Lecture 5 Artificial Selection R = h2 S

Applications of Artificial Selection Applications in agriculture and forestry Creation of model systems of human diseases and disorders Construction of genetically divergent lines for QTL mapping and gene expression (microarray) analysis Inferences about numbers of loci, effects and frequencies Evolutionary inferences: correlated characters, effects on fitness, long-term response, effect of mutations

Response to Selection Selection can change the distribution of phenotypes, and we typically measure this by changes in mean This is a within-generation change Selection can also change the distribution of breeding values This is the response to selection, the change in the trait in the next generation (the between-generation change)

The Selection Differential and the Response to Selection The selection differential S measures the within-generation change in the mean S = m* - m The response R is the between-generation change in the mean R(t) = m(t+1) - m(t)

Truncation selection uppermost fraction p chosen Within-generation change Between-generation change

The Breeders’ Equation: Translating S into R Recall the regression of offspring value on midparent value y O = π P + h 2 µ f m ° ∂ ( ) Averaging over the selected midparents, E[ (Pf + Pm)/2 ] = m*, E[ yo - m ] = h2 ( m* - m ) = h2 S Likewise, averaging over the regression gives Since E[ yo - m ] is the change in the offspring mean, it represents the response to selection, giving: R = h2 S The Breeders’ Equation

If males and females subjected to differing amounts of selection, Note that no matter how strong S, if h2 is small, the response is small S is a measure of selection, R the actual response. One can get lots of selection but no response If offspring are asexual clones of their parents, the breeders’ equation becomes R = H2 S If males and females subjected to differing amounts of selection, S = (Sf + Sm)/2 An Example: Selection on seed number in plants -- pollination (males) is random, so that S = Sf/2

Response over multiple generations Strictly speaking, the breeders’ equation only holds for predicting a single generation of response from an unselected base population Practically speaking, the breeders’ equation is usually pretty good for 5-10 generations The validity for an initial h2 predicting response over several generations depends on: The reliability of the initial h2 estimate Absence of environmental change between generations The absence of genetic change between the generation in which h2 was estimated and the generation in which selection is applied

The selection differential is a function of both the phenotypic variance and the fraction selected 20% selected Vp = 1, S = 1.4 50% selected Vp = 4, S = 1.6 20% selected Vp = 4, S = 2.8

The Selection Intensity, i As the previous example shows, populations with the same selection differential (S) may experience very different amounts of selection The selection intensity i provided a suitable measure for comparisons between populations, i = S p V P æ One important use of i is that for a normally-distributed trait under truncation selection, the fraction saved p determines i, i ' : 8 + 4 1 l n µ p ° ∂ ( )

Selection Intensity Versions of the Breeders’ Equation = h 2 S æ p i Expressed another way, R æ p = i h 2 Alternatively, R = i æ 2 A p

The Realized Heritability Since R = h2 S, this suggests h2 = R/S, so that the ratio of the observed response over the observed differential provides an estimate of the heritability, the realized heritability Obvious definition for a single generation of response. What about for multiple generations of response? Cumulative selection response = sum of all responses R C ( t = i 1 ) X

R ( t ) = h S + e b h = R ( T ) S P b = S ( ) R Cumulative selection differential = sum of the S’s S C ( t ) = 1 i X (1) The Ratio Estimator for realized heritability = total response/total differential, b h 2 r = R C ( T ) S (2) The Regression Estimator --- the slope of the Regression of cumulative response on cumulative differential P b = t S C ( ) R 2 Regression passes through the origin (R=0 when S=0). Slope = R C ( t ) = h 2 r S + e

Note x axis is differential, NOT generations Ratio estimator = 17.4/56.9 = 0.292 60 \ Cumulative Differential 5 10 15 20 Cumulative Response Slope = 0.270 = Regression estimator Note x axis is differential, NOT generations

Gene frequency changes under selection Genotype A1A1 A1A2 A2A2 Fitnesses 1 1+s 1+2s Additive fitnesses Let q = freq(A2). The change in q from one generation of selection is: ¢ q = s ( 1 ° ) + 2 ' w h e n j < D In finite population, genetic drift can overpower selection. In particular, when 4 N e j s < 1 drift overpowers the effects of selection

Strength of selection on a QTL Have to translate from the effects on a trait under selection to fitnesses on an underlying locus (or QTL) Suppose the contributions to the trait are additive: Genotype A1A1 A1A2 A2A2 Contribution to Character a 2a For a trait under selection (with intensity i) and phenotypic variance sP2, the induced fitnesses are additive with s = i (a /sP ) Thus, drift overpowers selection on the QTL when 4 N e j s = a i æ P < 1

D ¢ q ' 2 ( 1 ° ) [ + h ] More generally Change in allele frequency: Genotype A1A1 A1A2 A2A2 Contribution to trait a(1+k) 2a Fitness 1 1+s(1+h) 1+2s Change in allele frequency: D ¢ q ' 2 ( 1 ° ) [ + h ] s = i (a /sP ) Selection coefficients for a QTL h = k

Changes in the Variance under Selection The infinitesimal model --- each locus has a very small effect on the trait. Under the infinitesimal, require many generations for significant change in allele frequencies However, can have significant change in genetic variances due to selection creating linkage disequilibrium With positive linkage disequilibrium, f(AB) > f(A)f(B), so that AB gametes are more frequent With negativve linkage disequilibrium, f(AB) < f(A)f(B), so that AB gametes are less frequent Under linkage equilibrium, freq(AB gamete) = freq(A)freq(B)

± æ = ° V ( 1 ) = + d V ( 1 ) = + d d = æ ° h ± Changes in VA with disequilibrium Starting from an unselected base population, a single generation of selection generates a disequilibrium contribution d to the additive variance Under the infinitesimal model, disequilibrium only changes the additive variance. Additive genetic variance after one generation of selection Additive genetic variance in the unselected base population. Often called the additive genic variance disequilibrium V A ( 1 ) = a + d Changes in VA changes the phenotypic variance V P ( 1 ) = A + D E d h 2 ( 1 ) = V A P a + d d = æ 2 O ° P h 4 ± z The amount diseqilibrium generated by a single generation of selection is Changes in VA and VP change the heritability Within-generation change in the variance A decrease in the variance generates d < 0 and hence negative disequilibrium An increase in the variance generates d > 0 and hence positive disequilibrium ± æ 2 z = ° *

A “Breeders’ Equation” for Changes in Variance d(0) = 0 (starting with an unselected base population) Within-generation change in the variance -- akin to S New disequilibrium generated by selection that is passed onto the sext generation h 2 ( t ) = V A P a + d Decay in previous disequilibrium from recombination d(t+1) - d(t) measures the response in selection on the variance (akin to R measuring the mean) d ( t + 1 ) = 2 h 4 ± æ z æ 2 z ( t ) = 1 ° k Many forms of selection (e.g., truncation) satisfy k > 0. Within-generation reduction in variance. negative disequilibrium, d < 0 k < 0. Within-generation increase in variance. positive disequilibrium, d > 0 d ( t + 1 ) = 2 ° k h 4 æ z