Selection - Mutation - Drift

About this simulation

Many details about the worms and the model are the same as they are for the Drift and Mutation simulations.

• The worm genome is haploid.
• Worms reproduce asexually.
• Generations are non-overlapping.
• Population size is constant.

How it works

The simulation begins with a population of genetically identical driftworms. Each generation, new mutations are introduced. Mutations now affect fitness. So mutants can have a reproductive advantage or disadvantage, depending on your chosen value of s, the selection coefficient. Each generation, some of the worms reproduce asexually. Which worms reproduce is determined partly by chance (drift) and partly by natural selection.

Selection

First we assign a selection coefficient, s, to the mutations. In this model all mutations have the same selection value (this helps us illustrate selection but never happens in nature). The value of s can range from -1 to 1.

The absolute fitness of a worm is determined by the number of mutations it carries and the effect of each mutation (= s).

To calculate absolute fitness, start with 1, the fitness of a worm with no mutations. Each mutation will increase or reduce fitness by the amount s (the selection coefficient). So count the number of mutations and multiply by s, add this number to 1. Below, we start with the case of detrimental mutations.

Calculating absolute fitness
	s	# mutations	calculation	absolute fitness
	-0.1	3	1 + (- 0.1)(3)	0.7

Note: This is an additive model. As mutations accumulate, so do their effects on fitness. The effect of each mutation on fitness is the same, regardless whether it's the first mutation on a gene or the tenth.

The relative fitness of a worm is calculated by dividing the absolute fitness of that worm by the absolute fitness of the worm with the highest absolute fitness. Below, we continue looking at a case of detrimental mutations.

Calculating relative fitness
		s = - 0.1	M	absolute   fitness	relative fitness
1			3	0.7	0.7/1  =  0.7
2			1	0.9	0.9/1  =  0.9
3			0	1	1/1    =  1

Now worms are selected to reproduce. To select a worm, the computer generates a random number between 0 and N (1, 2, or 3 for the population above). Then the computer generates a random number between 0 and 1. If the random number is less than the relative fitness of the selected worm then that worm produces. The computer selects another potential parent until N worms have been produced.

Review of Drift and Mutation techniques

[change this ...]

Genetic Drift is simulated just as in the Drift simulation. N is the population size, which is constant. The worms are numbered 1 through N. In each generation, the computer draws N random digits, from 1 through N, which determine how many offspring each individual will leave in the next generation. This simulates drift. For example, in the graphic to the right, N = 5. The computer randomly drew a number from 1 to 5, five times. In this case, the computer drew the numbers 1, 5, 4, 3, and 1. Parent 1 had two offspring. Parents 3, 4, and 5 each had one offspring.

Mutation is simulated by introducing single base substitutions into the population. The probability that a base will change to another is the mutation rate (m) between 0 and 1, which is set by you.

The following is repeated each generation. For each of the 10 bases in each worm, the computer draws a random number between 0 and 1 (that's 10xN random numbers each generation). Each random number is compared to the mutation rate (m). If the random number is smaller than m, then that base changes to one of the other three bases which is chosen randomly.

For example, on the right, the computer drew random numbers. When m is greater than the random number (m>#), a mutation results. ... [graphic]

[the mutations do not affect the phenotype]

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Selection