Travelling waves due to negative plant-soil feedbacks in a model including tree life-stages.

The emergence and maintenance of tree species diversity in tropical forests is commonly attributed to the Janzen-Connell (JC) hypothesis, which states that growth of seedlings is suppressed in the proximity of conspecific adult trees. As a result, a JC distribution due to a density-dependent negative feedback emerges in the form of a (transient) pattern where conspecific seedling density is highest at intermediate distances away from parent trees. Several studies suggest that the required density-dependent feedbacks behind this pattern could result from interactions between trees and soil-borne pathogens. However, negative plant-soil feedback may involve additional mechanisms, including the accumulation of autotoxic compounds generated through tree litter decomposition. An essential task therefore consists in constructing mathematical models incorporating both effects showing the ability to support the emergence of JC distributions. In this work, we develop and analyse a novel reaction-diffusion-ODE model, describing the interactions within tropical tree species across different life stages (seeds, seedlings, and adults) as driven by negative plant-soil feedback. In particular, we show that under strong negative plant-soil feedback travelling wave solutions exist, creating transient distributions of adult trees and seedlings that are in agreement with the Janzen-Connell hypothesis. Moreover, we show that these travelling wave solutions are pulled fronts and a robust feature as they occur over a broad parameter range. Finally, we calculate their linear spreading speed and show its (in)dependence on relevant nondimensional parameters.

Process based modelling of plants-fungus interactions explains fairy ring types and dynamics.

Many mushroom-forming fungi can develop circular colonies affecting the vegetation in a phenomenon named fairy rings. Since the nineteenth century, several hypotheses have been proposed to explain how fairy ring fungi form ring-like shapes instead of disks and why they produce negative or positive effects on the surrounding vegetation. In this context, we present a novel process-based mathematical model aimed at reproducing the mycelial spatial configuration of fairy rings and test different literature-supported hypotheses explaining the suppressive and stimulating effects of fungi on plants. Simulations successfully reproduced the shape of fairy rings through the accumulation of fungal self-inhibitory compounds. Moreover, regarding the negative effects of fungi on vegetation, results suggest that fungal-induced soil hydrophobicity is sufficient to reproduce all observed types of fairy rings, while the potential production of phytotoxins is not. In relation to the positive effects of fungi on plants, results show that the release of phytostimulants is needed to reproduce the vegetation patterns associated to some fairy ring types. Model outputs can guide future experiments and field work to corroborate the considered hypotheses and provide more information for further model improvements.

Modelling how negative plant-soil feedbacks across life stages affect the spatial patterning of trees.

In this work, we theoretically explore how litter decomposition processes and soil-borne pathogens contribute to negative plant-soil feedbacks, in particular in transient and stable spatial organisation of tropical forest trees and seedlings known as Janzen-Connell distributions. By considering soil-borne pathogens and autotoxicity both separately and in combination in a phenomenological model, we can study how both factors may affect transient dynamics and emerging Janzen-Connell distributions. We also identify parameter regimes associated with different long-term behaviours. Moreover, we compare how the strength of negative plant-soil feedbacks was mediated by tree germination and growth strategies, using a combination of analytical approaches and numerical simulations. Our interdisciplinary investigation, motivated by an ecological question, allows us to construct important links between local feedbacks, spatial self-organisation, and community assembly. Our model analyses contribute to understanding the drivers of biodiversity in tropical ecosystems, by disentangling the abilities of two potential mechanisms to generate Janzen-Connell distributions. Furthermore, our theoretical results may help guiding future field data analyses by identifying spatial signatures in adult tree and seedling distribution data that may reflect the presence of particular plant-soil feedback mechanisms.

Adult conspecific density affects Janzen-Connell patterns by modulating the recruitment exclusion zones.

