Deterministic Process Research Articles

A comprehensive insight into the abundance and community of anammox bacteria in sediments of Hangzhou Bay, China

A total of 13 surface sediments were collected from Hangzhou Bay (HZB) for an investigation into the distribution and influencing factors of anammox bacterial community. The anammox bacterial 16S rRNA and hzo genes ranged between 2.34 × 105 to 9.22 × 105 copies/g and 3.68 × 105 to 1.70 × 106 copies/g, respectively. The results of high throughput sequencing (HTS) revealed that the obtained OTUs were affiliated with five known genera, named Ca. Scalindua, Ca. Jettenia, Ca. Brocadia, Ca. Kuenenia and Ca. Anammoxoglobus. RDA analysis indicated that salinity, pH, and water depth influenced the anammox bacterial community. Furthermore, network analysis identified Ca. Scalindua as a key genus. Neutral community model (NCM) and modified stochasticity ratio (MST) indicated that the deterministic process dominated the anammox bacterial community assembly. Overall, this study offers a more comprehensive understanding of the abundance and community of anammox bacteria in the sediments of HZB.

Spatial and temporal variation in lake macroinvertebrate communities is decreased by eutrophication

Eutrophication impacts freshwater ecosystems and biodiversity across the world. While temporal monitoring has shown changes in the nutrient inputs in many areas, how spatial and temporal beta diversity change along the eutrophication gradient under a changing context remains unclear. In this regard, analyses based on time series spanning multiple years are particularly scarce. We sampled benthic macroinvertebrates in 32 sites across three lake habitat types (MACROPHYTE, OPEN WATER, PHYTOPLANKTON) along the eutrophication gradient of Lake Taihu in four seasons from 2007 to 2019. Our purpose was to identify the relative contributions of spatial and temporal dissimilarity (i.e., inter-annual dissimilarity and seasonal dissimilarity) to overall benthic biodiversity. We also examined spatio-temporal patterns in community assembly mechanisms and how associated variation in benthic macroinvertebrate communities responded to nutrient indicators. Results showed that eutrophication caused macroinvertebrate community homogenization both along spatial and temporal gradients. Though spatial variability dominated the variation of species richness, abundance and community dissimilarity, seasons within years dissimilarity, inter-annual dissimilarity and seasonal dissimilarity were much more sensitive to eutrophication. Moreover, eutrophication inhibited a strong environmental control in benthic macroinvertebrate community assembly, including a dominant role of deterministic process in the spatial variation of macroinvertebrate communities and transition from stochastic to deterministic process in the temporal assembly of macroinvertebrate communities along the eutrophication gradient. In addition, some sites in PHYTOPLANKTON habitats showed similar spatial dissimilarity and spatial SES as sites in MACROPHYTE habitats, and the decreased spatial dissimilarity of three habitats implying that lake ecosystem recovery projects have achieved their goal at least to a certain degree.

Mean Square Exponential Stability of Semi-Linear Stochastic Perturbed Differential Equation Via Lyapunov Function Approach

In this work, a class of stochastically perturbed differential systems with standard Brownian motion of ordinary unperturbed differential system is considered and studied. The necessary conditions for the existence of a unique solution of the stochastic perturbed semi-linear system of differential equations are suggested and supported by concluding remarks. Some theoretical results concerning the mean square exponential stability of the nominal unperturbed deterministic differential system and its equivalent stochastically perturbed system with the deterministic and stochastic process as a random noise have been stated and proved. The proofs of the obtained results are based on using the stochastic quadratic Lyapunov function method. Form an application point of view of the proposed approach, an illustrative example is considered and implemented.

Determination of the most appropriate fertilizing method for apple trees using multi-criteria decision-making (MCDM) approaches.

