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Evolution in Sequence Space

Think of organisms as occupying a ``genotype space'' consisting of all possible sequences of all possible lengths of the elements of the genetic system (i.e., nucleotides or machine instructions). When the first organism begins replicating, a single self-replicating creature, with a single sequence of a certain length occupies a single point in the genotype space. However, as the creature replicates in the environment, a population of creatures forms, and errors cause genetic variation, such that the population will form a cloud of points in the genotype space, centered around the original point.

Because the new genotypes that form the cloud are formed by random processes, most of them are completely inviable, and die without reproducing. However, some of them are capable of reproduction. These new genotypes persist, and as some of them are affected by mutation, the cloud of points spreads further. However, not all of the viable genomes are equally viable. Some of them discover tricks to replicate more efficiently. These genotypes increase in frequency, causing the population of creatures at the corresponding points in the genotype space to increase.

Points in the genotype space occupied by greater populations of individuals will spawn larger numbers of mutant offspring, thus the density of the cloud of points in the genotype space will shift gradually in the direction of the more fit genotypes. Over time, the cloud of points will percolate through the genotype space, either expanding outward as a result of random drift, or by flowing along fitness gradients.

Most of the volume of this space represents completely inviable sequences. These regions of the space may be momentarily and sparsely occupied by inviable mutants, but the cloud will never flow into the inviable regions. The cloud of genotypes may bifurcate as it flows into habitable regions in different directions, and it may split as large genetic changes spawn genotypes in distant but viable regions of the space. We may imagine that the evolving population of creatures will take the form of wispy clouds flowing through this space.

Now imagine for a moment the situation that there were no selection. This implies that every sequence is replicated at an equal rate. Mutation will cause the cloud of points to expand outward, eventually filling the space uniformly. In this situation, the complexity of the structure of the cloud of points does not increase through time, only the volume that it occupies. Under selection by contrast, through time the cloud will take on an intricate structure as it flows along fitness gradients and percolates by drift through narrow regions of viability in a largely uninhabitable space.

Consider that the viable region of the genotype space is a very small subset of the total volume of the space, but that it probably exhibits a very complex shape, forming tendrils and sheets sparsely permeating the otherwise empty space. The complex structure of this cloud can be considered to be a product of evolution by natural selection. This thought experiment appears to imply that the intricate structure that the cloud of genotypes may assume through evolution is fully deterministic. Its shape is pre-defined by the physics and chemistry and the structure of the environment, in much the same way that the form of the Mandlebrot set is pre-determined by its defining equation. The complex structure of this viable space is inherent in the medium, and is an example of ``order for free'' [45].

No living world will ever fill the entire viable subspace, either at a single moment of time, or even cumulatively over its entire history. The region actually filled will be strongly influenced by the original self-replicating sequence, and by stochastic forces which will by chance push the cloud down a subset of possible habitable pathways. Furthermore, co-evolution and ecological interactions imply that certain regions can only be occupied when certain other regions are also occupied. This concept of the flow of genotypes through the genotype space is essentially the same as that discussed by Eigen [22] in the context of ``quasispecies''. Eigen limited his discussion to species of viruses, where it is also easy to think of sequence spaces. Here, I am extending the concept beyond the bounds of the species, to include entire phylogenies of species.

next up previous
Next: Natural Evolution in Up: What Natural Evolution Previous: What Natural Evolution

Thomas S.Ray
Thu Aug 3 13:59:36 JST 1995