### Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution

(2021)

#### Abstract:

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

*Studies in history and philosophy of biological and biomedical sciences*

**58**(2016) 107-116

#### Abstract:

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.### Robustness and stability of spin-glass ground states to perturbed interactions.

*Phys Rev E*

**107:1-1**(2023) 014126

#### Abstract:

Across many problems in science and engineering, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of ±J spin glasses at zero temperature by calculating the robustness of the ground states to flips in the sign of single interactions. For random graphs and the Sherrington-Kirkpatrick model, we find relatively large sets of bond configurations that generate the same ground state. These sets can themselves be analyzed as subgraphs of the interaction domain, and we compute many of their topological properties. In particular, we find that the robustness, equivalent to the average degree, of these subgraphs is much higher than one would expect from a random model. Most notably, it scales in the same logarithmic way with the size of the subgraph as has been found in genotype-phenotype maps for RNA secondary structure folding, protein quaternary structure, gene regulatory networks, as well as for models for genetic programming. The similarity between these disparate systems suggests that this scaling may have a more universal origin.### Predicting phenotype transition probabilities via conditional algorithmic probability approximations.

*Journal of the Royal Society, Interface*

**19:197**(2022) 20220694

#### Abstract:

Unravelling the structure of genotype-phenotype (GP) maps is an important problem in biology. Recently, arguments inspired by algorithmic information theory (AIT) and Kolmogorov complexity have been invoked to uncover*simplicity bias*in GP maps, an exponentially decaying upper bound in phenotype probability with the increasing phenotype descriptional complexity. This means that phenotypes with many genotypes assigned via the GP map must be simple, while complex phenotypes must have few genotypes assigned. Here, we use similar arguments to bound the probability

*P*(

*x*→

*y*) that phenotype

*x*, upon random genetic mutation, transitions to phenotype

*y*. The bound is [Formula: see text], where [Formula: see text] is the estimated conditional complexity of

*y*given

*x*, quantifying how much extra information is required to make

*y*given access to

*x*. This upper bound is related to the conditional form of algorithmic probability from AIT. We demonstrate the practical applicability of our derived bound by predicting phenotype transition probabilities (and other related quantities) in simulations of RNA and protein secondary structures. Our work contributes to a general mathematical understanding of GP maps and may facilitate the prediction of transition probabilities directly from examining phenotype themselves, without utilizing detailed knowledge of the GP map.

### The structure of genotype-phenotype maps makes fitness landscapes navigable.

*Nature ecology & evolution*

**6:11**(2022) 1742-1752