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1.
Sci Rep ; 12(1): 7549, 2022 May 09.
Article in English | MEDLINE | ID: mdl-35534510

##### ABSTRACT

Expression of numerous genes is precisely controlled in a cell in various contexts. While genetic and epigenetic mechanisms contribute to this regulation, how each mechanism cooperates to ensure the proper expression patterns of the whole gene remains unclear. Here, I theoretically show that the repetition of simple biological processes makes cells functional with the appropriate expression patterns of all genes if the inappropriateness of current expression ratios is roughly fed back to the epigenetic states. A learning pair model is developed, in which two factors autonomously approach the target ratio by repeating two stochastic processes; competitive amplification with a small addition term and decay depending on the difference between the current and target ratios. Furthermore, thousands of factors are self-regulated in a hierarchical-pair architecture, in which the activation degrees competitively amplify, while transducing the activation signal, and decay at four different probabilities. Changes in whole-gene expression during human early embryogenesis and hematopoiesis are reproduced in simulation using this epigenetic learning process in a single genetically-determined hierarchical-pair architecture of gene regulatory cascades. On the background of this learning process, I propose the law of biological inertia, which means that a living cell basically maintains the expression pattern while renewing its contents.

##### Subject(s)
Epigenesis, Genetic , Gene Expression Regulation , Computer Simulation , Gene Expression , Humans , Stochastic Processes
2.
Commun Biol ; 5(1): 424, 2022 May 06.
Article in English | MEDLINE | ID: mdl-35523944

##### ABSTRACT

Research on successions and community assembly both address the same processes such as dispersal, species sorting, and biotic interactions but lack unifying concepts. Recent theoretical advances integrated both research lines proposing a sequence of stochastic and deterministic processes along successional gradients. Shifts in ecosystem states along successional gradients are predicted to occur abruptly once abiotic and biotic factors dominate over dispersal as main driver. Considering the multidiversity composed of five organismal groups including plants, animals, and microbes, our results imply that stochastic, likely dispersal-dominated, processes are replaced by rather deterministic processes such as environmental filtering and biotic interactions after around 60 years of succession in a glacier forefield. The niche-based character of later successional processes is further supported by a decline in multi-beta-diversity. Our results may update concepts of community assembly by considering multiple taxa, help to bridge the gap between research on successions and community assembly, and provide insights into the emergence of multidiverse and complex ecosystems.

##### Subject(s)
Ecosystem , Plants , Animals , Ice Cover , Stochastic Processes
3.
J Math Biol ; 84(6): 50, 2022 May 05.
Article in English | MEDLINE | ID: mdl-35513730

##### ABSTRACT

We derive a stochastic SIS pairwise model by considering the change of the variables of this system caused by an event. Based on approximations, we construct a low-dimensional deterministic system that can be used to describe the epidemic spread on a regular network. The mathematical treatment of the model yields explicit expressions for the variances of each variable at equilibrium. Then a comparison between the stochastic pairwise model and the stochastic mean-field SIS model is performed to indicate the effect of network structure. We find that the variances of the prevalence of infection for these two models are almost equal when the number of neighbors of every individual is large. Furthermore, approximations for the quasi-stationary distribution of the number of infected individuals and the expected time to extinction starting in quasi-stationary are derived. We analyze the approximations for the critical number of neighbors and the persistence threshold based on the stochastic model. The approximate performance is then examined by numerical and stochastic simulations. Moreover, during the early development phase, the temporal variance of the infection is also obtained. The simulations show that our analytical results are asymptotically accurate and reasonable.

##### Subject(s)
Epidemics , Models, Biological , Computer Simulation , Humans , Stochastic Processes
4.
NPJ Biofilms Microbiomes ; 8(1): 31, 2022 Apr 27.
Article in English | MEDLINE | ID: mdl-35477734

