Spatial asymmetry of temporal ecological processes can shift in riverine macroinvertebrates responding to fluctuating climate conditions.

Exploring the temporal dynamics of biological communities can offer valuable insights into the underlying mechanisms driving changes in biodiversity in the context of short and long-term effects of climate fluctuations. However, an understanding of how such changes influence the spatial patterns of the temporary ecological processes that shape the pattern of community dynamics remains unexplored. This study examined the relative importance of temporary deterministic and stochastic processes (i.e., the influence of environmental filtering compared to stochastic variation within the same community) on community dynamics across watersheds in 15 rivers of the European Iberian Peninsula using 21 years of data. This study was divided into two time periods (i.e., 1997-2006 and 2007-2017). The climatic differences between the periods included decreasing levels and heightened variability of precipitation. Additionally, there were declining minimum temperatures and rising maximum temperatures, accompanied by reduced fluctuations in both minimum and maximum temperatures. Water quality and its variations also occur along an elevation pattern and changed over the time period studied. Spatial patterns of the relative importance of the ecological processes shifted between the two decades. The significance of stochastic processes increased with elevation in the earlier period, although no clear elevation pattern emerged in the later period. At the same time, the importance of deterministic processes decreased with elevation in the earlier period, and there was no clear pattern of elevation in the later period. An understanding of the patterns in community dynamics existing at various elevations over time can lay the groundwork for predicting and mitigating the impacts of short-term climate changes on biodiversity and guide appropriate conservation actions.

Seasonal dynamics of free-living (FL) and particle-attached (PA) bacterial communities in a plateau reservoir.

In terms of lifestyle, bacterioplankton can be classified as free-living (FL) and particle-attached (PA) forms, and both play essential roles in biogeochemical cycling in aquatic ecosystems. Structure, distribution, and community assembly of FL and PA bacteria in plateau riverine waterbodies are largely unknown. Therefore, we explored the seasonal dynamics of FLand PA bacterial communities in the Wujiangdu reservoir, Yungui Plateau using 16S rRNA gene high-throughput sequencing. Results revealed there was a significant environmental heterogeneity in Wujiangdu reservoir seasonally. The dominant phylum was Actinomycetota for FL and Pseudomonadota for PA bacteria. Species richness and diversity was higher in autumn and winter compared to spring and summer. In general, PA diversity was greater than FL, but with some temporal variations. Species turnover was the major contributor to ß-diversity of both FL and PA lifestyles, and significant differences were noticed between FL and PA bacterial community composition. Distinct co-occurrence network patterns implied that more connections exist between FL bacteria, while more complex PA networks were in parallel to their greater diversity and stronger interactions in biofilms on particles. Dispersal limitation was the major driving force for both FL and PA bacterial community assembly. Deterministic processes were of relatively low importance, with homogeneous selection for FL and heterogeneous selection for PA bacteria. Temperature was the most important environmental driver of seasonal bacterial dynamics, followed by nitrate for FL and Secchi depth for PA bacteria. This study allows for a better understanding of the temporal variability of different bacteria lifestyles in reservoirs in the vulnerable and rapidly changing plateau environment, facilitating further microbial research related to global warming and eutrophication.

Anthropogenic restoration exhibits more complex and stable microbial co-occurrence patterns than natural restoration in rubber plantations.

