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3.5 Relative Fitness

The selection coefficient is used to model the health of an individual relative to the health of the rest of the population.

The relative fitness of an individual, denoted w, is defined to be where n is the number of mutations the individual carries. Note that w is also a value between 0 and 1, where 1 indicates a perfectly healthy individual (no mutations) and values less than 1 are relatively unhealthy individuals. Note also that if s = 0, i.e. all mutations are harmless, then an individual's health is always 1.0, no matter how many mutations it carries. Similarly, if a single mutation is enough to kill the individual since w = 0 means the individual is too unhealthy to survive. This fitness value is an abstraction of the general rule of ``survival of the fittest'' since those individuals with a higher relative fitness are more likely to survive.

In sexual reproduction we may want to distinguish between recessive and dominant mutations, where recessive mutations have less of an effect. This will be a factor only at heterozygous loci, where an individual has one wild and one mutated gene. If we want the mutations to be recessive, we should scale the effect of the mutated gene by a dominance factor d. The fitness function then becomes

In this expression is the number of homozygous mutations, i.e. the mutations that occur in loci of type 11. is the number of heterozygous mutations. d is the dominance factor; if it is 1 the mutations are neither dominant nor recessive, and the equation reduces to . If d<1 the mutations are recessive and have slightly less effect, and if d>1 they are dominant and have greater effect.