##### ABSTRACT

Deterministic and stochastic forces both drive microbiota assembly in animals, yet their relative contribution remains elusive, especially in wild aquatic-insect-associated fungal communities. Here, we applied amplicon sequencing to survey the assembly mechanisms of the fungal community in 155 wild stonefly individuals involving 44 species of 20 genera within eight families collected from multiple locations in China. Analysis showed that fungal diversity and network complexity differed significantly among the eight stonefly families, and that the fungal communities in stoneflies exhibited a significant distance-decay pattern across large spatial scales. Both a structural equation model and variance partitioning analysis revealed that environmental factors (e.g., geographical, climatic) outweigh host attributes in shaping the fungal community of stoneflies. Using neutral and null model analyses, we also find that deterministic processes play a larger role than stochasticity in driving the fungal community assembly. However, the relative contribution of ecological processes including dispersal, drift, and selection, varied strongly with host taxonomy. Furthermore, environmental conditions also significantly affect the strength of these ecological processes. Overall, our findings illustrate that variations in host attributes and environment factors may moderate the relative influence of deterministic and stochastic processes to fungal community composition in wild stoneflies, which provides new insights into mechanisms of microbial community assembly in aquatic arthropods.

##### Subject(s)
Microbiota , Mycobiome , Animals , China , Humans , Insecta , Stochastic Processes
5.
Biol Cybern ; 116(2): 119-120, 2022 Apr.
Article in English | MEDLINE | ID: mdl-35471258

##### Subject(s)
Biological Clocks , Biology , Stochastic Processes
6.
J Math Biol ; 84(6): 41, 2022 Apr 25.
Article in English | MEDLINE | ID: mdl-35467160

##### ABSTRACT

We analyze the harvesting and stocking of a population that is affected by random and seasonal environmental fluctuations. The main novelty comes from having three layers of environmental fluctuations. The first layer is due to the environment switching at random times between different environmental states. This is similar to having sudden environmental changes or catastrophes. The second layer is due to seasonal variation, where there is a significant change in the dynamics between seasons. Finally, the third layer is due to the constant presence of environmental stochasticity-between the seasonal or random regime switches, the species is affected by fluctuations which can be modelled by white noise. This framework is more realistic because it can capture both significant random and deterministic environmental shifts as well as small and frequent fluctuations in abiotic factors. Our framework also allows for the price or cost of harvesting to change deterministically and stochastically, something that is more realistic from an economic point of view. The combined effects of seasonal and random fluctuations make it impossible to find the optimal harvesting-stocking strategy analytically. We get around this roadblock by developing rigorous numerical approximations and proving that they converge to the optimal harvesting-stocking strategy. We apply our methods to multiple population models and explore how prices, or costs, and environmental fluctuations influence the optimal harvesting-stocking strategy. We show that in many situations the optimal way of harvesting and stocking is not of threshold type.

##### Subject(s)
Models, Biological , Population Dynamics , Seasons , Stochastic Processes
7.
Bull Math Biol ; 84(6): 60, 2022 Apr 24.
Article in English | MEDLINE | ID: mdl-35461407

##### ABSTRACT

We show that the combination of Allee effects and noise can produce a stochastic process with alternating sudden decline to a low population phase, followed, after a random time, by abrupt increase in population density. We introduce a new, flexible, deterministic model of attenuated Allee effects, which interpolates between the logistic and a usual Allee model. Into this model, we incorporate environmental and demographic noise. The solution of the resulting Kolmogorov forward equation shows a dichotomous distribution of residence times with heavy occupation of high, near saturation, and low population states. Investigation of simulated sample paths reveals that indeed attenuated Allee effects and noise, acting together, produce alternating, sustained, low and high population levels. We find that the transition times between the two types of states are approximately exponentially distributed, with different parameters, rendering the embedded hi-low process approximately Markov.

##### Subject(s)
Mathematical Concepts , Models, Biological , Population Density , Population Dynamics , Stochastic Processes
8.
Math Biosci Eng ; 19(5): 4794-4811, 2022 Mar 14.
Article in English | MEDLINE | ID: mdl-35430841

##### ABSTRACT

We investigate a novel model of coupled stochastic differential equations modeling the interaction of mussel and algae in a random environment, in which combined effect of white noises and telegraph noises formulated under regime switching are incorporated. We derive sufficient condition of extinction for mussel species. Then with the help of stochastic Lyapunov functions, a well-grounded understanding of the existence of ergodic stationary distribution is obtained. Meticulous numerical examples are also employed to visualize our theoretical results in detail. Our analytical results indicate that dynamic behaviors of the stochastic mussel-algae model are intimately associated with two kinds of random perturbations.

