Contingency, convergence and hyper-astronomical numbers in biological evolution.

Counterfactual questions such as "what would happen if you re-run the tape of life?" turn on the nature of the landscape of biological possibilities. Since the number of potential sequences that store genetic information grows exponentially with length, genetic possibility spaces can be so unimaginably vast that commentators frequently reach of hyper-astronomical metaphors that compare their size to that of the universe. Re-run the tape of life and the likelihood of encountering the same sequences in such hyper-astronomically large spaces is infinitesimally small, suggesting that evolutionary outcomes are highly contingent. On the other hand, the wide-spread occurrence of evolutionary convergence implies that similar phenotypes can be found again with relative ease. How can this be? Part of the solution to this conundrum must lie in the manner that genotypes map to phenotypes. By studying simple genotype-phenotype maps, where the counterfactual space of all possible phenotypes can be enumerated, it is shown that strong bias in the arrival of variation may explain why certain phenotypes are (repeatedly) observed in nature, while others never appear. This biased variation provides a non-selective cause for certain types of convergence. It illustrates how the role of randomness and contingency may differ significantly between genetic and phenotype spaces.