Substitutional Load

    Substitutional Load is the theoretical loss of fitness to a population during the interval over which a deleterious allele is replaced ("substituted") by an advantageous allele. This load may be estimated as the difference between the observed Mean Fitness ("Wbar") and the optimal fitness (Wbar = 1.0) in any one generation of selection, summed over all generations during substitution. In the Pepper Moth (Biston betularia) exercise, over the first 10 generations, the population is at a slightly sub-optimal fitness because of the presence of the 'carbonaria' allele, which generates a small fraction of dark moths in an otherwise light population. Over the next 90 generations, when the environment changes to favour the dark form, the population is suddenly at a substantially lower fitness, because the predominant light form is less fit. The curve is that expected for a advantageous dominant allele replacing a disadvantageous recessive allele. At the 100th generation, relative fitness again reverses to favor the light moths over the dark. Under these circumstances the curve is that expected for an advantageous recessive allele replacing a disadvantageous dominant allele. Note that the cumulative substitutional load is much greater than in the previous allelic substitution.

    The actual effects of allelic substitution in a population are variable. In the first stage of the example, the presence of a small number of dark moths likely does not change the total population size N. Even in the second and third stages, population size is unlikely to be reduced as much as (1 - Wbar) = 30%, as N will tend to stay near the carrying capacity K despite increased predation on the non-cryptic form. That is, where natural selection is "soft", actual loss of population fitness may be negligible. On the other hand, the relatively sudden environmental change in stage 2 renders the large majority of the population liable to predation, and a drop in N at least initially might be expected. "Hard" selection occurs when the predator birds form a 'search image' that targets the non-cyptic form almost exclusively.

    Note that substitutional load could also be estimated by integrating the area above the curve from a knowledge of its generating function.