Appropriate tree fertilization with essential nutrients is considered as one of the major factors in enhancing the quality and quantity of horticultural crops. The most efficient way to fertilize trees is to dig holes around the trunks and fill them with appropriate chemical and organic fertilizer. Doing this operation with mechanized methods reduces costs and increases productivity compared to traditional methods. In the present study, multi-criteria decision-making (MCDM) methods, including deterministic analytical hierarchy process (AHP) and fuzzy analytical hierarchy process (FAHP), technique for order of preference by similarity to ideal solution (TOPSIS), fuzzy TOPSIS (FTOPSIS), and analytic network process (ANP), were used to score and select the appropriate fertilizing method for apple trees based on the growers and expert's perspectives. The criteria, including fertilizing operation cost, crop yield, the percentage of tree damages, ease of entering and moving fertilizing equipment in tree rows, field capacity (with or without machinery), comfort and safety of fertilizing operations, after-sales service, access to the required machinery and implements, crop selling price, and crop quality, were used in the above-mentioned methods. The fertilization methods (Hole digging) considered in the present study were traditional fertilization (Shovel), orchard Trencher, motor hole digger, fixed centerline tractor-mounted hole digger, and off-set tractor-mounted hole digger. Based on the results, the priority of mechanized fertilizing methods was determined as tractor-mounted hole diggers (AHP weight of 0.286, FAHP weight of 0.285, TOPSIS relative proximity of 0.65, and FTOPSIS relative proximity of 0.64), fixed centerline tractor-mounted hole diggers (AHP weight of 0.219, FAHP weight of 0.158, TOPSIS relative proximity of 0.56, and FTOPSIS relative proximity of 0.62), motor hole diggers (AHP weight of 0.171, FAHP weight of 0.079, TOPSIS relative proximity of 0.46, and FTOPSIS relative proximity of 0.31), and orchard trenchers (AHP weight of 0.12, FAHP weight of 0.057, TOPSIS relative proximity of 0.19, and FTOPSIS relative proximity of 0.20), respectively. Based on the ANP method, off-set and fixed centerline tractor-mounted hole diggers had the highest priority (weights of 0.43 and 0.27), followed by trencher (weight of 0.16), motor hole diggers (weight of 0.09), and the traditional method (weight of 0.04). Results showed that applying orchard tractors equipped with mounted diggers, especially off-set types, can play an important role in enhancing the quantity and quality of apples produced, as well as reducing the costs of fertilizing operations.

PEM-based random vibration analysis under service-braking conditions on an irregular track

PurposeAccording to relevant research, non-uniform speed has a significant impact on the vehicle-track systems. Up to now, research work on it is still very limited. In this paper, the PEM is adopted to further transform it into a deterministic process to solve the vehicle’s problem of running at a non-uniform speed.Design/methodology/approachThe multi-body vehicle model has 10 degrees of freedom and the track is regarded as a finite long beam supported by lumped sleepers and ballast blocks. They are connected via linear Hertz springs. The vertical track irregularity is a Gaussian stationary process in the space domain. It is transformed into a uniformly modulated nonstationary random process in the time domain with respect to the non-uniform vehicle speed. By solving the equation of motion of the coupled vehicle-track system with the pseudo-excitation method, the pseudo-response and consequently the power spectral density and the standard deviation of the structural response can be obtained.FindingsTwo kinds of vehicle braking programs are taken in the numerical example and some beneficial conclusions are drawn.Originality/valueThe pseudo-excitation method (PEM) was used to perform the random vibration analysis of a coupled non-uniform speed vehicle-track system. Transforming the track irregularity into a uniformly modulated nonstationary random process in time domain with respect to the non-uniform vehicle speed was undertaken. The pseudo-response of the coupled system is solved by applying the Newmark algorithm with constant space integral steps. The random vibration transfer mechanism of the coupled system is fully discussed.

Geographical distribution and driving force of micro-eukaryotes in the seamount sediments along the island arc of the Yap and Mariana trenches.

A distinct distribution pattern was shaped by a deterministic process. Enhanced vertical connectivity expanded the previous understanding of seamount effects. Parasitism and predation were prevalent in the seamounts.

