In charlotte-ngs/asmss2022: Applied Statistical Methods in Animal Science - Spring Semester 2022

knitr::opts_chunk$set(echo = FALSE)
knitr::knit_hooks$set(hook_convert_odg = rmdhelp::hook_convert_odg)

Administration

• Course: 2 hours of lecture (2 V)
• Plan: 2 V $\rightarrow$ 1 U + 1 V (i.e., 1 hour of lecture intersperced with time to do exercises)
• Exercises: Work on problems in R
• Material: course notes, slides, solution to exercises
• Exam: written, date: 30.05.2022, 08:15-10:00

Objectives

The students

• are familiar with the properties of fixed linear effects models
• are able to analyse simple data sets
• know why least squares cannot be used for genomic selection.
• know the statistical methods used in genomic selection, such as
  • BLUP-based approaches,
  • Bayesian procedures and
  • LASSO.
• are able to solve simple exercise problems using the statistical framework R.

Program

### # header names of tables
vecTableHeaders <- c("Week", "Date", "Topic")
# define course start date
dCourseStart <- as.Date("2022/02/21")
# set number of weeks in semester
nNrSemesterWeeks <- 15
# define columns for weaks, dates, and subjects
Week <- 1:nNrSemesterWeeks
Date <- format(seq(dCourseStart, by = "week", length.out = nNrSemesterWeeks), "%d.%m")
Topic <- vector(mode = "character", length = nNrSemesterWeeks)
# subjects per week
Topic[1] <- "Introduction"
Topic[2] <- "Linear Regression Models"
Topic[3] <- "Linear Fixed Effect Models"
Topic[4] <- "Model Selection"
Topic[5] <- "Pedigree BLUP"
Topic[6] <- "Variance Components"
Topic[7] <- "GBLUP - Marker-Effects Models"
Topic[8] <- "GBLUP - Breeding Value Models"
Topic[9] <- "__Easter Monday__"
Topic[10] <- "Lasso"
Topic[11] <- "SVM"
Topic[12] <- "Bayesian Approaches in Linear Regression Models"
Topic[13] <- "Bayesian Approaches in Linear Mixed Effects Models"
Topic[14] <- "Questions, Test Exam"
Topic[15] <- "Exams" 

dfCnTable <- data.frame(Week, Date, Topic, stringsAsFactors = FALSE)
colnames(dfCnTable) <- vecTableHeaders
knitr::kable(dfCnTable)

Information

• Website: https://charlotte-ngs.github.io/asmss2022
• Topics for master thesis: will follow
• Exam: 30.05.2022 08:15 -- 10:00

This Course

• Use dataset that is used to predict genomic breeding values and introduce four methods

• Fixed Linear Effects Models - Least Squares

• GBLUP - genomic version of BLUP
• LASSO - still fixed linear effects model, but modified parameter estimation
• Bayesian approach to estimate unknown parameter

Significance

• Why is this important?
• Is this only relevant for animal breeding?

• What about the rest of animal science?

• General trend of collecting data has led to development of Big Data

• Examples
  • Presidential campains in the US
  • Health care
  • Face recognition
  • Agriculture: Smart Farming
  • Animal Science

Face Recognition

#rmdhelp::use_odg_graphic(ps_path = 'odg/facerecog.odg')
knitr::include_graphics(path = "odg/facerecog.png")

Smart Farming

• Automated Milking Systems (AMS): Collection of data
• Sensor systems: SESAM (DigiDairy as follow-up)
• CFIT: automated gathering of feed intake data

SESAM

#rmdhelp::use_odg_graphic(ps_path = 'odg/farm-infrastrucutre.odg')
knitr::include_graphics(path = "odg/farm-infrastrucutre.png")

CFIT

Use video image analysis for

• cow identification
• collection of feed intake data

Traditional Animal Breeding

• Before 2006
• Data collected for other purposes were used to predict breeding values
• Predicted breeding values as side-product

Data Logistics

#rmddochelper::use_odg_graphic(ps_path = "odg/datalogistics.odg")
knitr::include_graphics(path = "odg/datalogistics.png")

Genomic Selection

• Same goal as in traditional breeding: Find animals with best genetic potential as parents of next generation
• New: use additional source of information
• Genomic information
  • spread accross whole genome
  • single nucleotide polymorphisms (SNP)
• Introduction:

\small "> Meuwissen THE, Hayes BJ, Goddard ME (2001) Prediction of total genetic value using genome-wide dense marker maps. Genetics 157:1819–1829"

• Popularisation:

\small "> L. R. Schaeffer. Strategy for applying genome-wide selection in dairy cat- tle. Journal of Animal Breeding and Genetics, 123(4):218–223, 2006. ISSN 09312668. doi: 10.1111/j.1439-0388.2006.00595.x."

SNP

#rmddochelper::use_odg_graphic(ps_path = "odg/snparchitecture.odg")
knitr::include_graphics(path = "odg/snparchitecture.png")

QTL

#rmddochelper::use_odg_graphic(ps_path = "odg/linkagesnpqtl.odg")
knitr::include_graphics(path = "odg/linkagesnpqtl.png")

Linkage

• Flanking SNPs and QTL not independent passed on from parents to progeny
• Favorable QTL-allele linked with a given SNP-allele
• QTL is unknown, but use SNPs close to QTL as information for selection

Monogenic Model

• Assume quantitative trait is influenced by one locus only
• Locus is bi-allelic $\rightarrow$ two alleles ($G_1$ and $G_2$) and three genotypes
• Look at Distribution of trait values for three different genotypes

Distribution No Effect

#rmddochelper::use_odg_graphic(ps_path = "odg/monogenicmodeltraitdistributionnoeffect.odg")
knitr::include_graphics(path = "odg/monogenicmodeltraitdistributionnoeffect.png")

Distribution With Effect

#rmddochelper::use_odg_graphic(ps_path = "odg/monogenicmodeltraitdistribution.odg")
knitr::include_graphics(path = "odg/monogenicmodeltraitdistribution.png")

Breeding Value

• Definition: Two times deviation from large number of offspring from population mean
• Assume: Hardy-Weinberg equilibrium
• Compute population mean as expected value of genotypic values
• Compute expected genotypic value of offspring for each of the three parental genotypes
• Assume purely additive loci, hence $d = 0$

Genomic Breeding Value

• Take into account many loci
• Approximate unknown QTL with linked SNP
• Estimate $a$-effects from monogenic model
• Compute genomic breeding values for all loci based on $a$ effects

Two Approaches

1. Two Step Procedure (used currently in Swiss Dairy Cattle)
2. Single Step

Two Step

#rmddochelper::use_odg_graphic(ps_path = "odg/twostepprocedure.odg")
knitr::include_graphics(path = "odg/twostepprocedure.png")

Single Step

• Combine all information into one single BLUP-based analysis
• Problem: Determine covariance between animals with and without genomic information

Summary: Traditional versus Genomic Selection

#rmddochelper::use_odg_graphic(ps_path = "odg/summarytraditionalvsgs.odg")
knitr::include_graphics(path = "odg/summarytraditionalvsgs.png")

charlotte-ngs/asmss2022 documentation built on June 7, 2022, 1:33 p.m.