##### Subject(s)
Bivalvia , Plants , Animals , Stochastic Processes
9.
Math Biosci Eng ; 19(5): 5169-5189, 2022 Mar 21.
Article in English | MEDLINE | ID: mdl-35430859

##### ABSTRACT

Coronavirus disease (COVID-19) has a strong influence on the global public health and economics since the outbreak in 2020. In this paper, we study a stochastic high-dimensional COVID-19 epidemic model which considers asymptomatic and isolated infected individuals. Firstly we prove the existence and uniqueness for positive solution to the stochastic model. Then we obtain the conditions on the extinction of the disease as well as the existence of stationary distribution. It shows that the noise intensity conducted on the asymptomatic infections and infected with symptoms plays an important role in the disease control. Finally numerical simulation is carried out to illustrate the theoretical results, and it is compared with the real data of India.

##### Subject(s)
COVID-19 , Epidemics , COVID-19/epidemiology , Computer Simulation , Disease Outbreaks , Humans , Stochastic Processes
10.
J R Soc Interface ; 19(189): 20220095, 2022 Apr.
Article in English | MEDLINE | ID: mdl-35414215

##### ABSTRACT

The stochastic processes underlying the growth and stability of biological and psychological systems reveal themselves when far-from-equilibrium. Far-from-equilibrium, non-ergodicity reigns. Non-ergodicity implies that the average outcome for a group/ensemble (i.e. of representative organisms/minds) is not necessarily a reliable estimate of the average outcome for an individual over time. However, the scientific interest in causal inference suggests that we somehow aim at stable estimates of the cause that will generalize to new individuals in the long run. Therefore, the valid analysis must extract an ergodic stationary measure from fluctuating physiological data. So the challenge is to extract statistical estimates that may describe or quantify some of this non-ergodicity (i.e. of the raw measured data) without themselves (i.e. the estimates) being non-ergodic. We show that traditional linear statistics such as the standard deviation, coefficient of variation and root mean square can break ergodicity. Time series of statistics addressing sequential structure and its potential nonlinearity: fractality and multi-fractality, change in a time-independent way and fulfil the ergodic assumption. Complementing traditional linear indices with fractal and multi-fractal indices would empower the study of stochastic far-from-equilibrium biological and psychological dynamics.

##### Subject(s)
Fractals , Humans , Stochastic Processes
11.
Philos Trans A Math Phys Eng Sci ; 380(2224): 20210162, 2022 May 30.
Article in English | MEDLINE | ID: mdl-35400179

##### ABSTRACT

The first part of this paper is a brief survey of the approaches to economic inequality based on ideas from statistical physics and kinetic theory. These include the Boltzmann kinetic equation, the time-reversal symmetry, the ergodicity hypothesis, entropy maximization and the Fokker-Planck equation. The origins of the exponential Boltzmann-Gibbs distribution and the Pareto power law are discussed in relation to additive and multiplicative stochastic processes. The second part of the paper analyses income distribution data in the USA for the time period 1983-2018 using a two-class decomposition. We present overwhelming evidence that the lower class (more than 90% of the population) is described by the exponential distribution, whereas the upper class (about 4% of the population in 2018) by the power law. We show that the significant growth of inequality during this time period is due to the sharp increase in the upper-class income share, whereas relative inequality within the lower class remains constant. We speculate that the expansion of the upper-class population and income shares may be due to increasing digitization and non-locality of the economy in the last 40 years. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

##### Subject(s)
Income , Physics , Entropy , Kinetics , Stochastic Processes , United States
12.
Philos Trans A Math Phys Eng Sci ; 380(2224): 20210158, 2022 May 30.
Article in English | MEDLINE | ID: mdl-35400191

##### ABSTRACT

In this paper, we propose a Boltzmann-type kinetic description of opinion formation on social networks, which takes into account a general connectivity distribution of the individuals. We consider opinion exchange processes inspired by the Sznajd model and related simplifications but we do not assume that individuals interact on a regular lattice. Instead, we describe the structure of the social network statistically, assuming that the number of contacts of a given individual determines the probability that their opinion reaches and influences the opinion of another individual. From the kinetic description of the system, we study the evolution of the mean opinion, whence we find precise analytical conditions under which a polarization switch of the opinions, i.e. a change of sign between the initial and the asymptotic mean opinions, occurs. In particular, we show that a non-zero correlation between the initial opinions and the connectivity of the individuals is necessary to observe polarization switch. Finally, we validate our analytical results through Monte Carlo simulations of the stochastic opinion exchange processes on the social network. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

