Aleix Arnau Soler
Master in Bioinformatics
Population Genomics Theory
25 November 2013
Exercise: Adaptive evolution and population size
The purpose of this exercise is to generate the fitness distribution of fixed mutations
for a population of variable size and discuss the relation between adaptive evolution
and population size. To achieve this goal we will assume a fitness distribution for new
mutations arising in the population and will use the formulae for the probability of
fixation and the rate of evolution that have been provided in the classroom to generate
the results with the help of Microsoft Excel.
Graph the fitness distribution of new mutations arising in the population:
Fitness distribution of new mutations
N = 500 and Ne = 50
30
proportion (%)
25
20
15
10
5
0
Fitness class
s (fitness coefficient)
Graph the fitness distribution of mutations fixed in the population:
Fitness distribution of mutations fixed in the population
N = 500 and Ne = 50
40
proportion ( %)
35
30
25
20
15
10
5
0
Fitness class
s (fitness coefficient)
Aleix Arnau Soler
Generate the corresponding graphs and compare the five distributions you have
generated: new mutations, mutations fixed with population size N = 500 and Ne =
50 (point 10), mutations fixed with population size N = 10000 and Ne = 1000, N =
500000 and Ne = 50000, N = 10000000 and Ne = 1000000.
Fitness distribution of new mutations
N = 500 and Ne = 50
proportion (%)
30
20
10
0,01
0,001
0,0001
0,00001
0,000001
0
-0,000001
-0,00001
-0,0001
-0,001
-0,01
-0,1
-0,5
0
Fitness class
s (fitness coefficient)
Fitness distribution of mutations fixed in the population
N = 500 and Ne = 50
Fitness distribution of mutations fixed in the population
N = 10000 and Ne = 1000
40
proportion (%)
0,01
0,001
0,0001
0,00001
0,000001
0
Fitness class
s (fitness coefficient)
Fitness distribution of mutations fixed in the population
N = 500000 and Ne = 50000
Fitness distribution of mutations fixed in the population
N = 10000000 and Ne = 1000000
30
25
Fitness class
s (fitness coefficient)
Fitness class
s (fitness coefficient)
0,01
0,001
0,0001
0,00001
0,000001
0
-0,000001
-0,00001
0
-0,0001
0,01
0,001
0,0001
0,00001
0,000001
0
-0,000001
-0,00001
-0,0001
-0,001
-0,01
-0,1
0
10
-0,001
5
-0,01
10
20
-0,1
15
-0,5
proportion (%)
20
-0,5
proportion (%)
-0,000001
-0,5
Fitness class
s (fitness coefficient)
-0,00001
0
0,01
0,001
0,0001
0,00001
0,000001
0
-0,000001
-0,00001
-0,0001
-0,001
-0,01
-0,1
-0,5
0
10
-0,0001
10
20
-0,001
20
30
-0,01
30
-0,1
proportion ( %)
40
Aleix Arnau Soler
Which conclusions can you derive about the relationship between adaptive
evolution and population size?
Looking at the first graph, it shows the fitness distribution of new mutations in a
population size of 500 individuals with an effective population size (Ne) of 50. We can see
that the highest proportion of new mutations appears when the fitness coefficient (s) is 0.
It coefficient give us information about the advantage or disadvantage of one mutation.
It’s also important to make attention in the little deviation into the negative side of the
fitness coefficient where the proportions of mutations are higher than in the positive side.
Moreover, there are a peak in these mutations whose s = -0.5.
We can explain it because usually, most of the mutations that appear are neutral (it can be
a mutation in the third position of a codon or in a non-coding site). They don’t give an
advantage or drawback to the specie. So, the highest proportion of mutations will be
when s = 0 or near it, where the mutations don’t provide a significant advantage or
drawback. Another thing to explain is that if all works right in the genome, when a
mutation appears, it’s often a drawback (the protein can become unfunctional, it can
break a pathway, etc. You are changing something that worked correctly) or it can be
deleterious. So, for that reason we see a deviation to the negative side of the fitness
coefficient. Although the more frequent mutations are neutral, when they aren’t, they are
often very disadvantageous. It explains the peak in s = -0,5.
In the second and third graphs we see a similar fitness distribution with the difference
that here the peak in s=-0,5 has disappeared. Because here, these graphs show the fitness
distribution of fixed mutations, then mutations which provide a big drawback or that are
deleterious will never be fixed in the population. Deleterious mutations will be removed
quickly from the population without fixing. Only mutations which provide an advantage
to the survival of the specie or those which give an insignificant drawback will tend to be
fixed. We also see that, bigger the population size is, smaller the proportion of
disadvantageous mutations is, too.
So, we note that the population size have an important role in the fixation of some
mutations and consequently in the evolution of species. If the population is bigger, there
will appear more mutation due to the bigger number of individuals contributing. Also,
when the population size increase, it’s very difficult for the disadvantageous mutations
(and for all mutations in general) to be fixed because not only the frequency of
appearance of a mutation is important for its finally fixation. Here what is also very
important to keep in mind is the natural selection or positive fitness of the mutation that
will tend to fix these mutations which provide an advantage to the species after one or
some generations. So, if the population size increase, the probability of appearance of
advantageous mutations will increase too. So, these species with a bigger Ne will be
expected to have a more adaptive evolution after generations because of more
advantageous mutations will be effectively selected and fixed, due in part to the natural
selection.
Then, looking at the fourth graph we see how the proportion of advantageous mutations
has increase significantly and basically those which are more positive, more attractive for
the natural selection have been fixed. It’s necessary a minimum number of individuals in
an effective population size for note an adaptive evolution after some generations. But it
doesn’t mean that always all advantageous mutations are fixed, there are some of them
which are lost on the way but they are more sensitive to be selected and then fixed. The
same happens with negative mutations, it’s possible to some of them be fixed due to
genetics drift or chance but this probability will be reduced with the increase of the
Aleix Arnau Soler
population size. Finally at the last graph we can see how in very big population sizes only
the mutations which have provided a really advantage to the specie have been fixed after
generations due to an adaptive evolution. The natural selection tends to keep and fix
these mutations which provide an advantage for the survival of the specie after
generations. On the other hand, there isn’t any disadvantageous mutation that has been
fixed.
After all that, something that can be also interesting is to compare population size and the rate of
evolution as it’s done in an article which I have read published in cell press called “Population size
and the rate of evolution” by Robert Lanfear, Hanna Kokko and Adam Eyre-Walker whose abstract
is it:
Does evolution proceed faster In larger or smaller populations? The relationship
between effective population size (Ne) and the rate of evolution has consequences
for our ability to understand and interpret genomic variation, and is central to
many aspects of evolution and ecology. Many factors affect the relationship
between Ne and the rate of evolution, and recent theoretical and empirical studies
have shown some surprising and sometimes counterintuitive results. Some
mechanisms tend to make the relationship positive, others negative, and they can
act simultaneously. The relationship also depends on whether one is interested in
the rate of neutral, adaptive, or deleterious evolution. Here, we synthesize
theoretical and empirical approaches to understanding the relationship and
highlight areas that remain poorly understood.
You can read it here:
http://web.natur.cuni.cz/zoologie/biodiversity/prednasky/EvolucniGenetika/clanky_20
13/Population-size-and-evolutionary-rate_TREE2013.pdf