scholarly journals Chaos and the (un)predictability of evolution in a changing environment

2017 ◽  
Author(s):  
Artur Rego-Costa ◽  
Florence Débarre ◽  
Luis-Miguel Chevin
Keyword(s):  
Evolutionary Dynamics ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Environmental Stochasticity ◽  
Phenotypic Evolution ◽  
Evolutionary System ◽  
Chaotic Oscillations ◽  
Changing Environment ◽  
Environmental Forcing ◽  
Evolutionary Trajectories

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency-dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution, by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability.

scholarly journals EXACT SOLUTION OF AN IRREVERSIBLE ONE-DIMENSIONAL MODEL WITH FULLY BIASED SPIN EXCHANGES

1996 ◽  
Vol 10 (25) ◽  
pp. 3451-3459 ◽  
Author(s):  
ANTÓNIO M.R. CADILHE ◽  
VLADIMIR PRIVMAN
Keyword(s):  
Exact Solution ◽  
Domain Wall ◽  
Nearest Neighbor ◽  
Spin Exchange ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Zero Temperature ◽  
Dimensional Model ◽  
One Dimensional ◽  
Temperature Dynamics

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑↓ (↓↑) can exchange to assume the configuration ↓↑ (↑↓), with rate β(α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such zero-temperature dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general, finite-temperature models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.

On New Aspects of Nested Carbon Nanotubes as Gigahertz Oscillators

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
R. Ansari ◽  
B. Motevalli
Keyword(s):  
Carbon Nanotubes ◽  
Initial Velocity ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Interaction Force ◽  
Arbitrary Length ◽  
Oscillatory Frequency ◽  
Analytical Expression ◽  
System Parameters ◽  
The Core

Nested carbon nanotubes exhibit telescopic oscillatory motion with frequencies in the gigahertz range. In this paper, our previously proposed semi-analytical expression for the interaction force between two concentric carbon nanotubes is used to solve the equation of motion. That expression also enables a new semi-analytical expression for the precise evaluation of oscillation frequency to be introduced. Alternatively, an algebraic frequency formula derived based on the simplifying assumption of constant van der Waals force is also given. Based on the given formulas, a thorough study on different aspects of operating frequencies under various system parameters is conducted, which permits fresh insight into the problem. Some notable improvements over the previously drawn conclusions are made. The strong dependence of oscillatory frequency on system parameters including the extrusion distance and initial velocity of the core as initial conditions for the motion is shown. Interestingly, our results indicate that there is a special initial velocity at which oscillatory frequency is unique for any arbitrary length of the core. A particular relationship between the escape velocity (the minimum initial velocity beyond which the core will leave the outer nanotube) and this specific initial velocity is also revealed.

scholarly journals The State-space Model of Micro-chaos

2021 ◽  
Vol 15 ◽  
pp. 184-189
Author(s):  
Gabor Csernak ◽  
Gabor Stepan
Keyword(s):  
Chaotic Systems ◽  
Initial Conditions ◽  
State Space Model ◽  
Unstable State ◽  
Considerable Influence ◽  
Chaotic Oscillations ◽  
Controlled System ◽  
Space Model ◽  
Digitally Controlled

Micro-chaos is the phenomenon when the sampling, the delay and the round-off lead to small amplitude chaotic oscillations in a digitally controlled system. It has been proved mathematically during the last few years in a couple of simple cases that the evolving vibrations are indeed chaotic. In this study, we partially generalize these results to the case when an originally unstable state of a system is stabilized by digital feedback control. It is pointed out that this type of systems are sensitive to initial conditions and there exists a finite attracting domain in their phase-space. We also show that the oscillations, related to micro-chaos may have a considerable influence on the accuracy and settling time of the control system. The application of numerical techniques is unavoidable in the case of chaotic systems. Several possibilities are highlighted in the paper for the numerical determination of important characteristics of microchaotic oscillations.

scholarly journals Noise-induced bistability in the quasineutral coexistence of viral RNA under different replication modes