Forest restoration is an effective method for restoring degraded soil ecosystems (e.g., converting primary tropical forests into rubber monoculture plantations; RM). The effects of forest restoration on microbial community diversity and composition have been extensively studied. However, how rubber plantation-based forest restoration reshapes soil microbial communities, networks, and inner assembly mechanisms remains unclear. Here, we explored the effects of jungle rubber mixed (JRM; secondary succession and natural restoration of RM) plantation and introduction of rainforest species (AR; anthropogenic restoration established by mimicking the understory and overstory tree species of native rainforests) to RM stands on soil physico-chemical properties and microbial communities. We found that converting tropical rainforest (RF) to RM decreased soil fertility and simplified microbial composition and co-occurrence patterns, whereas the conversion of RM to JRM and AR exhibited opposite results. These changes were significantly correlated with pH, soil moisture content (SMC), and soil nutrients, suggesting that vegetation restoration can provide a favorable soil microenvironment that promotes the development of soil microorganisms. The complexity and stability of the bacterial-fungal cross-kingdom, bacterial, and fungal networks increased with JRM and AR. Bacterial community assembly was primarily governed by stochastic (78.79 %) and deterministic (59.09 %) processes in JRM and AR, respectively, whereas stochastic processes (limited dispersion) predominantly shaped fungal assembly across all forest stands. AR has more significant benefits than JRM, such as a relatively slower and natural vegetation succession with more nutritive soil conditions, microbial diversity, and complex and stable microbial networks. These results highlight the importance of sustainable forest management to restore soil biodiversity and ecosystem functions after extensive soil degradation and suggest that anthropogenic restoration can more effectively improve soil quality and microbial communities than natural restoration in degraded rubber plantations.

A soluble model for synchronized rhythmic activity in ant colonies.

Synchronization is one of the most striking instances of collective behavior, occurring in many natural phenomena. For example, in some ant species, ants are inactive within the nest most of the time, but their bursts of activity are highly synchronized and involve the entire nest population. Here we revisit a simulation model that generates this synchronized rhythmic activity through autocatalytic behavior, i.e., active ants can activate inactive ants, followed by a period of rest. We derive a set of delay differential equations that provide an accurate description of the simulations for large ant colonies. Analysis of the fixed-point solutions, complemented by numerical integration of the equations, indicates the existence of stable limit-cycle solutions when the rest period is greater than a threshold and the event of spontaneous activation of inactive ants is very unlikely, so that most of the arousal of ants is done by active ants. Furthermore, we argue that the persistent oscillations observed in the simulations for colonies of finite size are due to resonant amplification of demographic noise.

Contrasting diversity patterns and drivers of aquatic macroinvertebrates in floodplain and non-floodplain wetlands.

Understanding diversity patterns and underlying drivers is one of the central topics in the fields of biogeography and community ecology. Aquatic macroinvertebrates are widely distributed in various wetlands and play vital ecological roles. Previous studies mainly have focused on macroinvertebrate diversity in a single type of wetland. Our understanding of the differences in diversity patterns and underlying drivers between different wetland types remains limited. Here, we compared diversity patterns and community assembly of floodplain wetlands (FWs) and non-floodplain wetlands (NWs) in the Sanjiang Plain, Northeast China. We found that the taxonomic richness and abundance were higher in NWs than those in FWs. Nineteen taxa were identified as habitat specialists in the NWs, whereas only four taxa were designated as habitat specialists in the FWs. In addition, the FW and NW assemblages exhibited contrasting compositions. Spatial and environmental variables explained the largest variations in the macroinvertebrate assemblages of NWs and FWs, respectively. Normalised stochasticity ratios and Sloan neutral models confirmed that the macroinvertebrate community assembly of both wetland types was driven largely by stochastic processes. Stochastic processes were more prominent in shaping macroinvertebrate communities of FWs, whereas a stronger dispersal limitation was detected in NWs. Our results revealed contrasting diversity patterns and assembly mechanisms of macroinvertebrate communities in FWs and NWs. We underscore the importance of flood disturbance in shaping wetland ecosystems in the Sanjiang Plain and highlight that conservation and restoration actions cover different types of wetland habitats.

Stochastic characterization of navigation strategies in an automated variant of the Barnes maze.

