PBG 650 Advanced Plant Breeding Module 12: Selection – Inbred Lines and Hybrids Selection for a high mean • Success is a function of – the population mean – the deviation of the best segregants from – ability to identify the best segregants • Advanced Cycle Breeding = “inbred recycling” – cross best by best (often related) – pedigree and backcross selection – emphasis on high mean at the expense of G2 – need methods for predicting Bernardo Chapt. 4 Probability of fixing favorable alleles during inbreeding Relative fitness 1 21 s 1 1 21 s (no dominance) A1A1 A1A2 A2A2 • Recombinant inbred from an F2 – without selection 1 2 – with selection 1 2 Standardized effect of a locus 2a si σP (Because p=1/2) 1 21 s • Three approaches to increase chances of fixing favorable alleles – selection before inbreeding – selection during inbreeding – one or more backcrosses to the better parent before inbreeding Mean with selfing Genotypic Value Frequency P a P d P a A1A1 A1A2 A2A2 p2+pqF 2pq(1-F) q2+pqF F0 p2 pqFP a 2 pq1 FP d q 2 pqFP a P a p - q 2 pq1 Fd • • Inbreeding decreases the mean if there is dominance At fixation (with no selection): RI P a p - q RI = recombinant inbred lines does not depend on dominance Mean of recombinant inbreds from a single-cross A P a pA - q A Means of the parents (for a single locus) B P a pB - q B Mean of recombinant inbreds derived from F2 of a single-cross RI ( AxB) P a 21 pA pB - 21 qA qB 21 A 21 B • The mean of recombinant inbreds derived from an F2 or backcross population can be predicted as a simple function of allele frequencies (the contribution of the parents) A = 6 t/ha B = 4 t/ha RI[(AxB)(A)BC1] = ¾*6 + ¼*4 = 5.5 t/ha Selfed families from a single-cross F2=S0 plant F3=S1 plant F3=S1 family represents S0 plant F4=S2 plant F4=S2 family represents S1 plant F5=S3 plant F5=S3 family represents S2 plant Selfed families from a single-cross F2 P a P d P a ¼A1A1 ½A1A2 ¼A2A2 2A 2 pqa d q - p 21 a 2 μ P 21 d 2 σD2 4 p 2q 2d 2 41 d 2 F3 ¼A1A1 Bernardo, Chapt. 9 ⅛A1A1 ¼A1A2 ⅛A2A2 ¼A2A2 G2 A2 D2 μ P 41 d Variance among and within selfed families F3 2Among ¼A1A1 1 4 ⅛A1A1 ¼A1A2 ⅛A2A2 ¼A2A2 μ P 41 d P a 2 21 P 21 d 2 41 P a 2 P 41 d 2 21 a2 161 d 2 2A 41 D2 2Avg.Within 41 0 21 2A D2 41 0 21 2A D2 2 F23plants 38 P a 41 P d 2 38 P a 2 P 41 d 2 34 a 2 163 d 2 32 2A 34 D2 Genetic variance with selfing Among families Within families Total σ 2A σD2 1/2 3/2 3/4 3/16 1/4 7/4 7/16 7/4 7/64 1/8 15/8 15/64 15/16 15/8 15/256 1/16 31/16 31/236 1 2 0 0 Generation F(g) σ 2A σD2 F3=S1 1/2 1 1/4 F4=S2 3/4 3/2 F5=S3 7/8 F6=S4 F∞=S∞ σ 2A , σD2 2 0 Inbreeding as a Selection Tool for OPVs • • • • More genetic variation among lines • Sets of inbred lines can be used to identify markerphenotype associations for important traits • Best lines can be intermated to produce synthetic varieties with defined characteristics Increased uniformity within lines Visual selection can be done for some traits Permits repeated evaluation of fixed genotypes in diverse environments, for many traits Testcrosses • The choice of tester will determine if an allele is favorable or not Testcross genotypic values with complete dominance Genotypic value of testcross Parent of cross A2A2 tester A1A1 tester A1A1 d a=d A1A2 ½(d - a) a=d -a a=d A2A2 Bernardo, Section 4.5 Effect of alleles in testcrosses Tester is an inbred line or population in HWE Genotypic Value Frequency P a P d P a A1A1 A1A2 A2A2 ppT pqT + pTq qqT T P a ppT qqT d pqT pT q qa d qT pT T 1 T2 -pa d qT pT - a d qT pT T T 1 T 2 Testcross mean of recombinant inbreds Testcross means of parental inbreds T P a pA pT - q AqT d pAqT q A pT A T P a pB pT - qB qT d pB qT qB pT B Testcross mean of recombinant inbreds derived from F2 of a single-cross T RI(AxB) • 21 T 21 T A B The testcross mean of recombinant inbreds derived from an F2 or backcross population can be predicted as a simple function of allele frequencies (the contribution of the parents) T=AxC and BxC For RI