Download Calculating Allele Frequencies

inFopulat!cns
AEEele
Frequencies
eaEeuNating
particularly
in populations,
as a means
equationprovidesa simplemathematical genotypefrequencies
The Hardy-Weinberg
The
use of the
measuring
their
rate.
gene
pool,
of
studying
changes
and
its
main
genetic
in
a
but
equilibrium
of
model
below.
equationis described
alleleand Hardy-Weinberg
in populationgeneticsis in.calculating
application
Punnettsquare
Aa
Frequencyof allele
co m b in a tio nAA in
th e p o p u la tio nis
representedas p'?
A
a
aA'
'\
Frequencyof allele
co m b in a tio na a in
th e p o p u la tio nis
representedas q'?
Frequencyof alleletypes
Frequencyof allelecombinations
p = Frequency of allele A
q = Frequencyof allele a
p2 = Frequency
dominant)
of AA (homozygous
2pq = Frequency
of Aa (heterozygous)
q2 = Frequency
recessive)
of aa (homozygous
Frequencyof allele combination
Aa in the population(add these
together to get 2pq)
The Hardy-Weinbery equation is applied ta populations with a simple genetic
situation: dominant and recessive alleles controlling a single trait.The frequency
of all of the dominant (A) and recessive alleles (a) equals the total genetic
complement, and adds up to 1 ot 100% of the alleles present.
How To Solve Hardy-Weinberg Problems
Worked example
ln most populations, the frequency of two alleles of interest
is calculated from the proportion of homozygous recessives
(q2 ), as this is the only genotype identifiabledirectly from its
phenotype. If onty the dominant phenotype is known, q2 may
be calculated (1 - the frequency of the dominantphenotype)The following steps outline the procedure for solving a
Hardy-Weinberg problem:
Amang Caucasians in the USA, approximately 70% of
people gan taste the chemical phenylthiocarbamide (PTC)
(the dominant phenotype), while 30% are non-tasters (the
recessivephenotype).
Answers
Determine the frequency of :
(a) Homozygousrecessivephenotype(q2).30% - provided
Remember that all calculations must be carried out using
proportions, NOT PERCENTAGES
!
"l. Examine the question to determine what piece of
you havebeengivenaboutthe population.
In
information
most cases,this is the percentageor frequencyof the
homozygousrecessivephenotypeq2, or the dominant
phenotypep2 + 2pq (see note above).
2. The firstobjectiveis to find out the valueof p or q, lf this
theneveryothervaluein the equationcan be
is achieved,
determinedby simplecalculation.
(b) The dominantallele(p).
45.2%
(c) Homozygoustasters(p2).
2Q.50k
(d) Heterozygoustasters(2pq).
49.5"k
Data: The frequencyof the dominantphenotype(70%tasters)
are provided.
and recessivephenotype(30%non-tasters)
Working:
Recessivephenotype:
q2
3. Takethe square root of q2 to find q.
therefore:
I
qf r om 1 ( i. e. p= 1 - q) .
4 . Dete rmine pbys ubt r ac t ing
therefore:
P
= 30%
use 0-30 for calculation
= 0.5477
^^,,^-^
^1v^.30
Jtl
U Ar
O I-^^+
VVL Wr
= 0.4523
1-q= p
p by itself (i.e.p2= p x p).
5. Determinep2 by multiplying
1 - 0 . 5 4 7 7 =A 4 5 2 3
p timesq times2.
6. Determine2pq by multiplying
Use p and q in the equation(top)to solveany unknown:
7. Checkthat your calculationsare correctby addingup the
valuesfor p2+ q2+ 2pq (thesum shouldequal1 or 100%).
HomozygouS
dominant p2
Heterozygous:
2pq
= 0.2046
(pxp = 0.4523x0.4523)
= 0.4953
A populationof hamstershas a gene consistingof 90% M alleles(black)and
10% m alleles(gray).Matingis random.
Data: Frequencyof recessiveallele(10% m) and dominantallele(90% M).
