Global dynamics of a mutualism–competition model with one resource and multiple consumers

Journal of Mathematical Biology - Recent simulation modeling has shown that species can coevolve toward clusters of coexisting consumers exploiting the same limiting resource or resources, with...     

Modeling nutrients,oxygen and critical phosphorus loading in a shallow reservoir in China with a coupled water quality – Macrophytes model

Many macrophyte-dominated clear lakes switch to a phytoplankton-dominated turbid state when the lake becomes eutrophic. An existing Yuqiao Reservoir Water Quality Model (YRWQM) and the macrophyte submodel were coupled to simulate the effect of submerged macrophytes on nutrients and dissolve oxygen cycles in a shallow reservoir in China. The level of phosphorus loading in a transition from a clear to turbid state was addressed using the integrated model. The model runs from seedling establishment until dying out, from March 1 to July 18 in 2009. The simulations were performed for a contingent range of P loadings, starting from three different initial conditions. The results indicated that the integrated model improves accuracy of predictions compared to YRWQM. The concentrations of nutrients declined slightly during the macrophyte growth period in the reservoir and dissolved oxygen increased slightly. Although nutrient concentrations increased by submerged macrophyte release during the extinction period, the effect on the nutrients was less than that of transfer with nutrient-rich water. More released nutrients may enhance increases in substantial abundance. The critical phosphorus loading level during a switch from the clear to turbid state was estimated by these scenarios. The threshold for the switch is ∼6.1 mgP m⁻² d⁻¹ with an initial total phosphorus concentration of 160 μg l⁻¹. Moreover, the results demonstrated that the switch was also dependent on the initial total phosphorus concentration. These results suggest that the reservoir in a clear water state is at risk of a switch as nutrient levels are close to the critical levels.     

Global dynamics and bifurcation analysis of a host–parasitoid model with strong Allee effect

In this paper, we study the global dynamics and bifurcations of a two-dimensional discrete time host–parasitoid model with strong Allee effect. The existence of fixed points and their stability are analysed in all allowed parametric region. The bifurcation analysis shows that the model can undergo fold bifurcation and Neimark–Sacker bifurcation. As the parameters vary in a small neighbourhood of the Neimark–Sacker bifurcation condition, the unique positive fixed point changes its stability and an invariant closed circle bifurcates from the positive fixed point. From the viewpoint of biology, the invariant closed curve corresponds to the periodic or quasi-periodic oscillations between host and parasitoid populations. Furthermore, it is proved that all solutions of this model are bounded, and there exist some values of the parameters such that the model has a global attractor. These theoretical results reveal the complex dynamics of the present model.     

The dynamics of irreversible evaporation of a water–protein droplet and the problem of structural and dynamic experiments with single molecules

The effect of isothermal and adiabatic evaporation on the state of a water–protein droplet is discussed. The considered problem relates to the design of various approaches for structural and dynamic experiments with single molecules involving X-ray lasers. The delivery of the sample into the X-ray beam is performed by a microdroplet injector in these experiments; and the approach time is in the microsecond range. A version of molecular-dynamics simulation for all-atom modeling of an irreversible isothermal evaporation process is developed. The parameters of the isothermal evaporation of a water–protein droplet that contains sodium and chloride ions at concentrations of approximately 0.3 M have been determined in computational experiments for different temperatures. The in silico experiments showed that the energy of irreversible evaporation at the initial stages of the process was virtually the same as the specific heat of evaporation for water. An exact analytical solution of the problem for the kinetics of irreversible adiabatic evaporation has been obtained in the limit of the high heat conductivity of the droplet (or a droplet size not exceeding ~100 Å). This solution contains parameters that were derived from simulation of the isothermal evaporation of the droplets. The kinetics of the evaporation and adiabatic cooling of the droplet were shown to be scalable according to the size of the droplet. Estimation of the rate of freezing of the water–protein droplet upon adiabatic evaporation in a vacuum chamber revealed the necessity of using additional procedures for stabilizing the temperature in the droplet nucleus that contains the protein molecule. Isothermal or quasi-isothermal conditions are more favorable for the investigation of macro-molecular structural rearrangements that are related to the functioning of the object. However, the effects of dehydration and a sharp increase in the ionic strength of the aqueous microenvironment of the protein must be taken into account in this case.     

