PBG 650 Advanced Plant Breeding Module 2: Inbreeding Genetic Diversity –A few definitions Small Populations –Random drift –Changes in variance, genotypes Mating Systems –Inbreeding coefficient from pedigrees –Coefficient of coancestry –Regular systems of inbreeding

Genetic Diversity Studies - Applications Highlight geographic areas for further germplasm collection Establish core collections –preserve genetic resources –representative samples for genetic studies Investigate theories regarding crop domestication and origin Determine genes involved in domestication –Lower diversity in domesticated species than in wild relatives Selection of parents for a breeding program –Identify untapped sources of genetic variation Establish effective breeding methods Define heterotic groups for inbred/hybrid development Take PBG 620, 621, 622!

Measures of Genetic Diversity Number of alleles or SNPs identified Average number of alleles per locus Effective alleles per locus = A e Major allele frequency = MAF Average expected heterozygosity (Nei’s genetic distance) = H e Observed heterozygosity = H o Polymorphic Information Content = PIC values Polymorphism or % of polymorphic loci= P j –A locus is considered polymorphic if the frequency of the major allele is less than 0.95 (or 0.99)

Average expected heterozygosity Also called Nei’s Genetic Distance –One locus (j), two alleles –One locus (j), with i alleles –Average across loci The average H e across loci measures extent of variation in a population

Steps in Diversity Analysis 1.Characterize the diversity –Genotyping –Phenotyping 2.Calculate relationships –Genetic distance 3.Express relationships with a classification and/or ordination method –Classification or clustering –Ordination (e.g., PCA)

Recent Studies of Crop Diversity Xu, X., et al., Resequencing 50 accessions of cultivated and wild rice yields markers for identifying agronomically important genes. Nature Biotechnology 30: 105–111.

Population size Sampling can lead to changes in gene frequency in small populations Changes are random in direction (dispersive), but predictable in amount –random drift – accumulation of small changes due to sampling over time –differences among subgroups of the population increase over time –increase in uniformity and level of homozygosity within subgroups (Wahlund effect) Two perspectives –changes in variances due to sampling –changes in genotype frequencies due to inbreeding Falconer, Chapt. 3

Dispersive process - idealized population Base population N =  2N 2N 2N 2N 2N 2N 2N gametes NNNNNNN 2N 2N 2N 2N 2N 2N 2N NNNNNNN sub-populations t=0 t=1 t=2

Idealized population assumptions Mating occurs within sub-populations Mating is at random (including self-fertilization) Sub-populations are equal in size Generations do not overlap No mutation, migration or selection  No change in the average gene frequency among sub-populations over generations

Random drift (genetic drift) Every generation, the sampling of gametes within each sub- population centers around a new allele frequency  changes accumulate over time Changes occur at a faster rate in smaller populations probability of obtaining k copies of an allele with frequency p in the next generation sampling process

Random drift (genetic drift) Gene frequencies in the sub- populations drift apart over time, until all frequencies become equally probable (steady state) Once the steady state is attained, the rate of fixation is 1/N in each generation The longterm effect of drift for a finite population is a loss of genetic variation Historical effects of drift are locked in (founder effect or bottleneck effect) Buri, Peter Gene frequency in small populations of mutant Drosophila. Evolution 10: eye color in Drosophila 105 populations, N=16 at t=0 f(bw)=f(bw 75 )=0.5

Dispersive process – effects on variance Variance in gene frequency among sub-populations at t=1 Variance among sub-populations increases in each generation. At time t:  p 0 q 0 at t = 

Change in genotype frequency As gene frequencies become more dispersed towards the extremes –there is an increase in homozygosity and decrease in heterozygosity within each sub-population –genetic uniformity increases within sub-populations

Definition of inbreeding inbreeding = mating of individuals that have common ancestors identical by descent (ibd) = alleles are direct descendents from a common ancestral allele (autozygous) identical in state = alleles have the same nucleotide sequence but descended from different ancestral alleles (allozygous) An individual is inbred if it has alleles that are identical by descent

Coefficient of inbreeding Probability that two alleles at any locus in an individual are ibd (also applies to alleles sampled at random from the population) Must be in relation to a base population Change in inbreeding in a single generation Inbreeding at generation t new old Recurrence equation

Inbreeding Remember: For a single generation At time t

Genotype frequencies with inbreeding What will genotype frequencies be when the sub-populations are completely inbred?

