Ard Louis

Abstract:

Modeling the rate at which adaptive phenotypes appear in a population is a key to predicting evolutionary processes. Given random mutations, should this rate be modeled by a simple Poisson process, or is a more complex dynamics needed? Here we use analytic calculations and simulations of evolving populations on explicit genotype–phenotype maps to show that the introduction of novel phenotypes can be “bursty” or overdispersed. In other words, a novel phenotype either appears multiple times in quick succession or not at all for many generations. These bursts are fundamentally caused by statistical fluctuations and other structure in the map from genotypes to phenotypes. Their strength depends on population parameters, being highest for “monomorphic” populations with low mutation rates. They can also be enhanced by additional inhomogeneities in the mapping from genotypes to phenotypes. We mainly investigate the effect of bursts using the well-studied genotype–phenotype map for RNA secondary structure, but find similar behavior in a lattice protein model and in Richard Dawkins’s biomorphs model of morphological development. Bursts can profoundly affect adaptive dynamics. Most notably, they imply that fitness differences play a smaller role in determining which phenotype fixes than would be the case for a Poisson process without bursts.

Abstract:

Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input-output maps. This phenomenon is known as simplicity bias. By viewing the parameters of dynamical systems as inputs, and the resulting (digitised) trajectories as outputs, we study simplicity bias in the logistic map, Gauss map, sine map, Bernoulli map, and tent map. We find that the logistic map, Gauss map, and sine map all exhibit simplicity bias upon sampling of map initial values and parameter values, but the Bernoulli map and tent map do not. The simplicity bias upper bound on the output pattern probability is used to make a priori predictions regarding the probability of output patterns. In some cases, the predictions are surprisingly accurate, given that almost no details of the underlying dynamical systems are assumed. More generally, we argue that studying probability-complexity relationships may be a useful tool when studying patterns in dynamical systems.

Abstract:

Biomorphs, Richard Dawkins’s iconic model of morphological evolution, are traditionally used to demonstrate the power of natural selection to generate biological order from random mutations. Here we show that biomorphs can also be used to illustrate how developmental bias shapes adaptive evolutionary outcomes. In particular, we find that biomorphs exhibit phenotype bias, a type of developmental bias where certain phenotypes can be many orders of magnitude more likely than others to appear through random mutations. Moreover, this bias exhibits a strong preference for simpler phenotypes with low descriptional complexity. Such bias towards simplicity is formalised by an information-theoretic principle that can be intuitively understood from a picture of evolution randomly searching in the space of algorithms. By using population genetics simulations, we demonstrate how moderately adaptive phenotypic variation that appears more frequently upon random mutations can fix at the expense of more highly adaptive biomorph phenotypes that are less frequent. This result, as well as many other patterns found in the structure of variation for the biomorphs, such as high mutational robustness and a positive correlation between phenotype evolvability and robustness, closely resemble findings in molecular genotype-phenotype maps. Many of these patterns can be explained with an analytic model based on constrained and unconstrained sections of the genome. We postulate that the phenotype bias towards simplicity and other patterns biomorphs share with molecular genotype-phenotype maps may hold more widely for developmental systems.