Calculation of multiple-trait sire reliability for traits included in a dairy cattle fertility index

The advent of genetic evaluations for fertility traits in the UK offers valuable information to farmers that can be used to control fertility problems and safeguard against involuntary culling. In addition to estimated genetic merit, proof reliabilities are required to make correct use of this genetic information. Exact reliabilities, based on the inverse of the coefficient matrix, cannot be estimated for large data sets because of computational restrictions. A method to calculate approximate reliabilities was implemented based on a six-trait sire model. Traits considered were interval between first and second calving, interval between first calving and first service, non-return rate 56 days post first service, number of inseminations per conception, daily milk yield at test nearest day 110 and body condition score. Sire reliabilities were calculated in four steps. Firstly, the number of effective daughters was calculated for each bull, separately for each trait, based on total number of daughters and daughter distribution across herd-year-seasons. Secondly, multiple-trait reliabilities were calculated, based on bull daughter contribution, applying selection index theory on independent daughter groups. Thirdly, (great-) grand-daughter contribution was added to the reliability of each bull, using daughter-based reliability of sons and maternal grandsons. An adjustment was made to account for the probability of bull and son or grandson having daughters in the same herd-year-season. Without the adjustment, reliabilities were inflated by proportionately 0·15 to 0·25. Finally, parent (sire and maternal grandsire) contribution was added to the reliability of each bull. The procedure was first tested on a data subset of 28 061 cow records from 285 bulls. Approximate reliabilities were compared with exact estimates based on the inverse of the coefficient matrix. Mean absolute differences ranged from 0·014 to 0·020 for the six traits and correlation between exact and approximate estimates neared unity. In a full-scale application, sire reliability for the fertility traits increased by proportionately 0·47 to 0·79 over single-trait estimates and the number of bulls with a reliability of 0·60 or more increased by 42 to 115%

Estimating variance components and predicting breeding values for eventing disciplines and grades in sport horses

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 12312 (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

Variance components for survival of piglets at farrowing using a reduced animal model

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

Genetic and environmental smoothing of lactation curves with cubic splines

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

Differences between primiparous and multiparous dairy cows in the inter-relationships between metabolic traits, milk yield and body condition score in the periparturient period

During the early postpartum period dairy cows mobilize fat and muscle to support lactation. This is associated with alterations in blood metabolite and hormone profiles which in turn influence milk yield and fertility. This study developed models to determine how metabolic traits, milk yield and body condition score were inter-related at different times in the periparturient period and to compare these relationships in primiparous (PP, n=188) and multiparous (MP, n=312) cows. Data from four previous studies which included information on blood metabolic parameters, parity, milk yield, body condition score and diet were collated into a single dataset. Coefficients of polynomial equations were calculated for each trait between -1 week pre-calving and week +7 postpartum using residual maximum likelihood modelling. The completed dataset was used in a multiple correlation model to determine how the best fit curves were related to each other over time. PP cows had higher concentrations of insulin-like growth factor-I and lower beta-hydroxybutyrate concentrations throughout, higher leptin concentrations pre-partum and both the peak in non-esterified fatty acids and the nadir in urea concentration occurred earlier after calving. These differences were associated with significantly lower milk production. Leptin concentrations fell at calving and were related to body condition score. Insulin was negatively correlated with yield in MP cows only. In MP cows the relationship between insulin-like growth factor-I and yield switched from negative to positive between weeks +4 and +7. Both beta-hydroxybutyrate and urea were positively related to yield in PP cows. In contrast, in MP cows beta-hydroxybutyrate was negatively correlated with yield and urea was strongly related to body condition score but not yield. These results suggest that there are differences in the control of tissue mobilization between PP and MP cows which may promote nutrient partitioning into growth as well as milk during the first lactation

Competition effects in a young Sitka spruce (Picea sitchensis, Bong. Carr) clonal trial

In the analysis of forestry experiments, there may be a need to adjust for competition between plots before predicting deployment performance in the field but there have been few attempts to investigate this. Our analysis looked at diameter data from a 19-year old Sitka spruce clonal trial growing in Scotland. Using a sequence of nested models, a likelihood ratio test indicated that fitting competition at both the genetic and residual level provided a significantly better fit than models which either ignored competition or fitted it at just the genetic or just the residual level. A strong negative genetic correlation of –0.93±0.05 was found between the direct genetic effects and competition effects. This was not significantly different from –1, indicating that competition is almost exactly proportional to the direct genetic effect and that a tree will exert a competitive effect which is closely related to its own genetic merit for size. At the residual level, the correlation between direct and competition effect was estimated as –0.17±0.03. We conclude that competition exists at both the genetic and environmental levels and including it in genetic evaluation systems gives a better prediction of future performance. Results also demonstrate that it is possible to obtain useful information about competition effects from a single-tree plot experiment

