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Register a new userUniversality of noise-induced resilience restoration in spatially-extended ecological systems
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Many systems may switch to an undesired state due to internal failures or external perturbations, of which critical transitions toward degraded ecosystem states are a prominent example. Resilience restoration focuses on the ability of spatially-extended systems and the required time to recover to their desired states under stochastic environmental conditions. While mean-field approaches may guide recovery strategies by indicating the conditions needed to destabilize undesired states, these approaches are not accurately capturing the transition process toward the desired state of spatially-extended systems in stochastic environments. The difficulty is rooted in the lack of mathematical tools to analyze systems with high dimensionality, nonlinearity, and stochastic effects. We bridge this gap by developing new mathematical tools that employ nucleation theory in spatially-embedded systems to advance resilience restoration. We examine our approach on systems following mutualistic dynamics and diffusion models, finding that systems may exhibit single-cluster or multi-cluster phases depending on their sizes and noise strengths, and also construct a new scaling law governing the restoration time for arbitrary system size and noise strength in two-dimensional systems. This approach is not limited to ecosystems and has applications in various dynamical systems, from biology to infrastructural systems.
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A new type of noise-induced synchronous behavior is described. This phenomenon, called incomplete noise-induced synchronization, arises for one-dimensional Ginzburg-Landau equations driven by common noise. The mechanisms resulting in the incomplete noise-induced synchronization in the spatially extended systems are revealed analytically. The different model noise are considered. A very good agreement between the theoretical results and the numerically calculated data is shown.
Noise through its interaction with the nonlinearity of the living systems can give rise to counter-intuitive phenomena. In this paper we shortly review noise induced effects in different ecosystems, in which two populations compete for the same resources. We also present new results on spatial patterns of two populations, while modeling real distributions of anchovies and sardines. The transient dynamics of these ecosystems are analyzed through generalized Lotka-Volterra equations in the presence of multiplicative noise, which models the interaction between the species and the environment. We find noise induced phenomena such as quasi-deterministic oscillations, stochastic resonance, noise delayed extinction, and noise induced pattern formation. In addition, our theoretical results are validated with experimental findings. Specifically the results, obtained by a coupled map lattice model, well reproduce the spatial distributions of anchovies and sardines, observed in a marine ecosystem. Moreover, the experimental dynamical behavior of two competing bacterial populations in a meat product and the probability distribution at long times of one of them are well reproduced by a stochastic microbial predictive model.
Ecologists have long suspected that species are more likely to interact if their traits match in a particular way. For example, a pollination interaction may be more likely if the proportions of a bees tongue fit a plants flower shape. Empirical estimates of the importance of trait-matching for determining species interactions, however, vary significantly among different types of ecological networks. Here, we show that ambiguity among empirical trait-matching studies may have arisen at least in parts from using overly simple statistical models. Using simulated and real data, we contrast conventional generalized linear models (GLM) with more flexible Machine Learning (ML) models (Random Forest, Boosted Regression Trees, Deep Neural Networks, Convolutional Neural Networks, Support Vector Machines, naive Bayes, and k-Nearest-Neighbor), testing their ability to predict species interactions based on traits, and infer trait combinations causally responsible for species interactions. We find that the best ML models can successfully predict species interactions in plant-pollinator networks, outperforming GLMs by a substantial margin. Our results also demonstrate that ML models can better identify the causally responsible trait-matching combinations than GLMs. In two case studies, the best ML models successfully predicted species interactions in a global plant-pollinator database and inferred ecologically plausible trait-matching rules for a plant-hummingbird network, without any prior assumptions. We conclude that flexible ML models offer many advantages over traditional regression models for understanding interaction networks. We anticipate that these results extrapolate to other ecological network types. More generally, our results highlight the potential of machine learning and artificial intelligence for inference in ecology, beyond standard tasks such as image or pattern recognition.
We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an age-structured multi-stage Markov process for approximating cell cycle time distributions. We further demonstrate that the resulting mean behaviour is equivalent, over large timescales, to the classical McKendrick-von Foerster integro-partial differential equation. We conclude by extending this framework to a spatial context, facilitating the modelling of travelling wave phenomena and cell-mediated pattern formation. More generally, this methodology may be extended to myriad reaction-diffusion processes for which the age of individuals is relevant to the dynamics.
A Belief Propagation approach has been recently proposed for the zero-patient problem in a SIR epidemics. The zero-patient problem consists in finding the initial source of an epidemic outbreak given observations at a later time. In this work, we study a harder but related inference problem, in which observations are noisy and there is confusion between observed states. In addition to studying the zero-patient problem, we also tackle the problem of completing and correcting the observations possibly finding undiscovered infected individuals and false test results. Moreover, we devise a set of equations, based on the variational expression of the Bethe free energy, to find the zero patient along with maximum-likelihood epidemic parameters. We show, by means of simulated epidemics, how this method is able to infer details on the past history of an epidemic outbreak based solely on the topology of the contact network and a single snapshot of partial and noisy observations.
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