Genetic Terms

1
Genetic Terms

• Gene - a unit of inheritance that usually is
  directly responsible for one trait or character.
• Allele - an alternate form of a gene. Usually
  there are two alleles for every gene, sometimes
  as many a three or four.
• Homozygous - when the two alleles are the same.
• Heterozygous - when the two alleles are
  different, in such cases the dominant allele is
  expressed.

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Genetic Terms

• Dominant - a term applied to the trait (allele)
  that is expressed irregardless of the second
  allele.
• Recessive - a term applied to a trait that is
  only expressed when the second allele is the same
  (e.g. short plants are homozygous for the
  recessive allele).
• Phenotype - the physical expression of the
  allelic composition for the trait under study.
• Genotype - the allelic composition of an
  organism.
• Punnett squares - probability diagram
  illustrating the possible offspring of a mating.

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Genetic Code
4
Example of Pedigree
5
Two alleles model

• Let us assume a gene containing two mutually
  exclusive allelesA1,A2.
• There are three possible combinationsA1/A1,A1/A2
  and A2/A2, with initial frequencies u,v and w.
• uvw1
• Let us compute their density after one division

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First generation
frequency Offsprings Mating type
2uv 0.5A1/A1 0.5A1/A2 A1/A1xA1/A2
2uw A1/A2 A1/A1xA2/A2
U2 A1/A1 A1/A1xA1/A1
V2 0.25A1/A10.5A1/A2 0.25A2/A2 A1/A2xA1/A2
2vw 0.5A1/A20.5A2/A2 A1/A2xA2/A2
w2 A2/A2 A2/A2xA2/A2
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In the next generation

• Hardy-Weinberg Equilibrium
• A1/A1u2uw0.25v2(u0.5v)2p12
• A2/A1uv2uw0.5v2vw2(u0.5v)(w0.5v)2p1p2
• A2/A20.25v2vww2(w0.5v)2p22

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Third generation
frequency Offsprings Mating type
2p13p2 0.5A1/A1 0.5A1/A2 A1/A1xA1/A2
p12p22 A1/A2 A1/A1xA2/A2
p14 A1/A1 A1/A1xA1/A1
4p12p22 0.25A1/A10.5A1/A2 0.25A2/A2 A1/A2xA1/A2
2p1p23 0.5A1/A20.5A2/A2 A1/A2xA2/A2
p24 A2/A2 A2/A2xA2/A2
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X linked loci

• If an allele is present in the X chromosome, the
  situation is more complicated.
• If qn is the allele frequency in women in the
  generation n, and rn the allele frequency in
  mens.
• Rnqn-1
• Qn0.5qn-10.5rn-1
• 2/3qn1/3rn2/3(0.5qn-10.5rn-1)1/3qn-1
• 2/3qn-11/3rn-1p
• Qn-p-0.5(qn-1-p)

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Dynamics to equilibrium
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When the Hardy-Weinberg Law Fails to Apply

• To see what forces lead to evolutionary change,
  we must examine the circumstances in which the
  Hardy-Weinberg law may fail to apply. There are
  five
• mutation
• gene migration
• genetic drift
• nonrandom mating
• natural selection

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Mutation

• The frequency of gene B and its allele b will not
  remain in Hardy-Weinberg equilibrium if the rate
  of mutation of B -gt b (or vice versa) changes.
• By itself, mutation probably plays only a minor
  role in evolution the rates are simply too low.
  But evolution absolutely depends on mutations
  because this is the only way that new alleles are
  created. After being shuffled in various
  combinations with the rest of the gene pool,
  these provide the raw material on which natural
  selection can act.

13
Gene Migration

• Many species are made up of local populations
  whose members tend to breed within the group.
  Each local population can develop a gene pool
  distinct from that of other local populations.
• However, members of one population may breed with
  occasional immigrants from an adjacent population
  of the same species. This can introduce new genes
  or alter existing gene frequencies in the
  residents. In many plants and some animals, gene
  migration can occur not only between
  subpopulations of the same species but also
  between different (but still related) species.
  This is called hybridization. If the hybrids
  later breed with one of the parental types, new
  genes are passed into the gene pool of that
  parent population. This process, is called
  introgression.