##### Subject(s)
Attitude , Social Networking , Humans , Monte Carlo Method , Probability , Stochastic Processes
13.
Chaos ; 32(3): 033126, 2022 Mar.
Article in English | MEDLINE | ID: mdl-35364848

##### ABSTRACT

A problem of the probabilistic analysis of stochastic phenomena in slow-fast dynamical systems modeling biochemical reactions is considered. We study how multiplicative noise induces systematic shifts of probabilistic distributions and forms "phantom" attractors in nonlinear enzymatic models. The mathematical analysis of the underlying probabilistic mechanism of such stochastic transformations is performed by the "freeze-and-average" method. Our theoretical results are supported by direct numerical simulation.

##### Subject(s)
Algorithms , Nonlinear Dynamics , Computer Simulation , Stochastic Processes
14.
J Acoust Soc Am ; 151(3): 2055, 2022 Mar.
Article in English | MEDLINE | ID: mdl-35364916

##### ABSTRACT

Several mathematical models of the human middle ear dynamics have been studied since the mid-twentieth century. Despite different methods applied, all of these models are based on deterministic approaches. Experimental data have shown that the middle ear behaves as an uncertain system due to the variability among individuals. In this context, stochastic models are useful because they can represent a population of middle ears with its intrinsic uncertainties. In this work, a nonparametric probabilistic approach is used to model the human middle ear dynamics. The lumped-element method is adopted to develop deterministic baseline models, and three different optimization processes are proposed and applied to the adjustment of the stochastic models. Results show that the stochastic models proposed can reproduce the experimental data in terms of mean and coefficient of variation. In addition, this study shows the importance of properly defining the acceptable range of each input parameter in order to obtain a reliable stochastic model.

##### Subject(s)
Ear, Middle , Humans , Stochastic Processes
15.
J Am Chem Soc ; 144(14): 6291-6297, 2022 Apr 13.
Article in English | MEDLINE | ID: mdl-35357150

##### ABSTRACT

Unraveling how chemistry can give rise to biology is one of the greatest challenges of contemporary science. Achieving life-like properties in chemical systems is therefore a popular topic of research. Synthetic chemical systems are usually deterministic: the outcome is determined by the experimental conditions. In contrast, many phenomena that occur in nature are not deterministic but caused by random fluctuations (stochastic). Here, we report on how, from a mixture of two synthetic molecules, two different self-replicators emerge in a stochastic fashion. Under the same experimental conditions, the two self-replicators are formed in various ratios over several repeats of the experiment. We show that this variation is caused by a stochastic nucleation process and that this stochasticity is more pronounced close to a phase boundary. While stochastic nucleation processes are common in crystal growth and chiral symmetry breaking, it is unprecedented for systems of synthetic self-replicators.

##### Subject(s)
Stochastic Processes , Gene Library
16.
Proc Natl Acad Sci U S A ; 119(14): e2116054119, 2022 04 05.
Article in English | MEDLINE | ID: mdl-35349334

##### ABSTRACT

SignificanceBiochemical reactions often occur in small volumes within a cell, restricting the number of molecules to the hundreds or even tens. At this scale, reactions are discrete and stochastic, making reliable signaling difficult. This paper shows that the transition between discrete, stochastic reactions and macroscopic reactions can be exploited to make a self-regulating switch. This constitutes a previously unidentified kind of reaction network that may be present in small structures, such as synapses.

##### Subject(s)
Calcium-Calmodulin-Dependent Protein Kinase Type 2 , Synapses , Dendritic Spines/physiology , Homeostasis , Neuronal Plasticity/physiology , Stochastic Processes , Synapses/physiology
17.
Math Biosci Eng ; 19(4): 4217-4236, 2022 02 21.
Article in English | MEDLINE | ID: mdl-35341295

##### ABSTRACT

In this paper, we propose a stochastic SIHR epidemic model of COVID-19. A basic reproduction number $R_{0}^{s}$ is defined to determine the extinction or persistence of the disease. If $R_{0}^{s} < 1$, the disease will be extinct. If $R_{0}^{s} > 1$, the disease will be strongly stochastically permanent. Based on realistic parameters of COVID-19, we numerically analyze the effect of key parameters such as transmission rate, confirmation rate and noise intensity on the dynamics of disease transmission and obtain sensitivity indices of some parameters on $R_{0}^{s}$ by sensitivity analysis. It is found that: 1) The threshold level of deterministic model is overestimated in case of neglecting the effect of environmental noise; 2) The decrease of transmission rate and the increase of confirmed rate are beneficial to control the spread of COVID-19. Moreover, our sensitivity analysis indicates that the parameters $\beta$, $\sigma$ and $\delta$ have significantly effects on $R_0/$.