Planktonic/benthic Bathyarchaeota as a “gatekeeper” enhance archaeal nonrandom co-existence and deterministic assembling in the Yangtze River

Archaea, the third proposed domain of life, mediate carbon and nutrient cycling in global natural habitats. Compared with bacteria, our knowledge about archaeal ecological modes in large freshwater environments subject to varying natural and human factors is limited. By metabarcoding analysis of 303 samples, we provided the first integrate biogeography about archaeal compositions, co-existence networks, and assembling processes within a 6000 km continuum of the Yangtze River. Our study revealed that, among the major phyla, water samples owned a higher proportion of Thaumarchaeota (62.8%), while sediments had higher proportions of Euryarchaeota (33.4%) and Bathyarchaeota (18.8%). A decline of polarization in phylum abundance profile was observed from plateau/mountain/hill to basin/plain areas, which was attributed to the increase of nutrients and metals. Planktonic and benthic Bathyarchaeota tended to co-occur with both major (e.g., methanogens or Thermoplasmata) and minor (e.g., Asgard or DPANN) taxa in the non-random networks, harboring the highest richness and abundances of keystone species and contributing the most positively to edge number, node degree, and nearest neighbor degree. Furthermore, we noted significantly positive contributions of Bathyarchaeota abundance and network complexity to the dominance of deterministic process in archaeal assembly (water: 65.3%; sediments: 92.6%), since higher carbon metabolic versatility of Bathyarchaeota would benefit archaeal symbiotic relations. Stronger deterministic assembling was identified at the lower-reach plain, and higher concentrations of ammonium and aluminum separately functioning as nutrition and agglomerator were the main environmental drivers. We lastly found that the Three Gorges Dam caused a simultaneous drop of benthic Bathyarchaeota abundance, network co-existence, and deterministic effects immediately downstream due to riverbed erosion as a local interference. These findings highlight that Bathyarchaeota are a “gatekeeper” to promote fluvial archaeal diversity, stability, and predictability under varying macroscopic and microscopic factors, expanding our knowledge about microbial ecology in freshwater biogeochemical cycling globally.

Core taxa, co-occurrence pattern, diversity, and metabolic pathways contributing to robust anaerobic biodegradation of chlorophenol

It is hard to achieve robustness in anaerobic biodegradation of trichlorophenol (TCP). We hypothesized that specific combinations of environmental factors determine phylogenetic diversity and play important roles in the decomposition and stability of TCP-biodegrading bacteria. The anaerobic bioreactor was operated at 35 °C (H condition) or 30 °C (L condition) and mainly fed with TCP (from 28 μM to 180 μM) and organic material. Metagenome sequencing was combined with 16S rRNA gene amplicon sequencing for the microbial community analysis. The results exhibited that the property of robustness occurred in specific conditions. The corresponding co-occurrence and diversity patterns suggest high collectivization, degree and evenness for robust communities. Two types of core functional taxa were recognized: dechlorinators (unclassified Anaerolineae, Thermanaerothrix and Desulfovibrio) and ring-opening members (unclassified Proteobacteria, Methanosarcina, Methanoperedens, and Rubrobacter). The deterministic process of the expansion of niche of syntrophic bacteria at higher temperatures was confirmed. The reductive and hydrolytic dechlorination mechanisms jointly lead to C–Cl bond cleavage. H ultimately adapted to the stress of high TCP loading, with more abundant ring-opening enzyme (EC 3.1.1.45, ∼55%) and hydrolytic dechlorinase (EC 3.8.1.5, 26.5%) genes than L (∼47%, 10.5%). The functional structure (based on KEGG) in H was highly stable despite the high loading of TCP (up to 60 μM), but not in L. Furthermore, an unknown taxon with multiple functions (dechlorinating and ring-opening) was found based on genetic sequencing; its functional contribution of EC 3.8.1.5 in H (26.5%) was higher than that in L (10.5%), and it possessed a new metabolic pathway for biodegradation of halogenated aromatic compounds. This new finding is supplementary to the robust mechanisms underlying organic chlorine biodegradation, which can be used to support the engineering, regulation, and design of synthetic microbiomes.

