Fluctuation Domains in Adaptive Evolution

We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this expression gives rise to the notion of fluctuation domains - parts of the fitness landscape where the rate of evolution is very predictable (due to fluctuation dissipation) and parts where it is highly variable (due to fluctuation enhancement). These fluctuation domains are determined by the curvature of the fitness landscape. Regions of the fitness landscape with positive curvature, such as adaptive valleys or branching points, experience enhancement. Regions with negative curvature, such as adaptive peaks, experience dissipation. We explore these dynamics in the ecological scenarios of implicit and explicit competition for a limiting resource

Evolutionary comparison between viral lysis rate and latent period

Marine viruses shape the structure of the microbial community. They are, thus, a key determinant of the most important biogeochemical cycles in the planet. Therefore, a correct description of the ecological and evolutionary behavior of these viruses is essential to make reliable predictions about their role in marine ecosystems. The infection cycle, for example, is indistinctly modeled in two very different ways. In one representation, the process is described including explicitly a fixed delay between infection and offspring release. In the other, the offspring are released at exponentially distributed times according to a fixed release rate. By considering obvious quantitative differences pointed out in the past, the latter description is widely used as a simplification of the former. However, it is still unclear how the dichotomy "delay versus rate description" affects long-term predictions of host-virus interaction models. Here, we study the ecological and evolutionary implications of using one or the other approaches, applied to marine microbes. To this end, we use mathematical and eco-evolutionary computational analysis. We show that the rate model exhibits improved competitive abilities from both ecological and evolutionary perspectives in steady environments. However, rate-based descriptions can fail to describe properly long-term microbe-virus interactions. Moreover, additional information about trade-offs between life-history traits is needed in order to choose the most reliable representation for oceanic bacteriophage dynamics. This result affects deeply most of the marine ecosystem models that include viruses, especially when used to answer evolutionary questions.Comment: to appear in J. Theor. Bio

Population aging through survival of the fit and stable

Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates. Individuals reproduce and die with a rate that is a property of each state, not necessarily related to its stability, and the offspring is born on the parent's state. The total population is limited by resources or space, as for example in a chemostat or a Petri dish. Our aim is to show that mutation rate and fitness become more correlated, \emph{even if they are completely uncorrelated for an isolated individual}, underlining the fact that the interaction induced by limitation of resources is by itself efficient for generating collective effects

Interplay between pleiotropy and secondary selection determines rise and fall of mutators in stress response

Dramatic rise of mutators has been found to accompany adaptation of bacteria in response to many kinds of stress. Two views on the evolutionary origin of this phenomenon emerged: the pleiotropic hypothesis positing that it is a byproduct of environmental stress or other specific stress response mechanisms and the second order selection which states that mutators hitchhike to fixation with unrelated beneficial alleles. Conventional population genetics models could not fully resolve this controversy because they are based on certain assumptions about fitness landscape. Here we address this problem using a microscopic multiscale model, which couples physically realistic molecular descriptions of proteins and their interactions with population genetics of carrier organisms without assuming any a priori fitness landscape. We found that both pleiotropy and second order selection play a crucial role at different stages of adaptation: the supply of mutators is provided through destabilization of error correction complexes or fluctuations of production levels of prototypic mismatch repair proteins (pleiotropic effects), while rise and fixation of mutators occur when there is a sufficient supply of beneficial mutations in replication-controlling genes. This general mechanism assures a robust and reliable adaptation of organisms to unforeseen challenges. This study highlights physical principles underlying physical biological mechanisms of stress response and adaptation

Irreversible thermodynamics of open chemical networks I: Emergent cycles and broken conservation laws

In this and a companion paper we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks "in a box", whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated to nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation $a + b = s^Y$ between the number of fundamental affinities $a$, that of broken conservation laws $b$ and the number of chemostats $s^Y$. We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction and of thermodynamic constraints for network reconstruction.Comment: 18 page

A general chemostat model with second-order Poisson jumps: asymptotic properties and application to industrial waste-water treatment

A chemostat is a laboratory device (of the bioreactor type) in which organisms (bacteria, phytoplankton) develop in a controlled manner. This paper studies the asymptotic properties of a chemostat model with generalized interference function and Poisson noise. Due to the complexity of abrupt and erratic fluctuations, we consider the effect of the second order Itô-Lévy processes. The dynamics of our perturbed system are determined by the value of the threshold parameter $\mathfrak{C}^{\star}_0$. If $\mathfrak {C}^{\star}_0$ is strictly positive, the stationarity and ergodicity properties of our model are verified (practical scenario). If $\mathfrak {C}^{\star}_0$ is strictly negative, the considered and modeled microorganism will disappear in an exponential manner. This research provides a comprehensive overview of the chemostat interaction under general assumptions that can be applied to various models in biology and ecology. In order to verify the reliability of our results, we probe the case of industrial waste-water treatment. It is concluded that higher order jumps possess a negative influence on the long-term behavior of microorganisms in the sense that they lead to complete extinction

Processes on the emergent landscapes of biochemical reaction networks and heterogeneous cell population dynamics: differentiation in living matters.

The notion of an attractor has been widely employed in thinking about the nonlinear dynamics of organisms and biological phenomena as systems and as processes. The notion of a landscape with valleys and mountains encoding multiple attractors, however, has a rigorous foundation only for closed, thermodynamically non-driven, chemical systems, such as a protein. Recent advances in the theory of nonlinear stochastic dynamical systems and its applications to mesoscopic reaction networks, one reaction at a time, have provided a new basis for a landscape of open, driven biochemical reaction systems under sustained chemostat. The theory is equally applicable not only to intracellular dynamics of biochemical regulatory networks within an individual cell but also to tissue dynamics of heterogeneous interacting cell populations. The landscape for an individual cell, applicable to a population of isogenic non-interacting cells under the same environmental conditions, is defined on the counting space of intracellular chemical composition