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Population GeneticsHalliburton Chapter 4-5

Recombinations:Any process which creates new combinations (genotypes) of existing alleles in theoffspring from sexual reproductions. Recombinations come from crossing overs duringmeiosis pro-phase 1. Unlike for mutations, no new genetic material is formed; insteadthere is a "re-use" of existing variant genes. Nonetheless, the offspring can possessnew 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 fourevolutionary 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 after7-8 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 inthe last decades ("Jeffrey's probes" for minisatellites").

The basis for these methods is the knowledge of the frequencies of different allelesin the population, an assumption that the loci used are not linked, and that the locihave many alleles (and thus many possible genotypes). In order to increase the statistical power of the conclusions, many polymorphic loci must be used. A multi-locus genotype (a "genetic profile") is established, which frequency in the reference which frequency in the reference population is the product of the frequencies of each single locus genotype.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 lociare used that the probability of a "match" in the reference group by pure chancebecomes 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 distributiondescribes the distribution of outcomes from n independent trials where each trial hastwo 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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BI 3010 H08Population Genetics

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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• the fitness concept• basic selection models

SELECTION

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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 anevolutionary force (cf Darwins' theory), three prerequisites must be fulfilled:

1. There must be phenotypic variation between the individuals in a population2. 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 multi-locus 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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FF SF SS NBefore selection 250 500 250 1000After selection 180 400 120 700Survival 180 / 250=0.72 400 / 500=0.80 120 / 250=0.48Relative survival 0.72 / 0.80=0.9 0.80 / 0.80=1.0 0.48 / 0.80=0.6Fitness coefficient (w) 0.9 1 0.6Seleksjonskoeffisient (s=1-w) 1.0 - 0.9 = 0.1 1.0 - 1.0 = 0.0 1.0 - 0.6 = 0.4

Fitness & Selection

Calculation of fitness - and selection coefficients for survival

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 frequencieschange 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):

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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See also formulae on slides 14 and 17

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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 breedingregimes 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-calledsickle cell anemia in man (se Halliburton chap. 5.3 and 5.4). While the selection type inthe moth resembles directional (or frequency-dependent), the sickle-cell anemia in Homosapiens in regions with malaria is a classical example of a balanced polymorphism.

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• 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 balancedpolymorphism.

The 3 types of selection are easily simulated with the distributed sofware PopG.exe and P14.exe)

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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."

"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 evolutionand selection always works to increase fitness, a population can be ”trapped” ona 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 neverreach 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’svariance 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 onlyone fitness component, e.g. survival until reproduction (next slide).

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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 individualsfrom reproducing, evolved into a more general eugenic thinking including races in humans.Many researchers made themselves spokesmen for the eradication of bad alleles throughstrict 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 thatthe 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 ineffectiveexercise, 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 tozero 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):

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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Documents

linked loci

single locus genotype

possible genotypes

polymorphic loci

binomial distributionbi

rich microsatellite

distribution of outcomes

reference population