This graph shows the results of natural selection and random drift. The thick purple line shows the predicted change in frequency of the red allele due to natural selection alone. It represents what would happen in an infinitely large population. The thin red lines are simulations that include both random drift and natural selection.
Set the relative fitness of one allele to 1.0, and set the relative fitness of the other allele to less than or equal to 1.0. When both fitnesses are 1.0, only random drift will operate; the results should be the same as on the previous web pages that showed the effects of random drift.
When one fitness is less than 1, the predicted result is that the allele with the higher fitness increases in frequency until it becomes fixed. Due to random drift, however, it may get lost instead. Try different combinations of fitnesses and population sizes. You should see that the results of the simulations fit the purple line quite closely when the population size is large or the difference in fitness is large. As the population gets smaller, the effect of random drift gets more important. Random drift is also more important when the selection coefficient (the difference in relative fitness between the two alleles) gets smaller.
Selection plus drift: haploid
To model the fate of a new allele, set the initial red allele frequency to 1/N; for example, if the number of haploid individuals is 100, set the allele frequency to 0.01. Try different fitnesses for the blue allele. You should see that even with really large selection coefficients, such as 0.5, the new red allele will be lost sometimes, even though it is more fit. As the selection coefficient gets smaller (as the relative fitness of the blue allele gets closer to 1), it is increasingly likely that the new red allele will be lost.
Try selection coefficients against the new allele that are around 1/N; for example, if N is 100, set the fitness of the red allele to 0.99. You should see that even though the red allele has lower fitness, its fate is about the same as if the two alleles had equal fitness: it has a probability of becoming fixed about equal to its initial frequency.
This page was last revised March 6, 2009. Its address is http://udel.edu/~mcdonald/evolseldrifthap.html.
©2009 by John H. McDonald. You can probably do what you want with this content; see the permissions page for details.