Plant-soil negative feedback (NF) is a well-established phenomenon that, by preventing the dominance of a single species, allows species coexistence and promotes the maintenance of biodiversity. At community scale, localized NF may cause the formation of exclusion zones under adult conspecifics leading to Janzen-Connell (JC) distribution. In this study, we explore the connection between adult density, either conspecifics or heterospecifics, on the probability of occurrence of JC distributions. Using an individual-based modelling approach, we simulated the formation of exclusion zones due to the build-up of NF in proximity of conspecific adult plants and assessed the frequency of JC distribution in relation to conspecifics and heterospecifics density ranging from isolated trees to closed forest stands. We found that JC recruitment distribution is very common in the case of an isolated tree when NF was strong and capable to form an exclusion zone under the parent tree. At very low NF intensity, a prevalence of the decreasing pattern was observed because, under such conditions, the inhibitory effect due to the presence of the mother tree was unable to overcome the clustering effect of the seed dispersal kernel. However, if NF is strong the JC frequency suddenly decreases in stands with a continuous conspecific cover likely as a result of progressive expansion of the exclusion zone surrounding all trees in closed forest stands. Finally, our simulations showed that JC distribution should not be frequent in the case of rare species immersed in a matrix of heterospecific adults. Overall, the model shows that a plant suffering from strong NF in monospecific stands can rarely exhibit a recruitment pattern fitting the JC model. Such counterintuitive results would provide the means to reconcile the well-established NF framework with part the forest ecologists' community that is still skeptical towards the JC model. Synthesis: Our model highlights the complex interconnection between NF intensity, stand density, and recruitment patterns explaining where and why the JC distribution occurs. Moreover, predicting the occurrence of JC in relation to stand density we clarify the relevance of this ecological phenomenon for future integration in plant community frameworks.

Effective conductivity of inertial flows through porous media.

We study two-dimensional incompressible inertial flows through porous media. At core (small) scale, we prove that the constitutive, nonlinear model can be rewritten into a linear one by means of a new parameter K^{★} which encompasses all the inertial effects. In natural (large-scale) formations, K^{★} is erratically changing, and we analytically compute its counterpart, which is coined generalized effective conductivity, by the self-consistent approach (SCA). In spite of its approximate nature, the SCA leads to simple results that are in good agreement with Monte Carlo simulations.

Metabolic flux analysis: a comprehensive review on sample preparation, analytical techniques, data analysis, computational modelling, and main application areas.

Metabolic flux analysis (MFA) quantitatively describes cellular fluxes to understand metabolic phenotypes and functional behaviour after environmental and/or genetic perturbations. In the last decade, the application of stable isotopes became extremely important to determine and integrate in vivo measurements of metabolic reactions in systems biology. 13C-MFA is one of the most informative methods used to study central metabolism of biological systems. This review aims to outline the current experimental procedure adopted in 13C-MFA, starting from the preparation of cell cultures and labelled tracers to the quenching and extraction of metabolites and their subsequent analysis performed with very powerful software. Here, the limitations and advantages of nuclear magnetic resonance spectroscopy and mass spectrometry techniques used in carbon labelled experiments are elucidated by reviewing the most recent published papers. Furthermore, we summarise the most successful approaches used for computational modelling in flux analysis and the main application areas with a particular focus in metabolic engineering.

A global report on the dynamics of COVID-19 with quarantine and hospitalization: A fractional order model with non-local kernel.

In this paper, a compartmental mathematical model has been utilized to gain a better insight about the future dynamics of COVID-19. The total human population is divided into eight various compartments including susceptible, exposed, pre-asymptomatic, asymptomatic, symptomatic, quarantined, hospitalized and recovered or removed individuals. The problem was modeled in terms of highly nonlinear coupled system of classical order ordinary differential equations (ODEs) which was further generalized with the Atangana-Balaeanu (ABC) fractional derivative in Caputo sense with nonlocal kernel. Furthermore, some theoretical analyses have been done such as boundedness, positivity, existence and uniqueness of the considered. Disease-free and endemic equilibrium points were also assessed. The basic reproduction was calculated through next generation technique. Due to high risk of infection, in the present study, we have considered the reported cases from three continents namely Americas, Europe, and south-east Asia. The reported cases were considered between 1st May 2021 and 31st July 2021 and on the basis of this data, the spread of infection is predicted for the next 200 days. The graphical solution of the considered nonlinear fractional model was obtained via numerical scheme by implementing the MATLAB software. Based on the fitted values of parameters, the basic reproduction number ℜ0 for the case of America, Asia and Europe were calculated as ℜ0≈2.92819, ℜ0≈2.87970 and ℜ0≈2.23507 respectively. It is also observed that the spread of infection in America is comparatively high followed by Asia and Europe. Moreover, the effect of fractional parameter is shown on the dynamics of spread of infection among different classes. Additionally, the effect of quarantined and treatment of infected individuals is also shown graphically. From the present analysis it is observed that awareness of being quarantine and proper treatment can reduce the infection rate dramatically and a minimal variation in quarantine and treatment rates of infected individuals can lead us to decrease the rate of infection.

