Dataset: EpiGen model

We modeled an individual based adaptive walk using a modified version of Fisher’s geometric adaptation model from Kronholm and Collins – the EpiGen model.

Fitness changes were driven by both LT (low transmission) modifications and HT (high transmission) modifications, where HT modifications were fixed and LT modifications reverted with probability urev (LT reversion rate). Model formulation: Phenotypic space was represented as an n-dimensional hypersphere where an individual’s phenotype, z, was characterized by its distance from the hypersphere origin with radius r.

Fitness for each individual (w) was calculated as: w(z) = e(-z^2)/2 (Eq. 1)
such that an individual located at the origin had an optimal fitness of 1 and fitness declined as a Gaussian function as the phenotype moved away from the origin of the hypersphere. The simulations began with z = r = 1 for all individuals in the population such that w = 0.6065.

The phenotype was altered through both LT and HT modifications which were represented  as mutational vectors with random directions and magnitudes in phenotypic space. A new phenotypic value, Zmut, was then calculated as:
zmut^2 = z^2 + m^2 + 2mzsin(sigma) (Eq. 2)
where m is the length of the mutational vector and sigma is the angle between the mutational vector and the vector running from the current phenotype to the origin (sigma is an element of [-pi/2, pi/2]).

For each new modification, sigma in n-dimensional space was drawn from the probability density (P):
P=Zcos(sigma)^(n-2) (Eq. 3)
where Z is a scaling constant and was calculated as:
integral[pi/2,−pi/2] Zcos(sigma)^(n-2) dsigma = 1 (Eq. 4)

All model parameters are given in Supplemental Table 1 in Walwort et al., 2020.

The model was initialized with a population of N uniform individuals: here N was varied  from N = 103 to N = 105. HT modifications (NHT =10) and LT modifications (NLT =90) were then introduced into the population. The modification supply (population size x modification rate) remained constant in each generation and no more than one LT and one HT modification per generation was allowed to occur in a single individual. Eq. 2 was used to calculate new mutant 2 phenotypes. Isotropic modifications in phenotypic space were represented through the uniform distribution of HT modifications, mht, between 0 and 2r, mht ~ U(0, 2r), which generated nonuniform fitness effects (2, 4). While LT modifications (mlt) were introduced in the same manner as HT modifications, the effects of LT modifications were smaller than HT modifications with a uniform distribution of me between 0 and l. Hence, mlt ~ U(0, l) instead of mht ~ U(0, 2r), where 2r is the maximum effect of HT modifications and l £ 2r is the maximum effect of LT modifications. Fitness for each mutant phenotype was then calculated using Eq. 1, and the next generation was then created by sampling from the current population with replacement.

Selection: In the ‘new’ environment, selection was based on fitness in the ‘new’ environment so the sampling probability of an individual was weighted by its fitness until N offspring had been produced. Selection in the ‘ancestral’ environment occurred through the stochastic removal of organisms with relatively more HT modifications (i.e. higher HT modification abundance), which corresponds to stabilizing selection. We assume that all modifications have an equal chance of being conditionally deleterious (being neutral or adaptive in the ‘selection’ or ‘new’ environment, but deleterious in some other environment) so that individuals who have accumulated a high number of modifications in the selection environment
have a higher probability of decreased fitness in the ‘ancestral’ environment.