L10 Variation I

Variation!-!I"

Dr. Gayle Ferguson"

Previously…"

Origin of genetic variation - mutations, recombination"

These processes bring about the variation

on which selection can act, resulting in evolution"

Understanding genetic variation"

Genetic variation is the foundation of evolution""

Understanding the processes of evolution requires knowledge of variation and how it is transmuted into evolutionary change"

Variation"

Genotypic" GxE"Environmental"

Variation can be due to our inheritance but also due to environmental conditions

like climate and diet"

Understanding genetic variation"

Environment directly affects phenotype and may be independent of genetics"

"> Sex determination in reptiles and fish"> Wing development in insects"> Congenital differences"

"

-  early in year"-  no wings"

-  late in year"-  wings"

Variation in aphids due to environment!

BUT:"Evolution depends on genetic variation"

Important to determine whether variation is genetic, environmental, or a combination of both

Distinguishing between sources! of variation"

Phenotypes can be experimentally crossed to F1 and F2 and backcross progeny."

Making use of Mendelian ratios as controls."

Correlation of phenotypic characteristics amongst and outside of kin."

This however needs to be controlled for similar environmental backgrounds of kin"

Common garden experiments in which offspring of phenotypically distinct parents are reared in a

common environment."

Predisposition for being tall is not enough if diet is not adequate."

Bonsai trees are genetically the same as their larger counterparts"

Environmental"

EPIGENETIC MECHANISMS are affected by these factors and processes: t Development (in utero, childhood) t Environmental chemicals t Drugs/Pharmaceuticals t Aging t Diet

CHROMOSOME

CHROMATIN

DNA

HISTONE TAIL

HISTONE TAIL

DNA accessible, gene active

DNA inaccessible, gene inactive Histones are proteins around which DNA can wind for compaction and gene regulation.

HISTONE

GENE

EPIGENETIC FACTOR

METHYL GROUP

DNA methylation Methyl group (an epigenetic factor found in some dietary sources) can tag DNA and activate or repress genes.

Histone modification The binding of epigenetic factors to histone “ tails” alters the extent to which DNA is wrapped around histones and the availability of genes in the DNA to be activated.

HEALTH ENDPOINTS t Cancer t Autoimmune disease t Mental disorders t Diabetes

Epigenetic!variation"

Getting back to basics"

In the most simplistic case a trait is controlled by a single gene

The gene can have two alleles, say A and a!

Hence the possible genotypes are:"

D H" R"Genotype frequencies in the population:"

So"

D+H+R!=!1"

A A

Homozygous for A!

Aa

Heterozygous"a a

Homozygous for a!

AA Aa

D H" R"

aa

What are the allele frequencies in the population?""Two alleles: A and a!!The frequency of A is represented as p!!The frequency of a is represented as q!" "

p + q = 1"

What is the frequency of the A allele ?"

AA Aa

D H" R"

aa


AA Aa

D H" R"

aa

p!=!D+H/2"


AA Aa

D H" R"

aa

p!=!D+H/2""

similarly!!

q = R+H/2"


AA Aa

D H" R"

aa

p!=!D+H/2""

similarly!!

q = R+H/2"

p+q!=1 q!=1-p!

But So"

we need to track only p!


AA Aa

D H" R"

aa

p!=!D+H/2""

similarly!!

q = R+H/2"

p+q!=1 q!=1-p!

But So"

we need to track only p!

Note that from the genotype frequencies one can always calculate the allele frequencies!

However,"the opposite is not true!!!"

A simple population genetics model"

AA !Aa" AA !Aa"aa" aa"A" a"

AA !Aa" AA !Aa"aa" aa"

If we know the frequency of allele A (i.e. p), then we can calculate the expected genotype frequencies in the next generation"

A" a"

A simple population genetics model"

A" a"

A"

a"

AA" Aa"

Aa" aa"

(sperm)"

(egg)"

p!

A"1-p!

a"

A"

a"

AA" Aa"

Aa" aa"

p!

1-p!

(sperm)"

(egg)"

p!

A"1-p!

a"

A"

a"

AA"P2!

"

Aa"p (1-p)"

"

Aa"(1-p) p!

"

aa"(1-p)2"

"

p!

1-p!

(sperm)"

(egg)"

AA !Aa !aa"p2 !2 p(1-p) !(1-p)2"

P’ !Q’ !R’"

Offspring proportions"

p!

A"1-p!

a"

A"

a"

AA"P2!

"

Aa"p (1-p)"

"

Aa"(1-p) p!

"

aa"(1-p)2"

"

p!

1-p!

(sperm)"

(egg)"

So what is the allele frequency in the next generation?"

AA !Aa !aa"p2 !2 p(1-p) !(1-p)2"

P’ !Q’ !R’"


p!

A"1-p!

a"

A"

a"

AA"P2!

"

Aa"p (1-p)"

"

Aa"(1-p) p!

"

aa"(1-p)2"

"

p!

1-p!

(sperm)"

(egg)"

So what is the allele frequency in the next generation?"So what is the allele frequency in the next generation?"

p’!=!D’+H’/2"=!p2 +![2 p(1-p)]/2"=!p2 +!p (1-p)"

=!p2 +!p - p2"

=!p (p+1-p)"

=!p!

p!

A"1-p!

a"

A"

a"

AA"P2!

"

Aa"p (1-p)"

"

Aa"(1-p) p!

"

aa"(1-p)2"

"

p!

1-p!