Recessiveallele:
Dominantallele:
v-
Determinethe proportionof offspringthat will be blackand the proportion
that will be gray (showyour working):
Recessivephenotype:
d2
Y-
Homozygous
dominant:
^2
l-{oiornzrrnnr
2no
rc'
=
2. You are workingwith pea plantsand found36 plantsout of 400 were dwarf.
Data: Frequencyof recessivephenotype(36 out o1469 = 9%)
(a) Calculatethe frequencyof the tall gene:
pea plants:
(b) Determinethe numberof heterozygous
ailete:
Recessive
Y-
allele:
Dominant
Y_
RecessivephenotyPe:
Y_
^2
i
dominant
Homozygous
v^2
ii
i
2pq =
I- .l,v(
6 lv,
a r n v&t
7 \/d n r
tq '
Yvvv,
'
J.
(PTC) is
In humans,the abilityto tastethe chemicalphenylthiocarbamide
Supposeyou foundout that
inheritedas a simpledominantcharacteristic.
360 out of 1000 collegestudentscould not tastethe chemical'
Data: Frequencyof recessivephenotype(360 out of 1000)'
allele:
Recessive
q
Dominantallele:
p
(a) Statethe frequencyof ihe gene for tastingPTC:
Recessivephenotype: q2
:
i.r
. , ,,.
Homozygousdominant:P2
studentsin this population:
(b) Determinethe numberof heterozygous
A
a,
A type of deformityappearsin 4'k of a large herd of cattle.Assumethe
deformitywas causedby a recessivegene.
Data:Frequencyof recessivephenotype(4% deformity).
(a) Calculatethe percentageof the herdthat are carriersof the gene:
Heterozygous:
Recessiveallele:
2pq =
,q
Dominantaliele:
Recessivephenotype: q2
Homozygousdominant:P2
(b) Determinethe frequencyof the dominantgene in this case;
Assumeyou placed50 pure bred blackguineapigs (dominantallele)with
50 albinoguineapigs (recessiveallele)and allowedthe populationto attain
geneticequilibrium(severalgenerationshavepassed).
Data:Frequencyof recessiveallele(50%)and dominantallele(50%)'
Determinethe proportion(%) of the populationthat becomeswhite:
Heterozygous:
zPq =
Recessiveallele:
q
Dominantallele:
p
Recessivephenotype: q2
Homozygousdominant:P2
o.
It is known lhal 64"k of a large populationexhibitthe recessivetrait of a
controlledby two alleles(one is dominantoverthe other).
characteristic
Data: Frequencyof recessivephenotype(64%).Determinethe following:
Heterozygous:
zpq =
(a) The frequencyof the recessiveallele:
(b) The percentagethat are heterozygousfor this trait:
(c) The percentagethat exhibitthe dominanttrait:
(d) The percentagethat are homozygousfor the dominanttrait:
(e) The percentagethat has one or more recessivealleles:
in humans.The frequencyol the albinoallelewas 10% in a population.
7. Albinismis recessiveto normalpigmentation
Data:Frequencyof recessiveallele(10% albinoallele).
=.:
Recessiveallele:
Q
Determinethe proportionof peoplethat you wouldexpectto be albino:
Dominantallele:
Recessivephenotype:
Homozygous
dominant:
l - l o i o r n zr r n n r
r c'
P
'
v^2
=,i
: ....
i : . . -, . ,
Pool
Gene
ofa5quirrel
Analysis
of albino(white)
In Olney,lllinois,there is a uniquepopulation
Between1977 and 1990,studentsat Olney
and gray squirrels.
They
CentralCollegecarriedout a study of this population.
