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Adaptive landscape and genetic algorithms

The adaptive landscape is a theoretical construct, typically visualized as a surface in 3D-space resembling a mountainous landscape. Adaptiveness is plotted on the z-axis and reaches one or more maxima, called adaptive peaks. The x- and y-axes (and any additional dimensions) represent quantitative or qualitative biological variability. 

Each individual occupies one point on the surface of the adaptive landscape, and each species occupies a typically contiguous area. Gene mutation and recombination randomly distribute new individuals at points generally not far from their parents, and selection rewards with a higher reproductive success the individuals located at higher z values. 

Intraspecific variability typically bridges only narrow adaptive valleys. Unless broad valleys prevent further evolution toward a peak, a species evolves ‘uphill’ and eventually reaches the peak, where continued selection keeps it in place. A species has no ‘knowledge’ of regions of the adaptive landscape it does not occupy, so nearby adaptive peaks may very well remain unoccupied. McGhee (2007) provided an extensive discussion of adaptive landscapes, their history, and related concepts.

In computer programming, genetic algorithms (GAs) were inspired by evolution and are interesting in this context. These algorithms were not developed as accurate models of evolution, and a comparison with evolution should therefore be applied with caution.

In GAs, parameters correspond to genes. Program execution starts with a population of candidate solutions, each storing slightly different parameter values. Values in the next generation are computed by applying recombination and mutation to the parents’ values. Finally, selection adjusts the probability of reproduction of each offspring, based on its optimality (z-value). 

With empirical adjustments for specific problems, genetic algorithms are often successful in solving engineering problems — and with good solutions. However, no underpinning theory clearly explains why.

Like evolution, GAs cannot reach a global optimum (highest adaptive peak) separated from the population by a broad low-optimality region. In this case, GAs lead the population no further than a local optimum. The No Free Lunch theorem in optimization theory states that none of the alternative GA modifications to mitigate this problem can be more efficient than all others in all problems, i.e. there is no general solution. 

The similarities of evolution with GAs suggest that evolution, in a rugged adaptive landscape, should be intrinsically poor in reaching far adaptive peaks, and cannot become much better. However, the ubiquitous occurrence of convergent evolution suggests that evolution is highly successful in reaching adaptive peaks (see Constructional morphology and morphodynamics). A proposed explanation involves generalist species, which occupy low-z regions and ‘hop’ among low adaptive peaks as stepping-stones to higher ones.

Another possible explanation for this disparity is that GAs fail to model evolution in critical respects: they make no distinction between genotype and phenotype, they cannot model gene interdependencies, and their solution space (the complete adaptive landscape) is static. Several evolutionary hypotheses rely instead on adaptive peaks that wander across the adaptive landscape. Some adaptive peaks may be continuously reshaped by evolution (e.g. once an ecological niche is occupied, it becomes less accessible to other species, or a numerically large population may deplete the resources on an adaptive peak and lower it, encouraging an exodus). Other peaks may be shaped by unalterable factors such as physical laws, and are sufficiently static to be reached multiple times. Wandering adaptive peaks may carry species across normally impassable valleys, and in this way allow species to reach even isolated static peaks. 

It is not clear at present, and should be investigated, whether a mixed static–dynamic adaptive landscape versus a fully static or fully dynamic one results in significantly different evolutionary patterns and tempos.


References

McGhee G R Jr (2007). The geometry of evolution. University Press, Cambridge, 200 p.

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