Download THE BASIC SELECTION MODEL ASSIGNMENT 1

THE BASIC SELECTION MODEL
ASSIGNMENT 1
The aim of this assignment set is to familiarize with natural selection as a concept in
population genetics. Selection = fitness differences of genotypes and/or alleles.
Recap the Hardy-Weinberg concept (pages 12-16).
One of the messages in HWE is that gene and genotype frequencies do not change
from one generation to another – if the assumptions are valid. Stochastics (genetic drift)
has a role (always), maybe also selection, which means that genes and/or genotypes do
not perform equally (their fitness-values differ). A question of its own is, whether
statistical deviation from HWE is a sensitive or practical measure for detecting such
evolutionary factors (it seldom is). We don´t consider that here. The point is that HWE is
a basic model, and based on this model, classical population genetics includes some
other basic models.
In practice (data analysis) the basic selection models have very little value. However, it
is good to know about them. Of special importance is the concept balancing selection
which maintains polymorphism. The amounts of polymorphisms are enormous and their
maintenance is enigmatic. The bulk of variation is neutral, but how much, and which
parts of them are maintained by selection.
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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THE BASIC SELECTION MODEL
Population growth, two haploid genotypes (like bacteria, or gametes of a diploid
individual), N individuals, is the finite rate of increase
Genotype A grows 3% per generation
= 1.03) and genotype B grows 1%
per generation ( = 1.01).
(a) Individuals of both genotypes
increase in number over time.
(b) Because the genotypes grow at
different rates, their relative
proportions in the total population
change over time. The solid line
shows the initial equal roportions.
Eventually, genotype A will
approach 100% and genotype B
0%.Genotype A is fixed and B
is lost and A-B polymorphism is
lost.
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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THE BASIC SELECTION MODEL
Haploid selection.
The top section of the
table gives expressions
for the general case.
The bottom part of the
table uses absolute and
relative fitness values
to show the change in
genotype proportions
for the first generation
of natural selection.
The absolute fitness of
the A genotype is
highest and is therefore
used as the standard of
comparison for relative
fitness.
The relative fitness can be used to determine the change in frequency of a genotype over
time p = pt+1 pt. In the haploid example, with relative fitnesses wA and wB,
p = ptwA / (ptwA + ptwB) - pt
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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THE BASIC SELECTION MODEL
Assumptions of a general model
• Diploid individuals
• One locus with two alleles
• Obligate sexual reproduction
• Generations do not overlap
• Mating is random
• Mechanism of natural selection is genotype-specific differences in
(fitness) that lead to variable genotype-specific growth rates,
termed viability selection
• Fitness values are constants that do not vary with time, over space,
or in the two sexes
• Infinite population size, so there is no genetic drift (stochastics)
• No population structure
• No gene flow
• No mutation
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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THE BASIC SELECTION MODEL
Expected frequencies of three genotypes in Hardy-Weinberg equilibrium, after natural
selection. The absolute fitness of the AA genotype is used as the standard of comparison
when determining relative fitness.
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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THE BASIC SELECTION MODEL
The general categories of relative fitness values for selection at a diallelic locus.
The selection coefficients (s, hs, t ) represent the decrease in viability of a genotype
compared to the maximum fitness 1 (fitness = 1 – selection coefficient).
wAA
wAa
waa
_______________________
Selection against a recessive phenotype
Selection against a dominant phenotype
General dominance
Heterozygote disadvantage (underdominance)
Heterozygote advantage (overdominance)
1
1–s
1
1
1- s
1
1–s
1 – hs
1–s
1
1- s
1
1- s
1
1–t
Change in allele frequency
p = [ (p2wAA + pq wAa ) / (p2wAA + 2pq wAa+ p2waa )] - p
Equilibrium
p=0
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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ALLELE AND GENOTYPE FREQUENCY CHANGES UNDER SELECTION
Selection against recessive phenotype.
Genotype aa has fitness 0.8. In the bottom
figure five initial allele frequency conditions.
Selection against dominant allele. The
dominant homozygote and heterozygote
have fitness 0.8.
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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ALLELE AND GENOTYPE FREQUENCY CHANGES UNDER SELECTION
General dominance, three cases. In all
cases the equilibrium allele frequency is
fixation or near fixation of allele A.
Heterozygote disadvantage.
Aa has fitness 0.9.
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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ALLELE AND GENOTYPE FREQUENCY CHANGES UNDER SELECTION:
OVERDOMINANCE, BALANCING SELECTION
Overdominance. Heterozygote has
fitness 1, and homozygotes have 0.9.
The classical (simple) selection scheme
which results in polymorphic equilibrium =
polymorphism is maintained in a population.
Frequency dependent selection models
(fitness-values are functions of allele
frequencies, not constants) can be shown to
lead to polymorphism maintenance (a genotype
becomes less fit as becomes more common).
Differing fitness values, temporally or spatially
(environment consists of patches, different
genotypes are fittest in different patches) also
form theoretically valid conditions for
polymorphism maintenance.
Balancing selection (although seldom
proved), is a widely used framework for
explaining polymorphism maintenance.
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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ASSIGNMENT 1
1.a. Derive the equilibrium allele frequency formulae for overdominance (see page 6).