Animals can use a repertoire of strategies to navigate in an environment, and it remains an intriguing question how these strategies are selected based on the nature and familiarity of environments. To investigate this question, we developed a fully automated variant of the Barnes maze, characterized by 24 vestibules distributed along the periphery of a circular arena, and monitored the trajectories of mice over 15 days as they learned to navigate towards a goal vestibule from a random start vestibule. We show that the patterns of vestibule visits can be reproduced by the combination of three stochastic processes reminiscent of random, serial, and spatial strategies. The processes randomly selected vestibules based on either uniform (random) or biased (serial and spatial) probability distributions. They closely matched experimental data across a range of statistical distributions characterizing the length, distribution, step size, direction, and stereotypy of vestibule sequences, revealing a shift from random to spatial and serial strategies over time, with a strategy switch occurring approximately every six vestibule visits. Our study provides a novel apparatus and analysis toolset for tracking the repertoire of navigation strategies and demonstrates that a set of stochastic processes can largely account for exploration patterns in the Barnes maze.

Higher genotypic diversity and distinct assembly mechanism of free-living Symbiodiniaceae assemblages than sympatric coral-endosymbiotic assemblages in a tropical coral reef.

While in hospite Symbiodiniaceae dinoflagellates are essential for coral health, ambient free-living counterparts are crucial for coral recruitment and resilience. Comparing free-living and in hospite Symbiodiniaceae communities can potentially provide insights into endosymbiont acquisition and recurrent recruitment in bleaching recovery. In this study, we studied coral-endosymbiotic and ambient free-living Symbiodiniaceae communities in the South China Sea. We collected samples from 183 coral and ambient plankton samples and conducted metabarcoding to investigate the diversity distribution, driving factors, and assembly mechanisms of the two groups of Symbiodiniaceae. Results revealed Cladocopium C1 and Durusdinium D1 as dominant genotypes. We detected a higher genotypic diversity in free-living than in hospite symbiodiniacean communities, but with shared dominant genotypes. This indicates a genetically diverse pool of Symbiodiniaceae available for recruitment by corals. Strikingly, we found that the cooler area had more Symbiodiniaceae thermosensitive genotypes, whereas the warmer area had more Symbiodiniaceae thermotolerant genotypes. Furthermore, in hospite and free-living Symbiodiniaceae communities were similarly affected by environmental factors, but shaped by different assembly mechanisms. The in hospite communities were controlled mainly by deterministic processes, whereas the ambient communities by stochastic processes. This study sheds light on the genetic diversity of source environmental Symbiodiniaceae and differential assembly mechanisms influencing Symbiodiniaceae inside and outside corals.IMPORTANCESymbiodiniaceae dinoflagellates play a pivotal role as key primary producers within coral reef ecosystems. Coral-endosymbiotic Symbiodiniaceae communities have been extensively studied, but relatively little work has been reported on the free-living Symbiodiniaceae community. Conducting a comparative analysis between sympatric coral-endosymbiotic and free-living Symbiodiniaceae communities can potentially enhance the understanding of how endosymbiont communities change in response to changing environments and the mechanisms driving these changes. Our findings shed light on the genetic diversity of source environmental Symbiodiniaceae and differential assembly mechanisms shaping free-living and in hospite Symbiodiniaceae communities, with implications in evaluating the adaptive and resilient capacity of corals in response to future climate change.

Analysis of a detailed multi-stage model of stochastic gene expression using queueing theory and model reduction.

We introduce a biologically detailed, stochastic model of gene expression describing the multiple rate-limiting steps of transcription, nuclear pre-mRNA processing, nuclear mRNA export, cytoplasmic mRNA degradation and translation of mRNA into protein. The processes in sub-cellular compartments are described by an arbitrary number of processing stages, thus accounting for a significantly finer molecular description of gene expression than conventional models such as the telegraph, two-stage and three-stage models of gene expression. We use two distinct tools, queueing theory and model reduction using the slow-scale linear-noise approximation, to derive exact or approximate analytic expressions for the moments or distributions of nuclear mRNA, cytoplasmic mRNA and protein fluctuations, as well as lower bounds for their Fano factors in steady-state conditions. We use these to study the phase diagram of the stochastic model; in particular we derive parametric conditions determining three types of transitions in the properties of mRNA fluctuations: from sub-Poissonian to super-Poissonian noise, from high noise in the nucleus to high noise in the cytoplasm, and from a monotonic increase to a monotonic decrease of the Fano factor with the number of processing stages. In contrast, protein fluctuations are always super-Poissonian and show weak dependence on the number of mRNA processing stages. Our results delineate the region of parameter space where conventional models give qualitatively incorrect results and provide insight into how the number of processing stages, e.g. the number of rate-limiting steps in initiation, splicing and mRNA degradation, shape stochastic gene expression by modulation of molecular memory.

