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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. In addition, if it possible to define the fitness of an allele as an average of individual fitness values, then, it must be possible to define the mean fitness of a whole population from such values.  

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. In addition, if it possible to define the fitness of an allele as an average of individual fitness values, then, it must be possible to define the mean fitness of a whole population from such values.  

[[Gaussian adaptation]] is based on the selection of individuals using definition given by Hartl, 1981. The fitness of the individual is 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. This definition is perhaps less useful in breeding programs, but may be useful in certain philosophical discussions about evolution. If the selection of individuals rules the enrichment of genes, then Gaussian adaptation will perhaps give a more reliable view of evolution.  

[[Gaussian adaptation]] is based on the selection of individuals using definition given by Hartl, 1981. The fitness of the individual is the probability s(x) that the individual having the n characteristic parameters x^T = (x₁, x₂, …, x_n) – where x^T is the transpose of x – will survive, i. e. become selected as a parent of new individuals in the progeny. This definition is perhaps less useful in breeding programs, but may be useful in certain philosophical discussions about evolution. If the selection of individuals rules the enrichment of genes, then Gaussian adaptation will perhaps give a more reliable view of evolution.  

The image below shows two different cases (upper and lower) of individual selection, where the green points with fitness = 1 - between the two lines - will be selected, while the red points outside with fitness = 0 will not. The centre of gravity, m, of the offspring is fat black and ditto of the parents and offspring in the new generation, m*  (according to the Hardy-Weinberg law), is fat red.  

The image below shows two different cases (upper and lower) of individual selection, where the green points with fitness = 1 - between the two lines - will be selected, while the red points outside with fitness = 0 will not. The centre of gravity, m, of the offspring is fat black and ditto of the parents and offspring in the new generation, m*  (according to the Hardy-Weinberg law), is fat red.  

http://www.evolution-in-a-nutshell.se/image001.gif

[http://www.evolution-in-a-nutshell.se/image001.gif]

Because the fraction of green feasible points is the same in both cases, Fisher’s theorem states that the increase in mean fitness in vertical direction is equal in both upper and lower case. But the phenotypic variance (not considered by Fisher) in the horizontal direction is larger in the lower case, causing m* to considerably move away from the point of intersection of the lines. Thus, if the lines are pushed towards each other (due to arms races between different species), the risk of getting stuck decreases. This represents a considerable increase in mean fitness (assuming phenotypic variances almost constant).  Because this gives room for more phenotypic disorder/entropy/diversity, we may expect diversity to increase according to the entropy law, provided that the mutation is sufficiently high.

Because the fraction of green feasible points is the same in both cases, Fisher’s theorem states that the increase in mean fitness in vertical direction is equal in both upper and lower case. But the phenotypic variance (not considered by Fisher) in the horizontal direction is larger in the lower case, causing m* to considerably move away from the point of intersection of the lines. Thus, if the lines are pushed towards each other (due to arms races between different species), the risk of getting stuck decreases. This represents a considerable increase in mean fitness (assuming phenotypic variances almost constant).  Because this gives room for more phenotypic disorder/entropy/diversity, we may expect diversity to increase according to the entropy law, provided that the mutation is sufficiently high.