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FROM GENOTYPES TO PHENOTYPES

Johanssen – in 1909 defined phenotype and genotype,delineating the difference between external expression and 

the underlying hereditary controls

Genetic basis of phenotypic variation originally documented with 'common garden' experiments

Turesson ‐ 1920's ecotype concept

Clausen, Keck & Heisey: Achillea lanulosa10 populations grown in a common garden 

Clausen, Keck & Heisey 1948. Experimental studies on the nature of species. III. Environmental responses of climatic races of Achillea. Washington, DC, Publication 581, Carnegie Institution of Washington

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P = G

P = G  +  E 

In a single environment, E refers to micro‐environmental variation or may be due to developmental instability

In multiple environments, E refers to phenotypic plasticity

P = G  +  E  +  G × E 

In multiple environments, G × E refers to genetic variation in phenotypic plasticity

Clausen, Keck & Hiesey

Reciprocal transplant gardens

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Clausen, Keck & Hiesey

Reciprocal transplant gardens

Achillea lanulosa

Clones grown at each of the 3 gardens

Sh d h b h i dShowed that both genetic and environmental effects were important

E is ubiquitous – phenotypes cannot be produced outside of context of environment 

E g DNA RNA & proteinsE.g., DNA, RNA & proteinsDNA unzips @ ~75°C

Proteins & enzymes have evolved to have their own optimal temps:

archaebacteria Thermus aquaticus, lives in 70°C hotsprings

Antarctic fish Pagothenia borchgrevinki lives @ ‐2°CDies of heat shock @ 6°C

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Modeling Evolutionary Change

2 major approaches: population and quantitative geneticsBoth created/elaborated by Fisher, Wright & Haldane

Population genetics deals with traits controlled by one or a few loci – it is a mathematical theory used to model evolutionary changes of allele frequencies in 

populations due to mutation and selection

Q tit ti ti d l ith th t itQuantitative genetics deals with those traits controlled polygenically ‐ it is a statistical approach which assumes that there are many loci involved, 

each with the same small additive effect on the trait. Mostly interested in effects of selection. 

Population Genetics

Centered on analyzing deviations from equilibrium(Castle‐Hardy‐Weinberg), where allele frequencies remain constant over time in absence of evolutionary ‘forces’

p + q =  1 where p and q are allele frequencies  

(p + q)  (p + q)  =  p2 + 2pq + q2 =  1

p2 and q2 are the frequencies of the homozygotes2pq is the frequency of the heterozygotes 

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Evolutionary ‘Forces’

mutation R

drift R

migration  R (NR)

(aka gene [allele] flow)

selection NR

assortative mating NRg

Pop gen equation is very flexible – terms can be inserted to examine effects of various evolutionary forces 

e.g.,  effect of mutation on allele frequencies

p + q = 1  p + (q μ1) + q + (p μ2)  =  1 where μ1 and μ2 are the back mutation rates

effect of selection on allele frequencieseffect of selection on allele frequencies

p + q = 1  p + q (1‐s)  = p + (q‐qs) = p2 + (2pq ‐ 2pqs) + (q2 ‐ 2q2s2  + q2s2)  = 1

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PopGen has been used to simulate many types of evolutionary scenarios.

Allele frequency change over time with selection.

Effects of genetic drift as a function of population size.

Migration models – stepping stone model, Island model

Sickle-cell anemia example - globin geneA - normal alleleS – sickle-cell allele (usually causes death before reproduction)

P l l f 12 387 d d l Population sample of 12,387 individuals. The genotype of each was determined.

and the genotype frequencies calculated as # observed/total sampled

e.g., for SS frequency = 29/12387 = .00234

The numbers for each genotype are tallied

Genotype Observed Individuals Frequency

SS 29 .002AS 2993 .242AA 9365 .756

sum 12387 1.000

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Worked example - 2

observed allele frequencies are calculated by summing the number of alleles of a particular form and dividing by the total alleles, e.g. for S

