Advective Environment Research Articles

Hopf bifurcations for a delayed discrete single population patch model in advective environments

Abstract In this paper, we consider a delayed discrete single population patch model in advective environments. The individuals are subject to both random and directed movements, and there is a net loss of individuals at the downstream end due to the flow into a lake. Choosing time delay as a bifurcation parameter, we show the existence of Hopf bifurcations for the model. In homogeneous non-advective environments, it is well known that the first Hopf bifurcation value is independent of the dispersal rate. In contrast, for homogeneous advective environments, the first Hopf bifurcation value depends on the dispersal rate. Moreover, we show that the first Hopf bifurcation value in advective environments is larger than that in non-advective environments if the dispersal rate is large or small, which suggests that directed movements of the individuals inhibit the occurrence of Hopf bifurcations.

Predator–prey systems with a variable habitat for predators in advective environments

AbstractCommunity composition in aquatic environments can be shaped by a broad array of factors, encompassing habitat conditions in addition to abiotic conditions and biotic interactions. This paper pertains to reaction–diffusion–advection predator–prey model featuring a variable predator habitat in advective environments, governed by a unidirectional flow. First, we establish the near‐complete global dynamics of the system. In instances where the functional response to predation conforms to Holling‐type I or II, we explore the uniqueness and stability of positive steady‐state solutions via the application of particular auxiliary techniques, the comparison principle for parabolic equations, and perturbation analysis. Furthermore, we obtain the critical positions at the upper and lower boundaries of the predator's habitat, which determine the survival of the prey irrespective of the predator's growth rate. Finally, we show how the location and length of the predator's habitat affect the persistence and extinction of predators and prey in the event of a small population loss rate at the downstream end. From the biological point of view, these results contribute to our deeper understanding of the effects of habitat on aquatic populations and may have applications in aquaculture and the establishment of protection zones for aquatic species.

Dynamics of a Diffusive Predator–Prey System with Fear Effect in Advective Environments

We explore a diffusive predator–prey system that incorporates the fear effect in advective environments. First, we analyze the eigenvalue problem and the adjoint operator, considering Constant-Flux and Dirichlet boundary conditions, as well as Free-Flow boundary conditions. Next, we use the principle of comparison to prove the non-negativity of the solution. Our investigation focuses on determining the direction and stability of spatial Hopf bifurcation, with the generation delay serving as the bifurcation parameter. Additionally, we examine the influence of both linear and Holling-II functional responses on the dynamics of the model. Through these analyses, we gain better understanding of the intricate relationship among advection, predation, and prey response in this system.

Dynamics of the epidemiological Predator-Prey system in advective environments.

This paper aims to establish the existence of traveling wave solutions connecting different equilibria for a spatial eco-epidemiological predator-prey system in advective environments. After applying the traveling wave coordinates, these solutions correspond to heteroclinic orbits in phase space. We investigate the existence of the traveling wave solution connecting from a boundary equilibrium to a co-existence equilibrium by using a shooting method. Different from the techniques introduced by Huang, we directly prove the convergence of the solution to a co-existence equilibrium by constructing a special bounded set. Furthermore, the Lyapunov-type function we constructed does not need the condition of bounded below. Our approach provides a different way to study the existence of traveling wave solutions about the co-existence equilibrium. The existence of traveling wave solutions between co-existence equilibria are proved by utilizing the qualitative theory and the geometric singular perturbation theory. Some other open questions of interest are also discussed in the paper.

Dynamics of reaction–diffusion–advection system and its impact on river ecology in the presence of spatial heterogeneity

This study considers a two-species reaction–diffusion–advection (RDA) model in a heterogeneous advective environment with zero Neumann boundary conditions. We suppose that two species compete for the same food resource but have different diffusion and advection rates. The primary objective of this study is to investigate the global asymptotic stability and coexistence of steady state based on different and unequal diffusion and advection rates through theoretical and numerical analysis. We establish the local stability of two semi-trivial steady states of the competing species. Also, the non-existence of coexistence steady state is proved with the help of some non-trivial assumptions. Finally, we show the global stability with the help of monotone dynamical systems and combine the local stability and non-existence of coexistence steady state. If one species adopts a smaller diffusion and advection rate, the competition’s result depends on the advection and diffusion rate ratio. If the ratio is smaller, then the species will prevail. Also, the species with higher diffusion and smaller advection will win. Lastly, the effectiveness of the model in one and two-dimensional situations is shown by a series of numerical calculations, which is particularly important for environmental consideration.