A Sight on Single-Cell Transcriptomics in Plants Through the Prism of Cell-Based Computational Modeling Approaches: Benefits and Challenges for Data Analysis.

Single-cell technology is a relatively new and promising way to obtain high-resolution transcriptomic data mostly used for animals during the last decade. However, several scientific groups developed and applied the protocols for some plant tissues. Together with deeply-developed cell-resolution imaging techniques, this achievement opens up new horizons for studying the complex mechanisms of plant tissue architecture formation. While the opportunities for integrating data from transcriptomic to morphogenetic levels in a unified system still present several difficulties, plant tissues have some additional peculiarities. One of the plants' features is that cell-to-cell communication topology through plasmodesmata forms during tissue growth and morphogenesis and results in mutual regulation of expression between neighboring cells affecting internal processes and cell domain development. Undoubtedly, we must take this fact into account when analyzing single-cell transcriptomic data. Cell-based computational modeling approaches successfully used in plant morphogenesis studies promise to be an efficient way to summarize such novel multiscale data. The inverse problem's solutions for these models computed on the real tissue templates can shed light on the restoration of individual cells' spatial localization in the initial plant organ-one of the most ambiguous and challenging stages in single-cell transcriptomic data analysis. This review summarizes new opportunities for advanced plant morphogenesis models, which become possible thanks to single-cell transcriptome data. Besides, we show the prospects of microscopy and cell-resolution imaging techniques to solve several spatial problems in single-cell transcriptomic data analysis and enhance the hybrid modeling framework opportunities.

A System Dynamics Approach to Model Photosynthesis at Leaf Level Under Fluctuating Light.

Photosynthesis has been mainly studied under steady-state conditions even though this assumption results inadequate for assessing the biochemical responses to rapid variations occurring in natural environments. The combination of mathematical models with available data may enhance the understanding of the dynamic responses of plants to fluctuating environments and can be used to make predictions on how photosynthesis would respond to non-steady-state conditions. In this study, we present a leaf level System Dynamics photosynthesis model based and validated on an experiment performed on two soybean varieties, namely, the wild type Eiko and the chlorophyll-deficient mutant MinnGold, grown in constant and fluctuating light conditions. This mutant is known to have similar steady-state photosynthesis compared to the green wild type, but it is found to have less biomass at harvest. It has been hypothesized that this might be due to an unoptimized response to non-steady-state conditions; therefore, this mutant seems appropriate to investigate dynamic photosynthesis. The model explained well the photosynthetic responses of these two varieties to fluctuating and constant light conditions and allowed to make relevant conclusions on the different dynamic responses of the two varieties. Deviations between data and model simulations are mostly evident in the non-photochemical quenching (NPQ) dynamics due to the oversimplified combination of PsbS- and zeaxanthin-dependent kinetics, failing in finely capturing the NPQ responses at different timescales. Nevertheless, due to its simplicity, the model can provide the basis of an upscaled dynamic model at a plant level.

A General Process-Based Model for Describing the Metabolic Shift in Microbial Cell Cultures.

The metabolic shift between respiration and fermentation at high glucose concentration is a widespread phenomenon in microbial world, and it is relevant for the biotechnological exploitation of microbial cell factories, affecting the achievement of high-cell-densities in bioreactors. Starting from a model already developed for the yeast Saccharomyces cerevisiae, based on the System Dynamics approach, a general process-based model for two prokaryotic species of biotechnological interest, such as Escherichia coli and Bacillus subtilis, is proposed. The model is based on the main assumption that glycolytic intermediates act as central catabolic hub regulating the shift between respiratory and fermentative pathways. Furthermore, the description of a mixed fermentation with secondary by-products, characteristic of bacterial metabolism, is explicitly considered. The model also represents the inhibitory effect on growth and metabolism of self-produced toxic compounds relevant in assessing the late phases of high-cell density culture. Model simulations reproduced data from experiments reported in the literature with different strains of non-recombinant and recombinant E. coli and B. subtilis cultured in both batch and fed-batch reactors. The proposed model, based on simple biological assumptions, is able to describe the main dynamics of two microbial species of relevant biotechnological interest. It demonstrates that a reductionist System Dynamics approach to formulate simplified macro-kinetic models can provide a robust representation of cell growth and accumulation in the medium of fermentation by-products.

