Noting that the normalized fitness values are ratios, a comparison for the fitness-landscapes shown in Figure 3 with those shown in Figure 4 indicates that the topologic relief of single-task landscapes is, on the average, 10 times greater than that of multi-task landscapes—that is, the fitnesses of phenotypic maxima with respect to the fitnesses of their ancestral condition are 10 times greater than the fitnesses of phenotypic optima with respect to their ancestral condition. Thus, the fitness of phenotypic optima apparently falls closer to the mean fitness of all the phenotypes within a landscape as the functional complexity of the phenotypes under selection increases. As noted, this result is consistent with engineering theory that indicates that the performance levels of artifacts designed to perform individual functional tasks are higher than those of artifacts designed to simultaneously perform two or more of the same tasks. Additionally, within both categories of fitness-landscapes, the relative fitness values of phenotypes occupying fitness peaks decreases as the number of peaks increases (r = 0.82; N = 25 maxima and optima)—that is, the number of phenotypic maxima (or optima) increases as the elevation of a landscape declines.

These observations are crudely summarized in Figure 5; they suggest that both the number and the accessibility of phenotypic optima increase as the number of functional obligations contributing to total fitness increases. Put differently, as the complexity of optimal phenotypes increases, the fitness of these optima falls closer to the mean fitness of all the phenotypes under selection. One implication of this conclusion is that the majority of walks over complex fitness-landscapes occurs over fitness plateaus and, therefore, is largely undirected by gradients of fitness until walks approach the foothills of fitness peaks.

Weaknesses and Strengths of Simulated Walks

However entertaining they may be, computer-simulated walks have four obvious weaknesses. First, "fitness" was measured in terms of comparatively few biological tasks that were further assumed to contribute to fitness in an independent and equal manner. The obvious epistatic relation between photosynthesis and reproduction (Gates, 1965; Nobel, 1983), therefore, was entirely neglected, as was the possibility that some tasks are more important to fitness than others (Franklin and Lewontin, 1970; Lewontin, 1974; Ewens, 1979). Second, walks were simulated as continuous processions among more fit phenotypes. Alternatively, plausible types of walks were not considered (Gillespie, 1983, 1984; Kauffman, 1993). Third, fitness-landscapes were assumed to be spatially stable in pointed neglect of evident changes in the environment that are predicted to shift the location of fitness optima



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