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Genetic Drift

• As we have seen, interbreeding often is limited
  to the members of local populations. If the
  population is small, hardy-Weinberg may be
  violated. Chance alone may eliminate certain
  members out of proportion to their numbers in the
  population. In such cases, the frequency of an
  allele may begin to drift toward higher or lower
  values. Ultimately, the allele may represent 100
  of the gene pool or, just as likely, disappear
  from it. Drift produces evolutionary change, but
  there is no guarantee that the new population
  will be more fit than the original one. Evolution
  by drift is aimless, not adaptive.

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Rate of Genetic Drift
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Nonrandom Mating

• One of the cornerstones of the Hardy-Weinberg
  equilibrium is that mating in the population must
  be random. If individuals (usually females) are
  choosy in their selection of mates the gene
  frequencies may become altered. Darwin called
  this sexual selection.
• Assortative mating -Humans seldom mate at random
  preferring phenotypes like themselves (e.g.,
  size, age, ethnicity). This is called assortative
  mating.

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Natural Selection

• If individuals having certain genes are better
  able to produce mature offspring than those
  without them, the frequency of those genes will
  increase. This is simple expressing Darwin's
  natural selection in terms of alterations in the
  gene pool. (Darwin knew nothing of genes.)
  Natural selection results from
• differential mortality and/or
• differential fecundity.

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Mortality Selection

• Certain genotypes are less successful than others
  in surviving through to the end of their
  reproductive period.
• The evolutionary impact of mortality selection
  can be felt anytime from the formation of a new
  zygote to the end (if there is one) of the
  organism's period of fertility. Mortality
  selection is simply another way of describing
  Darwin's criteria of fitness survival.

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Fecundity Selection

• Certain phenotypes (thus genotypes) may make a
  disproportionate contribution to the gene pool of
  the next generation by producing a
  disproportionate number of young. Such fecundity
  selection is another way of describing another
  criterion of fitness described by Darwin family
  size. In each of these examples of natural
  selection certain phenotypes are better able than
  others to contribute their genes to the next
  generation. Thus, by Darwin's standards, they are
  more fit. The outcome is a gradual change in the
  gene frequencies in that population.

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Effect of Natural Selection on Gene Frequencies.

• Let us define the frequency of each genotype in
  the population as w, and the initial allele
  distribution as p and q for A1 and A2.
• wA1/A11-r
• wA1/A21
• wA2/A21-s

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Fitness

• The average fitness is
• W(1-r)p22pq(1-s)q21-rp2-sq2
• DP((1-r)p2pq/W)-ppqs-(rs)p/W

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Hetrozygote Advantage

• Pn1-(s/(rs))(1-r)pn2pnq/W -(s/(rs))
• (1-r)pn2pnq-(s/(rs))W/W
• (1-r)pn2pnq-(s/(rs)) (1-rpn2-sqn2)/W
• (1-rpn-sqn)/Wpn-(s/(rs)
• The difference decreases to zero only for
  positive r and s. Thus the scenario in which both
  alleles can survive is Hetrozygote Advantage

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Recessive diseases

• If rgt0, and s0, the disadvantage appears only
  homozygotic A1.
• In this case pn1pn(1-rpn)/(1-rpn2)
• 1/pn1-1/pn1/pn(1-rpn2)/(1-rpn)-1
• r(1-pn2)/(1-rpn)
• 1/pn-1/p0nr

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Fitness Summary

• Third fix point is in the range 0,1 only if r
  and s have the same sign.
• It is stable only of both r and s are positive
• In all other cases one allele is extinct.
• If rgt0 and s0 then the steady state is still
  p0, but is is obtained with a rate
  pn1/(nr1/p0)

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Balance between Mutation and selection.

• Mutations can provide a balancing force to
  selection.
• Let us assume a mutation rate of m from A2 to A1.
  The dynamics equation is
• DP(1-r)p2pq/W-p(1-m)q
• An equilibrium is obtained when
• qpq(1-s)q2/W(1-m)?1m(1-s)/s

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Summary

• In the absence of selection an allele
  concentration equilibrium is obtained after one
  generation.
• In the presence of selection, usually a single
  allele survives.
• There are many mechanisms which can lead to the
  failure of the hardy weinberg equilibrium.