A Night at the OPERA: A Conceptual Framework for an Integrated Distributed Sensor Network-Based System to Figure out Safety Protocols for Animals under Risk of Fire.

Large scale wildfire events that occurred around the world involved a massive loss of animal lives, with a consequent economic impact on agricultural holdings and damages to ecosystems. Preparing animals for a wildfire evacuation requires an extra level of planning, preparedness and coordination, which is missing in the current practice. This paper describes a conceptual framework of an ICT system implemented to support the activities of the Regional Veterinary referral Center for non-epidemic emergencies (CeRVEnE) in the Campania Region for the twofold objectives. On the one hand, it realizes the monitoring of the wooded areas under risk of fire in the so-called "Mount Vesuvius' red zone". On the other hand, it determines the OPtimal Evacuation Route for Animals (OPERA) in case of fire, for each of the reported animal species living in the mentioned red zone. The main innovation of the proposed system lies in its software architecture that aims at integrating a Distributed Sensor Network (DSN), an ad-hoc software to generate timely simulations for fire risk modeling, and a GIS (Geographic Information System) for both the activities of web mapping and OPERA definition. This paper shows some effective preliminary results of the system implementation. The importance of the system mainly lies in its accordance with the so-called "Foresight approach" perspective, that provides models and tools to guarantee the prevention of systematic failure in disaster risk management, and becomes moreover critical in the case of Mount Vesuvius, which hosts a unique combination of both animal and anthropic elements within a delicate natural ecosystem.

One ring to rule them all: an ecosystem engineer fungus fosters plant and microbial diversity in a Mediterranean grassland.

Species coexistence in grasslands is regulated by several environmental factors and interactions with the soil microbial community. Here, the development of the Basidiomycetes fungus Agaricus arvensis, forming fairy rings, in a species-rich Mediterranean grassland, is described. Effects of the mycelial front on plants, fungi and bacteria were assessed by vegetation survey and next generation sequencing approaches. Our results showed a fungal-dependent shift in the community structure operated by a wave-like spread of fairy rings that decreased plant, fungal and bacterial diversity, indicating a detrimental effect of fairy rings on most species. The fairy rings induced successional processes in plants that enhanced the replacement of a community dominated by perennial plants with short-living and fast-growing plant species. In parallel, fungal and bacterial communities showed evident differences in species composition with several taxa associated within distinct sampling zone across the fairy rings. Notably, bacteria belonging to the Burkholderia genus and fungi of the genus Trichoderma increased in response to the advancing mycelium of A. arvensis. The profound changes in community composition and the overall increase in taxa diversity at ecosystemic scale suggest that fairy ring-forming fungi may act as ecosystem engineer species in Mediterranean grasslands.

Effects of limited volatiles release by plants in tritrophic interactions.

We introduce a mathematical model to describe the tritrophic interaction between crop,pest and the pest natural enemy where the release of Volatile Organic Compounds (VOCs) by crop istaken into account. The VOCs may be considered as an indirect defence mechanism of the plant asthey attract the pest natural enemies toward the attacked plants. The model dynamics is studied throughqualitative analysis and numerical simulations. The factors that may enhance pest disappearance areidentified. In particular, we show that VOCs may have a beneficial effect on the environment sincetheir release may be able to stabilize the model dynamics. Specifically, for the parameter values thatwe have explored, this effect can arise only when both the phenomena of VOCs basic plant release andVOCs plant release due to pest attack are present.

Bautin bifurcations in a forest-grassland ecosystem with human-environment interactions.

