Download Populations Student Notes Part 2

11-12-14
Populations
Mr. Korotash - MCHS
Hardy-Weinberg Principle and
Population Equilibrium
! Gene Pool: All of the genes that occur
in a given population
!   How
!
do we quantify a gene pool?
  How do we measure changes in a gene
pool over time (I.e. can we measure
evolution?)
!   Changes in gene pools are quantified by
measuring allele frequencies.
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!   Consider the following population of
moths for which there are 2 alleles:
!  A
!
= dark brown wings (dominant)
  a = white wings (recessive)
!
Phenotypes:
!
Genotypes:
AA
Aa
aa
# of Moths:
320
160
20
!
(total 500)
!
Genotype
Frequency:
!
# of A alleles: 320x2 = 640
# of a alleles: 320x0 = 0
!
! 
! 
320
500 = 0.64
160
500 = 0.32
160x1 = 160
160x1 = 160
A allele frequency = 800/1000 = 0.8
a allele frequency = 200/1000 = 0.2
20_
500 = 0.04
20x0 = 0 = 800
20x2 = 40 = 200
1000
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Hardy-Weinberg Principle
!   These patterns intrigued Reginald Punnett so
in 1908, he consulted with his friend and
colleague Godfrey Hardy, an eminent
mathematician, who wrote a solution without
hesitation on the nearest napkin…
!   German physician Wilhelm Weinberg
formulated the same solution independently
Hardy-Weinberg Principle
!   The Hardy-Weinberg Principle is a mathematical
relationship that shows that allele frequencies will not
change from generation to generation, as long as
certain conditions are met:
! 
The population is infinitely large (no genetic drift)
No migration occurs (no gene flow)
No mutations occur
No natural selection occurs
! 
Mating is random
! 
! 
! 
!   Useful for modeling a population at a given
moment in time
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Hardy-Weinberg Principle
!   For a gene with only two alleles (A and
a), the Hardy-Weinberg Principle can be
expressed using the following equation:
! 
If p = frequency of allele A and;
q = frequency of allele a then:
! 
! 
p+q=1
(p+q)2 = 12 and so…
p2 = frequency of genotype AA
2pq = frequency of gen. Aa
p2 + 2pq + q2 = 1
q2 = frequency of genotype aa
!
Phenotypes:
!
Genotypes:
AA
Aa
aa
# of Moths:
320
160
20
!
(total 500)
p2
!
Genotype
Frequency:
!
# of A alleles: 320x2 = 640
# of a alleles: 320x0 = 0
!
! 
! 
320
500 = 0.64
2pq
160
500 = 0.32
160x1 = 160
160x1 = 160
A allele frequency = 800/1000 = 0.8
a allele frequency = 200/1000 = 0.2
p
20_
500 = 0.04
q2
20x0 = 0 = 800
20x2 = 40 = 200
1000
q
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Hardy-Weinberg Principle
!   Example:
! 
A population has only two alleles, R and r, for a particular gene.
The allele frequency of R is 20%. What are the frequencies of RR,
Rr, and rr in the population? (Assume the population meets the
criteria for HW equilibrium)
! 
! 
! 
! 
! 
p = frequency of dominant allele R = 0.20
q = frequency of recessive allele r = 0.80
p2 = frequency of homozygous dominant (RR) = (0.2)2 = 0.04
2pq = frequency of heterozygous (Rr) = 2(0.2)(0.8) = 0.32
q2 = frequency of homozygous recessive (rr) = (0.8)2 = 0.64
Hardy-Weinberg Principle
!   Example:
!   A large population consists of 400 individuals, of
which 289 are homozygous dominant (MM), 102
are heterozygous (Mm), and 9 are homozygous
recessive (mm). Determine the allele frequencies
of M and m.
!   The gene pool of a certain population of fruit flies
contains only two eye-colour alleles: the dominant
red allele, R, and the recessive black allele, r.
Only 1% of the population has red eyes.
Determine the allele and genotype frequencies of
this population.
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How do Gene Pools Change?
Genetic Drift
(when population is small)
!   A certain allele
might get lost
from the
population due
to low
reproduction.
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Gene Flow
(when there is migration)
!   When individuals migrate brining their
alleles to another population.
Mutations
(as opposed to H-W no mutation rule)
!   If you don t know what a mutation is
by now, you re in trouble… study lots
before your final!
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Natural Selection
(As opposed to no Natural
selection in H-W rule)
!   Natural selection increases alleles that
are advantageous and vice versa.
Non-Random Mating
(As opposed to H-W
rule of random mating)
!   Random mating
theoretically preserves
gene pool…
!   Non-random
mating like
self-pollination or
choosing mates for
certain characteristics,
favors certain alleles.
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Founders Effect
!   When few individuals of a population
colonize a new area thereby only
bringing some of the alleles.
Bottleneck Effect
!   Bottleneck effect is
when pop. Is
reduced rapidly usually when a
species is driven
to extinction
!   Often followed by
genetic drift
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