Micro diversity

CHAPTER 6

POPULATION GENETICS



• A population is a localized group of individuals
belonging to the same species.

A species as a group of populations whose
individuals have the potential to interbreed
and produce fertile offspring in nature.

Gene pool is the complete set of genetic
information contained within the individuals
in a population. The gene pool includes all alleles present in the population.
Principal points
• Evolution is a process in which genetic variation
in a population changes over time.

Genetic variation originates when one allele
mutates to another.

Population genetics studies the origin of
variation, the transmission of variants from
parents to offspring generation after generation.
i.e., population genetics is the branch of genetics
that deals with frequencies of alleles and
genotypes in breeding populations.
Genotype frequency in a population is the proportion of organisms that have the particular genotype (eg. RR, Rr or rr ).

Allele frequency is the proportion of all alleles that are of the specified type (eg. R or r ).
Frequencies of Alleles & Genotypes
Suppose, these are diploid organisms:
+ There are only two allelic forms of the gene in the population.
+ There are a total of 1,000 copies of gene for flower color in the population of 500 individuals.
A gene has two alleles (R and r), their frequencies are represented:
p = 0.8 (frequency of R allele)
q = 0.2 (frequency of r allele)
p + q = 0.8 + 0.2 = 1
The frequency of homozygous individuals for dominant
allele (RR) is 320/500 = 0.64 = 64 %; and for recessive
allele (rr) is 0.04 (4%) in the population of 500 individuals.

+ The frequency of heterozygous individuals (Rr) in the
population is 0.32 = 32%.

The frequency of the R allele in the gene pool of this
population is p = 800/1,000 = 0.8 = 80%. And the r allele
must have a frequency of q = 0.2 = 20%.

+ The chance that the gamete will bear an R allele is 80%,
and the chance that the gamete will have an r allele is 20%.
Results of gene pool in parent population:
p + q = 1
p and q are the proportions of the two alleles of a gene in a population
- The relationship between p and q :
Gene pool of next generation
- The probability of picking two R alleles: p2 = 0.8x0.8 = 0.64,
i.e., about 64% of the plants have the genotype RR .

+ The frequency of rr individuals: q2 = 0.2 x 0.2 = 0.04 (4%)

+ And the frequency of heterozygous plants (Rr + rR):
2pq = 2 x 0.8 x 0.2 = 0.32 (32%)

The genotype frequencies add up to 1: 0.64+0.32+0.04=1
This is: (p + q)2 = p2 + 2pq + q2 = 1

The allele frequencies are the same as the allele frequencies
in the parent population. The chance that the gamete will
bear an R allele is 0.8, and the chance that the gamete will
have an r allele is 0.2. This is p + q = 1

The frequencies of alleles and genotypes remain the same between one generation (a) and the next generation (b)
Results of gene pool in next generation:
The Hardy-Weinberg law states that “allele and genotype frequencies in a population remain constant generation after generation if there is no selection, mutation, migration or random drift”

i.e.: the frequencies of three genotypes RR, Rr and rr for a locus with two alleles (R and r) will remain constant at p2, 2pq and q2 where p and q are the frequencies of alleles R and r, respectively.
Such populations are said to be at an equilibrium
Hardy – Weinberg law
Hardy-Weinberg equilibrium since their allele and genotype frequencies are constant or unchanging from one generation to the next
The Hardy-Weinberg allele frequencies:
p2 : frequency of homozygous dominant genotype
2pq : frequency of heterozygous individuals in the population
q2 : frequency of homozygous recessive genotype
p + q = 1
(p and q are the proportions of the two alleles of a gene in a population)

- The Hardy-Weinberg genotype frequencies:
(p + q)2 = p2 + 2pq + q2 = 1
Hardy – Weinberg principles
1. Very large population size; If that size is small, genetic drift, which can cause genotype frequencies to change over time.

2. No migration; If gene flow, the transfer of alleles between populations due to the movement of individuals or gametes, can increase the frequency of any genotype that is in high frequency among the immigrants.