The Contributions of Sub-Communities to the Assembly Process and Ecological Mechanisms of Bacterial Communities along the Cotton Soil-Root Continuum Niche Gradient.

Soil microbes are crucial in shaping the root-associated microbial communities. In this study, we analyzed the effect of the soil-root niche gradient on the diversity, composition, and assembly of the bacterial community and co-occurrence network of two cotton varieties. The results revealed that the bacterial communities in cotton soil-root compartment niches exhibited a skewed species abundance distribution, dominated by abundant taxa showing a strong spatial specificity. The assembly processes of the rhizosphere bacterial communities were mainly driven by stochastic processes, dominated by the enrichment pattern and supplemented by the depletion pattern to recruit bacteria from the bulk soil, resulting in a more stable bacterial community. The assembly processes of the endosphere bacterial communities were determined by processes dominated by the depletion pattern and supplemented by the enrichment pattern to recruit species from the rhizosphere, resulting in a decrease in the stability and complexity of the community co-occurrence network. The compartment niche shaped the diversity of the bacterial communities, and the cotton variety genotype was an important source of diversity in bacterial communities within the compartment niche. We suggest that the moderate taxa contribute to significantly more changes in the diversity of the bacterial community than the rare and abundant taxa during the succession of bacterial communities in the cotton root-soil continuum.

Nonlinear Growth Dynamics of Neuronal Cells Cultured on Directional Surfaces.

During the development of the nervous system, neuronal cells extend axons and dendrites that form complex neuronal networks, which are essential for transmitting and processing information. Understanding the physical processes that underlie the formation of neuronal networks is essential for gaining a deeper insight into higher-order brain functions such as sensory processing, learning, and memory. In the process of creating networks, axons travel towards other recipient neurons, directed by a combination of internal and external cues that include genetic instructions, biochemical signals, as well as external mechanical and geometrical stimuli. Although there have been significant recent advances, the basic principles governing axonal growth, collective dynamics, and the development of neuronal networks remain poorly understood. In this paper, we present a detailed analysis of nonlinear dynamics for axonal growth on surfaces with periodic geometrical patterns. We show that axonal growth on these surfaces is described by nonlinear Langevin equations with speed-dependent deterministic terms and gaussian stochastic noise. This theoretical model yields a comprehensive description of axonal growth at both intermediate and long time scales (tens of hours after cell plating), and predicts key dynamical parameters, such as speed and angular correlation functions, axonal mean squared lengths, and diffusion (cell motility) coefficients. We use this model to perform simulations of axonal trajectories on the growth surfaces, in turn demonstrating very good agreement between simulated growth and the experimental results. These results provide important insights into the current understanding of the dynamical behavior of neurons, the self-wiring of the nervous system, as well as for designing innovative biomimetic neural network models.

Functional Formulation of Quantum Theory of a Scalar Field in a Metric with Lorentzian and Euclidean Signatures.

We study the Schrödinger equation in quantum field theory (QFT) in its functional formulation. In this approach, quantum correlation functions can be expressed as classical expectation values over (complex) stochastic processes. We obtain a stochastic representation of the Schrödinger time evolution on Wentzel-Kramers-Brillouin (WKB) states by means of the Wiener integral. We discuss QFT in a flat expanding metric and in de Sitter space-time. We calculate the evolution kernel in an expanding flat metric in the real-time formulation. We discuss a field interaction in pseudoRiemannian and Riemannian metrics showing that an inversion of the signature leads to some substantial simplifications of the singularity problems in QFT.

