Transcript Evolution and Genetic Equilibrium

Evolution and
Genetic Equilibrium
and the HardyWeinberg Principle
Another way to look at evolution
• Evolution is not only the development
of new species from older ones, as
most people assume…
http://anthro.palomar.edu/synthetic/synth_2.htm
It is also the minor changes within a
species from generation to generation
over long periods of time that can result
in species.
http://anthro.palomar.edu/synthetic/synth_2.htm
• It is clear that the effects of evolution are
felt by individuals, but it is the population
as a whole that actually evolves.
Causes of Variation in Traits
• Mutation – random changes in genes passed to
offspring
• Recombination – reshuffling of genes in a diploid
organism (occurs during crossing-over in
prophase 1 of meiosis)
• Random pairing of gametes – Each organism
produces a large number of gametes; so the
union of a particular pair of gametes is a matter
of chance
The biological sciences now generally define
evolution as being the sum total of the
genetically inherited changes in the individuals
who are the members of a population's gene
pool. http://anthro.palomar.edu/synthetic/synth_2.htm
All the genes of a population
are referred to the gene pool.
The percentage of any allele
in that pool is the allele
frequency.
If there are no changes in
the allele frequencies, then
there is genetic equilibrium
evolution does not occur.
Calculating allele frequency
• Allele frequency is determined by dividing the
number of a certain allele by the total number of
alleles of all types in the population.
• Allele frequency is determined by dividing the
number of a certain allele by the total number of
alleles of all types in the population.
• Example: There are two alleles A and a in a set of
10 gametes. If 5 gametes carry allele A , we say
the allele frequency of A is 0.5 or 50%.
Modern Biology – Holt, Rhinehart & Winston pg 318
Next: The Dancing Alleles
Phenotypic frequencies
• A phenotypic frequency is equal to the number
of individuals with a particular phenotype
divided by the total number of individuals in the
population.
Examples: Calculated phenotypic frequencies of four-o’
clock flowers. Modern Biology – Holt, Rhinehart & Winston pg 319
4/8 = .5
4/8 = .5
Allele Frequency Calculations:
• Although the four-o’clock flowers differ
phenotypically from generation to generation,
the allele frequencies tend to remain the
same.
• Evolution is simply a change in
frequencies of alleles in the gene
pool of a population.
http://anthro.palomar.edu/synthetic/synth_2.htm
Let us assume that there is a trait that is
determined by the inheritance of a gene with two
alleles “ ” and “ ” http://anthro.palomar.edu/synthetic/synth_2.htm
If the parent generation has 92% B and 8% b
and their offspring have 90% B and 10% b,
evolution has
occurred between
generations.
The entire population’s gene pool
has evolved in the direction of a
higher frequency of the b allele --- it
was not those individuals who
inherited the b allele who evolved.
http://www.brooklyn.cuny.edu/bc/ahp/LAD/C21/C21_GenePool.html
• This definition of evolution was developed
largely as a result of independent work in the
early 20th century by Godfrey Hardy, an English
mathematician, and Wilhelm Weinberg, a
German physician. http://anthro.palomar.edu/synthetic/synth_2.htm
Gene shuffling during sexual reproduction
produces many gene combinations. But a
century ago, researchers realized that meiosis
and fertilization, by themselves, do not change
allele frequencies.
So hypothetically, a population of sexually
reproducing organisms could remain in genetic
equilibrium. “Biology” Miller and Levine (pg 491)
If a population is not evolving, allele
frequencies in its gene pool do not change,
which means that the population is in genetic
equilibrium. “Biology” Miller and Levine (pg 491)
Hardy, Weinberg, and the population geneticists who
followed them, came to understand that evolution will
not occur in a population if seven conditions are met:
1.
2.
3.
4.
5.
6.
mutation is not occurring
natural selection is not occurring
the population is infinitely large
all members of the population breed
all mating is random
everyone produces the same number
of offspring
7. There is no migration in or out of the
population http://anthro.palomar.edu/synthetic/synth_2.htm
• However, since it is highly unlikely that
any of these seven conditions, let alone
all of them, will happen in the real world,
evolution is the inevitable result.
http://anthro.palomar.edu/synthetic/synth_2.htm
Hardy-Weinberg Equilibrium Equation
Hardy & Weinberg developed a simple
equation which was helpful in discovering
the probable genotype frequencies in a
population and help track their changes
from generation to generation.
http://anthro.palomar.edu/synthetic/synth_2.htm
• By the outset of the 20th century, Punnett
squares were used to predict the probability of
offspring genotypes for particular traits based
on genotypes of their two parents when the
traits followed simple Mendelian rules of
dominance and recessiveness.
• The Hardy-Weinberg equation essentially
allowed geneticists to do the same thing for
entire populations.
• In this equation (p² + 2pq + q² = 1), p is
defined as the frequency of the
dominant allele and q as the frequency
of the recessive allele for a trait
controlled by a pair of alleles (A and a).
(and p + q = 1)
Let’s do a sample problem
• Albinism is due to an autosomal recessive allele. The
average human frequency of albinism in North America is
only 1 in 20,000.
• The frequency of homozygous recessive individuals (aa)
in a population is q²
so q² = 1/20,000 = .00005
the square root of .00005 = .007
so q = .007
If p + q = 1 ,
then p = 1 -q
p = 1 - .007
p = .993
• The frequency of the dominant, normal allele
(A) is, therefore, .993 or about 99 in 100.
• The next step is to plug the frequencies of p
and q into the Hardy-Weinberg equation:
p²
+ 2pq
+ q²
=1
(.993)² + 2 (.993)(.007) + (.007)² = 1
.986 + .014
+ .00005 = 1
• This gives us the frequencies for each of the
three genotypes for this trait in the
population:
• With a frequency of .005% (about 1 in 20,000),
albinos are extremely rare. However,
heterozygous carriers for this trait, with a
predicted frequency of 1.4% (about 1 in 72), are
far more common than most people imagine.
• There are roughly 278 times more carriers than
albinos.
• Clearly, though, the vast majority of humans
(98.6%) probably are homozygous dominant and
do not have the albinism allele.
http://anthro.palomar.edu/synthetic/sample.htm