Lecture 6: Inbreeding September 4, 2015

Last Time uCalculations  Measures of diversity and Merle patterning in dogs  Excel sheet posted uFirst Violation of Hardy-Weinberg assumptions: Random Mating uEffects of Inbreeding on allele frequencies, genotype frequencies, and heterozygosity

Important Points about Inbreeding uInbreeding affects ALL LOCI in genome uInbreeding results in a REDUCTION OF HETEROZYGOSITY in the population uInbreeding BY ITSELF changes only genotype frequencies, NOT ALLELE FREQUENCIES and therefore has NO EFFECT on overall genetic diversity within populations

Today uSelf-fertilization and mixed mating systems uInbreeding equilibrium uEstimating inbreeding coefficients from pedigrees uRelatedness and kinship

Nomenclature uD=X=P: frequency of AA or A 1 A 1 genotype uR=Z=Q: frequency of aa or A 2 A 2 genotype uH=Y: frequency of Aa or A 1 A 2 genotype up is frequency of the A or A 1 allele uq is frequency of the a or A 2 allele uAll of these should have circumflex or hat when they are estimates:

Effect of Inbreeding on Genotype Frequencies ufp is probability of getting two A 1 alleles IBD in an individual up 2 (1-f) is probability of getting two A 1 alleles IBS in an individual uInbreeding increases homozygosity and decreases heterozygosity by equal amounts each generation uComplete inbreeding eliminates heterozygotes entirely

Fixation Index uThe difference between observed and expected heterozygosity is a convenient measure of departures from Hardy-Weinberg Equilibrium Where H O is observed heterozygosity and H E is expected heterozygosity (2pq under Hardy-Weinberg Equilibrium)

uAssume completely inbred fraction (f) and noninbred fraction (1-f) in population uIf departures from Hardy Weinberg are entirely due to inbreeding, f can be estimated from Fixation Index, F IBD IBS

Effects of Inbreeding on Allele Frequencies uAllele frequencies do not change with inbreeding uLoss of heterozygotes exactly balanced by gain of homozygotes

Extreme Inbreeding: Self Fertilization uCommon mode of reproduction in plants: mate only with self uAssume selfing newly established in a population u½ of heterozygotes become homozygotes each generation uHomozygotes are NEVER converted to heterozygotes

Self Fertilization AA aa Aa A a aA Aa Self-Fertilizations AA A A AA AA Self-Fertilizations ½ Aa each generation ½ AA or aa (allele fixed within lineage)

Changes in Genotype Frequencies under Self-Fertilization

Decline of Heterozygosity with Self Fertilization uSteady and rapid decline of heterozygosity toward zero AA or aa Aa

If the population is infinite, how long will it take to eliminate heterozygotes in a population that becomes completely self-fertilizing?

Partial Self Fertilization uMixed mating system: some progeny produced by selfing, others by outcrossing (assumed random) uRate of outcrossing = T uRate of selfing = S uT+S=1 uHeterozygosity declines to equilibrium point aa AA Aa H-W Expectation Selfing Effect(from previous slide)

Inbreeding Equilibrium uProduction of heterozygotes by outcrossing balances loss of heterozygotes by selfing uFor any value of p and S, there is a characteristic equilibrium point, regardless of starting genotype frequencies uInbreeding coefficient also reaches equilibrium point, purely a function of selfing rate D eq H eq R eq See lab notes for derivations Outcross Combinations That Produce Heterozygotes AA x aa AA x Aa aa x Aa Aa x Aa gain loss

Estimating Selfing in Populations Level of selfing can be readily estimated from allele frequencies and observed heterozygosity: What are the assumptions of this calculation?

Estimating Inbreeding from Pedigrees uMost accurate estimate of f derived from direct assessment of relationships among ancestors Half First-Cousins CA: Common Ancestor

Estimating Inbreeding from Pedigrees uProbability P contains two A 1 alleles IBD uOverall: uThere are two alleles in the common ancestor, so there are two possibilities to inherit different alleles IBD uProbability P contains any alleles IBD is therefore:

Chain Counting uCount links to Common Ancestor starting with one parent of inbred individual and continuing down to other parent  D-B-CA-C-E  N=5 links For multiple common ancestors, m: If common ancestors are inbred as well: Where f CAi is inbreeding coefficient of common ancestor i

Kinship Coefficient CA 2 CA 1 D B C E uEstimate of relationship between two individuals in a population, D and E uProbability a randomly selected allele from each is Identical by Descent uEasiest to estimate as f of hypothetical progeny, p P

Relatedness uSewall Wright revolutionized study of inbreeding in 1922 uDefined coefficient of relationship (r)  Shared alleles between related individuals result in genetic correlation  Also the fraction of alleles that two individuals share IBD uCan be estimated as twice the inbreeding coefficient of possible offspring (i.e., twice the kinship) ry.org/unitarians/wright- sewall.html

Relatedness uRelatedness is twice the probability that two alleles, one chosen randomly from each individual, are IBD r=0.5 for parent–offspring and full sibs r=0.25 for half-sibs, and r=0.125 for first cousins. uCan be estimated from sharing of alleles conditioned on allele frequencies

Estimating Relatedness Without a Pedigree uMolecular markers provide indication of relatedness of individuals based on shared alleles uMore polymorphic markers are preferable: microsatellites Source: SilkSatDB Allozymes Microsatellites Lowe, Harris, and Ashton 2004

Estimating Relatedness Without a Pedigree uIn many cases, relationships among samples are unknown uRelationships can be estimated using multiple, highly polymorphic loci uQueller and Goodnight (1999, Mol Ecol. 8:1231) developed a program, KINSHIP, that estimates relatedness based on likelihood ratios (explained in more detail later) Number of Microsatellites Required to Distinguish Relationships

Relatedness in Natural Populations uWhite-toothed shrew inbreeding (Crocidura russula) (Duarte et al. 2003, Evol. 57: ) uBreeding pairs defend territory uSome female offspring disperse away from parents uHow much inbreeding occurs? u12 microsatellite loci used to calculate relatedness in population and determine parentage u17% of matings from inbreeding Number of matings Relatedness Parental Relatedness Offspring Heterozygosity