Only a certain proportion Pn of all mutation is
selectively neutral. P n may be estimated from the
number and frequency of rare alleles, i.e. those
whose frequency is lower than 0.01. Using this
method, pn for various enzymes and other proteins of both vertebrates and invertebrates has been
estimated as 0.14 ± 0.06 [211]. The value of pn
can be used to calculate the rate of occurrence
and fixation of neutral mutations from the total
mutation rate VT,
(4.8)
A neutral mutation is one that has no significant
effect on the fitness of an organism under a given
set of selection conditions. In contrast to the classical concept, according to which the strength of
positive selection determines the rate of evolution, the neutral theory maintains that it is the
characters without any fitness value, all mutations
of which are neutral, that show the maximal rate
of evolution and the highest polymorphism. The
more important a molecular character is for the
maintenance of structure and function of a
nucleic acid or protein, the greater is the restriction of its molecular evolution. As discussed in
section 4.6, this concept has been confirmed
many times. The highest rates of evolution are
found amongst the pseudo genes that are no longer expressed; non-coding DNA sequences
change quicker and are more polymorphic than
coding sequences (see Table 4.13, p.162), and
synonymous substitutions predominate over
amino acid exchanges in coding sequences. The
more complex the interaction of individual proteins with other cell components and the more
important their function for the whole organism,
the lower is their rate of evolution (see Table 4.12; p.161); thus, the amino acids that are
most frequently exchanged are those of lesser
importance for the structural and functional properties of the protein [440].
The following numerical example illustrates
the process of formation and fixation or elimination of neutral mutations. Consider a gene of
approximately 1000 nucleotides that codes for a
protein of about 330 amino acids; the effective
population size is Ne = 10 5 , and the neutral mutation rate Vo = 5 . 10- 9 per nucleotide and generation, corresponding to the value observed for
pseudogenes. Thus, one neutral mutation occurs
in this particular gene per generation and, in
most cases, will be randomly eliminated in the
course of about 24 generations. The probability
that the mutation will be fixed in the population
is approximately 1: 200000. It requires about
4.4.1 Neutral Theories of Molecular Evolution
141
400000 generations for the mutation to spread
throughout the whole population, and l/vo =
200 million generations before the mutated nucleotide is finally replaced by another. Many
speciation processes will, of course, occur within
this period. Therefore, neutral mutations are
usually very old, in fact mostly older than the
species in which they are found. The nucleotide
position (the mutation site) is polymorphic only
during the 400000 generations required for fixation; during the following 200 million generations it will be monomorphic. The probability of
polymorphy is correspondingly larger when the
numerous nucleotides of the whole gene are considered [210, 212]. The time required for the fixation of a useful mutation is comparatively short;
for a mutation with a selective advantage s (fitness = 1 + s), the time is given by (2/s)loge
(2Ne); with s = + 0.01 and Ne = 10 5 , the time
required is 2900 generations. Thus, advantageous
mutations in the phase of their fixation contribute very little to the polymorphism of the
population [294].
If we make the assumption that, in reality,
each mutation produces a new allele (the infinite
allele model), then the mean heterozygosity is
given by
(4.9a)
Taking into account the limited resolution of electrophoretic investigations (stepwise allele
model), then
H = 1- (1 + 8Nevotl12
(4.9b)
Where Nevo < 1, the two models give very similar
results, where Nevo is large, the value of H from
Eq. (4.9b) will be smaller [210, 212]. Extremely
low, almost undetectable heterozygosity results
when the population is very small (Ne < 1000), as
is often the case, for example, with large mammals [210, 212, 294]. According to Eq. (4.9a), in
very large populations H should approach 1.0,
whereas in fact the mean heterozygosity rarely
exceeds 0.3. The relatively low value of H = 0.177
in the tropical species Drosophila willistoni,
which includes thousands of millions of individuals, was used by Ayala as an argument against the
neutral theory of polymorphism. However, it is
also probably the case in this species that the
effective population size is much smaller than the
total number of individuals, and the polymorphism is heavily reduced by the frequent elimination
of local populations [210,212, 294]. Polymorphism can also be reduced by highly selected substitutions [201].