Is Drug Delivery System a Deterministic or Probabilistic Approach? A Theoretical Model Based on the Sequence: Electrodynamics–Diffusion–Bayes

Commonly, it is accepted that oncology treatment would yield outcomes with a certain determinism without any quantitative support or mathematical model that establishes such determinations. Nowadays, with the advent of nanomedicine, the targeting drug delivery scheme has emerged, whose central objective is the uptake of nanoparticles by tumors. Once they are injected into the bloodstream, it is unclear as to which process governs the directing of nanoparticles towards the desired target, deterministic or stochastic. In any scenario, an optimal outcome, small toxicity and minimal dispersion of drugs is expected. Commonly, it is expected that an important fraction of them can be internalized into tumor. In this manner, due to the fraction of nanoparticles that have failed to uptake, the success of the drug delivery scheme might be at risk. In this paper, a theory based on the sequence electrodynamics–diffusion–Bayes theorem is presented. The Bayesian probability that emerges at the end of the sequence might be telling us that dynamical processes based on the injection of electrically charged nanoparticles might be dictated by stochastic formalism. Thus, rather than expecting a deterministic process, the chain of events would convert the drug delivery scheme to be dependent on a sequence of conditional probabilities.

Soil salinity is the main factor influencing the soil bacterial community assembly process under long-term drip irrigation in Xinjiang, China.

Identifying the potential factors associated with the impact of long-term drip irrigation (DI) on soil ecosystems is essential for responding to the environmental changes induced by extensive application of DI technology in arid regions. Herein, we examined the effects of the length of time that DI lasts in years (NDI) on soil bacterial diversity as well as the soil bacterial community assembly process and the factors influencing it. The results showed that long-term DI substantially reduced soil salinity and increased soil bacterial diversity while affecting the soil bacterial community structure distinctly. Null model results showed that the soil bacterial community assembly transitioned from stochastic processes to deterministic processes, as NDI increased. Homogeneous selection, a deterministic process, emerged as the dominant process when NDI exceeded 15 years. Both random forest and structural equation models showed that soil salinity was the primary factor affecting the bacterial community assembly process. In summary, this study suggested that soil bacteria respond differently to long-term DI and depends on the NDI, influencing the soil bacterial community assembly process under long-term DI.

Analysis of the input material flow of the transport conveyor

Purpose. To develop a method for analyzing the material flow entering the input of a conveyor section, based on the decomposition of the input material flow into a deterministic material flow and a stochastic material flow. Methodology. The analysis of experimental data characterizing the input material flow was performed using the methods of the canonical Fourier representation of a random process. Findings. A method for representing a stochastic material flow as a combination of a deterministic process and a stationary random process with ergodic properties is proposed. Originality. The originality of the obtained results lies in the fact that, for the first time, a method of analysis based on the decomposition of the input material flow for a conveyor section has been proposed, which, unlike the existing methods of input flow typing for the mining industry, will allow us to independently perform deterministic flow typing and stochastic material flow typing in transport conveyors. The proposed approach makes it possible to highlight special characteristics separately for deterministic and stochastic material flows. This will make it possible to use the obtained regularities to increase the accuracy of the conveyor model and will accordingly increase the quality of the belt speed control systems and the flow of material coming from the input bunker. The obtained results are of particular importance due to the fact that the characteristics of the deterministic material flow are directly related to the technical or technological factors of material extraction. Practical value. The obtained results allow determining statistically stable regularities for the incoming flow, which makes it possible, based on these regularities from the set of available control algorithms, to choose the optimal control algorithm for the parameters of the operating conveyor section. This allows reducing the enterprise’s energy costs of the transportation of material. The proposed method can be successfully applied to build random number generators simulating the sequence of values of the input flow of material. The developed generators can be used both for validating existing belt speed control systems and creating new control systems based on neural networks. This opens perspectives for the design of effective systems for controlling the flow parameters of transport system, based on the transport conveyor model, which takes into account the stochastic nature of the incoming material flow.