The
albinos
gray
and
albino
squirrels.
of
frequency
recordedthe
only
as an albinophenotype
a mutantalleleexpressed
displayed
The datathey collected
recessivecondition.
in the homozygous
are provided in the table below. Using the Hardy-Weinberg
genotypefrequencies,
it was possible
equationfor calculating
to estimatethe frequencyof the normal'wild'allele(G) providing
of the mutantalbinoallele(g)
graytur coloring,and thefrequency
Thisstudyprovided
whitesquirrelswhenhomozygous.
producing
to
see howgenotype
could
use
real,firsthand,datathatstudents
population.
in
a
real
change
can
frequencies
Thanks io
Dr John
Stencel,
Olney Cental
College, Olney, lllinois, US, for providing ihe data for this exercise
Albinoformof graysquirrel
usualcolorform
Graysquirrel,
Populationof gray and white squirrels in Olney,lllinois(1977-1990)
.gg
Freq. of q
Freq. of G
23.21
48.18
51.82
50.00
25.18
50.1I
49.82
28.47
49.77
21.75
+o.o+
53.36
622
28.90
49.72
21.38
46.24
53.76
699
26.74
49.94
23.32
48.29
Jl./
IOY
31.01
49.35
19.64
44.31
6q AO
141
560
24.82
50.00
25.18
50.18
49.82
378
tu o
484
28.30
49.79
21.90
46.80
53.20
1985
448
tzJ
573
28.40
49.78
21.82
46.71
53.29
1986
536
155
oYl
zI-t
49.86
22.43
47.36
52.64
GG
Gg ,
784
z o.al c
49.93
172
683
24.82
482
134
o to
1980
489
taa
1981
'1982
536
to.t
618
tcl
1983
419
1984
Year
Gray
White
Total
1977
602
182
1978
511
1979
I
|
No data collected thisYear
1987
1988
652
122
774
36.36
47.88
15.76
39.70
60.30
1989
552
146
698
29.45
49.64
20.92
45.74
54.26
1990
603
111
a4
36.69
47.76
15.55
39.43
60,57
A
1. Graph population changes: Use the data in the first 3 columnsof the table aboveto plot a line graph.Thiswill show
Plot:
changesin the phenotypes:numbersof grayand white(albino)squirrels,as well as changesin the total population.
gray, white, and total for eachyear:
800
(a) Determineby how much (as a %) total
populationnumbershavefluctuatedoverthe
samplingperiod:
(b) Describethe overalltrend in total population
numbersand any patternthat may exist:
7oo
s, 600
o
L
L
_^^
ct
at,
= 400
o ^^^
.O UUU
E
z 200
100
f=c oo) oc \c 9$Lr ) ( o\99C J ) 9
co
co
co
Ff.-i\
bbboooooo) o) oo) o) o)
@
co
Year
@
@
A
A
co
o)
Graph genotype changes: Use the data in the genotype columns of the table on the opposite page to plot a line graph.This will
show changes in the allelecombinations(GG, Gg, gg). Plot:GG, Gg, and gg for each year:
Describethe overalltrendin the frequencyof:
(a) Homozygousdominant(GG)genotype:
o)
o
o50
c
o
u,
o40
(b) Heterozygous(Gg) genotype:
o
o
ct
o
o20,
o,
o
(c) Homozygousrecessive(gg) genotype:
o
c,
o
o-
ru
N@O)OC!CDStr)(o|.-@o)O
@
@
f'l'fO)
o)
o)
o)
O)
@
o)
@
O)
@
O)
@
o)
cO
O
@
O)
@
O)
@
O)
o)
O,
Year
pageto ploia linegraph.Thiswillshow
3. Graphallelechanges:Usethe datain the lasttwo columnsof thetableon ihe previous
for eachof the dominani(G) and recessive(g) alleles.
changesin the allelefrequencies
Plot:the frequencyof G and the frequencyof g:
(a) Describethe overalltrend in the frequencyof
the dominantallele(G):
70
() 60
o)
tE
o 50
a
o
(b) Describethe overalltrend in the frequencvof
the recessiveallele(g):
40
cr
o
o
ct)
(E
o
o
o
o-
30
20
10
n
Year
4. (a) Statewhich of the threegraphsbest indicatesthat a significantchangemay be takingplacein the gene poolof this
populationof squirrels:
(b) Give a reasonfor your answer:
5. Describea possiblecauseof the changesin allelefrequenciesoverthe samplingperiod: