One-way migration

1
One-way migration
2
Migration

• There are two populations (x and y), each with a
  different frequency of A alleles (px and py).
• Assume migrants are from population x, and
  residents are population x unidirectional).
• After migration, m is the migrant portion of the
  population y, and (1-m) is the resident portion
  of the population y. py is the p after
  migration
• py m x px (1-m) x py
• dpy m x px (1-m) x py py
• dpy m x px py m x py py
• dpy m x px m x py
• dpy m(px-py)

3
Change in allele frequency with one-way migration
(m 0.01)
4
Natural Selection

• The interaction between alleles and environment
  shapes the direction of the change in allele
  frequencies resulting in evolution of adaptable
  traits.

5
Fitness and coefficient of selection (s)

• Darwinian fitness is defined as the relative
  reproductive ability of a genotype.
• The genotype that produces the most offspring is
  assigned a fitness (W) value of 1. Selection
  coefficient (s) equals (1-W)
• AA produces on average 8 offspring
• Aa produces on average 4 offspring
• aa produces on average 2 offspring.
• WAA 1.0 sAA 1-1 0
• WAa 0.5 sAa 1-0.5 0.5
• Waa 0.25 saa 1-0.25 0.75

6
How to calculate change in allele frequency after
selection
AA Aa aa
Initial genotypic frequencies p2 2pq q2
Fitness WAA WAa Waa
Frequency after selection p2 WAA 2pq WAa q2 Waa
Relative frequency after selection p2 WAA/WMEAN 2pq WAa /WMEAN q2 Waa /WMEAN
Wmean p2 WAA 2pq WAa q2 Waa
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Possibilities

1. WAA WAa Waa no natural selection
2. WAA WAa lt 1.0 and Waa 1.0 natural
   selection and complete dominance operate against
   a dominant allele.
3. WAA WAa 1.0 and Waa lt 1.0 natural selection
   and complete dominance operate against a
   recessive allele.
4. WAA lt WAa lt 1.0 and Waa 1.0 heterozygote
   shows intermediate fitness natural selection
   operates without effects of complete dominance.
5. WAA and Waa lt 1.0 and WAa 1.0 heterozygote
   has the highest fitness natural
   selection/codominance favor the heterozygote
   (also called overdominance).
6. WAa lt WAA and Waa 1.0 heterozygote has lowest
   fitness natural selection favors either
   homozygote.

8
Selection against a recessive lethal phenotype

• Recessive trait result in reduced fitness.
• Frequency of the recessive allele decreases over
  time.
• Not completely eliminated since present in
  heterozygotes.

9
Heterozygote superiority

• Distribution of malaria and frequency of Hb-s
  allele leading to sickle cell disease in
  homozygotes.

10
Balance between mutation and selection

• When an allele becomes rare, changes in frequency
  due to natural selection are small.
• Mutation occurs at the same time and produces new
  rare alleles.
• For a complete recessive allele at equilibrium
• q vµ/s
• If homozygote recessive is lethal (s 1) then q
  vµ

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Model 1

• Simulate the change in allele frequencies
  directly by mathematical modeling of the forces
  that act on them.
• Set initial values for p and q
• Set initial sample size (effective population
  size)
• Set the HWE as the null model (p2 2pq q2
  1)
• Allow for forces such as mutation rate,
  migration, genetic drift, and selection to act on
  the null model.
• Estimate the change in allele frequencies over
  time using iterations (i.e., the program loops
  over for a number of generations as given by the
  arguments).

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Model 2

• Simulate individuals of a population(s) having
  DNA sequence polymorphisms, and allow them to
  evolve randomly or under certain forces.
• Set initial number of individuals (N at t 0,
  equals to the effective size of the population,
  Ne)
• Generate a null matrix for N x K x G, where K 2
  (diploid), and G equals to the number of genes
  considered (start with a single gene, if else
  assume genes are not linked for simplicity).
• Set the total number of alleles (Nk, start with
  Nk 2) for each G.
• Set the initial number of homozygotes,
  heterozygotes for G.
• Allow for the individuals mate randomly to
  produce offspring, iterate to simulate
  generations for simplicity assume that all
  individuals die after reproduction. E.g., annual
  plants where Nt1 bNt 0 Nt
• Allow for forces to act on the null model, and
  test their effects on the allelic evolution.