Quantitative Genetics as it Relates to Plant Breeding PLS 664 Spring 2011 D. Van Sanford Quantitative vs. Qualitative Qualitative Traits Discrete Classes Individuals in each class counted Little environmental influence on phenotype Controlled by few (< 3 genes)

Quantitative Traits Continuous Variation Individuals measured, not counted Significant environmental influence on phenotype Controlled by many genes Alleles whose effects result in continuous distribution of phenotype cannot be studied individually. Mean Variance Progeny segregating at quantitative loci usually

approximate a normal curve with a center point called a mean, and a spread called a variance. Quantitative alleles cannot be studied individually this comment must be qualified in light of recent studies of quantitative trait loci (QTL) over the past decade. The Mendelians concentrated on discrete inheritance and argued that evolutionary advance was based on sudden, mutational changes. Biometricians stressed the importance of continuous

variation as the most important basis for evolutionary change. Biometricians criticized Mendelian inheritance and believed the traits upon which it had been demonstrated were of no evolutionary consequence. East and the Multiple Factor Hypothesis East used Mendelian genetics to explain quantitative inheritance. His explanation was called the Multiple Factor hypothesis. East studied corolla length in tobacco. The demonstration that there was no conflict between

qualitative and quantitative inheritance was a watershed moment in genetics. All variation has a similar Mendelian basis, whether large mutations or slight individual differences. Progeny segregating at quantitative loci are typically measured in replicated, multi-environment trials. Progeny segregating at qualitative loci, in contrast, are frequently evaluated as unreplicated individual plants in a single environment.

The Swedish plant breeder Nilsson-Ehle (1911) was among the first to demonstrate Mendelian inheritance for a continuous trait--kernel color in wheat. He identified a 63:1 red:white segregation ratio in an F 2 population from a white x red cross. Mendelian Inheritance of Wheat Seed Color Red Parent White Parent R1R1R2R2R3R3

r1r1r2r2r3r3 F1 Hybrid Red R1r1R2r2R3r3 F2 Progeny 27/64 Red R1_R2_R3_

27/64 Dark Pink 2 R alleles, 1r 9/64 Light Pink 2 r alleles, 1 R 1/64 White

r1r1r2r2r3r3 In addition to 3 genes for Seed Color, the environment plays a big role. Pictured is very white seed from a dry NY environment in 2010. A wet year will result

in a much darker version of white. Effect of Increasing No. of Genes AA AABB Aa aa

aabb As number of loci increases, so does number of discrete genotypic classes. As number of classes increase, differences between their means decrease below the variation caused by environmental effects. At this stage, the genotypic classes overlap

phenotypically and the distribution curve assumes smoothness. Phenotypic Value P = G + E + GE Phenotypic value is what we measure in the field, lab, greenhouse, etc. It comprises three components: Genotypic effect Environmental effect G x E Interaction effect Genotypic Effect

i j i G = + a + aj + d i j Genotype AA

Aa aa Value 3 2 1

Frequency .25 .5 .25 Estimating the Genotypic Value Relative contribution of G to the value of P is heritability which will be discussed throughout the course.

Plant breeders try to estimate true genotypic value by testing in numerous environments to account for the E and G x E effects. In theory, if we test a line in enough environments we will approximate the true value of G. In the real world of a breeding program, this never happens. Heritability Quantifies the relative contribution of genotype to phenotype Converse: it tells us how important the environment is in determining the trait

Methods of Estimating Heritability ANOVA Parent- Offspring Regression Note: the regression coefficient estimates heritability. The term regression was developed in

this context: Galton noted that the progeny of tall parents regressed back toward the population mean. In parent-offspring heritability estimation the unit of selection is determined in the parental generation. A parental phenotype can be measured on a single plant,

or a plot. The offspring phenotypes can be based on single plants or a family of plants in plots. We assume no environmental covariance between the parent and offspring, thus the environments must be independent. If the parents and offspring are grown in two different years, they need to be grown in different locations in both years for the environments to be independent. If you measure individual plants in both generations, then a simple standardization of all data will remedy the problem of very different environments both years (Frey and Horner, 1957). Actually such a

procedure is equivalent to obtaining a correlation coefficient between data in parental and offspring generations. Definitions of Heritability Broad-Sense Heritability (H), is that portion of the phenotypic variance that is genetic in origin, 2 G 2 P

= 2 G 2 GE 2 2 G + + Correspondence between phenotypic values and genotypic values. If

the proportion is high, the genotype plays a large role in determining the observed phenotype; if the proportion is low, then the alternative is true Narrow-Sense Heritability (h2), which is that portion of the phenotypic variance that is due to variance in additive effects among the individuals in a population, or the ratio: 2 A 2

P = 2 A 2G. + 2GE + 2 In our breeding program, narrow-sense heritability for plant height and maturity is high in our F3:4 wheat lines, because we find that the short, early maturing lines we select will generally

produce short, early maturing F4:5 progeny. Heritability on a Per-Plot Basis Heritability can be reported on a per-plot basis; the plot being the lowest unit of observation, or selection. H (per-plot basis) 2G = 2G + 2GL + 2GY + 2GLY + 2

= 50 50 (19.8%) = =0198 . 50 + 20 + 32 + 50 + 100 252 We can estimate heritability of the trait based on the Entry Means over the number of observations (locs x reps x years) for each line. The formula is

H (entry mean basis) = = G2 2 2 2 2

G2 + GL + GY + GLY + l y ly lyr 50 50 = 20 32 50 100 100 50 + +

+ + 2 2 4 8 = 0.495 (or 49.5%). Heritability on a single plant basis would be estimated as: 2 G 2G + 2GL + 2GY + 2GLY + 2w

For convenience we utilize the variances from the previous example. Heritability on a per plant basis is estimated as: h2 = 50 50 + 20 + 32 + 50 + 250 = 0.12 (or 12%). BB Bb bb

100 80 40 Because of the environment, each of these genotypes has a distribution of values about the mean. So if we select individuals >100, most will be BB but some will be Bb and even bb, due to the effect of the environment. hR=R/S Predicting Selection Response We have just seen that Response is a product of heritability and selection

differential If we have not done the selection yet and have no selection differential, we can use the standardized selection differential Predicting Selection Response R=h2S Becomes 2 R = G = ih p

Where i= standardized selection differential and p = the phenotypic std deviation Indirect Selection Sometimes it is in our interest to improve one trait by selecting for another trait The second trait may be easier and cheaper to measure than the first trait Ex. Improve scab resistance by selecting molecular marker

Indirect Selection For indirect selection on trait 2 to be more effective than direct selection on trait 1 the following MUST be true: h2 (trait 2) > h2 (trait 1) Genetic correlation between the traits rg1,2 must be very high, such that h2 rg1,2 ( ) > 1 h1