Quantitative genetics and What is quantitative genetics? reaction norms Traits that seems to vary along a continuous • Demography - analyses sources for scale variation in fitness • Quantitative genetics - analyses the Growth rate in genetic reasons for variation in fitness trout – How much genetic variation – How is it conserved? – How is it expressed? • MICRO-EVOLUTION Methodically a way to formalise breeding programs in animal and plants: how to ”increase” quality?

What is quantitative genetics? Genetic Factors Affecting Quantitative Traits

• Statistical phenomenology • Additive Gene Action - Each allele has a specific metric value that it adds to the phenotype; generally this is the most important type of gene • Assumptions: traits are regulated by many action controlling quantitative traits genes - each with small effect • Dominant Gene Action - Homozygous dominant and heterozygous • Tries to quantify the importance of genes genotypes contribute the same to the phenotype. and environment in producing a genotype • Epistatic Gene Action - Interaction of two genes controlling a trait

• Assumes a genotype - phenotype link Phenotype = Genetic Factors + Environmental Factors • No hypotheses about the mechanisms

An example where two genes, A and B, control a trait. How can a trait vary on a A allele = 4 units a allele = 2 units

continuous scale? B allele = 2 units b allele = 1 units

1. The sum of ”many” genes each with little effect 2. Reaction norms.

1 Reaction norms Genotype-environment interactions

GxE

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y interaction

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h p No GxE interaction Environment

Reaction norms transforms environmental variation to phenotypic variation Environment

One example: Grayling (harr)

Grayling Variation - family level

Haugen & Vøllestad 2000

Genotype value (G) Two important concepts • Departure from the population mean • P (phenotype value) = G + E (environmental • Heritability (h2) and genetic correlation. effect; = 0 for the population) • First, we need some more basic concepts: Genotype aa Aa AA – Additive genetic variance – Breeding values – An alleles mean effect -a 0 d a – Genotype value Genotype value d - dominance (A ”dominates” over a) d = 0 - no dominance Full dominance: d = ± a Over-dominance: d > 1 or d < -1

2 Genes are transferred - not genotypes Breeding value

• An alleles mean effect: • Alleles combines in individuals. – Mean departure from the population mean for • The breeding value is the individuals mean values - individuals with a given allele, given the allele estimated from the mean values of its progeny. from the other parent is randomly distributed. • Called additive genetic effects, – We assume that effects of different genes are Genotype Frequency Value FxV independent and can be added. AA p2 +a p2a • heritability: the degree to which variation in a trait Aa 2pq d 2pqd is under genetic control! – Heritability needs variation 2 2 aa q -a -q a – Example: number of arms in humans has heritability = 0! A theoretical abstraction

Two types heritability Phenotypic variation (Vp) • ”Broad sense”: V / V • Vp = Vg + Ve g p – The propotion of phenotypic variation under genetic • Vg = Va + Vd + Vi control

– Vp = phenotypic variance – Includes maternal effects, effects of common environments and interaction between genes – Vg = genetic variance • ”Narrow sense”: h2 = V / V • Va = variation in breeding value / additive a p genetic variance – Phenotypic variation due to variation in ”breeding values” • Vd = dominance variance – Degree of similarity among relatives • Vi= interaction variance – Potential response to selection. – Ve = environmental variance

How to estimate these variance-components?

Parent - progeny regression To estimate heritability

• Similarity among relatives h2 = 0.91 – Parent - progeny regression R – Correlation between full- or halfsib • Controlled breeding experiments R = h2 S • Constant environment(s) • Variance analysis S • Response to selection – Direct estimation of the effect

3 How does heritability vary? Similarity between sibs • Lif history traits have in general lower h2 Environment A Environment B than morphological and physiological traits!

Dam 1 Dam 2 Dam 1 Dam 2 Strong selection removes genetic variation - traits Nested mixed-model ANOVA. strongly correlated with fitness is exposed to strong directional Sire 3 Y = µ + XE + X(dam; E) + X(sire; or stabilizing selection Sire 1 Sire 2 dam, E) + e

2 2 2 h = 4 σ sire / σ tot Individ #

Selection on quantitative traits The effect of selection

• Directional selection • Stabilising selection • Genes influencing traits under selection will be fixed! – Heritability (h2) will approach 0. • Time depends on sample size • Question: – How fast will the additive genetic variation be lost? – How can it be maintained over time?

How can genetic variation be Response to selection Trait maintained? • A balance between selection and mutation Limit to selection (mutation-selection balance) The effect of • Selection in ”patchy” environments new mutations • Genotype x environment interactions • Negative genetic correlations / pleiotropy Small N • Flat fitness-profiles Large N

Generations

4 Mutation vs. selection Selection in patchy environments

GENE FLOW • In large populations: mutation will counteract the effect of selection and genetic variation may be maintained. – Especially if many genes are involved – And if selection pressure varies in time and space • Common mutation rate: 10-4 pr locus and generation NOT FOR RARE ALLELS

Genotype X environment Negative genetic correlations interactions and pleiotropy • Environmental variation with the population • Pleiotropy: one gene - multiple traits • Crossing reaction norms • The genotype value for two traits are No single genotype will be most ”fit” reversed

Vøllestad and Quinn 2003

Flat fitness profiles Genetic covarians

Fitness • The genetisk correlation between two traits is the correlation between the ”breeding values” for the traits • The part of the correlation between traits due to additive genetic variation: 0 – Pleiotropy: one gene - severalt traits – Epistasis: several genes - the same trait – Linkage: different loci as if they are alleles at the same locus, even if the do not influence the same traits directly. Remember: covariance can be due to comparable Phenotype value 0 environments

5 Phenotypic vs genetic correlations Phenotypic and genetic correlations

Roff 2002 Reduced resource- rg = -1 allocation

Environmental Phenotypisk correlation correlation Genetic correlation increased resource- acquisition Genetic and phenotypic correlations can have different sign Van Noordwijk and de Jong 1986, Roff 2002.

How to measure the genetic rg correlation (rg) Good environment • Half- or fullsib design with simultaneous measurement of several traits. t

– Correlation between family means i a r

– Variance and covariance components T Crossing reaction norms • Parent-progeny regression • Response to selection • Very data intensive! • Varies in space and time, also during ontogeny Bad environment

Age

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