As an example we may mention the definition of fitness given by Maynard Smith, 1998, in the following way: ”Fitness is a property, not of an individual, but of a class of individuals – for example homozygous for allele A at a particular locus. Thus the phrase ’expected number of offspring’ means the average number, not the number produced by some one individual. If the first human infant with a gene for levitation were struck by lightning in its pram, this would not prove the new genotype to have low fitness, but only that the particular child was unlucky.”
Even if the definition is useful in breeding programs, it can hardly be of any use as a basis of a theory of an evolution selecting individuals. It seems to me that this definition denies the fitness of the individual. Nevertheless, the individual fitness is needed, because otherwise the “expected average number of offspring” from a certain class of individuals can’t be determined. Also, if the mean fitness of a class of individuals can be used as a fitness of a gene, it can’t be forbidden to use the fitness of individuals to determine the mean fitness of a whole population.
Therefore, since Gaussian adaptation is based on selection of individuals the definition given by Hartl, 1981, is preferred. The fitness of the individual is defined as the probability s(x) that the individual having the n characteristic parameters x’ = (x1, x2, …, xn) – where x’ is the transpose of x – will survive, i. e. become selected as a parent of new individuals in the progeny.
Even if the fitness of the individual is a very uncertain measure the mean fitness as defined by
integral s(x) N(m -x) dx
where N is a Gaussian probability density function and m its mean, it may be a reliable measure. Thus, even if it is less useful in breeding programs, it may be useful in certain philosophical discussions about evolution, because in reality evolution is a giant lottery. In principle, even the lightning may be considered.