Geology and elevation shape bacterial assembly in Antarctic endolithic communities

Ice free areas of continental Antarctica are among the coldest and driest environments on Earth, and yet, they support surprisingly diverse and highly adapted microbial communities. Endolithic growth is one of the key adaptations to such extreme environments and often represents the dominant life-form. Despite growing scientific interest, little is known of the mechanisms that influence the assembly of endolithic microbiomes across these harsh environments. Here, we used metagenomics to examine the diversity and assembly of endolithic bacterial communities across Antarctica within different rock types and over a large elevation range. While granite supported richer and more heterogeneous communities than sandstone, elevation had no apparent effect on taxonomic richness, regardless of rock type. Conversely, elevation was clearly associated with turnover in community composition, with the deterministic process of variable selection driving microbial assembly along the elevation gradient. The turnover associated with elevation was modulated by geology, whereby for a given elevation difference, turnover was consistently larger between communities inhabiting different rock types. Overall, selection imposed by elevation and geology appeared stronger than turnover related to other spatially-structured environmental drivers.Our findings indicate that at the cold-arid limit of life on Earth, geology and elevation are key determinants of endolithic bacterial heterogeneity. This also suggests that warming temperatures may threaten the persistence of such extreme-adapted organisms.

Markov decision processes approximation with coupled dynamics via Markov deterministic control systems

Abstract This article presents an approximation of discrete Markov decision processes with small noise on Borel spaces with an infinite horizon and an expected total discounted cost by the corresponding deterministic Markov process. In both cases, the dynamics evolve through a system consisting of two coupled difference equations. It is assumed that the difference equations of the system are perturbed by a small noise. Under our assumptions, a bound for the stability index is given, and the optimal cost convergence rate is estimated using a small perturbation parameter. Moreover, the convergence of the optimal policy on compact subsets is verified. Finally, two examples are presented to illustrate the developed theory.

Dominant role of rare bacterial taxa rather than abundant taxa in driving the tailing primary succession

Primary ecological succession is imperative for tailing vegetation, driven notably by microbes that enhance tailing nutrient status. Yet, the roles of abundant and rare taxa in tailing primary succession remain underexplored. This study investigates these subcommunities across three succession stages (i.e., original tailing, biological crusts, grasslands). Throughout primary succession, alpha diversity and functional gene abundances of the rare taxa (RT) group consistently rise from bare tailings to grasslands. Conversely, the abundant taxa (AT) group displays an opposing trend. Intriguingly, employing co-occurrence networks, keystone taxa, mantel tests, similarity percentage analysis, and structural equation model, the study uncovers that RT wields a more pivotal role than AT in driving tailing primary succession. Community assembly analysis reveals stochastic control of AT and deterministic control of RT. Additionally, primary succession reinforces stochastic processes in AT, while RT's deterministic process remains unaffected. By unveiling these dynamics, the research enriches our understanding of primary ecological succession in tailings. Recognition of unique diversity patterns and community assembly mechanisms for rare and abundant subcommunities advances tailing ecosystem comprehension and informs ecological restoration strategies. This study thus contributes valuable insights to the complex interplay of microbial taxa during tailing primary succession.

Rhizosphere shapes the associations between protistan predators and bacteria within microbiomes through the deterministic selection on bacterial communities.

The assembly of bacterial communities in the rhizosphere is well-documented and plays a crucial role in supporting plant performance. However, we have limited knowledge of how plant rhizosphere determines the assembly of protistan predators and whether the potential associations between protistan predators and bacterial communities shift due to rhizosphere selection. To address this, we examined bacterial and protistan taxa from 443 agricultural soil samples including bulk and rhizosphere soils. Our results presented distinct patterns of bacteria and protistan predators in rhizosphere microbiome assembly. Community assembly of protistan predators was determined by a stochastic process in the rhizosphere and the diversity of protistan predators was reduced in the rhizosphere compared to bulk soils, these may be attributed to the indirect impacts from the altered bacterial communities that showed deterministic process assembly in the rhizosphere. Interestingly, we observed that the plant rhizosphere facilitates more close interrelationships between protistan predators and bacterial communities, which might promote a healthy rhizosphere microbial community for plant growth. Overall, our findings indicate that the potential predator-prey relationships within the microbiome, mediated by plant rhizosphere, might contribute to plant performance in agricultural ecosystems.

Water table level controls methanogenic and methanotrophic communities and methane emissions in a Sphagnum-dominated peatland.