The needle mycobiome of Picea glauca – A dynamic system reflecting surrounding environment and tree phenological traits

Fungi play a crucial role in terrestrial Arctic ecosystems as symbionts of vascular plants and nutrient recyclers in soil, with many species persistently or temporarily inhabiting the phyllosphere of the vegetation.In this study we apply high-throughput sequencing to investigate the mycobiome of 172 samples of fresh (current year) and aged (3 year old) needles of Picea glauca from three sites over a distance of 500 km in Alaska (USA). We analysed Illumina-generated ITS2 sequences to relate mycobiome data with phenotypic tree traits, measures of genetic variation and climate variables obtained from long-term monitoring of the sites.Alpha-diversity declined with increasing environmental stress/climate harshness. Fungal communities differed in richness and taxonomic composition between sites, with a pronounced difference in the relative abundance of OTUs assigned to species of the rust genus Chrysomyxa, plant pathogens which seem to have been in an outbreak at two sites at the time of sampling.Beside climate parameters, needle age was the second strongest explanatory variable of the mycobiome composition, whereas we found no effect of tree genetic variation, indicating that environmental and tree trait specific variables mainly determined individual white spruce mycobiomes at Alaska's treelines.     

Rich dynamics in a predator–prey model with both noise and periodic force

A spatial version of the predator–prey model with Holling III functional response, which includes some important factors such as external periodic forces, noise, and diffusion processes is investigated. For the model only with diffusion, it exhibits spiral waves in the two-dimensional space. However, combined with noise, it has the feature of chaotic patterns. Moreover, the oscillations become more obvious when the noise intensity is increased. Furthermore, the spatially extended system with external periodic forces and noise exhibits a resonant pattern and frequency-locking phenomena. These results may help us to understand the effects arising from the undeniable susceptibility to random fluctuations in the real ecosystems.     

Environmental assessment of Smart City Solutions using a coupled urban metabolism—life cycle impact assessment approach

The International Journal of Life Cycle Assessment - The purpose of the study is to quantify the environmental performance of Smart City Solutions at urban system level and thus evaluate their...     

Analyzing the spatial dynamics of a prey–predator lattice model with social behavior

A lattice prey–predator model is studied. Transition rules applied sequentially describe processes such as reproduction, predation, and death of predators. The movement of predators is governed by a local particle swarm optimization algorithm, which causes the formation of swarms of predators that propagate through the lattice. Starting with a single predator in a lattice fully covered by preys, we observe a wavefront of predators invading the zones dominated by preys; subsequent fronts arise during the transient phase, where a monotonic approach to a fixed point is present. After the transient phase the system enters an oscillatory regime, where the amplitude of oscillations appears to be bounded but is difficult to predict. We observe qualitative similar behavior even for larger lattices. An empirical approach is used to determine the effects of the movement of predators on the temporal dynamics of the system. Our results show that the algorithm used to model the movement of predators increases the proficiency of predators.     

Transient spatio-temporal dynamics of a diffusive plant–herbivore system with Neumann boundary conditions

In many existing predator–prey or plant–herbivore models, the numerical response is assumed to be proportional to the functional response. In this paper, without such an assumption, we consider a diffusive plant–herbivore system with Neumann boundary conditions. Besides stability of spatially homogeneous steady states, we also derive conditions for the occurrence of Hopf bifurcation and steady-state bifurcation and provide geometrical methods to locate the bifurcation values. We numerically explore the complex transient spatio-temporal behaviours induced by these bifurcations. A large variety of different types of transient behaviours including oscillations in one or both of space and time are observed.     

Modeling the dynamics of woody plant–herbivore interactions with age-dependent toxicity

In this paper we study the effects that woody plant chemical defenses may have on interactions between boreal hares that in winter feed almost entirely on twigs. We focus particularly on the fact that toxin concentration often varies with the age of twig segments. The model incorporates the fact that the woody internodes of the youngest segments of the twigs of the deciduous angiosperm species that these hares prefer to eat are more defended by toxins than the woody internodes of the older segments that subtend and support the younger segments. Thus, the per capita daily intake of the biomass of the older segments of twigs by hares is much higher than their intake of the biomass of the younger segments of twigs. This age-dependent toxicity of twig segments is modeled using age-structured model equations which are reduced to a system of delay differential equations involving multiple delays in the woody plant-hare dynamics. A novel aspect of the modeling was that it had to account for mortality of non-consumed younger twig segment biomass when older twig biomass was bitten off and consumed. Basic mathematical properties of the model are established together with upper and lower bounds on the solutions. Necessary and sufficient conditions are found for the linear stability of the equilibrium in which the hare is extinct, and sufficient conditions are found for the global stability of this equilibrium. Numerical simulations confirmed the analytical results and demonstrated the existence of limit cycles over ranges of parameters reasonable for hares browsing on woody vegetation in boreal ecosystems. This showed that age dependence in plant chemical defenses has the capacity to cause hare-plant population cycles, a new result.     

