Population Genetics

How Much Genetic Variation Exists in Natural Populations?• Phenotypic variation - variation between

individuals in their structure– Environmental variation - differences in

phenotype can result from differences in environmental conditions

– Genetic variation - differences between individuals are often a result of differences in the alleles possessed by these individuals

Evidence for Genetic Variation among Populations

• Turesson experiments regarding differences among plant ecotypes: Responses to different environmental conditions or genetic differences?

• Sampled populations of the hare bell, Campanula rotundifolia, from 9 different geographic localities in Europe and grew them in plots in a common garden

• Hypothesis: If differences among plant groups persist in the same environment, then they are likely due to genetic differences among populations

Results

Differences among hare bell ecotypes persisted even when grown in the same environmental conditions

Evidence for Genetic Variation among Populations cont.

• Clausen and his associates took clones of several ecotypes of the flowering plant Potentilla glandulosa and grew them in 3 different experimental gardens: 30 m, 1400 m, and 3000 m

• Observed genetic differences among ecotypes

• Each plant clone responded differently to the 3 environmental garden types

Quantifying Genetic Variation

• At least 3 additional lines of evidence indicated substantial amounts of genetic variation within populations:

– Inbreeding Experiments

– Artificial Selection Experiments

– Molecular Genetics

Allozyme Electrophoresis• Allozymes are genetic variants of proteins coded for by different

alleles at a locus

• Tissue samples for individuals are homogenized in order to release enzymes and other proteins from the cells

• The homogenate supernatant is then placed in a gel and the gel is subjected to an electric current

• Each protein in the gel migrates in a direction and at a rate that depends on the protein’s net electric charge and molecular size

Allozyme Electrophoresis cont.

• After the gel is removed from the electric field it is treated with a chemical solution

enzyme

Substrate --------> product + salt -------> colored spot

- The genotype at the gene locus coding for the enzyme can be inferred for each individual in the sample from the number and positions of the spots observed in the gels

- There is a relationship between quaternary structure of the enzyme and the allozyme phenotype

DNA Fingerprinting

• There are duplicated noncoding regions of the DNA referred to as mini- and microsatellite sequences

• This DNA is similar among closely related organisms; there is a core sequence of nucleotides shared among closely related individuals

• However, each individual also has a rather unique sequence - these are highly variable regions and they experience random mutations through time giving

DNA Fingerprinting

a. DNA is isolated from cells and cleaved at specific sites with an endonucleaseb. The sample containing DNA fragments from each individual is placed in a gel where the fragments are separated by size and chargec. The DNA fragments are then denatured into single-stranded segments and transferred to a nitrocellulose membrane by a Southern blot transferd. The membrane is then washed with a solution containing single-stranded, radioactively labeled probes for the minisatellite DNA. The probe hybridizes with homologous fragments on the filtere. A piece of X-ray film is placed over the membrane and exposed. Each labeled hybrid fragment exposes the film and upon development shows up as a band. The pattern of bands comprises the individuals unique DNA fingerprint

Reporting Population Genetic Variation

• Polymorphism (P) - the proportion of variable loci in a population

• Two limitations: Arbitrary and imprecise

Reporting Population Genetic Variation cont.

• Heterozygosity - the average frequency of heterozygous individuals per locus of a population

• Heterozygosity is a good measure of variation because it estimates the probability that 2 alleles taken at random from the population for a locus are different

Reporting Population Genetic Variation cont.

• Genotype frequency - the proportion of the population that occurs in each genotype

Example

Phenotype Genotype # individuals Genotype frequency

Black BB 50 0.50

Gray Bb 25 0.25

White bb 25 0.25

100 1.00

Reporting Population Genetic Variation cont.

Allele frequency:

= frequency of homozygous individuals + 1/2 the frequency of heterozygotes for the allele

• Example– Frequency of B = 0.50 + 1/2 (0.25) = 0.625– Frequency of b = 0.25 + 1/2 (0.25) = 0.375

1.00

How reliable are estimates of genetic variation based on allozyme electrophoresis?

• Two conditions are required for making good estimates of genetic variation:

– A random sample of all gene loci must be obtained

– All alleles at every locus must be detected

Theoretical Population Genetics• How do we measure rates of change in the genetic composition

of populations?

• To proceed with this question it is important to address another question: How can we predict what allele frequencies will be in the absence of evolutionary change?

• In 1908, the mathematician G. H. HARDY and the geneticist T. WEINBERG, independently published what is now known as the HARDY-WEINBERG PRINCIPLE (LAW).

• It served as a null hypothesis; a mathematical description of the behavior of alleles in a population in the absence of evolution

Hardy-Weinberg Principle

• For a large population of diploid organisms in which mating is random and no evolutionary processes are occurring, allele and genotype frequencies reach a stable equilibrium after one generation and do not change thereafter.

