Partitioning of variance – Genetic models

Partitioning of variance – Genetic models Chapter 5, part 2

Basic genetic model Partitioning of variance P = G + E = µ + A + D + I + E P = µ + ½ As + ½ Ad +E Case 1: P = µ + ½ As + 0! If mated to random chosen females

Transmission model Half of the genes come from the sire. Half of the genes come from the dam. Which “half” is transmitted by sire or dam is unknown = Mendelian sampling

Mendelian sampling represents: Transmission model Variance • MS = Independent of everything else - uncertainty!! • Infinitesimal model: Variance of breeding values does not change from one generation to the next

Genetic model (for half sibs): Pij = phenotypic observation on offspring j of sire i • What is the resemblance between 2 half sibs, i.e. individuals with one parent in common ? • (paternal half sibs and maternal half sibs) • How to quantify resemblance?  covariance

Genetic model (for half sibs): What is the resemblance (covariance) in milk production between daughter 2 of sire 2 and daughter 5 of sire 2?

Genetic model (for half sibs): Why would their milk production be similar (show resemblance) ? They have the same father and therefore they will have partly the same “milk production genes”.

Genetic model (for half sibs):

Genetic model (for half sibs): What is the resemblance (covariance) in milk production between daughter 2 of sire 2 and daughter 5 of sire 2? Milk production:

Genetic model (for half sibs): Genetic model (for full sibs): Pijk = phenotypic observation on offspring k of sire I and dam ij What is the resemblance between full sibs, i.e. individuals with both parents in common ?

Genetic model for full sibs: What is the resemblance (covariance) in egg production between daughter 1 of sire i and dam ij and daughter 2 of the same sire and dam?

Genetic model for full sibs:

Individuals with the same (father and) mother also share part of their environment Common environment model Genetic model for half sibs Genetic model for full sibs ?

Common environment model

Common environment model • pigs in same litter are similar: • genetics (full sibs) • mother care • nutrition • same pen Individuals in this case resemble each other not only because the have genes in common but also because the have experienced some of the same environmental effects.

Common environment model • Is a common environmental effect important for the resemblance between: • half sib pigs ? • cross fostered full sib pigs? • full sib humans?

Common environment model Why do twins resemble each other? • The same father • The same mother • Common environment

Estimated parameters based on Dutch twins: • Purple = genetic, Green = common environment, Blue = age, Beige = environment

Common environment model Females males Age • Estimated parameters based on Dutch twins: • Purple = genetic, Green = common environment, Blue = age, Beige = environment

Genetic parameters for growth in Nile Tilapia Rutten, Komen and Bovenhuis (2004)

The repeatability model • Repeated measures of the same trait on the same individual. • repeated in time: weight of a fish on 122 days and 151 days. • measurement of backfat of a pig at different locations. • measure the strength of 2 eggs.

The repeatability model • Pij = phenotypic observation j on individual i • = overall mean • Gi = genetic value of individual 1 • = permanent environmental effect on individual i • = temporary environmental effect on repeated • observation j of individual i

The repeatability model Milk yield of cow 1 in lactation 1 and lactation 2: • The genotype and the permanent environmental effect of the cow have the same effect on lactation 1 and lactation 2. • Permanent environment Ep : • e.g. rearing conditions, diseases at young age

The repeatability model Milk yield of cow 1 in lactation 1 and lactation 2: Covariance between milk produced in lactation 1 and lactation 2?

The repeatability model Correlation between repeated observations: • i.e. the repeatability. • r  [0 …. 1] • r  h2 Repeatability is also being used to asses the quality of a measurement: if we redo a measurement does it give the same result?

Correlations between traits • Examples • Individuals that eat more also grow faster  positive relationship • Cows that produce more milk generally also have poorer fertility  negative relationship • Larger dogs have more HD  positive relationship. • Causes of similarity between traits • Genetics: Traits are affected by the same genes • genes increasing feed intake also increase growth rate • Environment: environmental effects work systematically in the same or opposite direction • better tasting feed increases both intake and growth rate

All genes of an animal All environmental effects affecting an animal Phenotype Trait 1 Trait 1 Trait 1 Pleiotropic genetic effects on trait 1 and 2 Environmental effects in common for trait 1 and 2 Trait 2 Trait 2 Phenotype Trait 2

Correlation between traits • Phenotypic correlation • Correlation between phenotypes for both traits • Strength of the relationship between the phenotypes for both traits • If I know the actual feed intake, how accurately do I know the growth rate?

Correlation between traits • (Additive) genetic correlation • Correlation between the (true) breeding values for both traits. • Strength of the relationship between the breeding values for both traits • If I know the breeding value for feed intake, how accurately do I know the breeding value for growth rate?

Correlation between traits • Environmental correlation • Correlation between the environmental effects on both traits (pl correct it in your reader, P5-11).

Multiple traits

Summary • Genetic Models • Basic genetic model • Transmission model • Common environmental model • Repeatability model • Multiple traits

Summary • Parameters: • Heritability • Common environmental effects • Repeatability • Phenotypic, genetic and environmental correlations

Partitioning of variance – Genetic models