Evolution, dispersal of genetics and Fishers equation

1
Evolution, dispersal of genetics and Fishers
equation
2
Charles Darwin (12 February 1809 19 April 1882)

• On the Origin of Species (1859)
• Many individuals of s species are destined to die
  before reaching reproduction age.
• Advantageous gene tends to be persevered, thus
  change the characteristics of the species
• Evolution by natural selection (slight
  modifications are passed on through generations)
• But how does it work?

3
Gregor Mendel (1822-1884)

• Study of the inheritance of traits in pea plants.
  Over a period of 7 years he bred and counted
  about 28,000 pea plants.
• Traits are passed through generations unchanged,
  a child can inherit the trait from either its
  mother or its father
• The trait is determined by two factors, one
  inherited from each parent, and it comes with
  probability from either parent
• For pairs of contrasting traits, one of the two
  is dominant and always overrules the other
  (recessive) factor
• Trait - a variant for a character
• Character - a heritable feature
• Factor Mendels factor is gene today

4
Experiments on Plant Hybridization, Gregor Mendel
(1865, Proceedings of the Natural History
Society) http//www.mendelweb.org/Mendel.html
(original paper)

• Mendel compared seven discrete traits
• Smoothness of the seeds.
• Color of the seeds.
• Color of the seed coats.
• Shape of the pods.
• Color of unripe pods.
• Position of flowers.
• Length of the stems.
• Through experimentation, Mendel discovered that
  one inheritable trait would invariably be
  dominant to its recessive alternative. This
  model, later known as Mendelian inheritance or
  Mendelian genetics, provided an alternative to
  blending inheritance, which was the prevailing
  theory at the time. Unfortunately, Mendel's work
  received little attention from the scientific
  community and was largely forgotten. It was not
  until the early 20th century that Mendel's work
  was rediscovered and his ideas used to help form
  the modern synthesis.

5
Plant material Mendel used sweet pea
6
Examples of Mendel traits
Difference in the color of the seed
albumen Yellow (I) and green (i) cotyledons
Difference in the form of the ripe seeds Round
(R) and wrinkled (r) cotyledons
Difference in the color of the seed coat Colored
(A) and white (a) flowers
Difference in the color of the unripe pods Green
(Gp) or yellow (gp) pod wall
7
(No Transcript)
8
(No Transcript)
9
Genetic Terms

• Phenotype - the outward, physical appearance of a
  particular trait (Pea round or wrinkled seed
  phenotype yellow or green seed phenotype)
• Genotype - genetic make-up of a particular trait,
  the specific allelic combination of a certain
  gene (AA, BB, or AB)
• Allele - one alternative form of a given allelic
  pair (A or B)
• Homozygote - an individual which contains only
  one allele at the allelic pair (AA or BB)
• Heterozygote - an individual which contains one
  of each member of the gene pair (AB)
• Dominant - the allele that expresses itself at
  the expense of an alternate allele the phenotype
  that is expressed in the F1 generation from the
  cross of two pure lines
• Recessive - an allele whose expression is
  suppressed in the presence of a dominant allele
  the phenotype that disappears in the F1
  generation from the cross of two pure lines and
  reappears in the F2 generation

10
More general, the probabilities (frequencies) of
allele A or a in a population can be p and q,
where pq1. Then the probability of each
genotype in F2 is AA p2 Aa 2pq aa
q2 Hardy-Weinbergs law the frequency remain
the same for each genotype
11
Wilhelm Weinberg (1862 1937)
G. H. Hardy (1877-1947)
12
Assumptions in Hardy-Weinbergs Law

• Expected sex ratio is independent of genotype
• Mating is random
• Fertility is independent of genotype
• Survivorship is independent of genotype
• There is no mutation or migration
• Different survival rate or fertility rate for the
  two genotypes could break Hardy-Weinbergs law

13
Evolution of genes under selectionFisher-Haldane
-Wright equation
14
Ronald Fisher (1890-1962)J. B. S. Haldane
(1892-1964)Sewall Wright (1889-1988)
Darwin-Wallace Medal is a medal awarded by the
Linnean Society of London every 50 years,
beginning in 1908, 50 years after the joint
presentation by Charles Darwin and Alfred Russel
Wallace of two scientific papers - On the
Tendency of Species to form Varieties and on the
Perpetuation of Varieties and Species by Natural
Means of Selection - to the Linnean Society of
London on 1 July 1858. It is awarded for "major
advances in evolutionary biology"
15
Some special cases
16
Evolution to advantageous gene numerical
solutions by Matlab
(upper) dominant and advantageous, left
s0.002, right s0.2 (lower) dominant and
recessive, left s0.002, right s0.2
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
Finally, Fishers equation with diffusion !
21
Traveling wave of Fishers equation
22
Finding Traveling wave solution
23
Phase portrait Analysis
24
Problem solved!