Exploiting the adaptation dynamics to predict the distribution of beneficial fitness effects

Adaptation of asexual populations is driven by beneficial mutations and therefore the dynamics of this process, besides other factors, depend on the distribution of beneficial fitness effects. It is known that on uncorrelated fitness landscapes, this distribution can only be of three types: truncated, exponential and power law. We performed extensive stochastic simulations to study the adaptation dynamics on rugged fitness landscapes, and identified two quantities that can be used to distinguish the underlying distribution of beneficial fitness effects. The first quantity studied here is the fitness difference between successive mutations that spread in the population, which is found to decrease in the case of truncated distributions, remain nearly a constant for exponentially decaying distributions and increase when the fitness distribution decays as a power law. The second quantity of interest, namely, the rate of change of fitness with time also shows quantitatively different behaviour for different beneficial fitness distributions. The patterns displayed by the two aforementioned quantities are found to hold for both low and high mutation rates. We discuss how these patterns can be exploited to determine the distribution of beneficial fitness effects in microbial experiments.Comment: Communicated to PLOS ON

Evolutionary dynamics on strongly correlated fitness landscapes

We study the evolutionary dynamics of a maladapted population of self-replicating sequences on strongly correlated fitness landscapes. Each sequence is assumed to be composed of blocks of equal length and its fitness is given by a linear combination of four independent block fitnesses. A mutation affects the fitness contribution of a single block leaving the other blocks unchanged and hence inducing correlations between the parent and mutant fitness. On such strongly correlated fitness landscapes, we calculate the dynamical properties like the number of jumps in the most populated sequence and the temporal distribution of the last jump which is shown to exhibit a inverse square dependence as in evolution on uncorrelated fitness landscapes. We also obtain exact results for the distribution of records and extremes for correlated random variables

Data from: Adaptive walks and distribution of beneficial fitness effects

We study the adaptation dynamics of a maladapted asexual population on rugged fitness landscapes with many local fitness peaks. The distribution of beneficial fitness effects is assumed to belong to one of the three extreme value domains, viz. Weibull, Gumbel, and Fréchet. We work in the strong selection-weak mutation regime in which beneficial mutations fix sequentially, and the population performs an uphill walk on the fitness landscape until a local fitness peak is reached. A striking prediction of our analysis is that the fitness difference between successive steps follows a pattern of diminishing returns in the Weibull domain and accelerating returns in the Fréchet domain, as the initial fitness of the population is increased. These trends are found to be robust with respect to fitness correlations. We believe that this result can be exploited in experiments to determine the extreme value domain of the distribution of beneficial fitness effects. Our work here differs significantly from the previous ones that assume the selection coefficient to be small. On taking large effect mutations into account, we find that the length of the walk shows different qualitative trends from those derived using small selection coefficient approximation

Simulation of adaptive walks on uncorrelated fitness landscapes

Starting from fitness f_0, the adaptive walk proceeds as per the transition probability (4) in the manuscript until it reaches a local fitness peak. The average fitness difference, selection co-efficient and the walk length are averaged over 10^6 iterations

Simulation of adaptive walks on correlated fitness landscapes

In our simulations, the initial fitness of each block is chosen independently such that their average equals f_0. From then on, the adaptive proceeds until the fitness of all blocks reach local fitness peaks. Over 10^5 iterations, various quantities like average fitness difference between steps and the selection coefficient are calculated for the every step of the adaptive walk

Figure shows the fitness increment in each time step for three different values of <i>κ</i> in two mutation regimes (SSWM and high mutation).

<p>In each case the data is fitted with the theoretically expected function given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151795#pone.0151795.e041" target="_blank">Eq (14)</a>, except for the exponential distribution for which we used the theoretical prediction by Park and Krug [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151795#pone.0151795.ref029" target="_blank">29</a>]. In all cases, the population starts with the same initial fitness <i>f</i>₀ = 0.5.</p