PBG 650 Advanced Plant Breeding

1. PBG 650 Advanced Plant Breeding Module 6: Quantitative Genetics • Environmental variance • Heritability • Covariance among relatives

2. More interactions • Interlocus interactions are important, but difficult to quantify • Many designs for genetic experiments lump dominance and epistatic interactions into one component called “non-additive” genetic variance For an individual G = A + D + I P = A + D + I + E For a population Two-locus interactions More than two loci….

3. Genetic variances from a factorial model Bernardo, Chapt. 5

4. Environmental variance • covariance would occur if better genotypes are given better environments • randomization should generally remove this effect from genetic experiments in plants P = G + E • genotype by environment interactions • differences in relative performance of genotypes across environments • experimentally, GE is part of E P = G + E + GE DeLacey et al., 1990 – summary of results from many crops and locations For a particular crop, only 10% of variation in phenotype is due to genotype! 70-20-10 rule E: GE: G

5. variation among observations on the same individual due to temporary environmental effects ( = special environmental variance) variation among individuals due to genetic differences and permanent environmental effects ( = general environmental variance) Repeatability • Multiple observations on the same individuals • May be repetitions in time or space (e.g. multiple fruit on a plant) Falconer & Mackay, pg 136

6. Repeatability Repeatability • Sets an upper limit on heritabilities • is easy to measure • To separate and , you must evaluate repeatability of genetically uniform individuals

7. Gain from multiple measurements fyi • Multiple measurements can increase precision and increase heritability (by reducing environmental and phenotypic variation) • Greatest benefits are obtained for measurements that have low repeatability (large )

8. Heritability • For an individual: P = A + D + I + E • For a population: • Broad sense heritability • degree of genetic determination • Narrow sense heritability • extent to which phenotype is determined by genes transmitted from the parents “heritability” Falconer & Mackay, Chapter 8

9. Narrow sense heritability – another view h2 = the regression of breeding value on phenotypic value h2=0.5 +1 +2 h2=0.3 h2 is trait specific, population specific, and greatly influenced by the choice of testing environments

10. Narrow sense heritability • Can be applied to individuals in a single environment (generally the case in animal breeding) • In plants, it is commonly expressed on a family (plot) basis, which are often replicated within and across environments

11. Heritability in plants - complications • Different mating systems, including varying degrees of selfing • Different ploidy levels • Annuals, perennials • For many crops, measurement of some traits is only meaningful with competition, in a full stand • variables such as yield are measured on a plot basis • other traits are averages of multiple plants/plot • plot size varies from one experiment to the next • Replicates are evaluated in different microenvironments • Genotype x environment interaction is prevalent for many important crop traits Nyquist, 1991; Holland et al., 2003

12. Heritability in plants - definition • Fraction of the selection differential that is gained when selection is practiced on a defined reference unit (Hanson, 1963) Selection Differential S=s-0 Selection Response R=1-0 Y=bX R=Sbyx R/S=h2=byx • Main purpose for estimating heritability is to make predictions about selection response under varying scenarios, in order to design the optimum selection strategy R=h2S

13. Applications in plant breeding • Selection in a cross-breeding population • Selection among purelines (with or without subsequent recombination) • Selection among clones • Selection among testcross progeny in a hybrid breeding program • Must specify the unit of selection, the selection method, and unit on which the response is measured

14. Heritability of a genotype mean GXE Error variance broad sense heritability narrow sense heritability or “heritability”

15. Resemblance between Relatives • Covariance between relatives measures degree of genetic resemblance • Variance among groups = covariance within groups Intraclass correlation of phenotypic values Strategy: • Determine expected covariance among relatives from theory, and compare to experimental observations • Estimate genetic variances and heritabilities Falconer & Mackay, Chapt. 9

16. Covariance between offspring and one parent CovOP=p2*2q(-qd)q+2pq[(q-p)+2pqd](1/2)(q - p) +q2[-2p(+pd)](-p) CovOP = pq2 = (1/2)σA2 This result is true for a single offspring and for the mean of any number of offspring

17. Resemblance between offspring and one parent • For parents and offspring, observations occur in pairs • Regression is more useful than the intraclass correlation as a measure of resemblance • does not depend on the number of offspring • does not require parents and offspring to have the same variance phenotypic variance of the parental population Estimate

18. Resemblance between offspring and mid-parent • Regression on mid-parent is twice the regression of offspring on a single parent • Number of offspring does not affect the covariance or the regression CovO,MP = pq2 = (1/2)σA2

19. Resemblance among half-sibs Covariance of half-sibs = variance among half-sib progeny CovHS = pq2[(1/2)(q - p)2+2pq] = pq2[(1/2)(p+q)2] =(1/2)pq2=(1/4)σA2

20. Resemblance among full-sibs CovFS= σFS2 = p4a2+4p3q[(1/2)(a+d)]2….+q4(-a)2 - 2 =pq[a+d(q-p)]2 + p2q2d2

21. Resemblance among full-sibs CovFS= σFS2 = p4a2+4p3q[(1/2)(a+d)]2….+q4(-a)2 - 2 =pq[a+d(q-p)]2 + p2q2d2

22. General formula for covariance of relatives • Unilineal relatives • Resemblance involves only • Bilineal relatives • Potential exist for relatives to have two common alleles that are identical by descent etc. (X1X3, X1X4, X2X3, orX2X4) A B Resemblance will also involve: X1X2 X3X4 etc. C D X1X3 X1X3

23. Covariance due to breeding values A B C D X Y (Ai Aj) (Ak Al)

24. Covariance due to dominance deviations A B C D X Y (Ai Aj) (Ak Al)

25. General formula for covariance of relatives A B C D X Y r = 2XY  = ACBD + ADBC Extended to include epistasis:

26. Adjusting coefficients for inbreeding