In Defence of Public Higher Education: Knowledge for a Successful Society (The Alternative White Paper for HE)

The present Conservative Government, like the Coalition Government that preceded it, has an ideological predisposition towards the market and its supposed benefits to consumers, but appears to have no vision of Higher Education and its benefits to students and to the whole of society. These wider societal benefits can be summarised under three aspects: * educating the next generation of the population * carrying out research to address social and scientific challenges * maintaining an independent platform for research into society and science to facilitate democratic debate. The last of these, sometimes drawn under the umbrella of ‘academic freedom’, is the basis of the historic contract between Universities and the State. We contend, following the UNESCO Recommendation (1997), that academic freedom must be sufficient to guarantee the independence of scientific inquiry, commentary and teaching. Pressures from funding agencies and the state are usually cited as the principal threats to academic independence. The last decade has seen the rise of a third threat, namely an increasing managerial interference in academic life deriving from the introduction of market imperatives. These three societal benefits are interconnected. Without independent research there can be no scientific independence and no cutting-edge teaching. Without a focus on critique and challenge, students may see ‘education’ as a mere process of accumulating ‘facts’ to meet test criteria. A narrow focus on the acquisition of qualifications undermines the education process itself. Employers have criticised graduate recruits for insufficient creativity, of being rote-taught and thus un-adaptable to a modern business subject to rapid technological change. Importantly, critical skills are necessary to meet the challenge of business and for inclusive democratic engagement. The idea of a University that unites these three aspects is undermined by a new model of Higher Education Institution that sees the investment in human capital only as a private benefit. The Government’s White Paper, Success as a Knowledge Economy, and associated legislative programme, consolidate a fee-loan (or debt-finance) model of funding which puts the costs of higher education onto new graduates and future taxpayers, while reducing taxes for current taxpayers – many of whom directly benefit from publicly-supported higher education, or from its wider public benefits. The Government suggests that it is merely replacing direct public funding with one that places the ‘student at the heart of the system’. But it proposes that public funding should be directed towards the realisation of the private benefits of higher education, and it fails to acknowledge the wider public benefits that higher education affords. In truth, the proposals place the market at the heart of the system and subordinate the student as a consumer of higher education, with loans functioning as a voucher to present at a university of choice (providing that the student has the grades required). It is our view that this new funding model is wrong in principle and deficient in practice. The regulatory framework that is being introduced in its wake will undermine the declared aims to improve teaching quality, to enhance social mobility, and to improve access and achievement. The extension of university title to for-profit providers will also threaten the wider public benefits of higher education, by allowing them to compete as single-function institutions, and giving them access to publicly-supported loans for their students without a guarantee of their longer term stability. This will intensify existing competition and encourage a ‘race to the bottom’. Our defence of an alternative vision of Higher Education takes place in the context of a dismal lack of leadership by the various mission groups representing universities in the sector – for example, Universities UK and the Russell Group – and other bodies responsible for the sector. Their willing advocacy of a fee-loan model of funding (to avoid possible cuts) has abdicated their leadership role in a proper debate on the values of public higher education. This failure to defend the values of the very public higher education they are chartered to provide is in marked contrast to representations made by another group. Lobbyists on behalf of for-profit providers are seeking a supposed ‘level-playing field’ in undergraduate degree provision, despite having no track record of success in the UK, a disastrous record in the USA, and no desire to provide any wider public benefit of their existence. The Government’s position is also in marked contrast to public attitudes. The British Social Attitudes Survey (NatCen) has, before and since the introduction of tuition fee changes, regularly asked questions about public attitudes to higher education and inequality. The majority of the population has consistently opposed high levels of student debt, believed that education has a value beyond simply providing the means to a better job, and maintained that inequality in Britain is an obstacle to the fulfillment of opportunities. Perhaps surprisingly, this commitment to the values of publicly-funded higher education is especially marked among those without graduate-level qualifications. Politicians who argue that the latter resent paying taxes to finance education for ‘middle-class people’ should seek evidence for this assertion. But the ‘debate’ among politicians, members of the BIS secretariat and corporate lobbyists over the issue has been remarkable for its superficial, un-evidenced character. It has also been remarkable for the absence of full public debate (Leach 2016). This Alternative White Paper aims to correct this imbalance. We need a proper debate about the future of UK Higher Education