Evolution, dispersal of Evolution, dispersal of genetics and Fisher’s genetics and Fisher’s

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Charles Darwin Charles Darwin (1809-1882)(1809-1882)

•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?

Gregor Mendel (1822-1884)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 – Mendel’s factor is gene today

Experiments on Plant HybridizationExperiments on Plant Hybridization, , Gregor Gregor Mendel Mendel

(1865, Proceedings of the Natural History Society)(1865, Proceedings of the Natural History Society) http://www.mendelweb.org/Mendel.htmlhttp://www.mendelweb.org/Mendel.html (original paper) (original paper)

Mendel compared seven discrete traits:Mendel compared seven discrete traits:• Smoothness of the seeds. Smoothness of the seeds. • Color of the seeds. Color of the seeds. • Color of the seed coats. Color of the seed coats. • Shape of the pods. Shape of the pods. • Color of unripe pods. Color of unripe pods. • Position of flowers. Position of flowers. • Length of the stems. Length of the stems.

Through experimentation, Mendel discovered that one inheritable Through experimentation, Mendel discovered that one inheritable trait would invariably be dominant to its recessive alternative. This trait would invariably be dominant to its recessive alternative. This model, later known as model, later known as MendelianMendelian inheritance inheritance or Mendelian or Mendelian genetics, provided an alternative to blending inheritance, which genetics, provided an alternative to blending inheritance, which was the prevailing theory at the time. Unfortunately, Mendel's was the prevailing theory at the time. Unfortunately, Mendel's work received little attention from the scientific community and work received little attention from the scientific community and was largely forgotten. It was not until the early 20th century that was largely forgotten. It was not until the early 20th century that Mendel's work was rediscovered and his ideas used to help form Mendel's work was rediscovered and his ideas used to help form the modern synthesisthe modern synthesis..

Plant material Mendel used: sweet Plant material Mendel used: sweet peapea

Examples of Mendel traitsExamples of Mendel traits

Difference in the form of the ripe seedsRound (R) and wrinkled (r) cotyledons

Difference in the color of the seed albumenYellow (I) and green (i) cotyledons

Difference in the color of the seed coatColored (A) and white (a) flowers

Difference in the color of the unripe podsGreen (Gp) or yellow (gp) pod wall

Genetic TermsGenetic Terms• PhenotypePhenotype - the outward, physical appearance of a particular trait - the outward, physical appearance of a particular trait

(Pea: round or wrinkled seed phenotype; yellow or green seed (Pea: round or wrinkled seed phenotype; yellow or green seed phenotypephenotype))

• GenotypeGenotype - - genetic make-up of a particular trait, the specific allelic genetic make-up of a particular trait, the specific allelic combination of a certain gene (AA, BB, or AB)combination of a certain gene (AA, BB, or AB)

• AlleleAllele - one alternative form of a given allelic pair - one alternative form of a given allelic pair (A or B)(A or B)

• HomozygoteHomozygote - an individual which contains only one allele at the - an individual which contains only one allele at the allelic pair (AA or BB)allelic pair (AA or BB)

• HeterozygoteHeterozygote - an individual which contains one of each member of - an individual which contains one of each member of the gene pair (AB)the gene pair (AB)

• DominantDominant - the allele that expresses itself at the expense of an - the allele that expresses itself at the expense of an alternate allele; the phenotype that is expressed in the F1 generation alternate allele; the phenotype that is expressed in the F1 generation from the cross of two pure linesfrom the cross of two pure lines

• RecessiveRecessive - an allele whose expression is suppressed in the presence - an allele whose expression is suppressed in the presence of a dominant allele; the phenotype that disappears in the F1 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 from the cross of two pure lines and reappears in the F2 generation generation

More general, the probabilities (frequencies) of allele A or a in a population can be p and q, where p+q=1. Then the probability of each genotype in F2 is

AA: p^2 Aa: 2pq aa: q^2

Hardy-Weinberg’s law: the frequency remain the same for each genotype

nnnnn

nnnnn

qqpqq

pqppp

22

1

22

1

21

21

(The equation at page 120 of Britton’s book is wrong.)

Assumptions in Hardy-Weinberg’s LawAssumptions in Hardy-Weinberg’s Law

• Expected sex ratio is independent of genotypeExpected sex ratio is independent of genotype

• Mating is randomMating is random

• Fertility is independent of genotypeFertility is independent of genotype

• Survivorship is independent of genotypeSurvivorship is independent of genotype

• There is no mutation or migrationThere is no mutation or migration

Different survival rate or fertility rate for the two genotypes Different survival rate or fertility rate for the two genotypes could break Hardy-Weinberg’s lawcould break Hardy-Weinberg’s law

Example: blood typeExample: blood type

• The ABO blood group in humans are The ABO blood group in humans are determined by a system of three determined by a system of three alleles, A, B and O. Genotype AA and alleles, A, B and O. Genotype AA and AO are group A, BB and BO are group B, AO are group A, BB and BO are group B, AB is group AB, and OO is group O. The AB is group AB, and OO is group O. The frequencies of blood groups in England frequencies of blood groups in England are 32.1% A, 22.4% B, 7.1% AB and are 32.1% A, 22.4% B, 7.1% AB and 38.4% O. Are these proportions 38.4% O. Are these proportions consistent with the assumptions of consistent with the assumptions of random mating?random mating?

Evolution of genes under selection:Evolution of genes under selection:Fisher-Haldane-Wright equationFisher-Haldane-Wright equation

Some special casesSome special cases

Evolution to advantageous gene: Evolution to advantageous gene: numerical solutions by Matlabnumerical solutions by Matlab

(upper): dominant and advantageous, left: s=0.002, right: s=0.2

(lower): dominant and recessive, left: s=0.002, right: s=0.2

Finally, Fisher’s equation with diffusion !Finally, Fisher’s equation with diffusion !

Traveling wave of Fisher’s Traveling wave of Fisher’s equationequation