The Hardy-Weinberg ratio explains quite easily why mutations or rare alleles are more likely to be spread in a small population than a large one:
H-W is one of the most basic principles in population genetics and yet is one of the most often misunderstood. H-W by itself does not address changes in allele frequency but describes what genotypes will be present at any given allele frequencies after one round of mating.
Let's say we have an allele with a frequency of q = 0.10 so that p = 1 - q = 0.90. What H-W says the genotypes would be AA = 0.81, Aa = 0.18, aa = .01. But notice that p still equals 0.90 and q still equals 0.10, no change in allele frequency. Without some force that changes the allele frequency, the frequency will remain q = 0.10.
Here's where H-W gets useful; let's say we find the population has an allele proportion of q = 0.10 and p = 0.90 but the measured genotype frequency is AA = 0.828, Aa = .162, aa = 0.028. We recognize this to be out of H-W equilibrium and so one of the 5 assumptions must not be valid
1. mating is random
2. population is infinitely large
3. no migration
4. no mutation
5. no selection
In this case, mating is not random but shows signs of inbreeding (the proportion of heterozygotes is reduced). We can estimate the inbreeding coefficient by F = (H
O-H
E)/H
O where H
O is heterozygotes observed and H
E is heterozygotes expected. In this case F = 0.10 which means 10% of the population is autozygous.
Now I was a little confused at first by the "reached after a single generation" comment, until I realized that this applies to each generation and changes with selection acting on the relative fitness of p and q.
Right, so we start with an allele frequency and determine the genotype. The population may then be subjected to selection which will remove an uneven proportion of alleles, ie. one allele will increase in frequency, the other will decrease. Selection models are kinda involved and I won't take time on it here, but let's say that the genotype aa is advantageous and the allele q increases from 0.10 to 0.15 because of selection. We now need to do the H-W calculation again to determine the genotypes of the next generation AA = 0.723, Aa = 0.255, aa = 0.022. So, an increase of 50% in allele frequency resulted in a 120% increase in 'aa' genotype frequency.
But certainly for a new mutation allele the q will be necessarily small, and thus it's relative proportion within the population will be overwhelmingly swamped by p in very large populations but not so much in very small populations.
Definitely true. Unless q confers a large fitness advantage, I would expect drift would be the primary process that would increase its frequency in a small population. Mutations can move to fixation in small populations rather rapidly, especialy when they have even a small fitness advantage.
If you are interested in a really good, easy to understand book on population genetics, I highly recommend
A Primer of Population Genetics. We used it in my Evolutionary Biology course and it is an excellent introduction to population genetics. Even if you have a more advanced understanding of the material, it is still a really good book.
HBD
Whoever calls me ignorant shares my own opinion. Sorrowfully and tacitly I recognize my ignorance, when I consider how much I lack of what my mind in its craving for knowledge is sighing for... I console myself with the consideration that this belongs to our common nature. - Francesco Petrarca
"Nothing is easier than to persuade people who want to be persuaded and already believe." - another Petrarca gem.
Ignorance is a most formidable opponent rivaled only by arrogance; but when the two join forces, one is all but invincible.