Stability against fluctuations: a two-dimensional study of scaling, bifurcations and spontaneous symmetry breaking in stochastic models of synaptic plasticity.

Stochastic models of synaptic plasticity must confront the corrosive influence of fluctuations in synaptic strength on patterns of synaptic connectivity. To solve this problem, we have proposed that synapses act as filters, integrating plasticity induction signals and expressing changes in synaptic strength only upon reaching filter threshold. Our earlier analytical study calculated the lifetimes of quasi-stable patterns of synaptic connectivity with synaptic filtering. We showed that the plasticity step size in a stochastic model of spike-timing-dependent plasticity (STDP) acts as a temperature-like parameter, exhibiting a critical value below which neuronal structure formation occurs. The filter threshold scales this temperature-like parameter downwards, cooling the dynamics and enhancing stability. A key step in this calculation was a resetting approximation, essentially reducing the dynamics to one-dimensional processes. Here, we revisit our earlier study to examine this resetting approximation, with the aim of understanding in detail why it works so well by comparing it, and a simpler approximation, to the system's full dynamics consisting of various embedded two-dimensional processes without resetting. Comparing the full system to the simpler approximation, to our original resetting approximation, and to a one-afferent system, we show that their equilibrium distributions of synaptic strengths and critical plasticity step sizes are all qualitatively similar, and increasingly quantitatively similar as the filter threshold increases. This increasing similarity is due to the decorrelation in changes in synaptic strength between different afferents caused by our STDP model, and the amplification of this decorrelation with larger synaptic filters.

Local Community Assembly Mechanisms and the Size of Species Pool Jointly Explain the Beta Diversity of Soil Fungi.

Fungi play vital regulatory roles in terrestrial ecosystems. Local community assembly mechanisms, including deterministic and stochastic processes, as well as the size of regional species pools (gamma diversity), typically influence overall soil microbial community beta diversity patterns. However, there is limited evidence supporting their direct and indirect effects on beta diversity of different soil fungal functional groups in forest ecosystems. To address this gap, we collected 1606 soil samples from a 25-ha subtropical forest plot in southern China. Our goal was to determine the direct effects and indirect effects of regional species pools on the beta diversity of soil fungi, specifically arbuscular mycorrhizal (AM), ectomycorrhizal (EcM), plant-pathogenic, and saprotrophic fungi. We quantified the effects of soil properties, mycorrhizal tree abundances, and topographical factors on soil fungal diversity. The beta diversity of plant-pathogenic fungi was predominantly influenced by the size of the species pool. In contrast, the beta diversity of EcM fungi was primarily driven indirectly through community assembly processes. Neither of them had significant effects on the beta diversity of AM and saprotrophic fungi. Our results highlight that the direct and indirect effects of species pools on the beta diversity of soil functional groups of fungi can significantly differ even within a relatively small area. They also demonstrate the independent and combined effects of various factors in regulating the diversities of soil functional groups of fungi. Consequently, it is crucial to study the fungal community not only as a whole but also by considering different functional groups within the community.

Microbial difference and its influencing factors in ice-covered lakes on the three poles.

Most lakes in the world are permanently or seasonally covered with ice. However, little is known about the distribution of microbes and their influencing factors in ice-covered lakes worldwide. Here we analyzed the microbial community composition in the waters of 14 ice-covered lakes in the Hoh Xil region of northern Qing-Tibetan Plateau (QTP), and conducted a meta-analysis by integrating published microbial community data of ice-covered lakes in the tripolar regions (the Arctic, Antarctica and QTP). The results showed that there were significant differences in microbial diversity, community composition and distribution patterns in the ice-covered tripolar lakes. Microbial diversity and richness were lower in the ice-covered QTP lakes (including the studied lakes in the Hoh Xil region) than those in the Arctic and Antarctica. In the ice-covered lakes of Hoh Xil, prokaryotes are mainly involved in S-metabolic processes, making them more adaptable to extreme environmental conditions. In contrast, prokaryotes in the ice-covered lakes of the Arctic and Antarctica were predominantly involved in carbon/nitrogen metabolic processes. Deterministic (salinity and nutrients) and stochastic processes (dispersal limitation, homogenizing dispersal and drift) jointly determine the geographical distribution patterns of microorganisms in ice-covered lakes, with stochastic processes dominating. These results expand the understanding of microbial diversity, distribution patterns, and metabolic processes in polar ice-covered lakes.