Coexistence and bistability of a modified Leslie–Gower predator–prey model with mixed movement for the predator and Holling-type II schemes

This paper centers on the analysis of the dynamics of a modified Leslie–Gower predator–prey model employing Holling-type II schemes, with the prey exhibiting pure random diffusion and the predator undergoing a mixed form of movement. The extinction of species and uniform persistence of this system are explored, and several conditions for the stability, uniqueness and multiplicity of positive steady-state solutions are derived. In contrast to the specialist and generalist predator–prey systems in open advective environments, the dynamics of this system are more intricate. It emerges that multiple positive steady-state solutions and the bistable phenomenon exist for this system when a small advection rate and a moderate predation rate are imposed. Numerical simulations reveal that the increase of diffusion rate for prey disadvantages the survival of itself and has no impact on predator invasion, while the increase of diffusion rate for predators favors the invasion of itself.

Dynamics of a generalist predator–prey model in closed advective environments

In this paper, we consider a two‐species generalist predator–prey model in closed advective environments. Compared with the model in open advective environments to the generalist predator–prey model, the dynamics of our system are different. It is easy to verify that the generalist predator can always invade. Meanwhile, we provide the dynamical behaviors of the model in terms of the intrinsic growth rates, the carrying capacity of both species, the predation rate, and the trophic conversion efficiency. More precisely, we establish the local/global stability of the semi‐trivial steady states and a unique positive equilibrium for the model.

Propagation dynamics of a free boundary problem in advective environments

In this paper, we study the equation ut=uxx−βux+f(x,u) in the domain {(t,x)∈R2:t≥0,x∈(−∞,h(t)]}, where h(t) is the free boundary and β≥0. The influence of the advection coefficient −β on the propagation dynamics of the solutions is considered. We find two parameters 2 and β∗ such that when 0≤β<2, only spreading happens; when 2≤β<β∗, there is a virtual spreading-transition-vanishing trichotomy result; when β≥β∗, only vanishing happens.

Diel Vertical Migrators Respond to Short‐Term Upwelling Events

AbstractPelagic organisms inhabiting coastal upwelling regions face a high risk of advection away from the nearshore productive habitat, potentially leading to mortality. We explored how animals remain in a productive yet highly advective environment in the Northern California Current System using the cabled observatory system located off the Oregon coast. Acoustic scatterers consistent with swimbladder‐bearing fish were only present during the downwelling season as these animals avoided the cold waters associated with strong upwelling conditions in summer and fall. Fish responded to short‐term upwelling events by increasing the frequency of diel vertical migration. Throughout the study, their vertical positions corresponded to the depth of minimum cross‐shelf transport, providing a mechanism for retention. The observed behavioral response highlights the importance of studying ecological processes at short timescales and the abilities of pelagic organisms to control their horizontal distributions through fine‐tuned diel vertical migration in response to upwelling.

On the role of advection in a spatial epidemic model with general boundary conditions

This paper is concerned with a reaction-diffusion-advection model for vector-borne disease with general boundary conditions and general incidences. Due to the boundary conditions, we first apply the eigenvalue theory of elliptic system to prove the existence and uniqueness of steady state for the model. The well-posedness of the model is established using an induction argument. By overcoming the difficulty of the associated elliptic eigenvalue problem, we originally derive the variational expression of the basic reproduction ratio R0. The asymptotic profiles and monotonicity of R0 with respect to the mobility and advection rates are investigated following the variational characterization of R0. Furthermore, the spatial dynamics of the model with Robin type boundary condition are categorized via classifying the level set of R0. This work provides new clues for further research on the spread of epidemics in open advective environments.

Dynamics of a competition system with lethal boundary conditions in advective environments

Dynamics of a competition system with lethal boundary conditions in advective environments

Reference Evapotranspiration Estimation Using Genetic Algorithm-Optimized Machine Learning Models and Standardized Penman–Monteith Equation in a Highly Advective Environment

Accurate estimation of reference evapotranspiration (ETr) is important for irrigation planning, water resource management, and preserving agricultural and forest habitats. The widely used Penman–Monteith equation (ASCE-PM) estimates ETr across various timescales using ground weather station data. However, discrepancies persist between estimated ETr and measured ETr obtained from weighing lysimeters (ETr-lys), particularly in advective environments. This study assessed different machine learning (ML) models in comparison to ASCE-PM for ETr estimation in highly advective conditions. Various variable combinations, representing both radiation and aerodynamic components, were organized for evaluation. Eleven datasets (DT) were created for the daily timescale, while seven were established for hourly and quarter-hourly timescales. ML models were optimized by a genetic algorithm (GA) and included support vector regression (GA-SVR), random forest (GA-RF), artificial neural networks (GA-ANN), and extreme learning machines (GA-ELM). Meteorological data and direct measurements of well-watered alfalfa grown under reference ET conditions obtained from weighing lysimeters and a nearby weather station in Bushland, Texas (1996–1998), were used for training and testing. Model performance was assessed using metrics such as root mean square error (RMSE), mean absolute error (MAE), mean bias error (MBE), and coefficient of determination (R2). ASCE-PM consistently underestimated alfalfa ET across all timescales (above 7.5 mm/day, 0.6 mm/h, and 0.2 mm/h daily, hourly, and quarter-hourly, respectively). On hourly and quarter-hourly timescales, datasets predominantly composed of radiation components or a blend of radiation and aerodynamic components demonstrated superior performance. Conversely, datasets primarily composed of aerodynamic components exhibited enhanced performance on a daily timescale. Overall, GA-ELM outperformed the other models and was thus recommended for ETr estimation at all timescales. The findings emphasize the significance of ML models in accurately estimating ETr across varying temporal resolutions, crucial for effective water management, water resources, and agricultural planning.

