## Haldane’s dilemma

Most models of evolution in the area of population genetics consider only *hard natural selection.* Consequently, geneticists occasionally encounter apparently unsolvable paradoxes. An example is **Haldane’s dilemma** (Haldane 1957), describing the substitution cost accompanying the replacement of one allele in the population by some other, more advantageous allele. The **substitution cost** *(L)* is defined by the equation

where *W*_{op}denotes the *fitness* of an individual with optimal genotype and *W* is the average fitness of individuals in the population i.e. a parameter expressing how many times the average *fitness* of individuals in the population is lower than would be the average *fitness* in a population formed exclusively of individuals with optimum genotype. In models describing *hard selection,* the magnitude of the *substitution cost* for the population is directly proportional to the number of *genetic deaths*, i.e. the number of organisms eliminated by *natural selection* in substituting a suboptimal allele by an optimal allele. If new alleles constantly appear in the population, increasing the fitness of their bearers, the relative fitness of all the bearers of the other alleles is reduced (*W _{op}*, i.e. the fitness of individuals with optimal phenotype is always set at 1), increasing the

*substitution cost*for the population. Haldane pointed out that, with simultaneous selection in favour of a greater number of suitable alleles from various genes, the

*substitution cost*for a particular population can attain unrealistically high values and the number of

*genetic deaths*can easily exceed the reproduction potential of the population.

However, when we take into consideration that the individual alleles can be eliminated by *soft selection*, the situation looks rather different. The *cost* is constant in each generation, i.e. actually equal to zero. *Natural selection* always eliminates a constant percentage of individuals from the population without regard to the specific values of the *average fitness of individuals in the population *(Nunney 2003). On the other hand, it is apparent that selection can occur simultaneously in favour of only a limited number of traits; if selection occurs to the benefit of a great many traits, the viability of the population is not endangered (as it would be if hard selection were active), but the effectiveness of the selection of the individual traits would be proportionally reduced, and the **Hill-Robertson effect**would be manifested. This effect is especially marked when there is a close genetic connection between the loci in which selection occurs, i.e., e.g., in asexually reproducing organisms or for loci in areas in which genetic recombination does not occur for some reason (Charlesworth & Charlesworth 2000). The reduced effectiveness of simultaneous selection for a greater number of traits can play a significant negative role in the evolutionary response of the population or species to a rapidly changing environment (Nunney 2003).