How do stochastic processes and genetic threshold effects explain incomplete penetrance and inform causal disease mechanisms?

Incomplete penetrance is the rule rather than the exception in Mendelian disease. In syndromic monogenic disorders, phenotypic variability can be viewed as the combination of incomplete penetrance for each of multiple independent clinical features. Within genetically identical individuals, such as isogenic model organisms, stochastic variation at molecular and cellular levels is the primary cause of incomplete penetrance according to a genetic threshold model. By defining specific probability distributions of causal biological readouts and genetic liability values, stochasticity and incomplete penetrance provide information about threshold values in biological systems. Ascertainment of threshold values has been achieved by simultaneous scoring of relatively simple phenotypes and quantitation of molecular readouts at the level of single cells. However, this is much more challenging for complex morphological phenotypes using experimental and reductionist approaches alone, where cause and effect are separated temporally and across multiple biological modes and scales. Here I consider how causal inference, which integrates observational data with high confidence causal models, might be used to quantify the relative contribution of different sources of stochastic variation to phenotypic diversity. Collectively, these approaches could inform disease mechanisms, improve predictions of clinical outcomes and prioritize gene therapy targets across modes and scales of gene function. This article is part of a discussion meeting issue 'Causes and consequences of stochastic processes in development and disease'.

Implementation of Adaptive-Bayesian DStoch technique for obtaining winds from MST radar covering higher altitudes.

It is challenging to estimate winds accurately from higher altitudes using VHF-MST radar. The current study introduces the Adaptive-Bayesian Deterministic Stochastics Technique (ADStoch), which implements an Empirical Bayesian 1D prediction method using stochastics to analyze radar signals. A new and robust estimator for empirical wavelet shrinkage with Gaussian prior of the nonzero mean for wavelet coefficients is presented, which makes the current prior different from other priors. The mean parameters and the prior covariance hyperparameters follow a pseudo maximum likelihood method for computation. Details on the implemented algorithm developed from scratch using C# are also presented. This technique outperforms contemporary techniques discussed in this context that can recover signals buried in noise established based on the analysis of moment and quality. The estimated Wind is cross-validated for accuracy with the observed wind from the GPS radiosonde operated simultaneously. This technique can consistently extract 3D wind that can reach the range of 25.5 km-28.2 km, improving the conventional maximum altitude of 21.2 km in real time for the MST radar. It is concluded that the ADStoch analysis technique can effectively obtain VHF-MST radar signals at significantly higher altitudes, which is helpful in various scientific investigations.

Stochastic transmission in epidemiological models.

Recent empirical evidence suggests that the transmission coefficient in susceptible-exposed-infected-removed-like (SEIR-like) models evolves with time, presenting random patterns, and some stylized facts, such as mean-reversion and jumps. To address such observations we propose the use of jump-diffusion stochastic processes to parameterize the transmission coefficient in an SEIR-like model that accounts for death and time-dependent parameters. We provide a detailed theoretical analysis of the proposed model proving the existence and uniqueness of solutions as well as studying its asymptotic behavior. We also compare the proposed model with some variations possibly including jumps. The forecast performance of the considered models, using reported COVID-19 infections from New York City, is then tested in different scenarios. Despite the simplicity of the epidemiological model, by considering stochastic transmission, the forecasted scenarios were fairly accurate.

Community assembly of organisms regulates soil microbial functional potential through dual mechanisms.