1.b. In November 1949 Linus Pauling (two Nobel prices) published in Science the paper
Sickle cell anemia, a molecular disease. In this paper he (with collaborators) showed
that hemoglobin from patients suffering from sickle cell anemia had a different electrical
charge than that from healtly individuals. This paper was seminal in two ways. First, it
showed that the cause of a disease could be traced to an alteration in the molecular
sturucture of a protein, raising the possibility that many other diseases might also be
explained in this way. Second, as this disease was known to inherited, the paper argued
that genes precisely determine the structure of proteins…. In 1957 it was shown that a
single amino acid difference between normal and sickle cell hemoglobin explained
electrical charge differences and around that time population genetics captured the
polymorphism, (co-existence of normal and sickle-cell alleles) in geographical areas
with malaria, as a stable balanced polymorphism.
Malaria has been among the most conspicuous selection pressures acting on the
human genome. Very recently (Nature 2010 September 23; vol. 467(7314):420-5.)
something interesting was publsihed about evolution of malaria. Explain briefly what.
1.c. Hemoglobin is not the only gene that is, and has been, under the selection
pressure of malaria. Find out some other example(s). Use PubMed. (Practical advise
next page)
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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ASSIGNMENT 1
1.d. Find out (PubMed) other examples of balanced polymorphisms in
humans and explain briefly what kind of arguments are given to support their
maintenance as balanced polymorphisms. Hints: there are very little concrete
evidence (as is with sickle cell anemia). There are, however, good reasons to
vote for balancing selection as maintaining evolutionary factor for HLA, ABO…
Using PubMed for screening papers is more practical within UH than at
home:
By performing PubMed-searches of your choice you get lists of
publications of which you can usually open only the abstract if you
are not at UH and also the full text within UH.
If you are not at UH you can, of course, pick up a reference from
PubMed, log in UH-library, e-journals, get the full text (see the
detailed instructions in Assignment 2)
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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Hardy-Weinberg ”equilibrium”, HWE
(to recap)
Summary of assumptions:
The organism is diploid and reproduces sexually.
Generations are nonoverlapping.
The gene under consideration has two alleles, A and a.
The allele frequencies, p and q, in the population, consisting of the
individuals (genotypes), AA, Aa, aa are identical in males and females.
Mating is random.
Population size is very large (infinite).
Migration is negligible.
Mutation at the gene locus we consider is so rare that can be ignored
(i.e. A mutating to a, or a to A).
Natural selection does not affect the alleles under consideration.
The assumption of infinite population means that random (stochastic) events can be
ignored. Negligible migration means that, if there is another population with different allele
frequencies, change of individuals (=migration) does not disturb the situation and violate
the assumption of a closed system. Natural selection here means that A and a, or AA, Aa,
aa perform equally well in reproduction, there are no fitness differences.
These assumptions summarize the Hardy-Weinberg model.
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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HWE
(to recap)
In Hardy-Weinberg model the relation between the allele frequencies,
p and q (p + q = 1), and the genotype frequencies is given by
AA : p2
Aa : 2pq
aa : q2 ,
The formation of one generation from the previous generation as an outcome of
repeated and independent trials (assuming random mating the choices of male gamete
and female gamete are independent trials):
pairs of gametes (carrying the alleles A and a), AA, Aa and aa, are
expected in proportions given by
( p + q )2 = p2 + 2pq + q2
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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HWE
(to recap)
Frequency of zygotes (progeny)
Mating
Frequency
of mating
AA
Aa
aa
AA x AA
P2
1
0
0
AA x Aa
2PQ
½
½
0
AA x aa
2PR
0
1
0
Aa x Aa
Q2
¼
½
¼
Aa x aa
2QR
0
½
½
aa x aa
R2
0
0
1
P´
Q´
R´
Totals
(next gen.)
P´ = P2 + (2PQ)/2 + Q2/4 = (P + Q/2)2 =
p2
Q´ = (2PQ)/2 + 2PR + Q2/2 + (2QR)/2 = 2(P + Q/2)(R + Q/2) = 2pq
R´ = Q2/4 + (2QR)/2 + R2 = (R + Q/2)2 =
q2
So, random mating of genotypes - random union of gametes - HWE.
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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HWE
(to recap)
With two alleles of gene, there are six possible types of matings (the left column in
the table)
When mating is random, the matings take place in proportion to the genotypic
frequencies in the population, and the types of mating pairs are given by successive
terms in the expansion of
(P AA + Q Aa + R aa)2
The proportion of AA x AA matings is P x P = P2 and the proportion of AA x Aa
matings is 2 x P x Q because the mating can be between either an AA female and an
Aa male (P x Q) or Aa female and AA male (Q + P). The frequencies of these and the
other types of matings are given in the second column.
The next generation (zygotes from which progeny follow): Mendel´s law of
segregation is taken into account.
Aa heterozygote produces and equal number of A-bearing and abearing gametes. AA and aa homozygotes produce only A and a
gametes, respectively.
The mating AA x aa produces all Aa zygotes, the mating
AA x Aa produces ½ AA and ½ Aa zygotes, Aa and Aa produces ¼ AA,
½ Aa, ¼ aa, etc.
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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HWE
(to recap)
Why a model with so many restrictive assumptions? Are all these assumptions likely to
be met in actual populations?
HWE is not meant to be an exact description of any actual population, although actual
populations often exhibit genotype frequencies predicted by it.
HWE provides a null model, a prediction based on a simplified or idealized situation
where no biological processes are acting and genotype frequencies are the result of
random combination.
Actual populations can be compared with this null model to test hypotheses about the
evolutionary forces acting on allele and genotype frequencies.
The important point and the original motivation for Hardy and Weinberg was to show
that the process of particulate inheritance itself does not cause any
changes in allele frequencies across generations.
Thus, changes in allele frequency or departures from HWE expected genotype
frequencies must be caused by processes that alter the outcome of basic inheritance.
The basic selection model - ASSIGNMENT 1 / Evol disease genes 2010 / SVarvio
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