Genetic drift

Question 1

What is genetic drift?

Answer 1

Natural Populations are finite in size

In finite populations there will be random changes in allele frequencies due especially to chance events, such as variation in the number of offspring between individuals.

This is Genetic Drift.

Question 2

Modelling Genetic Drift

Answer 2

The fate of an allele is governed by chance, and this is most pronounced in small populations

Simulation based on the Wright- Fisher Model (assume neutrality):
each new generation is obtained from the previous generation by repeating the following 3 steps:

1) choose an allele at random from among the 2N alleles in the parent generation.
2) make an exact copy of the allele
3) place the copy in the new generation.

[for N=20 (40 allele), repeat 40 times]

Note: the key is that each of the 2N alleles has an equal chance of having a copy appear in the next generation. This model is a simplification that predicts the real situation well.

Wright Fisher Model interactive site modelling with flies:
https://virtualbiologylab.org/NetWebHTML_FilesJan2016/GeneticDriftModel.html

Question 3

Implications of genetic drift

Answer 3

random changes in allele frequency - same start, different outcomes: evolution can never be repeated.

alleles are lost from the population, so genetic drift always removes variation from populations.

the direction of change is neutral.

Question 4

Diversity of 0.5:

Answer 4

A population of 4 results in loss of diversity after 20 generations

A population of 40 results in loss of diversity after 80 generations (but some is still retained after 100 generations)

A population of 400 results in a 20% reduction in diversity after 100 generations

Question 5

Decay of heterozygosity

Answer 5

Consider a simple model where there is just one hermaphroditic individual with the genotype Aa,
And the population size remains I.

Next generation the probability of being a heterozygote is 1/2 times the probability of being a heterozygote in the previous generation (because there ‘s half as many heterozygotes now)

In this simple model, probability of being a
heterozygote after t generations is (1/2)^t

Question 6

General case for sexual diploids

Answer 6

Ht=H0 (1-1/2Ne)^t

or

Ht=Ht-1 (1-1/2Ne)

Question 7

Effective Population Size (Ne)

Answer 7

Ne =The size of an ‘ideal population’ that would lose heterozygosity at the same rate as the real population.

A Wright-Fisher ideal population has constant size, random mating, discreet generations, sex ratio of 1, no migration, mutation or selection.

Another way to look at the loss of H in diploid, sexual species:

the chance that two identical alleles unite to form a zygote is:
1/ 2Ne
(^When they do, heterozygosity is lost).

The chance that they do not unite is:

1- (1/ 2Ne)

Ht+1 = (1- 1/ 2Ne) Ht

Question 8

Example: An empirical study on Drosophila melanogaster (Buri 1956 Evolution 10:367-402)

Answer 8

• Established 107 Drosophila populations.
• All founders were heterozygotes for the eye-color gene ‘brown’ (genotype: bw75/bw).
• No dominance
• Initial frequency of bw75 = 0.5
• Followed the populations for 19 generations, and kept the population size at 16 individuals
• Data followed Ne and not Nc
• Observed that all began heterozygous and over generations became more homozygous resulting in peaks at each end due to each fly being homozygous – having 0 or 1 rather than the 0.5 at the beginning

Question 9

What happens when a population is suddenly reduced in size?

Answer 9

This is a population bottleneck, and there are two consequences:
- first, a stochastic sampling of alleles
- second the loss of heterozygosity over time due to small population size.

Question 10

drift occurs on a timescale of 2Ne generations

Answer 10

but the Hardy Weinberg equilibrium can be reached after 2 generations of random mating

Therefore, the Hardy Weinberg equilibrium will only be greatly affected by drift when Ne is very small – Hardy Weinberg remains valid in spite of drift in most cases

Question 11

Mutation and Genetic Drift

Answer 11

If genetic drift is removing variation over time, why do natural populations retain variation?
MUTATION!!

u = the mutation rate = ~l x 10^-8 for mammals

Mutation introduces variation at a rate of 2Neu
(number of gametes recombining in a diploid
times the probability that one will include a
mutation)

Genetic drift gets rid of variation at a rate of 1/2Ne

Equilibrium is reached when the evolutionary
forces of drift (which eliminates variation) and
mutation (which adds variation), balance.

Since the average number of new mutations entering
the population each generation is 2Neu, and the
chance of fixation of the new mutation is 1/2Ne, the
average rate of substitution for Neutral mutations is:

2Neu X u

This means that for neutral mutations, the rate of
substitution depends only on the mutation rate, and
not on population size. Why? - because both drift
and mutation rate depend on population size in such a
way that this factor is cancelled out. This changes
when there is selection.