Peatlands are important sources of the greenhouse gas methane emissions equipoised by methanogens and methanotrophs. However, knowledge about how microbial functional groups associated with methane production and oxidation respond to water table fluctuations has been limited to date. Here, methane-related microbial communities and the potentials of methane production and oxidation were determined along sectioned peat layers in a subalpine peatland across four Sphagnum-dominated sites with different water table levels. Methane fluxes were also monitored at these sites. The results showed that mcrA gene copies for methanogens were the highest in the 10- to 15-cm peat layer, which was also characterized by the maximum potential methane production (24.53 ± 1.83 nmol/g/h). Copy numbers of the pmoA gene for type Ia and Ib methanotrophs were enriched in the 0-5 cm peat layer with the highest potential methane oxidation (43.09 ± 3.44 nmol/g/h). For the type II methanotrophs, the pmoA gene copies were higher in the 10- to 15-cm peat layer. Hydrogenotrophic methanogens and type II methanotrophs dominated the methane functional groups. Deterministic process contributed more to methanogenic and methanotrophic community assemblages in comparison with stochastic process. The level of water table significantly shaped methanogenic and methanotrophic community structures and regulated methane fluxes. Compared with vascular plants, Sphagnum mosses significantly reduced the methane emissions in peatlands. Collectively, these findings enhance a comprehensive understanding of the effect of the water table level on methane functional groups, with consequential implications for reducing methane emissions within peatland ecosystems.IMPORTANCEThe water table level is recognized as a critical factor in regulating methane emissions, which are largely dependent on the balance of methanogens and methanotrophs. Previous studies on peat methane emissions have been mostly focused on spatial-temporal variations and the relationship with meteorological conditions. However, the role of the water table level in methane emissions remains unknown. In this work, four representative microhabitats along a water table gradient in a Sphagnum-dominated peatland were sampled to gain an insight into methane functional communities and methane emissions as affected by the water table level. The changes in methane-related microbial community structure and assembly were used to characterize the response to the water table level. This study improves the understanding of the changes in methane-related microbial communities and methane emissions with water table levels in peatlands.

Probabilistic assessment of the safety profile of the Fischer–Tropsch process with a supercritical solvent

AbstractInherent safety assessment during the design stage of chemical processes is typically conducted based on average values for design parameters. Under those conditions, the single‐point deterministic process performance assessment may be affected by the phenomenon known as the ‘flaw of averages’ in the presence of irreducible sources of uncertainty (performance evaluated at average conditions does not represent average performance). In this work, an inherent process safety assessment developed under a probabilistic formulation is presented. An evaluation of the proposed approach is performed in the case of a gas‐to‐liquid process system using a supercritical solvent for Fischer–Tropsch reactor systems. The pertinent uncertainty analysis is carried out using Monte Carlo simulation techniques to account for the propagation of uncertainty through the inherent process safety model and the derivation of probability distribution profiles for the associated metrics, thus statistically characterizing ranges of potential performance outcomes. The response variables were the autothermal reactor and the syngas flows. The results show that the input variables associated to the autothermal flow potentially generate the most hazardous conditions for the process. The results also show how the metrics are affected when uncertainty is explicitly taken into account at the design stage of the process, offering a more nuanced assessment and characterization of the inherent process safety profile.

Elevational distribution and seasonal dynamics of alpine soil prokaryotic communities.