For a population to be in Hardy-Weinberg equilibrium, it must satisfy five main conditions:

3. No net mutations; If mutations can alter the gene pool by changing one allele into another.

4. Random mating; If individuals pick mates with certain genotypes, then the random mixing of gametes required for Hardy-Weinberg equilibrium does not occur.

5. No natural selection; If selection, differential survival and reproductive success of genotypes will alter their frequencies and may cause a detectable deviation from frequencies predicted by the Hardy-Weinberg equation.
Factors affecting gene frequencies
Small population size (Genetic drift)
e.g., the frequencies of the alleles for red (R ) and white (r ) flowers to change over the generations
A change in a population’s allele frequencies due to
chance, is called genetic drift.
This small wildflower population has a stable size of
only ten plants.
+ For generation 1, only the five boxed plants produce
fertile offspring.
+ In generation 2, only two plants manage to leave
fertile offspring.

Small population size can cause allele and genotype frequencies to change over time.
Over the generations, genetic drift can completely
eliminate some alleles, as is the case for the r allele
in generation 3 of this imaginary population.
Migration (Gene flow)
A population may gain or lose alleles by gene flow,
genetic exchange due to the migration of fertile
individuals or gametes between populations.
e.g. A population consists entirely of white-flowered individuals (rr) to grow near our wildflower population.

+ A windstorm may blow pollen from the rr population
to our wildflower population.

+ Result, the allele frequencies may change in
the next generation.
A mutation is a change in an organism’s DNA.

A new mutation that is transmitted in gametes
can immediately change the gene pool of a
population by substituting one allele for another.

Mutation is, very important to evolution because
it is the original source of the genetic variation
that serves as raw material for natural selection.
Mutation
Natural selection
Hardy-Weinberg equilibrium requires that all individuals
in a population be equal in their ability to survive and
produce viable, fertile offspring.
Populations consist of varied individuals, with some
variants leaving more offspring than others, which
Darwin meant by natural selection.
Selection results in alleles being passed along to the
next generation in numbers disproportionate to their
relative frequencies in the present generation.
eg. In wildflower population,

(i) White flowers (rr) are more visible to herbivorous
insects, so that more white flowers are eaten.
Therefore, plants with red flowers (RR or Rr) would
have more opportunity to produce offspring.

(ii) Red flowers may be more effective than white ones
in attracting the pollinators required for seed production.

Result:
- The frequency of the R allele would increase in the gene
pool, and the frequency of the r allele would decline.

This difference would disturb Hardy-Weinberg equilibrium.
Natural selection and
Genetic drift cause
most of the changes in allele frequencies
that we observe in evolving populations.
However, allele frequencies can also be changed by migration between populations or by mutation.
Application of the Hardy-Weinberg law
eg. One out of approximately 10,000 babies in the U.S. is born with Phenyl ketonuria (PKU). The disease is caused by a recessive allele; calculation of frequencies of recessive allele and heterozygous carriers in the population.
Applying the Hardy-Weinberg law, the frequency of individuals
in the U.S. population born with PKU corresponds to q2
(q2 : frequency of the homozygous recessive genotype).

- Given one PKU occurrence per 10,000 births, q2 = 0.0001.
+ The frequency of the recessive allele for PKU in the population is:

q = √0.0001 = 0.01 = 1%
+ The frequency of carriers, heterozygous people who
do not have PKU but may pass the PKU allele on to
offspring, is:

2pq = 2 x 0.99 x 0.01 = 0.0198 (≈ 2%)

+ The frequency of the dominant allele is:

p = 1 - q = 1 - 0.01 = 0.99
And about 2% of the U.S. population carries the
PKU allele.
Thus,
- There are 1% of the recessive allele in the population.
Explain the Hardy-Weinberg law with a suitable examples.
List the main conditions for a population to be in Hardy-Weinberg equilibrium. Explain Why ?
Discuss the effects of small population (genetic drift) and natural selection on gene frequencies.
Seven out of approximately 5,000 babies is born with PKU disease. The disease is caused by a recessive allele.
Calculation of frequencies of recessive allele and heterozygous carriers in the population
Questions and Problems