2018 ◽  
Author(s):  
Josep Sardanyés ◽  
Andreu Arderiu ◽  
Santiago F. Elena ◽  
Tomás Alarcón
Keyword(s):  
Viral Replication ◽  
Evolutionary Dynamics ◽  
Rna Viruses ◽  
Initial Conditions ◽  
Rna Replication ◽  
Viral Rna ◽  
Stochastic Simulations ◽  
Strong Impact ◽  
Deterministic Models ◽  
The Impact

Evolutionary and dynamical investigations on real viral populations indicate that RNA replication can range between two extremes given by so-called stamping machine replication (SMR) and geometric replication (GR). The impact of asymmetries in replication for single-stranded, (+) sense RNA viruses has been up to now studied with deterministic models. However, viral replication should be better described by including stochasticity, since the cell infection process is typically initiated with a very small number of RNA macromolecules, and thus largely influenced by intrinsic noise. Under appropriate conditions, deterministic theoretical descriptions of viral RNA replication predict a quasineutral coexistence scenario, with a line of fixed points involving different strands’ equilibrium ratios depending on the initial conditions. Recent research on the quasineutral coexistence in two competing populations reveals that stochastic fluctuations fundamentally alters the mean-field scenario, and one of the two species outcompetes the other one. In this manuscript we study this phenomenon for RNA viral replication modes by means of stochastic simulations and a diffusion approximation. Our results reveal that noise has a strong impact on the amplification of viral RNA, also causing the emergence of noise-induced bistability. We provide analytical criteria for the dominance of (+) sense strands depending on the initial populations on the line of equilibria, which are in agreement with direct stochastic simulation results. The biological implications of this noise-driven mechanism are discussed within the framework of the evolutionary dynamics of RNA viruses with different modes of replication.

scholarly journals A 15 million-year long record of phenotypic evolution in the heavily calcified coccolithophore <i>Helicosphaera</i> and its biogeochemical implications

2020 ◽  
Author(s):  
Luka Šupraha ◽  
Jorijntje Henderiks
Keyword(s):  
Cell Size ◽  
Resource Limitation ◽  
Tropical Indian Ocean ◽  
Adaptive Strategies ◽  
Cellular Level ◽  
Phenotypic Evolution ◽  
Environmental Forcing ◽  
Modern Species ◽  
Wide Range ◽  
Mean Size

Abstract. The biogeochemical performance of coccolithophores is defined by their overall abundance in the oceans, but also by a wide range in cell size, degree of calcification and carbon production rates between different species. Species’ sensitivity to environmental forcing has been suggested to relate to their cellular PIC : POC ratio and other physiological constraints. Understanding both the short and longer-term adaptive strategies of different coccolithophore lineages, and how these in turn shape the biogeochemical role of the group, is therefore crucial for modeling the ongoing changes in the global carbon cycle. Here we present data on the phenotypic evolution of a large and heavily-calcified genus Helicosphaera (order Zygodiscales) over the past 15 million years (Ma), at two deep-sea drill sites from the tropical Indian Ocean and temperate South Atlantic. The modern species Helicosphaera carteri, which displays eco-physiological adaptations in modern strains, was used to benchmark the use of its coccolith morphology as a physiological proxy in the fossil record. Our results show that, on the single-genotype level, coccolith morphology has no correlation with physiological traits in H. carteri. However, significant correlations of coccolith morphometric parameters with cell size and physiological rates do emerge once multiple genotypes or closely related lineages are pooled together. Using this insight, we interpret the phenotypic evolution in Helicosphaera as a global, resource limitation-driven selection for smaller cells, which appears to be a common adaptive trait among different coccolithophore lineages, from the warm and high-CO2 world of the middle Miocene to the cooler and low-CO2 conditions of the Pleistocene. However, despite a significant decrease in mean size, Helicosphaera kept relatively stable PIC : POC (as inferred from the coccolith aspect ratio) and thus highly conservative biogeochemical output on the cellular level. We argue that this supports its status as an obligate calcifier, like other large and heavily-calcified genera such as Calcidiscus and Coccolithus, and that other adaptive strategies, beyond size-adaptation, must support the persistent, albeit less abundant, occurrence of these taxa. This is in stark contrast with the ancestral lineage of Emiliania and Gephyrocapsa, which not only decreased in mean size but also displayed much higher phenotypic plasticity in degree of calcification while becoming globally more dominant in plankton communities.