selectively neutral. P n may be estimated from the
number and frequency of rare alleles, i.e. those
whose frequency is lower than 0.01. Using this
method, pn for various enzymes and other proteins of both vertebrates and invertebrates has been
estimated as 0.14 ± 0.06 [211]. The value of pn
can be used to calculate the rate of occurrence
and fixation of neutral mutations from the total
mutation rate VT,
(4.8)
A neutral mutation is one that has no significant
effect on the fitness of an organism under a given
set of selection conditions. In contrast to the classical concept, according to which the strength of
positive selection determines the rate of evolution, the neutral theory maintains that it is the
characters without any fitness value, all mutations
of which are neutral, that show the maximal rate
of evolution and the highest polymorphism. The
more important a molecular character is for the
maintenance of structure and function of a
nucleic acid or protein, the greater is the restriction of its molecular evolution. As discussed in
section 4.6, this concept has been confirmed
many times. The highest rates of evolution are
found amongst the pseudo genes that are no longer expressed; non-coding DNA sequences
change quicker and are more polymorphic than
coding sequences (see Table 4.13, p.162), and
synonymous substitutions predominate over
amino acid exchanges in coding sequences. The
more complex the interaction of individual proteins with other cell components and the more
important their function for the whole organism,
the lower is their rate of evolution (see Table 4.12; p.161); thus, the amino acids that are
most frequently exchanged are those of lesser
importance for the structural and functional properties of the protein [440].
The following numerical example illustrates
the process of formation and fixation or elimination of neutral mutations. Consider a gene of
approximately 1000 nucleotides that codes for a
protein of about 330 amino acids; the effective
population size is Ne = 10 5 , and the neutral mutation rate Vo = 5 . 10- 9 per nucleotide and generation, corresponding to the value observed for
pseudogenes. Thus, one neutral mutation occurs
in this particular gene per generation and, in
most cases, will be randomly eliminated in the
course of about 24 generations. The probability
that the mutation will be fixed in the population
is approximately 1: 200000. It requires about
4.4.1 Neutral Theories of Molecular Evolution
141
400000 generations for the mutation to spread
throughout the whole population, and l/vo =
200 million generations before the mutated nucleotide is finally replaced by another. Many
speciation processes will, of course, occur within
this period. Therefore, neutral mutations are
usually very old, in fact mostly older than the
species in which they are found. The nucleotide
position (the mutation site) is polymorphic only
during the 400000 generations required for fixation; during the following 200 million generations it will be monomorphic. The probability of
polymorphy is correspondingly larger when the
numerous nucleotides of the whole gene are considered [210, 212]. The time required for the fixation of a useful mutation is comparatively short;
for a mutation with a selective advantage s (fitness = 1 + s), the time is given by (2/s)loge
(2Ne); with s = + 0.01 and Ne = 10 5 , the time
required is 2900 generations. Thus, advantageous
mutations in the phase of their fixation contribute very little to the polymorphism of the
population [294].
If we make the assumption that, in reality,
each mutation produces a new allele (the infinite
allele model), then the mean heterozygosity is
given by
(4.9a)
Taking into account the limited resolution of electrophoretic investigations (stepwise allele
model), then
H = 1- (1 + 8Nevotl12
(4.9b)
Where Nevo < 1, the two models give very similar
results, where Nevo is large, the value of H from
Eq. (4.9b) will be smaller [210, 212]. Extremely
low, almost undetectable heterozygosity results
when the population is very small (Ne < 1000), as
is often the case, for example, with large mammals [210, 212, 294]. According to Eq. (4.9a), in
very large populations H should approach 1.0,
whereas in fact the mean heterozygosity rarely
exceeds 0.3. The relatively low value of H = 0.177
in the tropical species Drosophila willistoni,
which includes thousands of millions of individuals, was used by Ayala as an argument against the
neutral theory of polymorphism. However, it is
also probably the case in this species that the
effective population size is much smaller than the
total number of individuals, and the polymorphism is heavily reduced by the frequent elimination
of local populations [210,212, 294]. Polymorphism can also be reduced by highly selected substitutions [201].