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Recent advancements in next-generation sequencing have revolutionized our understanding of the human microbiome. Despite this progress, challenges persist in comprehending the microbiome's influence on disease, hindered by technical complexities in species classification, abundance estimation, and data compositionality. At the same time, the existence of macroecological laws describing the variation and diversity in microbial communities irrespective of their environment has been recently proposed using 16s data and explained by a simple phenomenological model of population dynamics. We here investigate the relationship between dysbiosis, i.e. in unhealthy individuals there are deviations from the "regular" composition of the gut microbial community, and the existence of macro-ecological emergent law in microbial communities. We first quantitatively reconstruct these patterns at the species level using shotgun data, and addressing the consequences of sampling effects and statistical errors on ecological patterns. We then ask if such patterns can discriminate between healthy and unhealthy cohorts. Concomitantly, we evaluate the efficacy of different statistical generative models, which incorporate sampling and population dynamics, to describe such patterns and distinguish which are expected by chance, versus those that are potentially informative about disease states or other biological drivers. A critical aspect of our analysis is understanding the relationship between model parameters, which have clear ecological interpretations, and the state of the gut microbiome, thereby enabling the generation of synthetic compositional data that distinctively represent healthy and unhealthy individuals. Our approach, grounded in theoretical ecology and statistical physics, allows for a robust comparison of these models with empirical data, enhancing our understanding of the strengths and limitations of simple microbial models of population dynamics., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Pasqualini et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Connecting the viscoelastic behavior of stressed ring melts to the various forms of entanglement that can emerge in such systems is still an open challenge. Here, we consider active ring melts, where stress is generated internally, and introduce a topology-based method to detect and track consequential forms of ring entanglements, namely, deadlocks. We demonstrate that, as stress accumulates, more and more rings are co-opted in a growing web of deadlocks that entrap many other rings by threading, bringing the system to a standstill. The method ought to help the study of topological aging in more general polymer contexts.

The common intuition among the ecologists of the midtwentieth century was that large ecosystems should be more stable than those with a smaller number of species. This view was challenged by Robert May, who found a stability bound for randomly assembled ecosystems; they become unstable for a sufficiently large number of species. In the present work, we show that May's bound greatly changes when the past population densities of a species affect its own current density. This is a common feature in real systems, where the effects of species' interactions may appear after a time lag rather than instantaneously. The local stability of these models with self-interaction is described by bounds, which we characterize in the parameter space. We find a critical delay curve that separates the region of stability from that of instability, and correspondingly, we identify a critical frequency curve that provides the characteristic frequencies of a system at the instability threshold. Finally, we calculate analytically the distributions of eigenvalues that generalize Wigner's as well as Girko's laws. Interestingly, we find that, for sufficiently large delays, the eigenvalues of a randomly coupled system are complex even when the interactions are symmetric.

Understanding the conditions of feasibility and stability in ecological systems is a major challenge in theoretical ecology. The seminal work of May in 1972 and recent developments based on the theory of random matrices have shown the existence of emergent universal patterns of both stability and feasibility in ecological dynamics. However, only a few studies have investigated the role of delay coupled with population dynamics in the emergence of feasible and stable states. In this work, we study the effects of delay on generalized Loka-Volterra population dynamics of several interacting species in closed ecological environments. First, we investigate the relation between feasibility and stability of the modelled ecological community in the absence of delay and find a simple analytical relation when intra-species interactions are dominant. We then show how, by increasing the time delay, there is a transition in the stability phases of the population dynamics: from an equilibrium state to a stable non-point attractor phase. We calculate analytically the critical delay of that transition and show that it is in excellent agreement with numerical simulations. Finally, following a similar approach to characterizing stability in empirical studies, we investigate the coefficient of variation, which quantifies the magnitude of population fluctuations. We show that in the oscillatory regime induced by the delay, the variability at community level decreases for increasing diversity. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Understanding of the pairing statistics in solutions populated by a large number of distinct solute species with mutual interactions is a challenging topic, relevant in modeling the complexity of real biological systems. Here we describe, both experimentally and theoretically, the formation of duplexes in a solution of random-sequence DNA (rsDNA) oligomers of length L = 8, 12, 20 nucleotides. rsDNA solutions are formed by 4L distinct molecular species, leading to a variety of pairing motifs that depend on sequence complementarity and range from strongly bound, fully paired defectless helices to weakly interacting mismatched duplexes. Experiments and theory coherently combine revealing a hybridization statistics characterized by a prevalence of partially defected duplexes, with a distribution of type and number of pairing errors that depends on temperature. We find that despite the enormous multitude of inter-strand interactions, defectless duplexes are formed, involving a fraction up to 15% of the rsDNA chains at the lowest temperatures. Experiments and theory are limited here to equilibrium conditions., Competing Interests: The authors have declared that no competing interests exist.