Dripping instability of a two-dimensional liquid film under an inclined plate

2021 ◽  
Vol 932 ◽  
Author(s):  
Guangzhao Zhou ◽  
Andrea Prosperetti
Keyword(s):  
Liquid Film ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Bond Number ◽  
Quasi Equilibrium ◽  
Two Dimensional ◽  
Inclined Plate ◽  
Maximum Value ◽  
Critical Curvature ◽  
Rayleigh Taylor Instability

It is known that the dripping of a liquid film on the underside of a plate can be suppressed by tilting the plate so as to cause a sufficiently strong flow. This paper uses two-dimensional numerical simulations in a closed-flow framework to study several aspects of this phenomenon. It is shown that, in quasi-equilibrium conditions, the onset of dripping is closely associated with the curvature of the wave crests approaching a well-defined maximum value. When dynamic effects become significant, this connection between curvature and dripping weakens, although the critical curvature remains a useful reference point as it is intimately related to the short length scales promoted by the Rayleigh–Taylor instability. In the absence of flow, when the film is on the underside of a horizontal plate, the concept of a limit curvature is relevant only for small liquid volumes close to a critical value. Otherwise, the drops that form have a smaller curvature and a large volume. The paper also illustrates the peculiarly strong dependence of the dripping transition on the initial conditions of the simulations. This feature prevents the development of phase maps dependent only on the governing parameters (Reynolds number, Bond number, etc.) similar to those available for film flow on the upper side of an inclined plate.

scholarly journals A 15-million-year-long record of phenotypic evolution in the heavily calcified coccolithophore <i>Helicosphaera</i> and its biogeochemical implications

2020 ◽  
Vol 17 (11) ◽  
pp. 2955-2969 ◽  
Author(s):  
Luka Šupraha ◽  
Jorijntje Henderiks
Keyword(s):  
Cell Size ◽  
Resource Limitation ◽  
Tropical Indian Ocean ◽  
Adaptive Strategies ◽  
Cellular Level ◽  
Phenotypic Evolution ◽  
Production Rates ◽  
Environmental Forcing ◽  
Modern Species ◽  
Mean Size

Abstract. The biogeochemical impact of coccolithophores is defined not only by their overall abundance in the oceans but also by wide ranges in physiological traits such as cell size, degree of calcification and carbon production rates between different species. Species' sensitivity to environmental forcing has been suggested to relate to their cellular PIC : POC (particulate inorganic carbon : particulate organic carbon) ratio and other physiological constraints. Understanding both the short-term and longer-term adaptive strategies of different coccolithophore lineages, and how these in turn shape the biogeochemical role of the group, is therefore crucial for modeling the ongoing changes in the global carbon cycle. Here we present data on the phenotypic evolution of a large and heavily calcified genus Helicosphaera (order Zygodiscales) over the past 15 million years (Myr), at two deep-sea drill sites in the tropical Indian Ocean and temperate South Atlantic. The modern species Helicosphaera carteri, which displays ecophysiological adaptations in modern strains, was used to benchmark the use of its coccolith morphology as a physiological proxy in the fossil record. Our results show that, on the single-genotype level, coccolith morphology has no correlation with growth rates, cell size or PIC and POC production rates in H. carteri. However, significant correlations of coccolith morphometric parameters with cell size and physiological rates do emerge once multiple genotypes or closely related lineages are pooled together. Using this insight, we interpret the phenotypic evolution in Helicosphaera as a global, resource-limitation-driven selection for smaller cells, which appears to be a common adaptive trait among different coccolithophore lineages, from the warm and high-CO2 world of the middle Miocene to the cooler and low-CO2 conditions of the Pleistocene. However, despite a significant decrease in mean coccolith size and cell size, Helicosphaera kept a relatively stable PIC : POC ratio (as inferred from the coccolith aspect ratio) and thus highly conservative biogeochemical output on the cellular level. We argue that this supports its status as an obligate calcifier, like other large and heavily calcified genera such as Calcidiscus and Coccolithus, and that other adaptive strategies, beyond size adaptation, must support the persistent, albeit less abundant, occurrence of these taxa. This is in stark contrast with the ancestral lineage of Emiliania and Gephyrocapsa, which not only decreased in mean size but also displayed much higher phenotypic plasticity in their degree of calcification while becoming globally more dominant in plankton communities.

