TBI 02-pfs-002
The Genotype-Phenotype Map
## 02-pfs-002

#
Abstract:

The Genotype-Phenotype Map

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## Peter F. Stadler

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 at least with
a notion of distance, for example, a Euclidean vector space. Recent
computational work on the biophysical genotype-phenotype model defined by
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. If recombination is taken
into account, an even weaker structure, known as neighborhood space, must
be used.

Patterns of phenotypic evolution - such as punctuation, irreversibility,
and modularity - result naturally from the properties of the
genotype-phenotype map, which, given the genetic accessibility structure,
defines accessibility in the phenotype space. The classical framework,
however, addresses these patterns by exclusively invoking natural selection
on suitably imposed fitness landscapes. We 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. The topological framework allows us to consider
e.g. the continuity of an evolutionary trajectory in an unambiguous way.

Lewontin's notion of ``quasi-independence'' of characters can be formalized
as the assumption that a region of the phenotype space is represented by
a product space of orthogonal factors. In this picture each character
corresponds to a factor of a region of the phenotype space. We consider any
region of the phenotype space that has a given factorization as a ``type'',
i.e., as a set of phenotypes that share the same set of phenotypic
characters. Using the notion of local factorizations a theory of character
identity can be developed that is based the correspondence of local factors
in different regions of the phenotype space.

**Keywords:**
Genotype-Phenotype Map,
Generalized Topology,
Evolutionary Trajectories, Continuity,
Characters

Presented at the *Altberg-Austin Workshop in Theoretical Biology*
on *"Biological Information: Beyond Metaphor: Causality, Explanation, and
Unification"*, 11-14 July 2002, Altenberg.

Return to 2002 working papers list.