The effectiveness of several biological and biotechnological processes relies on the remarkably selective pairing of nucleic acids in contexts of molecular complexity. Relevant examples are the on-target binding of primers in genomic PCR and the regulatory efficacy of microRNA via binding on the transcriptome. Here, we propose a statistical framework that enables us to describe and understand such selectivity by means of a model that is extremely cheap from a computational point of view. By re-parametrizing the hybridization thermodynamics on three classes of base pairing errors, we find a convenient way to obtain the free energy of pairwise interactions between nucleic acids. We thus evaluate the hybridization statistics of a given oligonucleotide within a large number of competitive sites that we assume to be random, and we compute the probability of on-target binding. We apply our strategy to PCR amplification and microRNA-based gene regulation, shedding new light on their selectivity. In particular, we show the relevance of the defectless pairing of 3' terminals imposed by the polymerase in PCR selection. We also evaluate the selectivity afforded by the microRNA seed region, thus quantifying the extra contributions given by mechanisms beyond pairing statistics.

We demonstrate that when power scaling occurs for an individual tree and in a forest, there is great resulting simplicity notwithstanding the underlying complexity characterizing the system over many size scales. Our scaling framework unifies seemingly distinct trends in a forest and provides a simple yet promising approach to quantitatively understand a bewilderingly complex many-body system with imperfectly known interactions. We show that the effective dimension, D tree , of a tree is close to 3, whereas a mature forest has D forest approaching 1. We discuss the energy equivalence rule and show that the metabolic rate-mass relationship is a power law with an exponent D /( D + 1) in both cases leading to a Kleiber's exponent of 3/4 for a tree and 1/2 for a forest. Our work has implications for understanding carbon sequestration and for climate science., (© The Author(s) 2022. Published by Oxford University Press on behalf of the National Academy of Sciences.)

One of the major challenges in stochastic thermodynamics is to compute the distributions of stochastic observables for small-scale systems for which fluctuations play a significant role. Hitherto much theoretical and experimental research has focused on systems composed of passive Brownian particles. In this paper, we study the heat fluctuations in a system of interacting active particles. Specifically we consider a one-dimensional harmonic chain of N active Ornstein-Uhlenbeck particles, with the chain ends connected to heat baths of different temperatures. We compute the moment-generating function for the heat flow in the steady state. We employ our general framework to explicitly compute the moment-generating function for two example single-particle systems. Further, we analytically obtain the scaled cumulants for the heat flow for the chain. Numerical Langevin simulations confirm the long-time analytical expressions for first and second cumulants for the heat flow for a two-particle chain.

Deoxyribonucleic acid (DNA) hybridization is at the heart of countless biological and biotechnological processes. Its theoretical modeling played a crucial role, since it has enabled extracting the relevant thermodynamic parameters from systematic measurements of DNA melting curves. In this article, we propose a framework based on statistical physics to describe DNA hybridization and melting in an arbitrary mixture of DNA strands. In particular, we are able to analytically derive closed expressions of the system partition functions for any number N of strings and explicitly calculate them in two paradigmatic situations: (i) a system made of self-complementary sequences and (ii) a system comprising two mutually complementary sequences. We derive the melting curve in the thermodynamic limit (N→∞) of our description, which provides a full justification for the extra entropic contribution that in classic hybridization modeling was required to correctly describe within the same framework the melting of sequences either self-complementary or not. We thus provide a thorough study comprising limit cases and alternative approaches showing how our framework can give a comprehensive view of hybridization and melting phenomena.

