From sequence to consequence and back

The genotype-phenotype relation is at the core of theoretical biology. It is argued why a mathematically based explanatory structure of this relation is in principle possible, and why it has to embrace both sequence to consequence and consequence to sequence phenomena. It is suggested that the primary role of DNA in the chain of causality is that its presence allows a living system to induce perturbations of its own dynamics as a function of its own system state or phenome, i.e. it capacitates living systems to self-transcend beyond those morphogenetic limits that exist for non-living open physical systems in general. Dynamic models bridging genotypes with phenotypic variation in a causally cohesive way are shown to provide explanations of genetic phenomena that go well beyond the explanatory domains of statistically oriented genetics theory construction. A theory originally proposed by Rupert Riedl, which implies that the morphospace that is reachable by the standing genetic variation in a population is quite restricted due to systemic constraints, is shown to provide a foundation for a mathematical conceptualization of numerous evolutionary phenomena associated with the phenotypic consequence to sequence relation. The paper may be considered a call to arms to mathematicians and the mathematically inclined to rise to the challenge of developing new formalisms capable of dealing with the deep defining characteristics of living systems.