Predicting population genetic change in an autocorrelated random environment: Insights from a large automated experiment

Most natural environments exhibit a substantial component of random variation, with a degree of temporal autocorrelation that defines the color of environmental noise. Such environmental fluctuations cause random fluctuations in natural selection, affecting the predictability of evolution. But despite long-standing theoretical interest in population genetics in stochastic environments, there is a dearth of empirical estimation of underlying parameters of this theory. More importantly, it is still an open question whether evolution in fluctuating environments can be predicted indirectly using simpler measures, which combine environmental time series with population estimates in constant environments. Here we address these questions by using an automated experimental evolution approach. We used a liquid-handling robot to expose over a hundred lines of the micro-alga Dunaliella salina to randomly fluctuating salinity over a continuous range, with controlled mean, variance, and autocorrelation. We then tracked the frequencies of two competing strains through amplicon sequencing of nuclear and choloroplastic barcode sequences. We show that the magnitude of environmental fluctuations (determined by their variance), but also their predictability (determined by their autocorrelation), had large impacts on the average selection coefficient. The variance in frequency change, which quantifies randomness in population genetics, was substantially higher in a fluctuating environment. The reaction norm of selection coefficients against constant salinity yielded accurate predictions for the mean selection coefficient in a fluctuating environment. This selection reaction norm was in turn well predicted by environmental tolerance curves, with population growth rate against salinity. However, both the selection reaction norm and tolerance curves underestimated the variance in selection caused by random environmental fluctuations. Overall, our results provide exceptional insights into the prospects for understanding and predicting genetic evolution in randomly fluctuating environments.

Non-Markovian decoherence of a two-level system in a Lorentzian bosonic reservoir and a stochastic environment with finite correlation time

In this paper we investigate non-Markovian evolution of a two-level system (qubit) in a bosonic bath under influence of an external classical fluctuating environment. The interaction with the bath has the Lorentzian spectral density, and the fluctuating environment (stochastic field) is represented by a set of Ornstein-Uhlenbeck processes. Each of the subenvironments of the composite environment is able to induce non-Markovian dynamics of the two-level system. By means of the numerically exact method of hierarchical equations of motion, we study steady states of the two-level system, evolution of the reduced density matrix and the equilibrium emission spectra in dependence on the frequency cutoffs and the coupling strengths of the subenvironments. Additionally, we investigate the impact of the rotating wave approximation (RWA) for the interaction with the bath on accuracy of the results.

Indirect Taxis on a Fluctuating Environment

In this article, we study a Patlak–Keller–Siegel (PKS) model of a community of two species placed in the inhomogeneous environment. We employ PKS law for modeling tactic movement due to interspecific taxis and in response to the environmental fluctuations. These fluctuations can arise for natural reasons, e.g., the terrain relief, the sea currents and the food resource distribution, and there are artificial ones. The main result in the article elucidates the effect of the small-scale environmental fluctuations on the large-scale pattern formation in PKS systems. This issue remains uncharted, although numerous studies have addressed the pattern formation while assuming an homogeneous environment. Meanwhile, exploring the role of the fluctuating environment is substantial in many respects, for instance, for predicting the side effects of human activity or for designing the control of biological systems. As well, it is necessary for understanding the roles played in the dynamics of trophic communities by the natural environmental inhomogeneities—those mentioned above, for example. We examined the small-scale environmental inhomogeneities in the spirit of Kapitza’s theory of the upside-down pendulum, but we used the homogenization instead of classical averaging. This approach is novel for the dynamics of PKS systems (though used commonly for other areas). Employing it has unveiled a novel mechanism of exerting the effect from the fluctuating environment on the pattern formation by the drift of species arising upon the homogenization of the fluctuations.