An algebraic approximation, of order K, of a polyhedron correlation function (CF) can be obtained from γ''(r), its chord-length distribution (CLD), considering first, within the subinterval [D i-1 , D i ] of the full range of distances, a polynomial in the two variables (r - D i-1 ) 1/2 and (D i - r) 1/2 such that its expansions around r = D i-1 and r = D i simultaneously coincide with the left and right expansions of γ''(r) around D i-1 and D i up to the terms O(r - D i-1 ) K/2 and O(D i - r) K/2 , respectively. Then, for each i, one integrates twice the polynomial and determines the integration constants matching the resulting integrals at the common end-points. The 3D Fourier transform of the resulting algebraic CF approximation correctly reproduces, at large q's, the asymptotic behaviour of the exact form factor up to the term O[q -(K/2+4) ]. For illustration, the procedure is applied to the cube, the tetrahedron and the octahedron.

We consider a general discrete state-space system with both unidirectional and bidirectional links. In contrast to bidirectional links, there is no reverse transition along the unidirectional links. Herein, we first compute the statistical length and the thermodynamic cost function for transitions in the probability space, highlighting contributions from total, environmental, and resetting (unidirectional) entropy production. Then we derive the thermodynamic bound on the speed limit to connect two distributions separated by a finite time, showing the effect of the presence of unidirectional transitions. Uncertainty relationships can be found for the temporal first and second moments of the average resetting entropy production. We derive simple expressions in the limit of slow unidirectional transition rates. Finally, we present a refinement of the thermodynamic bound by means of an optimization procedure. We numerically investigate these results on systems that stochastically reset with constant and periodic resetting rate.

In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then the process recommences. Hitherto, the resetting mechanism has been introduced as a symmetric reset about the preferred location. However, in nature, there are several instances where a system can only reset from certain directions, e.g., catastrophic events. Motivated by this, we consider a continuous stochastic process on the positive real line. The process is interrupted at random times occurring at a constant rate, and then the former relocates to a value only if the current one exceeds a threshold; otherwise, it follows the trajectory defined by the underlying process without resetting. An approach to obtain the exact nonequilibrium steady state of such systems and the mean first passage time to reach the origin is presented. Furthermore, we obtain the explicit solutions for two different model systems. Some of the classical results found in symmetric resetting, such as the existence of an optimal resetting, are strongly modified. Finally, numerical simulations have been performed to verify the analytical findings, showing an excellent agreement.

The chord-length distribution function [γ''(r)] of any bounded polyhedron has a closed analytic expression which changes in the different subdomains of the r range. In each of these, the γ''(r) expression only involves, as transcendental contributions, inverse trigonometric functions of argument equal to R[r, Δ 1 ], Δ 1 being the square root of a second-degree r polynomial and R[x, y] a rational function. As r approaches δ, one of the two end points of an r subdomain, the derivative of γ''(r) can only show singularities of the forms |r - δ| -n and |r - δ| -m+1/2 , with n and m appropriate positive integers. Finally, the explicit analytic expressions of the primitives are also reported.

We provide a strategy for the exact inference of the average as well as the fluctuations of the entropy production in nonequilibrium systems in the steady state, from the measurements of arbitrary current fluctuations. Our results are built upon the finite-time generalization of the thermodynamic uncertainty relation, and require only very short time series data from experiments. We illustrate our results with exact and numerical solutions for two colloidal heat engines.