(sperm)"

(egg)"

AA !Aa !aa"p2 !2 p(1-p) !(1-p)2"

P’ !Q’ !R’"


So what is the allele frequency in the next generation?"

p’!=!D’+H’/2" =!p2 +[2 p(1-p)]/2" =!p2 +p (1-p)"

=!p (p+1-p)"

=!p!Genotype frequency can change but allele frequency does not change over time"

Once in equilibrium both stay constant""

p!

A"1-p!

a"

A"

a"

AA"P2!

"

Aa"p (1-p)"

"

Aa"(1-p) p!

"

aa"(1-p)2"

"

p!

1-p!

(sperm)"

(egg)"

AA !Aa !aa"p2 !2 p(1-p) !(1-p)2"

P’ !Q’ !R’"


Hardy-Weinberg equilibrium"

The foundation on which almost all of the theory of population genetics is based"

If the genotype frequencies are away from the H-W equilibrium, in a single generation they regain it"

""

At equilibrium both genotype and allele frequencies remain constant over time"

However it is based on major assumptions of…"

"

> No selection "

> Random mating"

> Infinitely large population"

> No disturbance to the gene pool (migration, mutation, recomb.) "

> All individuals have equal probabilities of survival, reproduction"


Is it then even useful?"


Is it then even useful?"


Is the scarlet tiger moth population in H-W equilibrium?

E. B. Ford’s 1971 data" White spotted (A1A1) Intermediate (A1A2) Little spotting (A2A2)"

1469 138! ! ! ! 5" " Total # of alleles: 1612"

Genotype frequencies:" A1A1 = D = 1469/1612 = 0.911"A1A2 = H = 138/1612 = 0.085"A2A2 = R = 5/1612 = 0.004"

! !! ! 1.000 """

E. B. Ford’s 1971 data" White spotted (A1A1) Intermediate (A1A2) Little spotting (A2A2)"

1469 138! ! ! ! 5" "

Genotype frequencies:" A1A1 = D = 1469/1612 = 0.911"A1A2 = H = 138/1612 = 0.085"A2A2 = R = 5/1612 = 0.004"

! !! ! 1.000 """Allele frequencies:"

p(A1) = (2 x 1469 + 138)/ (2 x 1612) = 0.954"q(A2)= (2 x 5 + 138)/ (2 x 1612) = 0.046"

! ! ! ! 1.000 """

Total number of alleles in population A1A1 + A1A2"

A2A2 + A1A2 "

Calculate expected genotype frequencies under H-W principle "

Genotype frequencies AA Aa aa p2 2pq q2

Expected f 0.91 0.09 0.002 Expected no. 1467 145 3 (f x no of ind.)

Observed 1469 138 5

Allele frequencies:"p(A1) = (2 x 1469 + 138)/ (2 x 1612) = 0.954"q(A2)= (2 x 5 + 138)/ (2 x 1612) = 0.046"

! ! ! ! 1.000 """

AA !AA"AA !Aa"AA !aa"Aa !AA"Aa !Aa"Aa !aa"aa !AA"aa !Aa"aa !aa"

AA"Offspring

Aa" aa"Parents" Mating

probability"

Alternatively"


AA"Offspring

Aa" aa"

D2"

DH DR"DH H2"

HR DR"HR R2"

Parents" Mating probability"

Alternatively"


AA"Offspring

Aa" aa"

D2"

DH DR"DH H2"

HR DR"HR R2"


Alternatively"

D2"


AA"Offspring

Aa" aa"

D2"

DH DR"DH H2"

HR DR"HR R2"


Alternatively"

D2

DH/2""DH/2"


AA"Offspring


probability"

Alternatively"

D2"

DH/2""DH/2"H2/4"

"DH/2"DR"DH/2"H2/2"HR/2"DR"HR/2"

D2"

DH DR"DH "H2"

HR DR"HR "R2"

"H2/4"R2"

"HR/2"R2"


AA"Offspring


probability"

Alternatively"

D2"

DH/2""DH/2"H2/4"


D2"

DH DR"DH "H2"

HR DR"HR "R2"

"H2/4"R2"

"HR/2"R2"

D’!=!D2+DH/2+DH/2+H2/4 !"Remember p = D+H/2"


AA"Offspring


probability"

Alternatively"

D2"

DH/2""DH/2"H2/4"


D2"

DH DR"DH "H2"

HR DR"HR "R2"

"H2/4"R2"

"HR/2"R2"

D’!=!D2+DH+H2/4!" =!(D+H/2)2 " = !p2"

Remember p = D+H/2"


AA"Offspring


probability"

Alternatively"

D2"

DH/2""DH/2"H2/4"


D2"

DH DR"DH "H2"

HR DR"HR "R2"

"H2/4"R2"

"HR/2"R2"

p2" 2!p(1-p)" (1-p)2"


AA"Offspring


probability"

Alternatively"

D2"

DH/2""DH/2"H2/4"


D2"

DH DR"DH "H2"

HR DR"HR "R2"

"H2/4"R2"

"HR/2"R2"

p2" 2pq! q2"

This is the null hypothesis""If this is not satisfied then it means that probably something interesting

is happening!!"

e.g. non-random mating,"or selection,"

or migration etc !


Genetic and Environmental (as well as epigenetic) processes drive the variation in populations"

Hardy-Weinberg equilibrium is a fundamental

concept of population genetics"

The H-W equilibrium will hold true only if a number of assumptions are met"

These assumptions are expected to be violated in the real world thus leading us to interesting phenomena"

"I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.” - Hardy, G. H. (2004) [1940].

A Mathematician's Apology. Cambridge: University Press."

Summary"

Date post:	09-Dec-2015
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L10 Variation I

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