Ecosystems may be characterized by a complex dynamical behaviour where external disturbances and/or internal perturbations may trigger sudden/irreversible changes, called catastrophic shifts. Simple mathematical models in the form of ordinary and/or partial differential equations have been proposed to approximate in a qualitatively manner the observed complex phenomena, where catastrophic shifts are determined by bifurcation points. In this work, we show that in ecosystems, gradual/smooth changes may be transformed in sudden/catastrophic shifts as a consequence of codimension-2 bifurcations. We stress the importance of using the full arsenal of numerical bifurcation theory to systematically identify and characterize criticalities in ecological models in the 2D parameter space. For our demonstrations, we revisit the analysis of a simple model of a forest-grassland mosaic ecosystem constructing the 2D bifurcation diagram with respect to the impact of human influence and that of natural causes. Our numerical analysis reveals that this simple model is able to approximate both abrupt (catastrophic) and smooth transitions as the system undergoes Bautin bifurcations.

The Physiological Mechanisms Behind the Earlywood-To-Latewood Transition: A Process-Based Modeling Approach.

In extratropical ecosystems, the growth of trees is cyclic, producing tree rings composed of large-lumen and thin-walled cells (earlywood) alternating with narrow-lumen and thick-walled cells (latewood). So far, the physiology behind wood formation processes and the associated kinetics has rarely been considered to explain this pattern. We developed a process-based mechanistic model that simulates the development of conifer tracheids, explicitly considering the processes of cell enlargement and the deposition and lignification of cell walls. The model assumes that (1) wall deposition gradually slows down cell enlargement and (2) the deposition of cellulose and lignin is regulated by the availability of soluble sugars. The model reliably reproduces the anatomical traits and kinetics of the tracheids of four conifer species. At the beginning of the growing season, low sugar availability in the cambium results in slow wall deposition that allows for a longer enlargement time; thus, large cells with thin walls (i.e., earlywood) are produced. In late summer and early autumn, high sugar availability produces narrower cells having thick cell walls (i.e., latewood). This modeling framework provides a mechanistic link between plant ecophysiology and wood phenology and significantly contributes to understanding the role of sugar availability during xylogenesis.

Faster N Release, but Not C Loss, From Leaf Litter of Invasives Compared to Native Species in Mediterranean Ecosystems.

Plant invasions can have relevant impacts on biogeochemical cycles, whose extent, in Mediterranean ecosystems, have not yet been systematically assessed comparing litter carbon (C) and nitrogen (N) dynamics between invasive plants and native communities. We carried out a 1-year litterbag experiment in 4 different plant communities (grassland, sand dune, riparian and mixed forests) on 8 invasives and 24 autochthonous plant species, used as control. Plant litter was characterized for mass loss, N release, proximate lignin and litter chemistry by 13C CPMAS NMR. Native and invasive species showed significant differences in litter chemical traits, with invaders generally showing higher N concentration and lower lignin/N ratio. Mass loss data revealed no consistent differences between native and invasive species, although some woody and vine invaders showed exceptionally high decomposition rate. In contrast, N release rate from litter was faster for invasive plants compared to native species. N concentration, lignin content and relative abundance of methoxyl and N-alkyl C region from 13C CPMAS NMR spectra were the parameters that better explained mass loss and N mineralization rates. Our findings demonstrate that during litter decomposition invasive species litter has no different decomposition rates but greater N release rate compared to natives. Accordingly, invasives are expected to affect N cycle in Mediterranean plant communities, possibly promoting a shift of plant assemblages.

Effects of Hydraulic Soil Properties on Vegetation Pattern Formation in Sloping Landscapes.

Current models of vegetation pattern formation rely on a system of weakly nonlinear reaction-diffusion equations that are coupled by their source terms. While these equations, which are used to describe a spatiotemporal planar evolution of biomass and soil water, qualitatively capture the emergence of various types of vegetation patterns in arid environments, they are phenomenological and have a limited predictive power. We ameliorate these limitations by deriving the vertically averaged Richards' equation to describe flow (as opposed to "diffusion") of water in partially saturated soils. This establishes conditions under which this nonlinear equation reduces to its weakly nonlinear reaction-diffusion counterpart used in the previous models, thus relating their unphysical parameters (e.g., diffusion coefficient) to the measurable soil properties (e.g., hydraulic conductivity) used to parameterize the Richards equation. Our model is valid for both flat and sloping landscapes and can handle arbitrary topography and boundary conditions. The result is a model that relates the environmental conditions (e.g., precipitation rate, runoff and soil properties) to formation of multiple patterns observed in nature (such as stripes, labyrinth and spots).