derived from the F2 of AxB TA = 8 t/ha TRI(AxB) = ½*8 + ½*6 = 7 t/ha TB = 6 t/ha Testcross means Genotype A1A1 A1A2 A2A2 • Frequency Testcross Mean p2+pqF 2pq(1-F) q2+pqF T+qT T+½(q - p)T T - pT Testcross mean of the heterozygote is half-way between the two homozygotes • Cross “good” by “good” • But, the correlation between the performance of inbred lines per se and their performance in testcrosses is very poor for yield and some other agronomic traits Heterosis or Hybrid Vigor • Quantitative genetics: – superiority over mean of parents • Applied definition – superiority over both parents – economic comparisons need to be made to nonhybrid cultivars • Various types – population cross – single-, three-way, and double-crosses – topcrosses – modified single-cross Bernardo, Chapt. 12 Heterosis P a P a A1A1 x A2A2 A1A2 P d F1 F2 ¼A1A1 ½A1A2 ¼A2A2 μ P 21 d • Amount of heterosis due to a single locus = d • 50% is lost with random-mating Theories for Heterosis • Dominance theory: many loci with d a – Should be possible to obtain inbred single-cross – Expect skewed distribution in F2 (may not be the case if many loci control the trait) • • Overdominance theory: d > a Pseudo-overdominance - decays over time +1 -2 A1 B2 A1 B2 X -1 +2 A2 B1 +1 A1 B2 A2 B1 A2 B1 +2 • tight, repulsion phase linkages • partial to complete dominance Heterosis – some observations • Experimental evidence suggests that heterosis is largely due to partial or complete dominance • Yields of inbred lines per se are poor predictors of hybrid performance – due to dominance – hybrids from vigorous lines may be too tall, etc. – due to heritability <1 • Heterosis generally increases with level of genetic divergence between populations, however…. – There is a limit beyond which heterosis tends to decrease – A high level of divergence does not guarantee that there will be a high level of heterosis Heterosis – more observations • Epistasis can also contribute to heterosis – does not require d>0 • Selection can influence heterosis – Iowa Stiff Stalk Synthetic (BSSS) – Iowa Corn Borer Synthetic (BSCB1) – High density SNP array shows increasing divergence over time in response to reciprocal recurrent selection Gerke, J.P. et al., 2013 arXiv:1307.7313 [q-bio.PE] Heterotic groups • Parents of single-crosses generally come from different heterotic groups • Two complementary heterotic groups are often referred to as a “heterotic pattern” • Temperate maize – ‘Reid Yellow Dent’ x ‘Lancaster Sure Crop’ – Iowa Stiff Stalk x Non Stiff Stalk • Tropical maize – Tuxpeño x Caribbean Flint Identifying heterotic patterns • • Diallel crosses among populations • Use molecular markers to establish genetic relationships, and make diallel crosses among dissimilar groups Crosses to testers representing known heterotic groups – initial studies were disappointing – markers must be linked to important QTL Exploiting heterosis • • Recycle inbreds within heterotic groups Evaluate testcrosses between heterotic groups – elite inbreds often used as testers • BLUP can predict performance of new singlecrosses using data from single-crosses that have already been tested – fairly good correlations between observed and predicted values What is a synthetic? • Lonnquist, 1961: – Open-pollinated populations derived from the intercrossing of – • selfed plants or lines Subsequently maintained by routine mass selection procedures from isolated plantings Poehlman and Sleper: – Advanced generation of a seed mixture of strains, clones, – – – inbreds, or hybrids Propagated for a limited number of generations by openpollination Must be periodically reconstituted from parents Parents selected based on combining ability or progeny tests Predicting hybrid performance Three-way crosses AxBxC 21 YAxB YAxC Double-crosses AxBx CxD 41 YAxC YAxD YBxC YBxD Synthetics Synthetic Yii ' Yi Yii ' n Yii ' = avg yield of all F1 hybrids Yi = avg yield of parents Wright’s Formula n = number of parents