Calculation of F from population data F can be viewed as the deficiency in observed heterozygotes relative to expectation: H = observed frequency of heterozygotes H e = expected frequency of heterozygotes

F statistics – relative deficiency of heterozygotes (1-F IT )=(1-F IS )(1-F ST ) I = individual S = sub-population T = total Base population N =  2N 2N 2N NNN t=0 Generation t ….. Individuals in a subpopulation F IT F IS F ST

What population sizes are needed for breeding? 1. Calculate the population size needed to have the expectation of obtaining one ideal genotype For a trait controlled by 10 unlinked loci: (1/4) 10 in an F 2, so N = 4 10 = 1,048,576 (1/2) 10 in an inbred line, so N = 2 10 = Consider how to stabilize variance of allele frequencies Bernardo, Chapt. 2 Would be more critical for a long-term recurrent selection program than for a particular F 2 population

Effective population size Number of individuals that would give rise to the calculated sampling variance, or rate of inbreeding, if the conditions of an idealized population were true Falconer, Chapt.4

Effective population size unequal numbers in successive generations –effects of a bottleneck persist over time different numbers of males and females Falconer, Chapt.4 harmonic mean

Half-sib recurrent selection in meadowfoam Year 1 – create half-sib families 500 spaced plants in nursery outcross  half-sibs families self  S 1 families Year 2 – evaluate families in replicated trials Year 3 - Should I go back to remnant half-sib seed of selected families or use the selfed seed for recombination?

Migration How many new introductions do I need in my breeding program to counteract the loss of genetic diversity due to inbreeding (genetic drift)? m is the migration rate (frequency) N e m is the number of individuals introduced each generation  A few new introductions each generation can have a large impact on diversity in a breeding population

Inbreeding coefficients from pedigrees ABABACACBXBXCXCX Prob. a1a1 a1a1 a1a1 a1a1 (½) 4 a2a2 a2a2 a2a2 a2a2 a1a1 a2a2 a1a1 a2a2 a2a2 a1a1 a2a2 a1a1 A BC X x a1a2a1a2 F X =2*(½) 4 +2*(½) 4 *F A =(½) 3 +(½) 3 F A = (½) 3 (1+F A ) n = number of individuals in path including common ancestor Falconer Chapt. 5; Lynch and Walsh pgs

Inbreeding coefficients from pedigrees B E D G H C J A Paths of Relationshipn F of common ancestor Contribution to F J EBACH50(1/2) 5 EBADGH60(1/2) 6 EBCH40(1/2) 4 ECADGH60(1/2) 6 ECBADGH70(1/2) 7 ECHECH3 1/4 (1/2) 3 *(1+0.25) FJ=FJ= E is inbred but this does not contribute to F J No individual can appear twice in the same path Path must represent potential for gene transmission (BCA is not valid, for example)

Coefficient of coancestry identical by descent (ibd) = alleles descended from a common ancestral allele inbreeding coefficient = probability that alleles in C are ibd coefficient of coancestry probability that alleles in A are ibd with alleles in B aka coefficient of kinship, parentage or consanguinity AB C x Note:  AB = f AB in Bernardo’s text

Coefficient of coancestry ABC x alleles received by A and B alleles sampled from A and B (to go to offspring) alleles received by C alleles sampled from C (to go to offspring)

Formal calculation of coancestry AB C x a1a2a1a2 b1b2b1b2 ab c1c2c1c2

Rules of coancestry A x B E x C x D G H

Coancestry: selfing Aa1a2Aa1a2 x Aa1a2Aa1a2 X ¼ a 1 a 1 ½ a 1 a 2 ¼ a 2 a 2

Derivation of the rules: another example A x B E x C x D G H Alleles from EAlleles from C 1/4a1a1 1/2c1c1  AC 1/4a1a1 1/2c2c2  AC 1/4a2a2 1/2c1c1  AC 1/4a2a2 1/2c2c2  AC 1/4b1b1 1/2c1c1 BCBC 1/4b1b1 1/2c2c2 BCBC 1/4b2b2 1/2c1c1 BCBC 1/4b2b2 1/2c2c2 BCBC

Coancestry of full sibs A x BC x D E A C xB D E with no prior inbreeding Note: could get same result by calculating F E

Tabular method for calculating coancestries A B C D E F G Can accommodate different levels of inbreeding in parents Can incorporate information from molecular markers about the contribution of parents to offspring (may vary from 0.5 due to segregation during inbreeding) Can be automated contribution of E to G = 0.5 Excel

Regular systems of inbreeding Same mating system applied each generation All individuals in each generation have the same level of inbreeding Purpose is to achieve rapid inbreeding Develop recurrence equations to predict changes over time A B Example: repeated selfing

Regular systems of inbreeding ACB DEG HJ Mating systemCoancestry No prior inbreeding Recurrence equation full sibs  EG =(1/4)(2  BC +  BB +  CC ) 1/4F t =(1/4)(1+2F t-1 +F t-2 ) half sibs  DE =(1/4)(  AB +  AC +  BB +  BC ) 1/8F t =(1/8)(1+6F t-1 +F t-2 ) parent-offspring  AD =(1/2)(  AA  AB ) 1/4F t =(1/2)(1+F t-2 ) backcrossing F H =  BD =(1/2)(  BB +  AB ) 1/4F t =(1/4)(1+F B +2F t-1 ) selfing  BB =(1/2)(1+F B ) 1/2F t =(1/2)(1+F t-1 )