LT2 Selection at a single gene

Selection at a Single Gene

Population Genetics
Dynamics of alleles at one or few loci Predict allele frequency change
Frequency change Infer population parameters/processes
Directed effects: selection
Stochastic effects: genetic drift
Quantitative Genetics
Genetic contribution to phenotypic variation
No direct representation of genes and alleles
Variance components: genetic and environmental
Phylogenetics
Long term evolution
DNA substitutions
Calculate species distances
Reconstruct trees



Discrete Traits Continuous traits
One or few loci Most often polygenic, multifactorial
Large alleic effects Meristic traits: quantitative but not
Discontinuous distribution infinite range (eg. number of eggs laid)
Threshold traits: small number of discrete
phenotypic classes (eg. Type II diabetes –
people have a combination of alleles at
different loci  continuous range for
varying levels of libability)
Small alleic effects
Central Limit Theorem


Single-gene traits

 Antibiotic resistance to bacteria
 Resistance to insecticides, pesticides
 Plant heavy metal tolerance
 Human resistance to malaria (sickle cells)
 Human genetic diseases (cystic fibrosis, Huntingtons)

Peppered moth Biston betularia

 2 morphs = typica (camouflaged among lichen, conspicuous on dark bark) and
carbonaria (camouflaged on dark bark, conspicuous among lichen)

, During Industrial Revolution (1800s) – heavy air pollution led to soot deposition on
trees, sulphur dioxide killed lichens = result was that trees turned dark
 Tree colour and predation effects observed through a mark-recapture experiment:
in polluted areas carbonaria had higher %capture than typical (vice versa in clean
areas) (Kettlewell, 1956)
 Melanic carbonaria form had increased survival and the dark phenotype spread
 Manchester: (1848) First carbonaria found, by 1895 98% moth carbonaria
 Rapid evolution still contiguous today (post-industrial revolution – air is cleaner

Forming a Model (ie. a mathematical description of biology)

 Moth pigmentation has a simple genetic determinism – one locus, 2 alleles
 Carbonaria is dominant (CC or Cc), typical is recessive (cc)
 Modelling frequency of C alleles over time – predict evolution (eg. frequency of C in
the future), estimate force of selection, test biological
scenarios

1. Define a life cycle
- Between the change in frequencies of individuals
within a population, life cycle events of organisms
(and alleles) occur (eg. at time t = 13/24 typica, at
time t+1 = 8/24 typica)
- What is happening between time t and t+1?
Reproduction, Survival, Dispersal, Cooperation –
how and where does selection intervene?
- Non-overlapping generations = Birth Survival 
Reproduction  Death

2. Tracking Frequencies

Genotypic frequency change through selection

- Relative fitness: Probability of survival
relative to reference genotype
- Probability of survival relative to population
average
- Frequencies of p + q of alleles C and c assumed
to affect survival
- Frequencies of C and c among survivors
obtained by multiplying frequencies
before selection by probabilities of
survival = pw1 and qw2

, - Dividing these by proportion of population that has survived ensures frequencies
add up to 1
- Proportion of survivors = mean fitness of population: wbar = pw 1 + qw2
- New frequencies: p’= pw1/wbar q’=qw2/wbar

Alleic frequency change through selection




Fitting the model to data

Manchester: carbonaria from 1% to 98% in 47 years

q20 = 99% = 0.99
q0 = sqrt(0.99) = ~0.995
p0 = 1-q0 = 0.005

Selective advantage (s)  what is s, the
relative reduction in typical survival?

In more general terms…

Frequency dynamics

Frequency of A changes fastest when:

- Selection is strong
- When frequencies are intermediate
- For recessive A alleles (h=1) , when p is large
- For dominant alleles (h=0), when p is small

 For models to predict dynamics of allele frequencies
and to infer parameters (fit models to data), model assumptions must be met