• Assumptions:– The absence of evolutionary processes (e.g., mutation,

migration, drift, selection)

– Random mating - the probability of mating between individuals is independent of their genetic constitution

– Large population size

Step 1: Calculate the allele frequencies in the current generation from the genotype frequencies

Flower color genotype number genotype frequency

Red RR 60 0.60 Red Rr 20 0.20 White rr 20 0.20

100 1.00

Therefore,

frequency of R (or p) allele = 0.60 + 1/2 (0.20) = 0.70

frequency of r (or q) allele = 0.20 + 1/2 (0.20) = 0.30 1.00

Now we have the genotype and allele frequencies for our population in generation 1

Step 2: Calculate the frequencies of genotypes among the progeny of this population after one round of random mating.

• There are 9 possible mating types; each of these mating types produces offspring with a characteristic ratio of genotype frequencies

• To determine the genotype frequencies of the offspring in our population we need 2 pieces of information: the probability of each mating type and the number offspring of each genotype produced by each mating type.

• What are the possible genotypes of the offspring (second generation) in our example population?

Step 2 Short-cut: Because diploid organisms make haploid gametes, we can apply the allele frequency values

• Individuals from our example population can produce two types of gametes: R gametes or r gametes• The frequency of each type of allele in the gametes is the same as the frequency of each type of allele in the parental population. • The frequency of the R allele in our population is 0.7, so the frequency of R gametes is also 0.7. • Similarly, the frequency of the r allele in our population is 0.3, so the frequency of a gametes is also 0.3.

Step 2 cont. • The probability of a R (p) gamete from a male uniting with a R (p) gamete from a female is simply the frequency of R (p) male gametes times the frequency of R (p) female gametes (p x p, or p2) • The probability of a r (q) gamete from a male uniting with a r (q) gamete from a female is simply the frequency of r (q) male gametes times the frequency of r (q) female gametes

(q x q, or q2) • R (p) and r (q) gametes can come together in two ways: 1) a R from a male and a r from a female; 2) r from a male and a R from a female. The probability of a R male gamete uniting with a r female gamete is p x q, and the probability of a r male gamete uniting with a R female gamete is also q x p.

(p x q) + (q x p), or 2pqThe genotype frequencies in the offspring (second generation) is given by the binomial expansion: (p + q)2 = p2 + 2pq + q2 = 1.

Example

• Recall that the frequency of R was 0.7 and that the frequency of r was 0.3. • The genotype frequencies of the offspring are then:

p2 = frequency of RR = (0.7)2 = 0.492pq = frequency of Rr = 2(0.7)(0.3) = 0.42q2 = frequency of aa = (0.3)2 = 0.09

Determining whether populations conform to HW equilibrium

Observed genotype frequencies:

Genotype # individuals frequency MM 114 0.57 MN 76 0.38 NN 10 0.05

Expected values based on HW Equilibrium:

1. Calculate the frequency of M and N

M = 0.57 + 1/2 (0.38) = 0.76N = 0.05 + 1/2 (0.38) = 0.24

2. Calculate the expected genotype frequencies

MM = p2 = (0.76)2 = 0.58MN = 2pq = 2(0.76)(0.24) = 0.36NN = q2 = (0.24)2 = 0.06

Expected values based on HW Equilibrium cont.

3. Expected genotypes (number of individuals)

MM = 0.58 x 200 = 116MN = 0.36 x 200 = 72NN = 0.06 x 200 = 12

4. Perform a Chi-square (2) analysis

2 = (O-E)2

E= (114 - 116)2 + (76 - 72)2 + (10 - 12)2

116 72 12

= 0.034 + 0.222 + 0.333 = 0.589

The Hardy-Weinberg Law for 3 alleles

• The model can be easily expanded to take account of three or more alleles at a single locus. • Assume there are 3 alleles designated as A1, A2, and A3 or p, q, and r respectively• For three alleles, the genotype frequencies in the second generation can be determined by the multinomial expansion:

(p + q + r)2 = p2 + 2pq + 2pr + q2 + 2qr + r2 = 1.

The Hardy-Weinberg Law for 3 alleles cont.

• Six genotypes are possible with three alleles:

0.2 0.1 0.3 0.1 0.2 0.1A1 A1 A1 A2 A1 A3 A2 A2 A2 A3 A3 A3

p2 2pq 2pr q2 2qr r2

where p is the frequency of A1, q is the frequency of A2, and r is the frequency of A3. • Allele frequencies:

p or A1 = 0.2 + 1/2 (0.1) + 1/2 (0.3) = 0.4q or A2 = 0.1 + 1/2(0.1) + 1/2(0.2) = 0.25r or A3 = 0.1 + 1/2(0.3) + 1/2(0.2) = 0.35

Sex-Linked Genes• In the case of sex linked genes, the homogametic sex carries 2/3 of all genes (on the 2 Xs) in the population; the heterogametic sex carries only 1/3 (on one X)• Assume that there are 2 alleles (A and a or p and q) in a population and that the frequency of A is pf among the females and pm among the males

The frequency of A in the whole population will be

p = 2/3pf + 1/3pm

Similarly, q = 2/3qf + 1/3qm

Sex-Linked Genes cont.• When the allele frequencies at sex linked loci are different between males and females, the population does not reach the equilibrium frequency in a single generation• Rather, the frequency of a given allele among the males in a given generation is the frequency of that allele among females in the previous generation