Selection and Random Genetic Drift

Let's assume there are two alleles in a population of diploid organisms: A₁ and A₂.

Models to describe selection in population genetics terms:

CO-DOMINANCE

Genotype:	A1A1	A1A2	A2A2
Fitness (ability to survive and reproduce)	1	1+s	1+2s
	w11	w12	w22

where s is selection coefficient.

OVER-DOMINANCE (heterozygous advantage)

Genotype:	A1A1	A1A2	A2A2
Fitness (ability to survive and reproduce)	1	1+s1	1+s2

where s₁ > s₂ > 0

Whether mutation that has arisen in population is fixed or lost can be due to chance alone (due to Random Genetic Drift).

Simulation Explorations (using JAVA applets of Kent Holsinger):

1. Genetic Drift: play with population size N
2. Selection and Drift: play with p and N. Default settings (P=0.01, N=50) are quite interesting: Even though the allele conveys a strong selective advantage of 10%, the allele has a rather large chance to go extinct quickly.

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Let's assume there is no selection (s=0) in a diploid population of size N. There are total 2N allelic copies of each gene.

If mutation rate (per gene/per unit of time) is μ, frequency with which new alleles are generated in a diploid population of size N is equal to μ*2N.

Probability of fixation for each new allele is 1/(2N) [simply its frequency in the population after it has arisen by mutation, since s=0].

Substitution rate = frequency with which allele is generated * Probability of fixation= μ*2N *1/(2N) = μ

Therefore: The substitution rate (rate of fixation of mutations) is independent of population size and equals to the mutation rate! That is, about the same number of neutral mutations are fixed every generation. This is the theoretical basis for molecular clock.

It has been shown that fixation time of a neutral allele due to genetic drift is on average 4N generations. That is, new alleles continuously arise due to mutation; many are lost quickly due to genetic drift and ~ every 4N generations, one allele is fixed.

Neutral Theory of Evolution

Neutral Theory of Evolution was developed in 1960s by Motoo Kimura.

It states that the vast majority of observed sequence differences between members of a population are neutral and fixed by random genetic drift. Some mutations are strongly counter selected (this is why there are patterns of conserved residues). Only very seldom is a mutation under positive selection.

The neutral model is often rejected when tested with real data. => Nearly neutral theory was proposed (allows for both slightly deleterious and slightly advantageous mutations)

Measuring Selection in Genes

H₀: neutral evolution. Under neutral evolution, synonymous substitutions should occur at rate equal to mutation rate AND amino acid substitutions (non-synonymous substitutions) should occur at rate equal to mutation rate.

Number of synonymous substitutions per synonymous site: d_S or K_S

Number of non-synonymous substitutions per non-synonymous site: d_N or K_A

ω = d_N/d_S. ω = 1: no selection. ω < 1: purifying selection; ω >1 : positive selection

Different models:

• One ω for the whole tree
• Branch model: different ω for every branch or several ω per tree
• Site Model: detect specific sites in the protein under selection

Example

One example where this kind of analyses worked really well is the evolution of the hemagglutinin gene -the gene that codes for the major influenza surface protein.

News piece from UC Irvine from December 1999

Newer analyses:

e.g., Shih et al. 2007, Suzuki, 2008, Valli et al, 2010 (H1N1).