Transcript E-Halliburton chapter 4

BI 3010 H08
Population Genetics
Halliburton Chapter 4-5
Recombinations:
Any process which creates new combinations (genotypes) of existing alleles in the
offspring from sexual reproductions. Recombinations come from crossing overs during
meiosis pro-phase 1. Unlike for mutations, no new genetic material is formed; instead
there is a "re-use" of existing variant genes. Nonetheless, the offspring can possess
new phenotypic traits that were not present in any of the parents.
Linkage:
Two loci are linked if they are localized sufficiently near each other on the
same chromsome, so that the recombination frequency is < 50%. Linked
loci thus tend to be inherited together (i.e. in the same gamete).
D = gametic (linkage) disequilibrium:
For example HW-equilibrium at each of two loci, but non-random distribution of locus-1
genotypes among locus-2 genotypes. This can be brought about by any of the four
evolutionary forces. If the responsible evolutionary force is relaxed, D will be reduced
by time (generations). For a recombination frequency of 0.5, D approaches zero after
7-8 generations. Dt = (1-r)tD0
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Genetic identification:
In forensics it can be crucial to be able to link a perpetrator to the crime scene.
Traditionally, fingerprinting has been the method of choise. However, molecular
genetic techniques (blood types, isozymes, DNA) have been increasingly used in
the last decades ("Jeffrey's probes" for minisatellites").
The basis for these methods is the knowledge of the frequencies of different alleles
in the population, an assumption that the loci used are not linked, and that the loci
have many alleles (and thus many possible genotypes). In order to increase the
statistical power of the conclusions, many polymorphic loci must be used. A multilocus genotype (a "genetic profile") is established, which frequency in the reference
population is the product of the frequencies of each single locus genotype.
If each single locus genotype is rare due to the presence of many alleles at that locus,
a multilocus profile can easily be extremely rare. In forensics genetics, so many loci
are used that the probability of a "match" in the reference group by pure chance
becomes extremely low, even in mankind as a whole.
The development of DNA techniques has offered an enormous pool of allele-rich
microsatellite loci for use in forensic laboratories. Tests of fatherhood are based on the
same principles and techniques, and are equally extremely reliable.
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Important distributions:
Binomial distribition
Normal distribution
Chi-squared distribution
F-distribution
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The binomial distribution
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The binomial distribution
describes the distribution of outcomes from n independent trials where each trial has
two possible outcomes.
Let the probability of one outcome (success) be p, and for the other (failure) 1-p.
Further, let X be a random variable which denotes the number of successes in n trials.
Hence, X can take the values 1,2,3,...n. The binomial distribution describes the
probability (Pr) for each of the possible outcomes (i.e. number of successes in n trials).
If x symbols one specific outcome for X, then
Pr(X=x) = [ n! / (x!(n-x)! ] [ px(1-p)n-x ]
(remember: 0! =1, and 10 = 1)
Example: The probability of obtaining a "1" when throwing a dice once is 1/6. The
probability to get exactly two "1"s (x=2) in five trials (n=5) is then:
Pr(X=2) = [5! / 2!3!] [ (1/6)2 (5/6)3] = 0.16
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Halliburton Chapter 4-5
Standard normal distribution
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Standard normal distribution cont'd
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2 (Chi-squared)
distribution
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F-distribution
(Anova)
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Halliburton Chapter 4-5
SELECTION
• the fitness concept
• basic selection models
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Natural selection I
Basic models
Evolution can be caused by several of the 4 evolutionary forces, either single or in concert.
Selection is only one of them. Natural selection works on phenotypes. For selection to be an
evolutionary force (cf Darwins' theory), three prerequisites must be fulfilled:
1. There must be phenotypic variation between the individuals in a population
2. The variation must result in individual fitness differences (survival, reproduction success)
3. The variation must, at least partly, be heritable (i.e. have a genetic basis)
In population genetics, the term relative fitness denotes indidual genotypic performance relative
to other genotypes on the same polymorphic locus (or for the same polymorphic loci for multilocus traits). An example of how to calculate relative fitness for 2 traits can be found in Table 5.1
on page 131 in Halliburton.