Possible dynamic anchor points in a benzoxazinone derivative–human oxytocin receptor system — a molecular docking and dynamics calculation

In this study, we performed a molecular docking and dynamics simulation for a benzoxazinone–human oxytocin receptor system to determine the possible hydrophobic and electrostatic interaction points in the dynamic complex. After the homology modeling, the ligand was docked into the putative active using AutoDock 3.05. After the application of energetic and structural filters, the complexes obtained were further refined with a simulated annealing protocol (AMBER8) to remove steric clashes. Three complexes were selected for subjection to the molecular dynamics simulation (5 ns), and the results on the occurrence of average anchor points showed a stable complex between the benzoxazinone derivative and the receptor. The complex could be used as a good starting point for further analysis with site-directed mutagenesis, or further computational research. Figure The location of the ligands (complex B – blue; complex E – red; and complex F – green) in the transmembrane regions (TM1 – red; TM2 – blue; TM3 – yellow; TM4 – purple; TM5 – orange; TM6 – cyan; TM7 – pink) of the hOTR. For clarity, the EC and IC loops are not shown Electronic Supplementary Material Supplementary material is available at     

Soil carbon dynamics and aquatic metabolism of a wet–dry tropics wetland system

Freshwater wetlands are a key component of the global carbon cycle. Wet–dry tropics wetlands function as wet-season carbon sinks and dry-season carbon sources with low aquatic metabolism controlled by predictably seasonal, yet magnitude-variable flow regimes and inundation patterns. However, these dynamics have not been adequately quantified in Australia’s relatively unmodified wet–dry tropics freshwater wetlands. A baseline understanding is required before analysis of land-use or climate change impacts on these aquatic ecosystems can occur. This study characterises geomorphology and sedimentology within a seasonally connected wet–dry tropics freshwater wetland system at Kings Plains, Queensland, Australia, and quantifies soil carbon stocks and wet- and dry-season aquatic metabolism. Soil carbon stocks derived from loss-on-ignition on samples to 1 m depth were 51.5?±?7.8 kg C m^?2, higher than other wet–dry tropics wetlands globally, with potential for long-term retention at greater depths. Gross primary productivity of phytoplankton (GPP) and planktonic respiration (PR) measured through biological oxygen demand bottle experiments in the water column of sediment inundated under laboratory conditions show overall low GPP and PR in both wet- and dry-season samples (all wetland samples were heterotrophic with GPP/PR?<?1). Despite the short-term dominance of aquatic respiration processes leading to net release of carbon in the water column under these conditions, there is appreciable long-term storage of carbon in sediment in the Kings Plains wetlands. This demonstrates the importance of wet–dry-tropics wetland systems as hotspots of carbon sequestration, locally, regionally and globally, and consideration should be given to their conservation and management in this context.

     

Temporal dynamics of natural enemy–pest interactions in a changing environment

Agroecosystems contain complex networks of interacting organisms and these interaction webs are structured by the relative timing of key biological and ecological events. Recent intensification of land management and global changes in climate threaten to desynchronize the temporal structure of interaction webs and disrupt the provisioning of ecosystem services, such as biological control by natural enemies. It is therefore critical to recognize the central role of temporal dynamics in driving predator–prey interactions in agroecosystems. Specifically, ecological dynamics in crop fields routinely behave as periodic oscillations, or cycles. Familiar examples include phenological cycles, diel activity rhythms, and crop-management cycles. The relative timing and the degree of overlap among ecological cycles determine the nature and magnitude of the ecological interactions among organisms, and ultimately determine whether ecosystem services, such as biological control, can be provided. Additionally, the ecological dynamics in many cropping systems are characterized by a pattern of frequent disturbances due to management actions such as harvest, sowing and pesticide applications. These disturbance cycles cause agroecosystems to be dominated by dispersal and repopulation dynamics. However, they also serve as selective filters that regulate which animals can persist in agroecosystems over larger temporal scales. Here, we review key concepts and examples from the literature on temporal dynamics in ecological systems, and provide a framework to guide biological control strategies for sustainable pest management in a changing world.     

Fusing spatial resource heterogeneity with a competition–colonization trade-off in model communities

Two commonly cited mechanisms of multispecies coexistence in patchy environments are spatial heterogeneity in competitive abilities caused by variation in resources and a competition–colonization trade-off. In this paper, a model that fuses these mechanisms together is presented and analyzed. The model suggests that spatial variation in resource ratios can lead to multispecies coexistence, but this mechanism by itself is weak when the number of resources for which species compete is small. However, spatial resource heterogeneity is a powerful mechanism for multispecies coexistence when it acts synergistically with a competition–colonization trade-off. The model also shows how resource supply can control the competitive balance between species that are weak competitors but superior colonizers and strong competitors/inferior colonizers. This provides additional theoretical support for a possible explanation of empirically observed hump-shaped relationships between species diversity and ecological productivity.     