The alpine grassland ecosystem is a biodiversity hotspot of plants on the Qinghai-Tibetan Plateau, where rapid climate change is altering the patterns of plant biodiversity along elevational and seasonal gradients of environments. However, how belowground microbial biodiversity changes along elevational gradient during the growing season is not well understood yet. Here, we investigated the elevational distribution of soil prokaryotic communities by using 16S rRNA amplicon sequencing along an elevational gradient between 3,200 and 4,200 m, and a seasonal gradient between June and September in the Qinghai-Tibetan alpine grasslands. First, we found soil prokaryotic diversity and community composition significantly shifted along the elevational gradient, mainly driven by soil temperature and moisture. Species richness did not show consistent elevational trends, while those of evenness declined with elevation. Copiotrophs and symbiotic diazotrophs declined with elevation, while oligotrophs and AOB increased, affected by temperature. Anaerobic or facultatively anaerobic bacteria and AOA were hump-shaped, mainly influenced by moisture. Second, seasonal patterns of community composition were mainly driven by aboveground biomass, precipitation, and soil temperature. The seasonal dynamics of community composition indicated that soil prokaryotic community, particularly Actinobacteria, was sensitive to short-term climate change, such as the monthly precipitation variation. At last, dispersal limitation consistently dominated the assembly process of soil prokaryotic communities along both elevational and seasonal gradients, especially for those of rare species, while the deterministic process of abundant species was relatively higher at drier sites and in drier July. The balance between deterministic and stochastic processes in abundant subcommunities might be strongly influenced by water conditions (precipitation/moisture). Our findings suggest that both elevation and season can alter the patterns of soil prokaryotic biodiversity in alpine grassland ecosystem of Qinghai-Tibetan Plateau, which is a biodiversity hotspot and is experiencing rapid climate change. This work provides new insights into the response of soil prokaryotic communities to changes in elevation and season, and helps us understand the temporal and spatial variations in such climate change-sensitive regions.

The cultivation regimes of Morchella sextelata trigger shifts in the community assemblage and ecological traits of soil bacteria.

The successful large-scale cultivation of morel mushrooms (Morchella sextelata) requires a comprehensive understanding of the soil bacterial communities associated with morel-farming beds, as the interactions between fungi and bacteria play a crucial role in shaping the soil microbiome. In this study, we investigated the temporal distribution and ecological characteristics of soil bacteria associated with morel fruiting bodies at different stages, specifically the conidial and primordial stages, under two cropping regimes, non-continuous cropping (NCC) and continuous cropping (CC). Our findings revealed a significant reduction in the yield of morel primordia during the third year following 2 years of CC (0.29 ± 0.25 primordia/grid), in comparison to the NCC regime (12.39 ± 6.09 primordia/grid). Furthermore, inoculation with morel mycelia had a notable impact on soil bacterial diversity, decreasing it in the NCC regime and increasing the number of generalist bacterial members in the CC regime. The latter regime also led to the accumulation of nutrients in the soil beds, resulting in a shift from a stochastic to a deterministic process in the composition of the bacterial community, which differed from the NCC regime. Additionally, mycelial inoculation had a positive effect on the abundance of potential copiotrophic/denitrifying and N-fixing bacteria while decreasing the abundance of oligotrophic/nitrifying bacteria. Interestingly, this effect was more pronounced in the NCC regime than in the CC regime. These results suggest that the increase in potential copiotrophic/denitrifying and N-fixing bacteria facilitated the decomposition of nutrients in exogenous nutrient bags by morel mushrooms, thereby maintaining nitrogen balance in the soil. Overall, our study provides valuable insights into the interactions between morel mycelia and the associated soil bacteriome as well as the influence of different cultivation regimes on these interactions. These findings contribute to our understanding of the complex dynamics of the soil microbiome and can inform strategies for optimizing morel mushroom cultivation.

Fluctuations of the local times of the self-repelling random walk with directed edges

AbstractIn 2008, Tóth and Vető defined the self-repelling random walk with directed edges as a non-Markovian random walk on $\unicode{x2124}$ : in this model, the probability that the walk moves from a point of $\unicode{x2124}$ to a given neighbor depends on the number of previous crossings of the directed edge from the initial point to the target, called the local time of the edge. Tóth and Vető found that this model exhibited very peculiar behavior, as the process formed by the local times of all the edges, evaluated at a stopping time of a certain type and suitably renormalized, converges to a deterministic process, instead of a random one as in similar models. In this work, we study the fluctuations of the local times process around its deterministic limit, about which nothing was previously known. We prove that these fluctuations converge in the Skorokhod $M_1$ topology, as well as in the uniform topology away from the discontinuities of the limit, but not in the most classical Skorokhod topology. We also prove the convergence of the fluctuations of the aforementioned stopping times.