Evolutionary topology of adaptive landscapes

In the previous example we have seen that it is possible to construct more and more complicated evolutionary scenarios in an adaptive landscape simply by adding additional adaptive peaks. Now let us consider the possible shapes and arrangements of those peaks. If you go hiking in the mountains, you immediately notice that not all mountains are alike. Some are very high, with precipitous slopes. Others are lower, and have more gently rounded slopes. Just as in a real landscape, the peaks and hills in an adaptive landscape may come in different sizes, shapes, and arrangements.

The theoretician Stuart Kauffman (1993, 1995) has conducted extensive computer simulations of evolution via the process of natural selection in what he calls 'NK fitness landscapes'. In NK fitness landscape models, N is the number of genes under consideration and K is the number of other genes which affect each of the N genes. The fitness of any one of the N genes is thus a function of its own state plus the states of the K other genes which affect it, allowing one to model epistatic genetic interactions. Such interactions can be extremely complex, yet still can be modelled with the computer.

Kauffman's computer simulations have demonstrated that two end-member landscapes exist in a spectrum of NK fitness landscapes: a 'Fujiyama' landscape at K equal to zero, and a totally random landscape at K equal to N minus one, which is the maximum possible value of K. In the Fujiyama landscape a single adaptive peak with a very high fitness value exists, with smooth slopes of fitness falling away from this single peak (Fig. 2.12). Such a fitness landscape exists where there are no epistatic interactions between genes, where each gene is independent of all other genes. At the other extreme, every gene is affected by every other gene, and a totally random fitness landscape results, a landscape comprised of numerous adaptive peaks all with very low fitness values.

Morphological Trait

Figure 2.12. Contrasting topologies of adaptive landscapes. The dashed line depicts a 'Fujiyama' landscape, with a single adaptive peak with very high adaptive value, versus the solid line depicting a 'rugged' landscape, with multiple peaks of varying height but all of much lower adaptive value than the Fujiyama peak.

Morphological Trait

Figure 2.12. Contrasting topologies of adaptive landscapes. The dashed line depicts a 'Fujiyama' landscape, with a single adaptive peak with very high adaptive value, versus the solid line depicting a 'rugged' landscape, with multiple peaks of varying height but all of much lower adaptive value than the Fujiyama peak.

In a Fujiyama landscape a single adaptive maximum occurs, in a random landscape any area in the landscape is just about the same as any other area. Between these two extremes exists a spectrum of landscapes, ranging from 'smooth' (a few large peaks) to increasingly 'rugged' (multiple smaller peaks; Fig. 2.12), and from 'isotropic' (landscapes where the large peaks are distributed uniformly across the landscape; Fig. 2.13) to 'nonisotropic' (landscapes where the large peaks tend to cluster together; Fig. 2.13).

Kauffman (1993, 1995) has argued that the process of evolution on Earth appears to have taken place on rugged fitness landscapes and not on Fujiyama landscapes, smooth landscapes of high peaks that he characterizes as the Darwinian gradualist ideal. Computer simulations of the process of evolution via natural selection in rugged fitness landscapes reveals on the one hand that the rate of adaptive improvement slows exponentially as the evolving population climbs an adaptive peak, but on the other hand that the highest peaks in the landscape can be climbed from the greatest number of regions! The latter conclusion is in accord with the empirical observation that the phenomenon of convergent morphological evolution has been extremely common in the evolution of life on Earth, a phenomenon that we shall examine in more detail in the next chapter.

Figure 2.13. Contrasting topologies of adaptive landscapes. The top figure depicts an 'isotropic' landscape, where the adaptive peaks are uniformly distributed across the landscape. The bottom figure depicts a 'nonisotropic' landscape, where the adaptive peaks cluster near one another in several groups.

Morphological Trait 1

Figure 2.13. Contrasting topologies of adaptive landscapes. The top figure depicts an 'isotropic' landscape, where the adaptive peaks are uniformly distributed across the landscape. The bottom figure depicts a 'nonisotropic' landscape, where the adaptive peaks cluster near one another in several groups.

If life has evolved on rugged fitness landscapes then epistatic interactions must be the norm, and the fitnesses of morphological character states must be correlated. Kauffman (1993, 1995) has argued that the more interconnected the genes are the more conflicting constraints arise. These conflicting constraints produce the multipeaked nature of the rugged landscape (Fig. 2.12). There exists no single superb solution as in a Fujiyama landscape. The conflicting constraints of the inter-correlated genes produce large numbers of compromise, less than optimum, solutions instead. A rugged landscape results, a landscape with numerous local peaks with lower altitudes.

Kauffman's computer simulations are based on models of genetic interactions and their consequences. However, we can take his fitness landscapes and transform them to adaptive landscapes by simply changing their dimensions (as we saw in Chapter 1), and use them to explore the consequences of the different adaptive landscape topologies for the evolution of morphology. In doing so, we must keep in mind the caveat of Arnold et al. (2001) that a complex fitness landscape of genotypes does not automatically produce a corresponding complex adaptive landscape of phenotypes. We shall be exploring the morphological effects of geometry, not genetics.

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