Buffl

Definitionen & Stoff

CS
von Carina S.

Wright-Fisher Model


  • used to construct null hypothesis for the change of allele frequencies in populations. These hypothesis are then tested against data

  • Rejection of the simple Writh-Fisher model is then taken as evidence that something more interesting than “just mutation and drift” acts in the population, e.g. selection

  • assumes haploid (or diploid) population without sexes, in which each individual reproduces without the need of finding a mate

  • finite population size

  • discrete generations

  • random transmission to the next generation with equal probability

1) Allele frequencies changed within populations

  • some will not reproduce, some will have multiple offspring -> allele frequencies will fluctuate and eventually one of the two alleles get fixed and the other one lost

  • trace back: all individuals come from common ancestor

2) Variation in allele frequency increased across populations, mean stays the same

  • Genetic diversity within population gets lost

  • the colonies will diverge only very slowly if the population size is large

3) The probability of fixation and the time it takes

  • in absence of mutation, any allele must eventually be lost or fixed

  • the average amount of time it will take for a single allele to fix within a population is given by twice the number of alleles within a population. Hence, in a population of haploid individuals it will take 2N, for diploids 4N generations

4) Genetic drift erodes genetic variation

  • genetic variance within a population decreases

  • drift is mostly potent in small populations, in large populations it erodes genetic variation only very slowly


-> under simplifying assumptions the model could predict the state of a population in the next generation



Wolf - Lecture 3 - Genetic Drift

Role of drift in adaptation: Wright vs. Fisher


  • concept of adaptive landscape: with peaks and valleys

  • Scenario Wright:

    • Adaptation is a multi-step process that follows from the interplay of three basic evolutionary forces: drift, selection, migration.

    • efficient selection cannot be by (mutation and) selection alone. Solution: Shifting balance theory.

    • Evolution to a new adaptive peak is a 3 step process:

      • Drift: Just by chance, one of many medium-sized subpopulations may drift off the historical fitness peak

      • Individual Selection: natural selection then sweeps this subpopulation to some new and higher optimum

      • Migration: migrants from the better adapted subpopulation spread the adaptation to the entire population

  • Scenario Fisher:

    • Adaptation is a simple hill-climbing process that is driven by selection as the allmighty force. This is the classical adaptationist view.

    • Shifting Balance does not work: because it needs a subtle balance of evolutionary forces that is unlikely to be widespread

  • Other solutions to the problem (Fisher?):

    • multiple fitness peaks only exist if there are non-additive gene effects (epistasis)

    • the analogy at the walk on the 2D surface max be misleading: for most traits there are not only 2 loci, but many

    • adaptive landscapes are not rigid objects, but should be thought of as variable as environmental conditions change


  • Most evolutionists today do not believe that shifting balance is necessary (or likely) for adaptation on the trait level, which are influenced by many genes. At this level, selection is thought to be often stronger and interactions among genes less likely to create local peaks.




Wolf - Lecture 7 - Selection

Recombination


  • Recombination frequencies differ between species and sexes, but also differ significantly among chromosomes within species

  • recombination rate tends to be elevated in small chromosomes

  • Recombination also varies along the genome, often with strongly reduced recombination in regions of dense heterochromatin (e.g. around centromere)

  • Recombination is a central parameter for many aspects of evolution

  • Recombination generates phenotypic diversity (e.g. height, not either or but different heights)

  • In case of linkage one has to wait longer, but eventually recombination will unlink loci and introduce novel combinations

  • number of gametes generated by recombination: 2^n gametes from n loci

  • number of genotypes generated by recombination: 2^n-1 (2^n + 1)

  • Recombination speeds up adaptation:

    • with recombination favourable mutations at different loci can be combined

    • if there are two favourable mutations at different loci, they compete and the haplotype with the mutation conferring less of a selective advantage will eventually be lost from the population

    • in a sexual population with recombination, they combine and so both advantageous mutations survive

  • With recombination selection will thus act on the locus, without recombination it will act on the entire haplotype

