Lecture 6: Transmission Genetics at the population level

I.Importance:

-fundamental to understanding of evolution

-fundamental to understanding of crop/animal domestication and IMPROVEMENT

-fundamental to understanding virulence of diseases and resistance

-fundamental to understanding gene function

-

II. First case- No change- Hardy-Weinberg

definitions:

phenotype frequency- proportion of individuals in a pop with a particular trait (red vs pink vs white flowers)

genotype frequency- proportion of individuals in a pop of a particular genotype (RR, Rr, rr)

allele frequency- proportion of all alleles in a population that are of a particular type (R vs. r)

Five Assumptions of Hardy-Weinberg:

1.population is large

2.

2.individuals mate completely at random

3.

3.no new mutations

4.

4.no migration into or emigration out of the population

5.

5.each genotype has an equal chance of survivorship and equal reproductive output

Consider the alternatives

1.small population= drift

2.non random mating;

3. mutations

4. effect of movement of genotypes

5. selection

Helpful tips:

p + q = 1;

(p + q)(p + q) = p² + 2pq + q²

Hardy-Weinberg:

1.Allele frequencies do not change from generation to generation in a population in HW equilibrium

2.A HW population achieves the genotype frequencies

p² + 2pq + q²

in JUST ONE generation and maintains those frequencies in subsequent generations

Determining allele frequencies, and frequencies of carriers assuming Hardy-Weinberg

Frequency of PKU in Caucasians in North America

1/3600 born with disease

disease is manifestation of homozygous recessive mutation

autosomal

eliminates activity of of enzyme that converts aa phenyalanine to aa tyrosine

buildup of phenyalanine leads to abnormal brain development

III. Effect of small population size

Sampling variance – example with coin flip

IV. Selection

Fitness- the RELATIVE ability of an individual to survive and reproduce compared to other individuals in the SAME population;

abbreviated as w

Selection- differences in survivorship and reproduction among individuals associated with the expression of

specific values of traits or combinations of traits

natural selection- selection exerted by the natural environment

artificial selection- selection exerted by humans

abbreviated as s;

w = 1-s

Sickle Cell Anemia:

freq of s allele (q) = 0.17

0.17 = s1/(s1 + s2)

if s2 = 1, then s1 = 0.2

then the advantage of Ss heterozygotes is 1/0.8 = 1.25 over the SS homozygote

IV. Selection-Mutation balance

if selection acts to remove deleterious alleles, why do you see deleterious alleles in the population at relatively high

frequencies???

Assume NO heterozygote Advantage &

imagine if R mutates to r and rr is a lethal condition,

q = freq (r)

change of q (complete selection against homozygote, complete dominance of R)

= spq²/mean w

but mutation introduces r at rate u, thus:

change q = [-spq² + u(1-q)]/mean w

but mutation introduces r at rate u, thus:

change q = [-spq² + u(1-q)]/mean w

we want to know what happens at EQUILIBRIUM condition

when there is no change, so we set equation to 0:

WHAT IS THE FREQUENCY OF r WHEN SELECTION AND

MUTATION ARE AT A BALANCE

change q = [-spq² + u(1-q)]/mean w = 0 OR

[-spq² + u(1-q)]= 0

q (equilibrium) =

if u = 1/million, and s = 1, what is equilibrium q???, go to board

V. Quantitative Variation

Most traits are controlled by many genes

This is known as multifactorial inheritence or the trait is under polygenic control

Environmental effects contribute to the expression of quantitative traits

A.Genetic and Environmental Variation

B.

What is the shape of the distribution and why?

Central Limit Theorem:

the distribution of the means of random variables

or

the distribution of the sum of random variables

is

NORMAL

example of several loci with 2 alleles

. Heritability

the proportion of the phenotypic variation attributable to the segregation of alleles

h² = V_G/(V_G + V_E) = V_G/V_P

C. Measuring Heritability

genetic relatedness- the fraction of common alleles shared by two individuals

Father- Daughter, Father- son ??;

Mother- Daughter, Mother- Son ???;

brother with another brother etc.????

Measure the resemblance among relatives for a trait

Compare phenotypic variation among relatives versus phenotypic variation among all individuals, can determine the extent to which genes and environment influence a trait

Example of partitioning variance:

D. Heritability and Environment, e.g.,

HT,

IQ

E. Heritability and Evolution

R = h² S

R is the response to selection ACROSS generations

S is the strength of selection, measured as the difference of the mean of the selected group and the group BEFORE

selection

. Where does variation come from for response to selection?

-Recombination!!!!!!!!, &

Mutations!!!!!!!!!

VI. Conclusions

Selection is a powerful force for the both the change and maintenance of allele frequencies and subsequently

phenotypic change and stasis

Drift- the random fluctuation of allele frequencies associated with sampling of gametes is strongest in small

populations

Most traits of evolutionary and economic value are controlled by many loci with profound environmental effects.

The heritability of a trait determines whether it will respond to selection.

Mutation affecting traits controlled by many genes is important for long-term evolution and selection response

Key Concepts etc: HW law (application), microevolution vs. macroevolution, fitness, natural and artificial selection, how to use selection equations (they will be provided), drift, phenotypic and genotypic variation, heritability, parent offspring regression, QTL. Figures: 2, 3, 5, , 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18. and Table 1 (important).