We consider the paradigm of an overdamped Brownian particle in a potential well, which is modulated through an external protocol, in the presence of stochastic resetting. Thus, in addition to the short range diffusive motion, the particle also experiences intermittent long jumps that reset the particle back at a preferred location. Due to the modulation of the trap, work is done on the system and we investigate the statistical properties of the work fluctuations. We find that the distribution function of the work typically, in asymptotic times, converges to a universal Gaussian form for any protocol as long as that is also renewed after each resetting event. When observed for a finite time, we show that the system does not generically obey the Jarzynski equality that connects the finite time work fluctuations to the difference in free energy. Nonetheless, we identify herein a restricted set of protocols which embraces the relation. In stark contrast, the Jarzynski equality is always fulfilled when the protocols continue to evolve without being reset. We present a set of exactly solvable models, demonstrate the validation of our theory and carry out numerical simulations to illustrate these findings. Finally, we have pointed out possible realistic implementations for resetting in experiments using the so-called engineered swift equilibration.

Variability on external conditions has important consequences for the dynamics and the organization of biological systems. In many cases, the characteristic timescale of environmental changes as well as their correlations play a fundamental role in the way living systems adapt and respond to it. A proper mathematical approach to understand population dynamics, thus, requires approaches more refined than, e.g., simple white-noise approximations. To shed further light onto this problem, in this paper we propose a unifying framework based on different analytical and numerical tools available to deal with "colored" environmental noise. In particular, we employ a "unified colored noise approximation" to map the original problem into an effective one with white noise, and then we apply a standard path integral approach to gain analytical understanding. For the sake of specificity, we present our approach using as a guideline a variation of the contact process-which can also be seen as a birth-death process of the Malthus-Verhulst class-where the propagation or birth rate varies stochastically in time. Our approach allows us to tackle in a systematic manner some of the relevant questions concerning population dynamics under environmental variability, such as determining the stationary population density, establishing the conditions under which a population may become extinct, and estimating extinction times. We focus on the emerging phase diagram and its possible phase transitions, underlying how these are affected by the presence of environmental noise time-correlations.

Background: Mixed dispersal syndromes have historically been regarded as a bet-hedging mechanism that enhances survivorship in unpredictable environments, ensuring that some propagules stay in the maternal environment while others can potentially colonize new sites. However, this entails paying the costs of both dispersal and non-dispersal. Propagules that disperse are likely to encounter unfavorable conditions, while non-dispersing propagules might form inbred populations of close relatives. Here, we investigate the conditions under which mixed dispersal syndromes emerge and are evolutionarily stable, taking into account the risks of both environmental unpredictability and inbreeding., Results: Using mathematical and computational modeling, we show that high dispersal propensity is favored whenever environmental unpredictability is low and inbreeding depression high, whereas mixed dispersal syndromes are adaptive under high environmental unpredictability, more particularly if inbreeding depression is small. Although pure dispersal is frequently adaptive, mixed dispersal represents the optimal strategy under many different parameterizations of our models, indicating that this strategy is likely to be favored in a wide variety of contexts. Furthermore, monomorphic populations go inevitably extinct when environmental and genetic costs are high, whilst mixed strategies can maintain viable populations even under very extreme conditions., Conclusions: Our models support the hypothesis that the interplay between inbreeding depression and environmental unpredictability shapes dispersal syndromes, often resulting in mixed strategies. Moreover, mixed dispersal seems to facilitate persistence whenever conditions are critical or nearly critical for survival.

Empirical evidence suggesting that living systems might operate in the vicinity of critical points, at the borderline between order and disorder, has proliferated in recent years, with examples ranging from spontaneous brain activity to flock dynamics. However, a well-founded theory for understanding how and why interacting living systems could dynamically tune themselves to be poised in the vicinity of a critical point is lacking. Here we use tools from statistical mechanics and information theory to show that complex adaptive or evolutionary systems can be much more efficient in coping with diverse heterogeneous environmental conditions when operating at criticality. Analytical as well as computational evolutionary and adaptive models vividly illustrate that a community of such systems dynamically self-tunes close to a critical state as the complexity of the environment increases while they remain noncritical for simple and predictable environments. A more robust convergence to criticality emerges in coevolutionary and coadaptive setups in which individuals aim to represent other agents in the community with fidelity, thereby creating a collective critical ensemble and providing the best possible tradeoff between accuracy and flexibility. Our approach provides a parsimonious and general mechanism for the emergence of critical-like behavior in living systems needing to cope with complex environments or trying to efficiently coordinate themselves as an ensemble.