The Effects of a Rapidly-Fluctuating Random Environment on Systems of Interacting Species

Some models of interacting species in a random environment are analyzed. Approximate solutions of the stochastic differential or delay-differential equations describing the systems are obtained, on the assumption that the random environment is fluctuating rapidly

Phenotypic diversity and population growth in fluctuating environment: a MBPRE approach

Organisms adapt to fluctuating environments by regulating their dynamics, and by adjusting their phenotypes to environmental changes. We model population growth using multitype branching processes in random environments, where the offspring distribution of some organism having trait t\in\cT in environment e\in\cE is given by some (fixed) distribution $\Upsilon_{t,e}$ on \bbN. Then, the phenotypes are attributed using a distribution (strategy) $\pi_{t,e}$ on the trait space \cT. We look for the optimal strategy $\pi_{t,e}$, t\in\cT, e\in\cE maximizing the net growth rate or Lyapounov exponent, and characterize the set of optimal strategies. This is considered for various models of interest in biology: hereditary versus non-hereditary strategies and strategies involving or not involving a sensing mechanism. Our main results are obtained in the setting of non-hereditary strategies: thanks to a reduction to simple branching processes in random environment, we derive an exact expression for the net growth rate and a characterisation of optimal strategies. We also focus on typical genealogies, that is, we consider the problem of finding the typical lineage of a randomly chosen organism.Comment: 21 page

Protein-mediated DNA Loop Formation and Breakdown in a Fluctuating Environment

Living cells provide a fluctuating, out-of-equilibrium environment in which genes must coordinate cellular function. DNA looping, which is a common means of regulating transcription, is very much a stochastic process; the loops arise from the thermal motion of the DNA and other fluctuations of the cellular environment. We present single-molecule measurements of DNA loop formation and breakdown when an artificial fluctuating force, applied to mimic a fluctuating cellular environment, is imposed on the DNA. We show that loop formation is greatly enhanced in the presence of noise of only a fraction of $k_B T$, yet find that hypothetical regulatory schemes that employ mechanical tension in the DNA--as a sensitive switch to control transcription--can be surprisingly robust due to a fortuitous cancellation of noise effects

Stochastic thermodynamics of active Brownian particles

Examples of self propulsion in strongly fluctuating environment is abound in nature, e.g., molecular motors and pumps operating in living cells. Starting from Langevin equation of motion, we develop a fluctuating thermodynamic description of self propelled particles using simple models of velocity dependent forces. We derive fluctuation theorems for entropy production and a modified fluctuation dissipation relation, characterizing the linear response at non-equilibrium steady states. We study these notions in a simple model of molecular motors, and in the Rayleigh-Helmholtz and energy-depot model of self propelled particles.Comment: 8 pages, version accepted in Phys. Rev.

How self-regulation, the storage effect and their interaction contribute to coexistence in stochastic and seasonal environments

Explaining coexistence in species-rich communities of primary producers remains a challenge for ecologists because of their likely competition for shared resources. Following Hutchinson's seminal suggestion, many theoreticians have tried to create diversity through a fluctuating environment, which impairs or slows down competitive exclusion. However, fluctuating-environment models often only produce a dozen of coexisting species at best. Here, we investigate how to create richer communities in fluctuating environments, using an empirically parameterized model. Building on the forced Lotka-Volterra model of Scranton and Vasseur (Theor Ecol 9(3):353-363, 2016), inspired by phytoplankton communities, we have investigated the effect of two coexistence mechanisms, namely the storage effect and higher intra- than interspecific competition strengths (i.e., strong self-regulation). We tuned the intra/inter competition ratio based on empirical analyses, in which self-regulation dominates interspecific interactions. Although a strong self-regulation maintained more species (50%) than the storage effect (25%), we show that none of the two coexistence mechanisms considered could ensure the coexistence of all species alone. Realistic seasonal environments only aggravated that picture, as they decreased persistence relative to a random environment. However, strong self-regulation and the storage effect combined superadditively so that all species could persist with both mechanisms at work. Our results suggest that combining different coexistence mechanisms into community models might be more fruitful than trying to find which mechanism best explains diversity. We additionally highlight that while biomass-trait distributions provide some clues regarding coexistence mechanisms, they cannot indicate unequivocally which mechanisms are at play.Comment: 27 pages, 9 figures, Theor Ecol (2019

Active-to-absorbing state phase transition in the presence of fluctuating environments: Weak and strong dynamic scaling

We investigate the scaling properties of phase transitions between survival and extinction (active-to-absorbing state phase transition, AAPT) in a model, that by itself belongs to the directed percolation (DP) universality class, interacting with a spatio-temporally fluctuating environment having its own non-trivial dynamics. We model the environment by (i) a randomly stirred fluid, governed by the Navier-Stokes (NS) equation, and (ii) a fluctuating surface, described either by the Kardar-Parisi-Zhang (KPZ) or the Edward-Wilkinson (EW) equations. We show, by using a one-loop perturbative field theoretic set up, that depending upon the spatial scaling of the variance of the external forces that drive the environment (i.e., the NS, KPZ or EW equations), the system may show {\em weak} or {\em strong dynamic scaling} at the critical point of active to absorbing state phase transitions. In the former case AAPT displays scaling belonging to the DP universality class, whereas in the latter case the universal behavior is different.Comment: 17 pages, 2 figures, accepted in PR

Probing charge fluctuator correlations using quantum dot pairs

We study a pair of quantum dot exciton qubits interacting with a number of fluctuating charges that can induce a Stark shift of both exciton transition energies. We do this by solving the optical master equation using a numerical transfer matrix method. We find that the collective influence of the charge environment on the dots can be detected by measuring the correlation between the photons emitted when each dot is driven independently. Qubits in a common charge environment display photon bunching, if both dots are driven on resonance or if the driving laser detunings have the same sense for both qubits, and antibunching if the laser detunings have in opposite signs. We also show that it is possible to detect several charges fluctuating at different rates using this technique. Our findings expand the possibility of measuring qubit dynamics in order to investigate the fundamental physics of the environmental noise that causes decoherence.Comment: 9 pages, 13 figure

Fluctuating selection models and Mcdonald-Kreitman type analyses

It is likely that the strength of selection acting upon a mutation varies through time due to changes in the environment. However, most population genetic theory assumes that the strength of selection remains constant. Here we investigate the consequences of fluctuating selection pressures on the quantification of adaptive evolution using McDonald-Kreitman (MK) style approaches. In agreement with previous work, we show that fluctuating selection can generate evidence of adaptive evolution even when the expected strength of selection on a mutation is zero. However, we also find that the mutations, which contribute to both polymorphism and divergence tend, on average, to be positively selected during their lifetime, under fluctuating selection models. This is because mutations that fluctuate, by chance, to positive selected values, tend to reach higher frequencies in the population than those that fluctuate towards negative values. Hence the evidence of positive adaptive evolution detected under a fluctuating selection model by MK type approaches is genuine since fixed mutations tend to be advantageous on average during their lifetime. Never-the-less we show that methods tend to underestimate the rate of adaptive evolution when selection fluctuates