Fitness coefficient (w): The relative fitness of a genotype compared to the fitness of the best
genotype is denoted by w, which value is fraction between 0 and 1.
Selection coefficient (s): Defined as [ 1 – w ]. E.g.; if w=0.8, then s = 0.2.
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The fitness concept
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The efficiency of selection, measured as the change in allele frequency per generation, depends not only
on the size of the selection coefficients, but also on the allele frequency itself (the change per genaration is
largest for allele frequencies around 0.5). This can be seen from the formula for the average fitness for the
population for a single locus trait, where the allele frequencies are incorporated as follows:
Wmean = p2 WFF + 2pqWFS + q2 WSS
From this formula we can (under some heroic assumptions) derive the "mean fitness" for each allele as:
WF-mean = pWFF + qWFS, and WS-mean = pWFS + qWSS
After some algebra the above formulas can be combined to give p; the change in allele frequency per
generation due to selection:
p = pq [WF-mean – WS-mean] / Wmean
which states that the speed of change in allele frequency per generation is proportional to the frequency (pq)
of heterozygotes, which in turn is largest at allele frequencies around 0.5. At extreme allele frequencies
(approaching 0 or 1), the change per generation will be small.
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Fitness & Selection
Calculation of fitness - and selection coefficients for survival
Before selection
After selection
Survival
Relative survival
Fitness coefficient (w)
Seleksjonskoeffisient (s=1-w)
FF
250
180
180 / 250=0.72
0.72 / 0.80=0.9
0.9
1.0 - 0.9 = 0.1
SF
500
400
400 / 500=0.80
0.80 / 0.80=1.0
1
1.0 - 1.0 = 0.0
SS
250
120
120 / 250=0.48
0.48 / 0.80=0.6
0.6
1.0 - 0.6 = 0.4
N
1000
700
The table shows a case of selection of type ”balanced polymorphism”
(stabilizing selection, overdominans), i.e. the heterozygote has the highest
relative fitness.
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Is the fitness of natural populations increasing?
Populations adapt genetically to their environments, i.e. the allele frequencies
change by time. The change in allele frequency (Δp) is related to the relative
fitness value of alleles and the mean relative fitness coefficient of the
population):
See also formulae
on slides 14 and 17
Directional selection will allway increase the mean fitness of a population. With
over- and underdominance the frequency of the favoured allele will change in a
direction that increases the mean fitness.
However, natural selection forces are probably not constant over time, life
stages and seasons, and even not between sexes. It has been suggested that
many of the polymorphisms that can be seen today are maintained by shifting
selection regimes. There is also reason to emphasize the difference between
absolute and relative fitness. The relative fitness of a certain genotype may
increase evem if the absolute fitness of the population as a whole decreases
(e.g. due to poorer life conditions).
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Fitness can have many components, e.g.:
• Viability (survival, longeivity)
• Fecundity
• Mating ability (competetiveness)
• Reproduction success (offspring number)
• Gamete competition
Selection changes the genotypic composition and the allele frequencies within and
between generations. The magnitude of the changes depends on the relative
fitness of the genotypes. The change in the allele frequency (p) per generation
given on slide 14 can also be written as:
 p = pt+1 - p = [ (p2w11 + pqw12) / (mean W) ] - p
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The 3 main types of selection
1. Directional selection (heterozygote fitness intermedate between homozygotes)
2. Balanced polymorphism (heterozygot superiority, overdominance)
3. Disruptive selection (heterozygote inferiority; its w is lower than both homozyg.)
Directional selection and disruptive selection will, after some time, lead to fixation of
one allele and loss of the others, i.e reduction of genetic variability.
Artificial selection (breeding) for productivity or exteriour traits works through selecting
individuals with the preferred traits to be parents for the next generation. The traits are
usually quantitative, like growth, age at maturity, disease resistence. Efficient breeding
regimes will effectively change allele frequencies by directional selection. Again, this leads
to loss of genetic variability.
