In this talk, I will discuss two factors that affect the probability of fixation of adaptive mutations: demography and levels of selection.
The fate of a new beneficial mutation within a population was first addressed by Fisher, Haldane, and Wright in the 1920's and 1930's.
In his 1927 paper, Haldane proved the classic result that the probability of fixation of a new beneficial mutation (P) is approximately 2s in a large population of constant size.
Haldane used a branching process to calculate P, noting that for an allele to be lost, all offspring copies of the allele must also be lost.
By assuming that the number of offspring per parent is, on average, one in a population of constant size, is 1+s for a new beneficial mutant, and is Poisson distributed,
When s is small,
With changing population size, what is the probability of fixation of an allele and how does this affect the rate of evolution of a species?
In this case,
When r>0, beneficial mutations will fix at a faster rate.
When r<0, beneficial mutations will fix at a slower rate.
Why? In a growing population, every individual has more offspring on average, which protects the new mutation from loss while rare.
By solving the inhomogeneous branching process,
This reduces to 2(s+r) when the population is far from carrying capacity and to 2s at carrying capacity.
We therefore define a fixation effective population size (Ne) such that:
Importantly, Ne may be used in Kimura's more general diffusion equation for the probability of fixation:
This equation may be used to determine the probability of fixation for
Growing populations incorporate more beneficial mutations and fewer deleterious mutations than predicted based on current population size.
Shrinking populations incorporate fewer beneficial mutations and more deleterious mutations than predicted based on current population size.
Evolutionary forces are likely to reinforce, rather than counteract, externally caused changes in population size, such as those currently caused by humans.
The alleles that survive in a population will reflect past demographic changes of the population as well as their own selective effects.
In particular, selection within an individual is a powerful force, since it is compounded over many cell divisions during an individual generation.
When a mutation first appears within a developing individual, it creates a genetic mosaic and generates genetic variability among cells upon which selection can act.
When single-cell offspring are produced in subsequent generations, however, the genetic variability within an individual is lost and selection among cells becomes ineffective.
Can selection within an individual have an impact on the fate of an allele even if it only acts in the first generation in which a mutant appears?
What evidence is there for such selection?
Mutations that are recessive lethal at the individual level were studied at the cellular level. Homozygous cells within heterozygous individuals grew more slowly or not at all in 23 out of 39 cases.
Example 2. Barley (Gaul 1958).
Gaul irradiated barley seeds and watched their development. Tillers that developed late and that had more time to experience within-individual selection had 23-33% fewer mutations.
Example 3. Variegated maple (Whitham and Slobodchikoff 1981).
Wildtype revertants on a variegated maple tree spread and took over 95% of the tree's foliage within ten years.
Example 4. Drosophila (Dearolf 1988).
After irradiating larvae heterozygous for a recessive lethal mutation, mutant homozygous cells were observed 0% - 60% as often as wildtype homozygous cells in the adult.
) of adult cells that carry a mutation.
To calculate , we assume that development occurs by a series of binary cell divisions.
The first step is to find the probability (Px) that the mutation happens in cell generation (x):
where k1 is the number of cell divisions per generation for non-mutant cells.
If a mutation occurs at the xth cell division, there will be 1-x/k1 of a generation left in which time the number of mutant cells will reach:
where k2 is the number of cell divisions per generation for mutant cells.
Similarly, the number of non-mutant cells in the adult will reach:
The expected proportion of mutant cells in the adult is then:
), is
relative to () in the absence of selection.
The proportion of mutant cells grows or declines nearly exponentially with the strength of selection and the number of cell divisions.
Cell-lineage selection can dramatically increase the rate of fixation of beneficial mutations and decrease the observed rate of deleterious mutations, both of which will help a population adapt to its environment.
Evolution should maximize opportunities for cell-lineage selection.
When might these conclusions be false?
If cell fitness and individual fitness are in opposition, then selection among cells would favor those mutations that decrease fitness at the individual level and evolution should minimize opportunities for cell-lineage selection.
For a multicellular organism to become complex with highly differentiated tissues, the organism must limit the ability of some cells to become reproductive tissues. Cell-lineage selection will then only be able effective within the germ-line.
That is, there exists a potential trade-off between the evolutionary advantages of cellular specialization and the evolutionary advantages of cell-lineage selection.
The probability of incorporation depends strongly on the current population size relative to future population sizes, with growing populations incorporating more of the beneficial mutations and fewer of the deleterious mutations that appear over time.
The probability of incorporation also depends strongly on the degree of selection within an individual. The rate of evolution in organisms with many cell divisions per generation is potentially much higher for mutations that affect fitness at the cellular level as well as the individual level.