1. Basic concepts on population genetics
OUTLINE
Allele frequency and genotypic frequency
Hardy Weinberg equilibrium
Linkage and Linkage disequilibrium (LD)

2. Allele and genotypic frequency under HW
Characteristics of a population
 Genotypic frequencies
 Allele frequencies
‘n’ diploid plants are equivalent to ‘2n’ alleles
In F1 and F2 generations p and (1-p)=0.5 at all loci that differ between the two parental inbreeds.
What is the Hardy-Weinberg Equilibrium?

3. How about for genotypes with respect to loci considered jointly?
HARDY-WEINBERG EQUILIBRIUM FOR ONE LOCUS OR SEVERAL LOCI CONSIDERED SEPARATELY
3 KEY FEATURE
Allele frequencies [p and q=(1-p)] remain constant from generation to generation
Square of the array of allele=array of genotypic frequency
If allele frequency change, one generation of random mating would lead to a new set of equilibrium in genotypic frequency for all loci considered separately (one locus).
How about for genotypes with respect to loci considered jointly?

4. Assumptions of HW model
DIPLOID
SEXUAL REPRODUCTION
TWO ALLELES
MATING IS AT RANDOM
LARGE POPULATION SIZE NO MUTATION, NO MIGRATION
NATURAL SELECTION DOES NOT AFFECT THE ALLELES UNDER CONSIDERATIONS

5. Linkage and lack or random mating Small population sizes
Geneticists and breeders use procedures that cause deviation from HW equilibrium
Linkage and lack or random mating
Small population sizes
Assortative mating
Selection
Inbreeding
INBREEDING and SMALL POPULATION SIZES affects all loci in the population
SELECTION affect only certain loci

6. Frequency of Heterozygous at HW
The HW principle has important implications for the frequency of heterozygous carrying rare alleles 1
A2A2
A1A1
Genotype
Freq.
A1A2
0.5
0.5
0.5 1
p = Freq. allele A1

7. When p=(1- p)=0.5 maximum Freq. of A1A2 in F2 Pop. When p>0.667 
When p or (1-p) are rare (low frequency) there will be in the heterozygous 1
A2A2
A1A1
Genotype
Freq.
A1A2
0.5
0.5
0.5 1
= Freq. A1

8. HW for more than one locus
Two populations with two alleles at two loci. Equal number of individuals from both populations are mixed and mate at random
A1A1B1B1 x A2A2B2B2
A1A2B1B2
From 9 possible genotypes, in the first generation, there will be three types of genotypes
A1A1B1B1, A1A2B1B2 , A2A2B2B2
whereas all the other 6 possible genotype classes are ‘missings’

9. 9 possible genotypes
A1A1B1B1 A1A1B1B2 A1A1B2B2 A1A2B1B1 A1A2B1B2 A1A2B2B2 A2A2B1B1 A2A2B1B2 A2A2B2B2

10. More than 1 generation of random mating
The missing genotypes would appear in subsequent generations.
If the two loci are linked then HW equilibrium will take longer because the appearance of the missing genotypes depends on the RECOMBINATION between the two loci.
Disequilibrium with respect to two or more loci is called LINKAGE DISEQUILIBRIUM this is regardless of whether the loci are linked or not

11. LINKAGE DISEQUILIBRIUM
When alleles at locus A are in random association with alleles in locus B?
LINKAGE EQUILIBRIUM
A1B pA1pB1
A1B pA1pB2
A2B pA2pB1
A2B pA2pB2
When alleles at locus A are NOT in random association with alleles in locus B?
LINKAGE DISEQUILIBRIUM
D=[Observed frequency of gamete A1B1 ]–[pA1pB1]
D=pA1B1 –[pA1pB1]

12. Linkage Causes of linkage
Random association of alleles of different loci  linkage equilibrium D=0
Non Random association of alleles of different loci  linkage disequilibrium D≠0
For unlinked loci D decreases by ½ in each generation meiosis
For linked loci D decreases by c (recombination frequency) in each generation meiosis
Causes of linkage
 loci in the same chromosome
 Admixture of populations with different allele frequencies
Natural selection differentially favoring some genotypes

13. Decay of LD in a population (in LD) mating at random
In this case the amount of disequilibrium is progressively reduced with successive generation of random mating.
The rate at which LD reduces depends on the frequency of gametic types in two successive generations.
Assume two loci are linked in the same chromosome.
The Disequilibrium D in the progeny can be obtained from the frequency of the four gametic types

14. The Haldane (1919) function
The Haldane function establishes that the recombination (c) frequency between a QTL and its closest marker can be expressed as
where x is the map distance in centiMorgans
between the QTL and its closest marker

15. The Haldane (1919) function
From the Haldane function we get
This equation relates the recombination frequency (c) with the map distance (x) in centiMorgan
This indicates that if c=1/2 the value of x is undefined
For this reason a QTL not linked to a marker must have a c close to 1/2