##### Subject(s)
COVID-19 , Epidemics , Basic Reproduction Number , COVID-19/epidemiology , Humans , Population Density , Stochastic Processes
18.
Math Biosci Eng ; 19(4): 3526-3563, 2022 02 07.
Article in English | MEDLINE | ID: mdl-35341263

##### ABSTRACT

Many real world problems depict processes following crossover behaviours. Modelling processes following crossover behaviors have been a great challenge to mankind. Indeed real world problems following crossover from Markovian to randomness processes have been observed in many scenarios, for example in epidemiology with spread of infectious diseases and even some chaos. Deterministic and stochastic methods have been developed independently to develop the future state of the system and randomness respectively. Very recently, Atangana and Seda introduced a new concept called piecewise differentiation and integration, this approach helps to capture processes with crossover effects. In this paper, an example of piecewise modelling is presented with illustration to chaos problems. Some important analysis including a piecewise existence and uniqueness and piecewise numerical scheme are presented. Numerical simulations are performed for different cases.

##### Subject(s)
Stochastic Processes
19.
J Theor Biol ; 542: 111088, 2022 Jun 07.
Article in English | MEDLINE | ID: mdl-35339514

##### ABSTRACT

Stochasticity is often associated with negative consequences for population dynamics since a population may die out due to random chance during periods when population size is very low (stochastic fade-out). Here we develop a coupled social-ecological model based on stochastic differential equations that includes natural expansion and harvesting of a forest ecosystem, and dynamics of conservation opinions, social norms and social learning in a human population. Our objective was to identify mechanisms that influence long-term persistence of the forest ecosystem in the presence of noise. We found that most of the model parameters had a significant influence on the time to extinction of the forest ecosystem. Increasing the social learning rate and the net benefits of conservation significantly increased the time to extinction, for instance. Most interestingly, we found a parameter regime where an increase in the amount of system stochasticity caused an increase in the mean time to extinction, instead of causing stochastic fade-out. This effect occurs for a subset of realizations, but the effect is large enough to increase the mean time to extinction across all realizations. Such "stochasticity-induced persistence" occurs when stochastic dynamics in the social system generates benefits in the forest system at crucial points in its temporal dynamics. We conclude that studying relatively simple social-ecological models has the benefit of facilitating characterization of dynamical states and thereby enabling us to formulate new hypothesis about mechanisms that could be operating in empirical social-ecological systems.

##### Subject(s)
Ecosystem , Forests , Humans , Models, Biological , Models, Theoretical , Population Dynamics , Stochastic Processes
20.
Biol Cybern ; 116(2): 219-234, 2022 Apr.
Article in English | MEDLINE | ID: mdl-35320405

##### ABSTRACT

Seminal work by A. Winfree and J. Guckenheimer showed that a deterministic phase variable can be defined either in terms of Poincaré sections or in terms of the asymptotic (long-time) behaviour of trajectories approaching a stable limit cycle. However, this equivalence between the deterministic notions of phase is broken in the presence of noise. Different notions of phase reduction for a stochastic oscillator can be defined either in terms of mean-return-time sections or as the argument of the slowest decaying complex eigenfunction of the Kolmogorov backwards operator. Although both notions of phase enjoy a solid theoretical foundation, their relationship remains unexplored. Here, we quantitatively compare both notions of stochastic phase. We derive an expression relating both notions of phase and use it to discuss differences (and similarities) between both definitions of stochastic phase for (i) a spiral sink motivated by stochastic models for electroencephalograms, (ii) noisy limit-cycle systems-neuroscience models, and (iii) a stochastic heteroclinic oscillator inspired by a simple motor-control system.

##### Subject(s)
Noise , Stochastic Processes