Observed fs = = 0.123

29 individuals homozygous SS, thus 229 S alleles,

(2 × 29) + 299312387 × 2

2993 AS individuals, thus 12993 S alleles. Total alleles is 212387, 2 alleles for each diploid individual.

expected genotype frequencies are calculated from the Hardy-Weinberg equation

Expected fss = q2 = .01513

# of SS individuals then = = 187.4

= (0.123)2

(0.123)2 × 12387

Genotype Observed Expected

Individuals Frequency Individuals Frequency Fitness s or tSS 29 .002 187.4 .015 1-t = .138 .862AS 2993 .242 2672.4 .216 1 0AA 9365 .756 9527.2 .769 1-s = .877 .123

sum 12387 1.000 12387 1.00

Worked example for Sickle-cell anemia

Genotype Observed Individuals Frequency

Population sample of 12,387 individuals.

p q fp fq

58 877 123

H-W expectations

Individuals Frequency SS 29 .002AS 2993 .242AA 9365 .756

sum 12387 1.000

58 .877 .1232993 2993

18730 p2 2pq q2

21723 3051 .769 .216 .015

Compare observed with expected - Χ2 test

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Fitnesses are calculated as the ratio of observed/expected frequenciesIn this example AS has the highest fitness: .242/.216 = 1.12SS = .002/.015 = 0.133 ; AA = .756/.769 = 0.983

Then all fitnesses are relativized by dividing by the highest fitness

Worked example - 3

Then all fitnesses are relativized by dividing by the highest fitness. AS = 1.12 / 1.12 = 1.00 SS = .133 / 1.12 = 0.138AA = .983 / 1.12 = 0.877

Selection coefficients are calculated as (1 - relative fitness)

Genotype Observed Expected Genotype Observed Expected

Individuals Frequency Individuals Frequency Fitness sSS 29 .002 187.4 .015 .138 .862AS 2993 .242 2672.4 .216 1 0AA 9365 .756 9527.2 .769 .877 .123

sum 12387 1.00 12387 1.00

p + q = 1  p0 = 0.877, q0 = 0.123p2 (1‐s) + 2pq + q2 (1‐t) = 1

Sickle-cell anemia exampleLet s be selection on homozygous normal

and t be selection on homozygous sickle cell

p2 (1‐0.123) + 2pq + q2 (1‐0.862) = 10.877p2 + 2pq + 0.138q2 = 1

p2 (1‐s) + 2pq + q2 (1‐t) = 10.877 (0.756) + 0.242 + (0.123)(0.002) = 

p2 + 2pq + q2

0 663 0 242 0 0002 0 9052 ( 1)0.663 + 0.242 + 0.0002 = 0.9052 (≠ 1).663/.905 = .732,

p2 + 2pq + q2

.732 + .267 + .0003 = 1

p1 = 0.789, q1 = 0.211

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Quantitative Genetics

Focus on analyzing changes in phenotypes using statistical models. Genetic basis of phenotypes is estimated

Polygenic traits: trait expression is assumed to be controlled by many genes, each of small effect

QG use variances and covariances among traits

Genetic architecture: refers to the relationships among genes, among traits and among genes and traits 

Questions of interest:

Quantitative Genetics

What traits can and cannot respond to selection?

What is the genetic architecture of traits?  

What maintains genetic variation in populations?

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VP = VG + VE + VG*E

VG = VA + VD + VI

A ‐ additive, D ‐ dominance, I ‐ epistasis 

additive – effects of alleles are added to each other

A1 = 2cm and A2 = 3cm  A1A1  = 4cm; A2A2 = 6cm; A1A2 = 5cm

heterozygote is intermediate between homozygotes

dominance is non‐additive

A1 = 2cm and A2 = 3cm  A1A1  = 2cm; A2A2 = 3cm; A1A2 = 3cm

epistasis – interaction of genes controls trait expression 

gene regulation will produce epistasis; cascades, pathways.

For additive traits, linear regression explains all of variation

For non‐additive traits, there is unexplained variance

NOTE ! – the assignment of effects in QG is purely statistical,there is no actual assessment of the real genetics of the genes controlling traits 

It is the (statistically) additive variance that will determine response to selective forces, i.e., VAp A