Generating Novel Variation
Additive genetic variance in fitness (i.e. differences in the average fitness of alleles at a locus) is the basic fuel upon which evolution acts in a sexual population.
Yet, in most of the models we've discussed, selection exhausts this variation. Eventually:
Generation | Heritability (high line) | Heritability (low line) |
1-9 | 0.32 | 0.50 |
10-25 | 0.34 | 0.23 |
26-52 | 0.11 | 0.10 |
53-76 | 0.12 | 0.15 |
(From Dudley, 1977; See Ridley p. 239).
What prevents evolution from grinding to a halt?
Mutation is the ultimate source of novel genetic variation.
Mutation: Spontaneous change from one allele to another allele due to
The error rate in DNA replication per generation varies from organism to organism:
Species | Genome size (basepairs) | Mutation rate per basepair | Mutation rate per genome |
Bacteriophage lambda | 4.7 104 |
2.4 10-8 | 0.001 |
Escherichia coli | 3.8 106 |
4 10-10 | 0.002 |
Neurospora crassa | 4.5 107 |
5.8 10-11 | 0.003 |
Drosophila melanogaster | 4.0 108 |
2.3 10-9 | 0.93 |
(Estimates per generation. From Drake 1974; See also Futuyma, 1998)
The genome of an organism is not faithfully replicated from generation to generation.
EXAMPLE: Humans have a diploid genome size of 6.8 109 basepairs. Assuming a generation time of 20 years and an est. mutation rate per year of 3.5 10-9 (Li, 1997), this suggests that 300-500 new mutations appear somewhere within the genome each generation.
The spontaneous mutation rate also varies from gene to gene:
Species and locus | Mutations per 100,000 gametes (or cells) |
Escherichia coli | |
|---|---|
Streptomycin resistance | 0.00004 |
Resistance to T1 phage | 0.003 |
Arginine independence | 0.0004 |
Drosophila melanogaster | |
Yellow body | 12 |
Brown eyes | 3 |
Eyeless | 6 |
Homo sapiens | |
Retinoblastoma | 1.2-2.3 |
Achondroplasia | 4.2-14.3 |
Huntington's chorea | 0.5 |
(From Dobzhansky, 1970; See also Futuyma, 1998)
The mutation rate also depends on the alleles involved:
e.g. Coat color mutations in mice (Russell 1963; Schlager and Dickie 1971)
Mutations disturbing wildtype function (forward mutations) often occur at higher rates than mutations restoring wildtype function (back mutations).
Roughly, in multicellular organisms, mutations occur at an approximate rate of 10-9 - 10-8 per basepair per year or 10-6 - 10-4 per gene per generation.
How does mutation affect the maintenance of variation?
Let:
is the mutation rate from A to a
is the mutation rate from a to A
:
=0 and =1 are NOT equilibria. Fixation is not stable when mutations recur.
However, the population approaches equilibrium at a rate of only
+.
VERY SLOW!
Example:
With =
= 10-6, the population will eventually reach the equilibrium of =1/2.
With a starting frequency of p[0]=0
This occurs over such a long time frame that other forces such as
selection (even very weak selection) or sampling error
in finite populations are likely to overwhelm evolution of the system to
.
In the vast majority of cases, these changes are deleterious (= reduce fitness), e.g. the many mutations causing severe human genetic diseases.
(From Cavalli-Sforza and Bodmer, 1971)
Only rarely will a mutation produce a more fit individual.
To what extent will selection be effective at eliminating deleterious mutations from a population?
NOTE: I will use "mutation" to refer to a new alteration in the DNA. I will use mutant to refer to the allele produced by mutation. A mutant allele may remain in a population long after it originated by mutation.
Let selection act against the mutant a allele, with the relative fitnesses of diploid individuals equaling:
s measures the selection coefficient against the mutation and h measures the dominance of the mutation.
We will assume that s is larger than the mutation rate, , to a.
If we add mutation to the model of diploid selection, we find that the population rapidly evolves towards fixation on A, but rather than a being lost entirely, it reaches a mutation-selection balance:
Mutant alleles are generally so rare that the mutant allele is almost always found in heterozygotes.