Spatial Self-Organization of Vegetation Subject to Climatic Stress-Insights from a System Dynamics-Individual-Based Hybrid Model.

In simulation models of populations or communities, individual plants have often been obfuscated in favor of aggregated vegetation. This simplification comes with a loss of biological detail and a smoothing out of the demographic noise engendered by stochastic individual-scale processes and heterogeneities, which is significant among others when studying the viability of small populations facing challenging fluctuating environmental conditions. This consideration has motivated the development of precise plant-centered models. The accuracy gained in the representation of plant biology has then, however, often been balanced by the disappearance in models of important plant-soil interactions (esp. water dynamics) due to the inability of most individual-based frameworks to simulate complex continuous processes. In this study, we used a hybrid modeling approach, namely integrated System Dynamics (SD)-Individual-based (IB), to illustrate the importance of individual plant dynamics to explain spatial self-organization of vegetation in arid environments. We analyzed the behavior of this model under different parameter sets either related to individual plant properties (such as seed dispersal distance and reproductive age) or the environment (such as intensity and yearly distribution of precipitation events). While the results of this work confirmed the prevailing theory on vegetation patterning, they also revealed the importance therein of plant-level processes that cannot be rendered by reaction-diffusion models. Initial spatial distribution of plants, reproductive age, and average seed dispersal distance, by impacting patch size and vegetation aggregation, affected pattern formation and population survival under climatic variations. Besides, changes in precipitation regime altered the demographic structure and spatial organization of vegetation patches by affecting plants differentially depending on their age and biomass. Water availability influenced non-linearly total biomass density. Remarkably, lower precipitation resulted in lower mean plant age yet higher mean individual biomass. Moreover, seasonal variations in rainfall greater than a threshold (here, ±0.45 mm from the 1.3 mm baseline) decreased mean total biomass and generated limit cycles, which, in the case of large variations, were preceded by chaotic demographic and spatial behavior. In some cases, peculiar spatial patterns (e.g., rings) were also engendered. On a technical note, the shortcomings of the present model and the benefit of hybrid modeling for virtual investigations in plant science are discussed.

Self-DNA inhibitory effects: Underlying mechanisms and ecological implications.

DNA is usually known as the molecule that carries the instructions necessary for cell functioning and genetic inheritance. A recent discovery reported a new functional role for extracellular DNA. After fragmentation, either by natural or artificial decomposition, small DNA molecules (between ∼50 and ∼2000 bp) exert a species specific inhibitory effect on individuals of the same species. Evidence shows that such effect occurs for a wide range of organisms, suggesting a general biological process. In this paper we explore the possible molecular mechanisms behind those findings and discuss the ecological implications, specifically those related to plant species coexistence.

A novel process-based model of microbial growth: self-inhibition in Saccharomyces cerevisiae aerobic fed-batch cultures.

BACKGROUND: Microbial population dynamics in bioreactors depend on both nutrients availability and changes in the growth environment. Research is still ongoing on the optimization of bioreactor yields focusing on the increase of the maximum achievable cell density. RESULTS: A new process-based model is proposed to describe the aerobic growth of Saccharomyces cerevisiae cultured on glucose as carbon and energy source. The model considers the main metabolic routes of glucose assimilation (fermentation to ethanol and respiration) and the occurrence of inhibition due to the accumulation of both ethanol and other self-produced toxic compounds in the medium. Model simulations reproduced data from classic and new experiments of yeast growth in batch and fed-batch cultures. Model and experimental results showed that the growth decline observed in prolonged fed-batch cultures had to be ascribed to self-produced inhibitory compounds other than ethanol. CONCLUSIONS: The presented results clarify the dynamics of microbial growth under different feeding conditions and highlight the relevance of the negative feedback by self-produced inhibitory compounds on the maximum cell densities achieved in a bioreactor.