric functions of time. In this model, only a few parameters need to be estimated, and the residual variance is then a continuous function of time. The analysis of a sample data set illustrates this methodology.

Most approaches to modeling lactation curves involve parametric curves with fixed or random coefficients. In either case, the resulting models require the specification of an underlying parametric curve. The fitting of splines represents a semiparametric approach to the problem. In the context of animal breeding, cubic smoothing splines are particularly convenient because they can be incorporated into a suitably constructed mixed model. The potential for the use of splines in modeling lactation curves is explored with a simple example, and the results are compared with those using a random regression model. The spline model provides greater flexibility at the cost of additional computation. Splines are shown to be capable of picking up features of the lactation curve that are missed by the random regression model.

Cattle breeders, farmers and vets believe that the decline in fertility seen in recent years can be partially attributed to changes in rump angle with selection being for more angular cows. This suggests that animals with pin bones that sit above the hip bones (high rump angle) will have poorer fertility. Few studies have shown a significant relationship between fertility and rump traits. This study investigates the popular belief that high rump angle equates to poor fertility by examining the genetic and phenotypic correlation between rump angle and fertility traits. The relationship between rump angle and fertility was also examined to see if there was an intermediate optimum or threshold of rump angle for good/bad fertility. The correlation of other type traits (udder and composite traits) with fertility was also examined to see if they had potential to add information to the estimation of fertility breeding values.

1. As a pilot study, descriptions of the vegetation and soil sampling were carried out on 20 forest sites to investigate the soil factors likely to be of importance in assessing soil quality for silvicultural/ecological purposes, and to see how useful indicator species were in predicting soil factors. 2. Soil analytical properties, mostly expressed in units of kg ha -1 , were examined statistically by principal components analysis. 3. The vegetation descriptions were treated numerically by assigning to each plant species Ellenberg indicator values for F (soil moisture), R (soil reaction) and N (soil nitrogen). The indicator values were weighted either using the Domin scores for abundance or the frequency of each species in the vegetation. 4. Measures of nitrogen availability (especially mineralizable NO 3 and NH 4 ) and pH were the most important variables loading Principal Component 1 (PC1). 5. The site mean indicator values for R (mR) and N (mN) were combined (mR + mN) to provide a simple proxy for 'soil nutrient regime', and the site mean indicator value for F (mF) was used as a proxy for 'soil moisture regime'. 6. The scores for each site on PC1 were related to the values of mR + mN. 7. A grid formed from mF and (mR + mN) was used to ordinate the sites in terms of 'soil quality' (soil nutrient regime and soil moisture regime). 8. Further work along similar lines is proposed to enable local (British) ecological indicator values for plant species to be developed.

The effects of ditch spacing (10, 20 and 40 m) and depth (60 and 90 cm) on watertable depth were measured in a Sitka spruce plantation before and after drainage and finally after part of the plantation had been clearfelled. No significant differences in watertable depth were recorded between drainage treatments mainly because the ditch spacings were too large but also because of inadequate calibration of the site before the drainage treatments were applied. By the time of felling, the site had been thoroughly calibrated for the behaviour of the watertable, enabling sensitive comparisons to be made, and a significant rise in the watertable was recorded after felling.

SUMMARY Samples of air or water were extracted daily from porous pots buried within the rooting zone of trees planted on a deep peat soil. For most pots, the O2 concentration in the fluid increased with the number of samples taken each day, presumably because air was drawn into the pot from shallower depths. Sampling frequency should therefore be chosen as a compromise between the needs to increase precision and to minimize introduced bias.

Post-mixing aggression in commercially housed pigs can be intense and often results in the accumulation of skin lesions. The number of lesions (lesion score, LS) has often been used as a proxy indicatorofpost-mixingaggression.Therehasbeennopreviousattempttoquantifytheroleofdifferent behaviours in the accumulationof lesions. The objective ofthis work was to investigate the factors that contribute to LS in order to assess the validity of LS as a measure of individual aggressiveness. After mixingintonewgroupsof12,thedurationsofreciprocalfightingandbullying,theproportionsoffights initiated,wonandlostandphysicalattributesofthepigswereinvestigatedfortheirimpactonLSusing multipleregressiononasampleof342growingpigs.Pigliveweightwasthesinglegreatestdeterminant of LS.The duration spent in reciprocalfighting and being bullied were also significantdeterminants of the LS and contributed to the total LS in proportions of 0.17 and 0.14, respectively. The proportion of

First, second and third lactation curves of 21,885 first lactation dairy cows were allowed to vary depending on the months in milk at which the cow became pregnant. The curves were modelled using a 4th degree polynomial of days in milk. In the models for second and third lactation daily yield, days open in the previous lactation was included as a quadratic regression. Allowing the curve coefficients to depend on the month in milk when pregnancy occurred significantly improved the goodness of fit of the model to the data. The linear and quadratic coefficients of second and third lactation daily milk yield on days open in first and second lactation, respectively, were also significant. We suggest that, in the evaluation of test day milk yield, the shape of lactation curves are allowed to vary depending on the months in milk when pregnancy occurs and that days open in the previous lactation, if appropriate, is included in the model.

Mixing of commercial pigs frequently leads to intense aggression. Considerable phenotypic variation exists between individuals and selection against aggressiveness may offer a long-term reduction in aggression without incurring additional costs to the primary producer. The genetic contribution to aggressiveness was quantified in this study using the number of skin lesions as an indicator of involvement in aggression. A sample of 1132 pigs were mixed at an average weight of 27·9 (s.d. 4·6) kg into 96 pens on a commercial sire line nucleus unit. Post-mixing aggressiveness of pigs was assessed using the lesion score (LS) approach. Growth rate, between 27·9 and 91·9 kg, and backfat depth at 91·9 kg were recorded for a subsample of 658 pigs. With a pedigree file of 1947 animals, a heritability of 0·22 was estimated for the LS trait. No significant genetic or phenotypic correlations were found between LS and growth rate or backfat depth, but standard errors of estimates were large. The response to selection, when all selection pressure was placed on the LS trait, was a 25% reduction in LS per generation. It is therefore technically possible to select for a reduced LS without substantially inhibiting genetic progress in growth rate or backfat depth through antagonistic genetic relationships.

Several statistical models have been proposed for the genetic evaluation of production traits in dairy cattle based on test-day records. Three main approaches have been put forward in the literature: random regression, orthogonal polynomials, and, more recently, character process models. The aim of this paper is to show how these different approaches are related, to compare their performance for the genetic analysis of lactation curves, and to assess equivalence between sire and animal models for repeated measures analyses. It was found that, with an animal model, a character process model with 11 parameters performed better, regarding the likelihood criterion, than a quartic random regression model (with 31 parameters). However, although the likelihood was higher, the genetic variance was very different with the character process model from the unstructured model, which raises important issues concerning model selection criteria. There are advantages in combining methodologies. A quadratic random regression model for the environmental part, combined with a character process model for the residual, performed better than the quartic random regression model and had fewer parameters. A character process structure allowing for a correlation pattern modeled the residual better than a simple quadratic variance, and had only one extra parameter.