Potential plan for the course - to be deliberated by participants and teachers. - There is not room for all the mentioned topics !

1 What is assumed known when starting the course (Tormod Ådnøy). * Mixed Model (MM) y = Xb +Zu + e, with G R V. * Fixed and Random. * Classification (ANOVA) and Regression. * BLUP with known variance components (g r). That GLS and MME are equivalent. * Pedigree based relationship A (G = g*A). * Various MM and consequences for Z, G, R : Animal Model, Reduced animal model, Repeated measures, Maternal effects, Multitrait models (MMM). * Random Regression (RR), polynomials (Taylor, Legendre, ... )

2 Programming. Numerical issues (Xijiang Yu, Ulf Indahl, ...). ** Programs : Excel, R, Julia, SAS, DMU, asreml, R (BLR), ... * You need to choose to do your term paper. ** Numeric : Alternative methods to theoretical inverse solution of MME/GLS : projections in linear spaces, SVD, Q R, Gram Schmidt, ...

Presentation of datasets and intentions for term papers (all participants). * 5-10 minutes oral or with slides.

3 Including genomic info (Theo Meuwissen). * Base population, gene frequencies, equilibria, - . * Estimating genomic relationship. * Single Step method (pedigree + genomic). 

4 Estimation of variance components (Tormod Ådnøy, Theo Meuwissen, Gareth Difford, ... ). * Requirements for structure of data (to estimate g and r G and R need to span separatable linear spaces). EMS from analyses of variance (LS) to estimate variances (g and r). * Likelihood. * REML. * Frequentist / Bayes.

Presentation of progression for term papers (all participants). * Potential models and programming languages.

5 Choice of programming language. Efficiency and accuracy. (Xijiang Yu, ... ). * Efficiency, both for human beings and computers. For human beings, a program should be easy to learn and write.  The developing cycle shouldn't be long.  For computers, a program should also run fast. * Numeric accuracy. Requirements for data. * Validation : Simulations. Crossvalidations. Leave one out (LOO). * Bias.

6 MMM - bruk av spekterinfo (Binyam Dagnachew, Tormod Ådnøy, Gareth Difford, ... ). * Spektra as information about other (chemical) traits. * Principal components (PC), PLS, PLSR. * Indirect Prediction (IP), Direct Prediction (DP). 

Presentation of results of analyses in term papers (all participants). * *With slide presentations of results (plots / graphs).

7 Modeling of G * E interations (?, ... )

8 Neural networks and other machine learning techniques (Arne Gjuvsland, Ulf Indahl, ... ) 

9 Monte Carlo Markov Chain (MCMC) methods (Jørgen Ødegård)

10 ' The Shaky Foundations of Fisherian Genetics' (Tormod Ådnøy, ... ) The infinitessimal gene effect model has been used for a hundred years and is still alive ... * Hardy Weinberg (HW), Random Mating (R!), Equilibrium (E!, not LD, ... ), additiv independent gene effects, ...

Knowledge

You will get knowledge on theory for prediction of breeding values based on mixed models, genomic and pedigree based relationship, including estimation of variance components.

Skills

You will be able to calculate breeding or genetic values for plant and animal breeding organisations for real data and with industry data programs.

General competence

In general you will have better competency in data handling, programming, linear algebra, and estimation theory; and understanding of plant and animal breeding programs

See Course contents.

The lectures and presentations in the course and assigned scientific papers.

Curriculum partly depends on needs and wishes of the participants in the course.

Chapter 27 in Lynch and Walsh (1998) : 'Genetics and Analysis of Quantitative Traits'  shows some parts of the curriculum intended.

Some papers on estimation of variance components. Manuals for vce/pest, asreml, dmu, R (BLR), or other variance component estimation programs also are important sources of information.

BIN301. Plant or animal breeding up to PhD level. Linear algebra. Matrix handling.

MSc students that want more challenges in breeding beyond what is given in other breeding courses may consider taking this course together with PhD students.

Animal or plant breeding to MSc level, including pedigree and genomic based relationship.

Some linear algebra. Vector and matrix handling.

Some data programming.

Participation in colloquia.

Presentation of calculation of breeding values in an own data set of size relevant for plant or animal breeding organizations.

Commenting / being opponent to / other participants' presentations.

Evalutation of term paper showing results of calculations of breeding values for real data with state of the art programs used by breeding organizations like DMU, asreml, R (BLR), ...

Passed / Failed

The course is given when there are enough interested participants. Lectures and colloquia initiated by the teacher will be held for more than 4 participants. If fewer students, some teacher supervision may be provided.

MSc students with enough relevant background may participate (with course code BIN303).