Natural selection for single-locus characters is excellently demonstrated by the so-called
"industrial melanism" in the peppered moth (Biston betularia) in England, and the so-called
sickle cell anemia in man (se Halliburton chap. 5.3 and 5.4). While the selection type in
the moth resembles directional (or frequency-dependent), the sickle-cell anemia in Homo
sapiens in regions with malaria is a classical example of a balanced polymorphism.
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The 3 types of selection are easily
simulated with the distributed
sofware PopG.exe and P14.exe)
• Directional selection (homozygote superiority or
inferiority)
• Balanced selection (heterozygote superiority,
balanced polymorphism, like the human sickle
cell (HbS) disease and malaria; see figure ----------->)
• Disruptive selection (heterozygote inferiority)
Human HbS; an example of a balanced
polymorphism.
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Halliburton Chapter 4-5
"Industrial melanism"
During the period when the number of coal-burning factories in England was increasing (during the so-called Industrial
Revolution) it was noticed that the number of melanic individuals of the species of Peppered Moth (Biston betularia) was
becoming more common. Originally rare in the population of normally light-colored moths, the frequency of the melanic form
increased in polluted areas until it was over 90%. This change in color has come to be known as "industrial melanism."
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Formulae for fitnesses and
equilibrium allele frequency
values are often more simple
if we use allelic fitnesses
rather than genotypic
fitnesses, as shown in the
box on the left.
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Sewall Wright’s shifting balance theory and adaptive landscapes:
Sewald Wright formulated in 1932 the theory on "adaptive landscapes" of peaks
and valleys, where the peaks represented points of maximal fitness. As evolution
and selection always works to increase fitness, a population can be ”trapped” on
a local peak (i.e. trapped at a certain allele frequency and genotypic composition).
To escape such a peak and continue the fitness increas, natural selection would
have to relax its strive towards increasing fitness, and allow the population to cross
valleys lower fitness. However this will not happen, so the populations may never
reach a global fitness maximum (see Halliburton Chapter 5.9 and 5.10).
Ronald Fisher's fundamentale teorem om naturlig seleksjon:
The rate of increase in a population’s fitness is proportional to the population’s
variance for fitness.
Components of fitness:
Many components works together to shape an individual fitness; the fertility
Of mother and father, fecundity of mother, survival, age at sexual maturation,
mating ability of parents, number of offspring etc.
A model for calculating of fitness coefficients can be very simple if focusing on only
one fitness component, e.g. survival until reproduction (next slide).
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Population Genetics
Halliburton Chapter 4-5
Eugenics ("racial hygienics")
Between World War I and II, eugenics had considerable support (much more than we
like to acknowledge) in Europe as well as in the USA. The background was in part the
discovery that many human diseases (e.g. the bleeder disease) were heritable and
surface under certain circumstances. The frequencies of deleterious recessive alleles are
usually low, but increased homozygosity can arise from mating of close relatives.
Actually, it is now known that each human is heterozygous for in average 8 alleles which
can be lethal in double dose, or cause certain physical or mental diseases.
From here, the idea that such diseases could be controlled by preventing certain individuals
from reproducing, evolved into a more general eugenic thinking including races in humans.
Many researchers made themselves spokesmen for the eradication of bad alleles through
strict human breeding programs. Adolf Hitler incorporated this in his nazi ideology.
However, these ideas were not based on sound population genetics theory. It is a fact that
the harmful alleles ”hide” in heterozygotes which can be without symptoms. It can easily
be shown that the eradication of harmful alleles in a population is a hopelessly ineffective
exercise, since the frequency of heterozygotes is so much larger than the frequency of
the double recessive ("visible") homozygotes.
The course of a eradication process can easily be simulated with the computer program
PopG.exe (uploaded to It’s learning), setting the fitness of one of the homozygotes to
zero and the population size to e.g. 10000 (cf next slide).
Eugenics has lost most of its former momentum in our days (see chapter 5.5 and 5.6).
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Two simulations of an eugenics program
(PopG.exe screenshots):
Population Genetics
Halliburton Chapter 4-5
Even after 10 generations ( ~300 years), there's a fairly high frequency of the bad allele (and heterozygotes)
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Last slide
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