The topology of the possible:
Formal spaces underlying patterns of evolutionary change
Author(s):
Bärbel M. R. Stadler, Peter Stadler, Günter Wagner, Walter Fontana
Submitted to:
J. Theor. Biol.
Abstract:
The current implementation of the Neo-Darwinian model of evolution typically assumes that the set of possible phenotypes is organized into a highly symmetric and regular space equipped with a notion of distance, for example, a Euclidean vector space. Recent computational work on a biophysical genotype-phenotype model based on the folding of RNA sequences into secondary structures suggests a rather different picture. If phenotypes are organized according to genetic accessibility, the resulting space lacks a metric and is formalized by an unfamiliar structure, known as a pretopology. Patterns of phenotypic evolution - such as punctuation, irreversibility, modularity - result naturally from the properties of this space. The classical framework, however, addresses these patterns by exclusively invoking natural selection on suitably imposed fitness landscapes. We propose to extend the explanatory level for phenotypic evolution from fitness considerations alone to include the topological structure of phenotype space as induced by the genotype-phenotype map. We introduce the mathematical concepts and tools necessary to formalize the notion of accessibility pretopology relative to which we can speak of continuity in the genotype-phenotype map and in evolutionary trajectories. We connect the factorization of a pretopology into a product space with the notion of phenotypic character and derive a condition for factorization. Based on anecdotal evidence from the RNA model, we conjecture that this condition is not globally fulfilled, but rather confined to regions where the genotype-phenotype map is continuous. Equivalently, local regions of genotype space on which the map is discontinuous are associated with the loss of character autonomy. This is consistent with the importance of these regions for phenotypic innovation. The intention of the present paper is to offer a perspective, a framework to implement this perspective, and a few results illustrating how this framework can be put to work. The RNA case is used as an example throughout the text.
Keywords: Evolution, Genotype-Phenotype Map, Character, Pretopology
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DESTAQUE DESTE BLOGGER:
“A further mechanistic consequence of the topological interpretation of major evolutionary transitions is that natural selection does not provide a complete explanation for their occurrence. Natural selection is a sufficient explanation for the outcome of an evolutionary process, if the genetic variation contributing to the derived phenotype is easily accessible. Whether a transition occurs, then only depends (to a first approximation) on the strength and direction of selection. If major transitions, however, require specially poised genotypic/developmental realizations of the ancestral phenotype, then the transition critically depends on factors not under the control of selection, since different genetic realizations of the same ancestral phenotype lie on a neutral network and are not distinguishable by selection on phenotypes.” p. 54.
NOTA BENE:
A seleção natural é impotente para explicar as principais transições evolucionárias.
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