A GENERALIZATION OF THE DETERMINISTIC ANNEALING EM ALGORITHM BY MEANS OF NON-EXTENSIVE STATISTICAL MECHANICS

2003 ◽  
Vol 17 (29) ◽  
pp. 5525-5539 ◽  
Author(s):  
JUN-ICHI INOUE ◽  
KATSUMI TABUSHI
Keyword(s):  
Em Algorithm ◽  
Initial Conditions ◽  
Marginal Likelihood ◽  
Strong Dependence ◽  
Large Data ◽  
Gaussian Mixture ◽  
Local Maxima ◽  
The Em Algorithm ◽  
Estimation Problems ◽  
Extensive Property

We extend the EM algorithm to overcome its bottleneck, that is to say, the problem of local maxima of the marginal likelihood due to its strong dependence of initial conditions. As an alternative posterior distribution appearing in the so-called Q function, we use the distribution that maximizes the non-extensive Tsallis entropy. The distribution we introduce has a parameter q which represents the non-extensive property of the entropy. We control the parameter q so as to weaken the influence of the initial conditions. In order to investigate its performance, we apply our algorithm to Gaussian mixture estimation problems under some additive noises. In large data limit, we derive the averaged update equations with respect to hyper-parameters, marginal likelihood etc. analytically. Our analysis supports usefulness of our algorithm.

scholarly journals Noise-induced bistability in the quasi-neutral coexistence of viral RNAs under different replication modes

2018 ◽  
Vol 15 (142) ◽  
pp. 20180129 ◽  
Author(s):  
Josep Sardanyés ◽  
Andreu Arderiu ◽  
Santiago F. Elena ◽  
Tomás Alarcón
Keyword(s):  
Evolutionary Dynamics ◽  
Rna Viruses ◽  
Initial Conditions ◽  
Rna Replication ◽  
Viral Rna ◽  
Stochastic Simulations ◽  
Strong Impact ◽  
Deterministic Models ◽  
Viral Rnas ◽  
The Impact

Evolutionary and dynamical investigations into real viral populations indicate that RNA replication can range between the two extremes represented by so-called ‘stamping machine replication’ (SMR) and ‘geometric replication’ (GR). The impact of asymmetries in replication for single-stranded (+) sense RNA viruses has been mainly studied with deterministic models. However, viral replication should be better described by including stochasticity, as the cell infection process is typically initiated with a very small number of RNA macromolecules, and thus largely influenced by intrinsic noise. Under appropriate conditions, deterministic theoretical descriptions of viral RNA replication predict a quasi-neutral coexistence scenario, with a line of fixed points involving different strands' equilibrium ratios depending on the initial conditions. Recent research into the quasi-neutral coexistence in two competing populations reveals that stochastic fluctuations fundamentally alter the mean-field scenario, and one of the two species outcompetes the other. In this article, we study this phenomenon for viral RNA replication modes by means of stochastic simulations and a diffusion approximation. Our results reveal that noise has a strong impact on the amplification of viral RNAs, also causing the emergence of noise-induced bistability. We provide analytical criteria for the dominance of (+) sense strands depending on the initial populations on the line of equilibria, which are in agreement with direct stochastic simulation results. The biological implications of this noise-driven mechanism are discussed within the framework of the evolutionary dynamics of RNA viruses with different modes of replication.

Sign in / Sign up

Export Citation Format

Share Document