Stochastic tunneling across fitness valleys can give rise to a logarithmic long-term fitness trajectory

Abstract

Adaptation, where a population evolves increasing fitness in a fixed environment, is typically thought of as a hill-climbing process on a fitness landscape. With a finite genome, such a process eventually leads the population to a fitness peak, at which point fitness can no longer increase through individual beneficial mutations. Instead, the ruggedness of typical landscapes due to epistasis between genes or DNA sites suggests that the accumulation of multiple mutations (via a process known as stochastic tunneling) can allow a population to continue increasing in fitness. However, it is not clear how such a phenomenon would affect long-term fitness evolution. By using a spin-glass type model for the fitness function that takes into account microscopic epistasis, we find that hopping between metastable states can mechanistically and robustly give rise to a slow, logarithmic average fitness trajectory.

The effect of weak clonal interference on average fitness trajectories in the presence of macroscopic epistasis

“…Although we have only considered adaptation dynamics on fitness-parameterized landscapes, it is possible for such macroscopic epistasis to arise from a microscopic model of fitness landscape that explicitly takes into account interactions between genes (i.e. microscopic epistasis) [11,30]. Furthermore, in many of these microscopic models, the rate of beneficial mutations decreases as the population climbs up the fitness landscape.…”

Evolution of Microbial Growth Traits Under Serial Dilution

“…For small populations, mutations generally arise and either fix or go extinct one at a time, a regime known as strong-selection weak-mutation (SSWM) ( Gillespie 1984 ). In this case, we expect the fixation probability of a beneficial mutation with selection coefficient to be ( Wahl and Gerrish 2001 ; Wahl and Zhu 2015 ; Guo et al 2019 ) This is similar to the standard Wright–Fisher fixation probability of ( Crow and Kimura 1970 ), but with a different prefactor due to averaging over the different times in the exponential growth phase at which the mutation can arise (Supplemental Methods, section VIII). Indeed, we see this predicted dependence matches the simulation results for the small population size of ( Figure 2C ).…”

“…We have investigated a model of microbial evolution under serial dilution, which is both a common protocol for laboratory evolution experiments ( Luckinbill 1978 ; Lenski et al 1991 ; Elena and Lenski 2003 ; Levy et al 2015 ; Kram et al 2017 ) as well as a rough model of evolution in natural environments with feast–famine cycles. While there has been extensive work to model population and evolutionary dynamics in these conditions ( Gerrish and Lenski 1998 ; Wahl and Gerrish 2001 ; Desai 2013 ; Baake et al 2019 ; Guo et al 2019 ), these models have largely neglected the physiological links connecting mutations to selection. However, models that explicitly incorporate these features are necessary to interpret experimental evidence that mutations readily generate variation in multiple cellular traits, and that this variation is important to adaptation ( Vasi et al 1994 ; Novak et al 2006 ; Reding-Roman et al 2017 ; Li et al 2018 ).…”

Evolutionary dynamics of asexual hypermutators adapting to a novel environment

“…For example, the modes of adaptation in complex environments may vary greatly due to the presence of a more rugged fitness landscape, additional paths available for fitness improvement, the presence of multiple spatial or nutritional niches, or more complicated genetic interactions. (Handel and Rozen 2009;Lynch 2010a;Ochs and Desai 2015;Guo et al 2019). Therefore, it is necessary to study adaptive processes in more complex and heterogeneous environments to determine whether the principles observed in simpler environments still apply.…”