  • Recombination counters the accumulation of deleterious mutations

    • individuals free of mutation = individuals with fittest genotype -> will eventually be lost by genetic drift and can never be recovered -> decreasing the fitness of the entire population. Unless there is backmutation or recombination recreating mutation-free haplotypes the expectation in the long run is that the population will go extinct



Merill - Lecture 1 - Recombination

Linkage Disequilibrium


  • correspondence or non-random association of alleles at two or more loci / at different loci within a population

  • Loci are said to be in linkage disequilibrium when the frequency of association of their different alleles is higher or lower than what would be expected if the loci were independent and associated randomly

  • depends on multiple factors like local recombination rate, non-random mating, mutation rate, genetic drift, population structure

  • Linkage Disequilibrium ≠ physical linkage (but physical linkage of loci can lead to linkage disequilibrium) -> contrary to linkage due to a physical connection of neighboring loci on the same chromosome, Linkage Disequilibrium can even occur between loci on different chromosomes

    • alleles on different chromosomes can be in LD

  • Quantifying Linkage Disequilibrium

    • Linkage Disequilibrium can be thought of as a deviation from a null model of Linkage Equilibrium (|D|)

    • Linkage Equilibrium assumes: no selection, random mating, free recombination, large populations

    • Linkage Disequilibrium can be thought of as a measure of the excess of coupling (AB/ab) over repulsion (Ab/aB) gametes

    • D = 0: two alleles segregate independently -> they are in linkage equilibrium

    • D > 0: there are more coupling gametes than expected by random assortment

    • D < 0: there are more repulsion gametes than expected

  • Linkage equilibrium => strongest possible linkage disequilibrium

  • LD will break down over time

  • Factors affecting LD:

    • genetic drift

    • bottleneck

    • random mating

    • assortative mating -> increase LD

    • selection

  • Change of LD over time - the effect of recombination

    • c = recombination fraction between 2 loci / describes degree of recombination in the 2 loci / describes the genetic distance between 2 loci on a map / number of recombinations / fraction of recombinant gametes (Ab|aB) produced in heterozygotes (AB|ab)

    • ranges from not recombination (c=0) to a maximum (c=0.5, two loci recombine freely)

    • small c = recombination unlikely -> LD maintained

    • large c = recombination likely -> LD broken down






Merill - Lecture 2 - Linkage Disequilibrium

Hill-Robertson interference




Parsch - Lecture 8 - Genomics 2

  • provides an explanation as to why there may be an evolutionary advantage to genetic recombination.

  • n a population of finite but effective size which is subject to natural selection, varying extents of linkage disequilibria (LD) will occur. These can be caused by genetic drift or by mutation, and they will tend to slow down the process of evolution by natural selection

  • This is most easily seen by considering the case of disequilibria caused by mutation: Consider a population of individuals whose genome has only two genes, a and b. If an advantageous mutant (A) of gene a arises in a given individual, that individual's genes will through natural selection become more frequent in the population over time. However, if a separate advantageous mutant (B) of gene b arises before A has gone to fixation, and happens to arise in an individual who does not carry A, then individuals carrying B and individuals carrying A will be in competition. If recombination is present, then individuals carrying both A and B (of genotype AB) will eventually arise. Provided there are no negative epistatic effects of carrying both, individuals of genotype AB will have a greater selective advantage than aB or Ab individuals, and AB will hence go to fixation. However, if there is no recombination, AB individuals can only occur if the latter mutation (B) happens to occur in an Ab individual. The chance of this happening depends on the frequency of new mutations, and on the size of the population, but is in general unlikely unless A is already fixed, or nearly fixed. Hence one should expect the time between the A mutation arising and the population becoming fixed for AB to be much longer in the absence of recombination. Hence recombination allows evolution to progress faster. There tends to be a correlation between the rate of recombination and the likelihood of the preferred haplotype (in the above example labeled as AB) goes into fixation in a population.


Author

Carina S.

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