Unraveling the influence of community assembly processes on soil ecosystem functioning presents a major challenge in the field of theoretical ecology, as it has received limited attention. Here, we used a series of long-term experiments spanning over 25 years to explore the assembly processes of bacterial, fungal, protist, and nematode communities using high-throughput sequencing. We characterized the soil microbial functional potential by the abundance of microbial genes associated with carbon, nitrogen, phosphorus, and sulfur cycling using GeoChip-based functional gene profiling, and determined how the assembly processes of organism groups regulate soil microbial functional potential through community diversity and network stability. Our results indicated that balanced fertilization (NPK) treatment improved the stochastic assembly of bacterial, fungal, and protist communities compared to phosphorus-deficient fertilization (NK) treatment. However, there was a nonsignificant increase in the normalized stochasticity ratio of the nematode community in response to fertilization across sites. Our findings emphasized that soil environmental factors influenced the assembly processes of the biotic community, which regulated soil microbial functional potential through dual mechanisms. One mechanism indicated that the high phosphorus levels and low soil nutrient stoichiometry may increase the stochasticity of bacterial, fungal, and protist communities and the determinism of the nematode community under NPK treatment, ultimately enhancing soil microbial functional potential by reinforcing the network stability of the biotic community. The other mechanism indicated that the low phosphorus levels and high soil nutrient stoichiometry may increase the stochastic process of the bacterial community and the determinism of the fungal, protist, and nematode communities under NK treatment, thereby enhancing soil microbial functional potential by improving the ß-diversity of the biotic community. Taken together, these results provide valuable insights into the mechanisms underlying the assembly processes of the biotic community that regulate ecosystem functioning.

Higher stochasticity in comammox Nitrospira community assembly in upland soils than the adjacent paddy soils at a regional scale.

Understanding the assembly mechanisms of microbial communities, particularly comammox Nitrospira, in agroecosystems is crucial for sustainable agriculture. However, the large-scale distribution and assembly processes of comammox Nitrospira in agricultural soils remain largely elusive. We investigated comammox Nitrospira abundance, community structure, and assembly processes in 16 paired upland peanuts and water-logged paddy soils in south China. Higher abundance, richness, and network complexity of comammox Nitrospira were observed in upland soils than in paddy soils, indicating a preference for upland soils over paddy soils among comammox Nitrospira taxa in agricultural environments. Clade A.2.1 and clade A.1 were the predominant comammox Nitrospira taxa in upland and paddy soils, respectively. Soil pH was the most crucial factor shaping comammox Nitrospira community structure. Stochastic processes were found to predominantly drive comammox Nitrospira community assembly in both upland and paddy soils, with deterministic processes playing a more important role in paddy soils than in upland soils. Overall, our findings demonstrate the higher stochasticity of comammox Nitrospira in upland soils than in the adjacent paddy soils, which may have implications for autotrophic nitrification in acidic agricultural soils.

The probability of epidemic burnout in the stochastic SIR model with vital dynamics.

We present an approach to computing the probability of epidemic "burnout," i.e., the probability that a newly emergent pathogen will go extinct after a major epidemic. Our analysis is based on the standard stochastic formulation of the Susceptible-Infectious-Removed (SIR) epidemic model including host demography (births and deaths) and corresponds to the standard SIR ordinary differential equations (ODEs) in the infinite population limit. Exploiting a boundary layer approximation to the ODEs and a birth-death process approximation to the stochastic dynamics within the boundary layer, we derive convenient, fully analytical approximations for the burnout probability. We demonstrate-by comparing with computationally demanding individual-based stochastic simulations and with semi-analytical approximations derived previously-that our fully analytical approximations are highly accurate for biologically plausible parameters. We show that the probability of burnout always decreases with increased mean infectious period. However, for typical biological parameters, there is a relevant local minimum in the probability of persistence as a function of the basic reproduction number [Formula: see text]. For the shortest infectious periods, persistence is least likely if [Formula: see text]; for longer infectious periods, the minimum point decreases to [Formula: see text]. For typical acute immunizing infections in human populations of realistic size, our analysis of the SIR model shows that burnout is almost certain in a well-mixed population, implying that susceptible recruitment through births is insufficient on its own to explain disease persistence.