Analysis on a Spatial SIS Epidemic Model with Saturated Incidence Function in Advective Environments: I. Conserved Total Population

Analysis on a Spatial SIS Epidemic Model with Saturated Incidence Function in Advective Environments: I. Conserved Total Population

Dynamical Behavior of a Spatiotemporal Model in Open Advective Environments

Dynamical Behavior of a Spatiotemporal Model in Open Advective Environments

Dynamics of a diffusive mussel-algae system in closed advective environments

In this paper, we are concerned with a diffusive system modeling the interaction of mussel and algae in the water layer overlying the mussel bed, where the algae are the main food source for mussels, and the advection pushes algaes in one direction but not out of the domain. We present a threshold result on the global extinction and persistence of mussels. It shows that the condition for persistence depends on the principal eigenvalue of a scalar boundary value problem, which is related to the diffusion, the speed of the tidal flow, the conversion rate of algae to mussel production, and mussel mortality rate. We further investigate the asymptotic profile of the positive steady state when it exists.

Population Dynamics in an Advective Environment

Population Dynamics in an Advective Environment

Effects of diffusion and advection on predator-prey dynamics in closed environments

We investigate the dynamics and the asymptotic profiles of positive steady states of a specialist predator-prey model and a generalist predator-prey model in closed advective environments. The threshold dynamics are determined by the mortality rate of the specialist predators and the predation rate of the generalist predators, respectively. We demonstrate that, no matter how large advection and diffusion rates are, the specialist predators can successfully invade as long as the mortality rate is sufficiently small, while the generalist predators can take-over the prey if the predation rate is relatively large. Finally, we explore the impacts of diffusion and advection on the asymptotic profiles of positive steady states. Our results imply that large advection rates and small diffusion rates will lead to the concentration of the species at the downstream or the upstream. Moreover, if the diffusion rates are large, then the densities of the species will be less spatial heterogeneous.

Global dynamics of a Leslie–Gower predator–prey model in open advective environments

This paper investigates the global dynamics of a reaction–diffusion–advection Leslie–Gower predator–prey model in open advective environments. We find that there exist critical advection rates, intrinsic growth rates, diffusion rates and length of the domain, which classify the global dynamics of the Leslie–Gower predator–prey system into three scenarios: coexistence, persistence of prey only and extinction of both species. The results reveal some significant differences with the classical specialist and generalist predator–prey systems. In particular, it is found that the critical advection rates of prey and predator are independent of each other and the parameters about predation rate have no influence on the dynamics of system. The theoretical results provide some interesting highlights in ecological protection in streams or rivers.

On a competition model in stream environments: The effects of seasonal pulses and advection

A diffusion-advection competition model with different pulses has been investigated in order to understand how the impulsive intervention affects the dynamics and alters the competition state of two competitors in open advective environments. The threshold values are introduced as the principal eigenvalues of the periodic problems with pulses and defined by the spectral radius of a time-T map. We have obtained two critical advection curves depending on pulses that determine the stability of the periodic steady states and have computed these numerically. The dynamics of two competitors in open advective environments such as competition exclusion, co-extinction, coexistence and bistability have been classified. By applying different impulsive effects, simulation analysis shows interesting scenarios, and reveals that a tradeoff between two different impulsive interventions and movements can be found in order to improve sustainable ecological development and economic benefits.

Evolution of Dispersal in Advective Patchy Environments

We study a two-species competition model in a patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches and there are losses of individuals in the downstream end (e.g., due to the flow into a lake or ocean). The two competing species are assumed to have the same growth rates but different advection and random dispersal rates. We focus our studies on the properties of an associated eigenvalue problem which characterizes the extinction/persistence dynamics of the underlying patch population model. We also derive conditions on the advection and random dispersal rates under which a mutant species can or cannot invade the resident species.