Consumer–resource dynamics of indirect interactions in a mutualism–parasitism food web module

Food web dynamics are well known to vary with indirect interactions, classic examples including apparent competition, intraguild predation, exploitative competition, and trophic cascades of food chains. Such food web modules entailing predation and competition have been the focus of much theory, whereas modules involving mutualism have received far less attention. We examined an empirically common food web module involving mutualistic (N ₂) and parasitic (N ₃) consumers exploiting a resource of a basal mutualist (N ₁), as illustrated by plants, pollinators, and nectar robbers. This mutualism–parasitism food web module is structurally similar to exploitative competition, suggesting that the module of two consumers exploiting a resource is unstable. Rather than parasitic consumers destabilizing the module through (?,?) indirect interactions, two mechanisms associated with the mutualism can actually enhance the persistence of the module. First, the positive feedback of mutualism favors coexistence in stable limit cycles, whereby (+,?) indirect interactions emerge in which increases in N ₂ have positive effects on N ₃ and increases in N ₃ have negative effects on N ₂. This (+,?) indirect interaction arising from the saturating positive feedback of mutualism has broad feasibility across many types of food web modules entailing mutualism. Second, optimization of resource exploitation by the mutualistic consumer can lead to persistence of the food web module in a stable equilibrium. The mutualism–parasitism food web module is a basic unit of food webs in which mutualism favors its persistence simply through density-dependent population dynamics, rather than parasitism destabilizing the module.     

The dynamics of the lynx–hare system: an application of the Lotka–Volterra model

The Lotka–Volterra model of predator–prey dynamics was used for approximation of the wellknown empirical time series on the lynx–hare system in Canada that was collected by the Hudson Bay Company in 1845–1935. The model was assumed to demonstrate satisfactory data approximation if the sets of deviations of the model and empirical data for both time series satisfied a number of statistical criteria (for the selected significance level). The frequency distributions of deviations between the theoretical (model) trajectories and empirical datasets were tested for symmetry (with respect to the Y-axis; the Kolmogorov–Smirnov and Lehmann–Rosenblatt tests) and the presence or absence of serial correlation (the Swed–Eisenhart and “jumps up–jumps down” tests). The numerical calculations show that the set of points of the space of model parameters, when the deviations satisfy the statistical criteria, is not empty and, consequently, the model is suitable for describing empirical data.     

Fractional optimal control dynamics of coronavirus model with Mittag–Leffler law

Most countries around the world are battling to limit the spread of severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2). As the world strives to get an effective medication to control the disease, appropriate control measures for now remains one of the effective measures to reduce the spread of the disease. In this study, a fractional optimal control model is formulated in Atangana-Baleanu-Caputo derivative sense. The reproduction number and steady state of disease free of the Coronavirus model are examined and found to be globally stable. The existence and uniqueness of solution of the fractional Coronavirus model is established by using the Banach fixed point theorem approach. Three controls are considered in the model and Pontryagins Maximum Principle is used to establish the necessary conditions for optimal control solution. The numerical solution suggests that the best strategy is found to be the utilization of all three controls at the same time.     

The complex dynamics of a diffusive prey–predator model with an Allee effect in prey

This paper investigates complex dynamics of a predator–prey interaction model that incorporates: (a) an Allee effect in prey; (b) the Michaelis–Menten type functional response between prey and predator; and (c) diffusion in both prey and predator. We provide rigorous mathematical results of the proposed model including: (1) the stability of non-negative constant steady states; (2) sufficient conditions that lead to Hopf/Turing bifurcations; (3) a prior estimates of positive steady states; (4) the non-existence and existence of non-constant positive steady states when the model is under zero-flux boundary condition. We also perform completed analysis of the corresponding ODE model to obtain a better understanding on effects of diffusion on the stability. Our analytical results show that the small values of the ratio of the prey's diffusion rate to the predator's diffusion rate are more likely to destabilize the system, thus generate Hopf-bifurcation and Turing instability that can lead to different spatial patterns. Through numerical simulations, we observe that our model, with or without Allee effect, can exhibit extremely rich pattern formations that include but not limit to strips, spotted patterns, symmetric patterns. In addition, the strength of Allee effects also plays an important role in generating distinct spatial patterns.     

Global dynamic modes of peristaltic-ciliary flow of a Phan–Thien–Tanner hybrid nanofluid model

Biomechanics and Modeling in Mechanobiology - In this paper, the tools of dynamical systems theory are applied to examine the streamline patterns and their local and global bifurcations for...     

Dating and localizing an invasion from post-introduction data and a coupled reaction–diffusion–absorption model

Journal of Mathematical Biology - Invasion of new territories by alien organisms is of primary concern for environmental and health agencies and has been a core topic in mathematical modeling, in...