Question 12

de novo variation introduced by mutation, is then
modified by subsequent forces of selection and drift.

Answer 12

Eventually, the measured rate will reflect new variants
shared by all members of the population (the
substitution rate), which can be more than an order of
magnitude lower than the de novo mutation rate.
See: Hoelzel & Lynch (2023) The raw material of
Evolution. Science 381, 942-943

As new mutations go to extinction or fixation over time,
there will be a lot of variation in natural populations that
reflects the transient representation of new alleles
(from Hoelzel & Dover 1991)

Question 13

Neutral Theory of Evolution

Answer 13

proposes that most DNA variation is neutral, and that this is the basis for evolution
Kimura & Ohta (1971) Nature 229:467-469

“A population that is free from selection can accumulate many polymorphic neutral alleles. Then, if a change in ecological circumstances occurs, some of the neutral alleles will no longer be neutral but deleterious, against which purifying selection may operate. After these alleles are removed, the population will become more adapted to its new circumstances than before.”
Kimura (The Natural Theory of Molecular Evolution, 1983)

“I am inclined to suspect that we see, at least in some of these polymorphic genera, variations which are of no service or disservice to the species(neutral), and which consequently have not been seized on and rendered definite by natural selection.”

Charles Darwin (The Origin of Species)

Question 14

Predictions

Answer 14

Previously we saw how sequence data from the ADH gene supports a prediction from neutral theory: that there should be high levels of variation in natural populations.

Another prediction is that change should accumulate gradually over time (provided that mutation is random, neutral, and selection acts primarily to purge deleterious variation).

Genetic drift explains the high level of variation we observe despite the fact that natural evolution drives species with purifying selection

Question 15

DNA Sequencing improved accuracy

Answer 15

The advent Of DNA sequencing made the assessment of change over time more accurate, and provided the
opportunity to compare change at synonymous
(dashed line) vs non- synonymous sites

as seen in the example in notes: a study on the insulin gene (Li et al. 1985 in Molecular Evolutionary Genetics)

Question 16

Example: The Hawaiian Islands

Answer 16

Example: The Hawaiian Islands
Volcanic – formed over a period of time
5 million years ago there was only one island
As more islands form increased diversification resulted
Linear relationship

So the observed rate of change did seem to be very constant, and evolving as a kind of Molecular Clock.

Given varying environments, natural selection would be expected to create a more erratic pattern of substitutions.

Furthermore, the observed average rate of change by amino acid substitution in genes was measured to be about 10-9, very close to the estimated neutral mutation rate at the nucleotide level (and remember the prediction that the substitution rate should be determined only by the mutation rate).

However, the derivation of substitution rate k = u was in units of generations, so the substitution rate should be constant per generation, rather than per year.

This means that animals with shorter generation times should evolve more quickly – the generation time effect - a prediction of the neutral theory. This was observed in non-coding DNA, but not in proteins.

Implication: something slowed down the rate of evolution in proteins, and this led to the theory that most amino acid substitution were not neutral but slightly deleterious -> Nearly Neutral Theory

Question 17

Proportion of mutations according to different theories

Answer 17

Selection theory: mostly deleterious, some advantageous

Neutral theory: almost half deleterious and half neutral with a few advantageous

Nearly neutral theory: approx 1/3 deleterious, 1/3 neutral, 1/3 nearly neutral with a few advantageous

Bromham & Penny (2003) DOI: 10.1038/nrg1020

Question 18

Summary

Answer 18

l) Genetic Drift: In finite populations there will be random changes in allele frequencies due to chance events, such as variation in the number of offspring between individuals.

2) Important implications: Evolution is unpredictable; generic drift removes variation from population; the direction of change is neutral.

3) Heterozygosity is lost in finite populations over time according to the following formula:

Ht = Ht-1 (1-(1/2Ne))
(Ne in this formula is the - the Of an ideal population that
would show the same rate of decay in heterozygosity as the observed population.)

4) At equilibrium the probability that two alleles differ by origin and by state is:
H = 4Neu/(1 + 4Neu)

5) Mutation introduces variation at a rate of 2Ncu. where u is the mutation rate to neutral alleles, and genetic drift gets rid of variation at a rate of so under the neutral theory average rate of substitution is 2Neu x 1/2Ne = u