Only if the mutation is completely recessive (h=0) will homozygous mutants be common. In this special case (where only the aa genotype is selected against), the frequency of the mutant allele tends toward:
 |
Much that we know about the dynamics of mutations comes from the pioneering work in population genetics done by J. B. S. Haldane in the 1920's. |
"J.B.S. Haldane is reported to have said that his great pleasure was to see his ideas widely used even though he was not credited with their discovery."
For example, Haldane was the first to estimate mutation rates using the above equations.
EXAMPLE: Albinism is a recessive condition that occurs in humans at a frequency of 1/20,000 (=q2). If albinos have a relative fitness of 0.9 (s = 0.1), then the mutation rate to the albino allele would be = 5 10-6.
EXAMPLE: Achondroplasia is a dominant condition causing dwarfing, which occurs at a frequency of 1/10,000.
Since it is dominant, most carriers are heterozygotes.
Therefore 2pq = 1/10,000 and q is approximately 1/20,000.
Affected individuals have an estimated relative fitness of 0.2 (s = 0.8).
The mutation rate to achondroplasia can then be estimated as = 0.8 1/20,000 = 4 10-5, which is consistent with the rate at which achondroplasia spontaneously appears within a population.
Mean relative fitness is therefore highest when q=0 and no mutant alleles exist in the population.
However, the population doesn't go towards q=0 (where the mean fitness equals 1) but rather to q=/hs (assuming that a is not completely recessive).
At the mutation-selection balance, the mean fitness equals:
Mutations reduce the mean fitness below the maximum possible by an amount equal to the mutation rate per diploid set of genes.
Oddly, the decrease in mean fitness caused by deleterious mutations does not depend on the fitness effects of the mutations.
More severe mutations will exist at a lower frequency, while less severe mutations will reach a higher frequency, but the fraction of deaths caused by mutation will be the same in both cases.
Point 1 The mean fitness at equilibrium is not the maximum possible.
Point 2 The reduction in mean fitness due to mutation is not that great at one locus alone, but it may be substantial with mutations occurring throughout the genome (= "Mutation Load").
Point 3 Mean fitness can decrease over time. Whenever the population starts nearer q=0 than
q=/hs, the mean fitness will decline towards 1-2.
While deleterious mutations decrease the mean fitness of a population, they are potentially an important source of genetic variation in the face of environmental change.
, what are the fitness effects of deleterious mutations throughout the genome?
If there are no fitness interactions among genes (no epistasis), then the average fitness of an individual would be (1-2 )# loci 
e-2 (# loci) = e-U, where U is the sum total deleterious mutation rate in a diploid genome.
What is U?
Current estimates of U for multicellular animals and plants are roughly 0.2-2.0 (Lynch and Walsh 1998), but more data are sorely needed.
These estimates suggest a major fitness cost:
U | Average fitness = e-U | Mutation load (= 1-fitness) |
0.2 | 0.82 | 0.18 |
0.6 | 0.55 | 0.45 |
2.0 | 0.14 | 0.86 |
[If assumptions are accurate.]
For certain quantitative traits, researchers have estimated the amount of new additive genetic variance arising by mutation each generation.
A common method to estimate variance due to new mutations is to take a genetically uniform population (where VG = 0 and VP = VE) and subject it to selection.
The response of the population to selection can be used to determine h2m, the "mutational heritability" which equals the amount of new VA caused by one generation of mutation divided by VE.
(h2m will give the narrow sense heritability after one generation of mutation in a population with no genetic variance.)
Species and trait | h2m |
Drosophila melanogaster | |
|---|---|
0.0035 | |
Ethanol resistance | 0.0009 |
Viability | 0.0003 |
Mouse | |
Length of limb bones | 0.0234 |
6-week weight | 0.0034 |
Rice | |
Plant size | 0.0112 |
Reproductive traits | 0.0073 |
(From Lynch and Walsh, 1998.)
If the genetic variability in a population is exhausted (e.g. by inbreeding or following a period of strong selection), which of the above traits would you expect to show the highest longer-term response to selection?
Why might some traits have a higher mutational heritability than others?
SOURCES:
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