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A parabolic–elliptic Keller–Segel model for multipopulations in a two‐dimensional unit ball will be considered in this paper. For the initial boundary value problem with mutually attractive populations, the global existence of bounded solutions has been proved through the logarithmic Hardy–Littlewood–Sobolev inequality for system when the initial masses satisfy the subcritical condition. Moreover, based on the moments technique, there exists a blow‐up solution when the initial masses satisfy the supercritical case. In a word, a critical mass phenomenon has been established in this multispecies chemotaxis system. [ABSTRACT FROM AUTHOR]

The fall armyworm (FAW), Spodoptera frugiperda (Lepidoptera: Noctuidae), poses a global threat to agriculture, causing significant economic losses in numerous cash crops. Various control methods, including chemical insecticides, have proven insufficient against S. frugiperda, leading to a demand for alternative strategies, such as biological control. In this context, laboratory experiments were conducted to evaluate the parasitism of Trichogramma foersteri (Hymenoptera: Trichogrammatidae) and Telenomus remus (Hymenoptera: Scelionidae) on egg masses of S. frugiperda with one and two layers. Additionally, the potential synergistic use of both species against the fall armyworm were assessed. Although both species parasitized single and double‐layered egg masses of S. frugiperda, Te. remus showed higher parasitism compared to T. foersteri. The parasitism of Te. remus was not affected by the competition with T. foersteri. Conversely, an increase in parasitism of T. foersteri was observed due to competition with Te. remus, especially when both species had simultaneous access to S. frugiperda egg masses. The total number of parasitized eggs was significantly higher when Te. remus was allowed to parasitize first, and when both parasitoids had simultaneous access to the egg masses. These results are crucial for the development of biological control programs using T. foersteri and Te. remus, as they indicate that both parasitoids could be used, either individually or in combination, against S. frugiperda. [ABSTRACT FROM AUTHOR]

Initial-boundary value problems for a linear diffusion-advection-reaction equation are considered, with general nonhomogeneous linear boundary conditions and general linear nonlocal boundary conditions. Analytical solutions are obtained using an embedding method. The solutions are expressed in terms of time-varying functions that satisfy coupled linear Volterra integral equations of the first kind. A boundary element method is applied to numerically solve the integral equations. Three examples are given to demonstrate the accuracy of the numerical solutions when compared with the analytical solutions. The embedding method is applicable to problems with bounded and unbounded spatial domains. [ABSTRACT FROM AUTHOR]

The article provides information on the fib Model Code for Concrete Structures (2020), which focuses on sustainability and the impact of concrete on climate change. It covers various aspects such as social performance, safety, durability, and reducing CO2 emissions. The code also offers guidance on structural design, seismic design, durability, and structural assessment. The article mentions upcoming events like the fib Symposium in Christchurch and the International Conference on Concrete Sustainability in Portugal. Additionally, it highlights the birthdays of Mario Chiorino and Michael Fardis, both influential figures in the field of concrete structures. The document also includes information about Michael Fardis, a professor and researcher in earthquake engineering, and Andrzej Cholewicki, a respected scientist specializing in precast concrete structures who passed away in 2024. Lastly, it provides a list of upcoming congresses and symposia related to structural concrete. [Extracted from the article]

This paper considers the inverse problem of determining the time‐dependent coefficient in the time‐fractional diffusion‐wave equation. In this case, an initial boundary value problem was set for the fractional diffusion‐wave equation, and an additional condition was given for the inverse problem of determining the coefficient from this equation. First of all, it was considered the initial boundary value problem. By the Fourier method, this problem is reduced to equivalent integral equations. Then, using the Mittag‐Leffler function and the generalized singular Gronwall inequality, we get a priori estimate for solution via unknown coefficient which we will need to study of the inverse problem. The inverse problem is reduced to the equivalent integral of equation of Volterra type. The principle of contracted mapping is used to solve this equation. Local existence and global uniqueness results are proved. The stability estimate is also obtained. [ABSTRACT FROM AUTHOR]

In this research, two systems of nonlinear Volterra integral equation and Volterra integro‐differential equation were considered. New results in sense of Ulam stabilities in relation to these two systems were proved on a finite interval. The proof of the results on the Ulam stabilities of that classes of the equations are based on the nonlinear alternative related to Banach's contraction principle. The outcomes of this research give new contribution to the theory of Ulam stabilities. [ABSTRACT FROM AUTHOR]

The sigmoid functional response in the predator–prey model was posed in 1977. But its dynamics has not been completely characterized. This paper completes the classification of the global dynamics for the classical predator–prey model with the sigmoid functional response, whose denominator has two different zeros. The dynamical phenomena we obtain here include global stability, the existence of the heteroclinic and homoclinic loops, the consecutive canard explosions via relaxation oscillation, and the canard explosion to a homoclinic loop among others. As we know, the last one is a new dynamical phenomenon, which has never been reported previously. In addition, with the help of geometric singular perturbation theory, we solve the problem of connection between stable and unstable manifolds from different singularities, which has not been well settled in the published literature. [ABSTRACT FROM AUTHOR]

A class of two‐dimensional fractional Volterra integral equations (2D‐FVIEs) of the second kind is considered. The solution may have unbounded derivatives near the integral domain boundary. Therefore, smoothing transformations are employed to change the original 2D‐FVIEs into new transformed 2D‐FVIEs with better regularity. The novelty in this research concerns both the theoretical investigation of the bivariate modified Bernstein–Kantorovich (B‐MBK) operators and the numerical application of these operators for approximating the unknown solution of 2D‐FVIEs. In this regard, an algorithm is given utilizing the B‐MBK operators and discretization that approximates the solution of the transformed discretized equation. Further, an inverse transformation is applied to obtain the solution of the original equation. Additionally, we illustrate the applicability of the proposed method on examples from the literature. [ABSTRACT FROM AUTHOR]

We propose an Adomian decomposition method to solve a class of nonlinear differential equations of fractional‐order with modified Caputo derivatives and integral boundary conditions. Our approach uses the integral boundary conditions to derive an equivalent nonlinear Volterra integral equation before establishing existence and uniqueness of solution and a recursion scheme for the solution. The convergence of the method is proved and an error analysis given. Two numerical examples are solved by obtaining a rapidly converging sequence of analytical functions to the solution. [ABSTRACT FROM AUTHOR]

In this paper, a second‐order accurate scheme is considered for the temporal discretization of the abstract Volterra integrodifferential equation with a weakly singular kernel. The time discrete scheme is constructed by the Crank–Nicolson method for approximating the time derivative and product integration (PI) rule for approximating the integral term. The proposed scheme employs a graded mesh for time to compensate for the singular behavior of the exact solution at t=0$$ t=0 $$. Under the suitable assumptions, the stability and convergence are established by the energy argument, and the error is of order k2$$ {k}^2 $$, where k$$ k $$ is the parameter for the time grids. Numerical experiments validate the theoretical estimate. [ABSTRACT FROM AUTHOR]

This paper considers the Galerkin spectral method for solving linear second‐kind Volterra integral equations with weakly singular kernels on large intervals. By using some variable substitutions, we transform the mentioned equation into an equivalent semi‐infinite integral equation with nonsingular kernel, so that the inner products from the Galerkin procedure could be evaluated by means of Gaussian quadrature based on scaled Laguerre polynomials. Furthermore, the error analysis is based on the Gamma function and provided in the weighted L2$$ {L}^2 $$‐norm, which shows the spectral rate of convergence is attained. Moreover, several numerical experiments are presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

Aim: Intraspecific variation in species relative abundance is shaped by a complex interplay of abiotic and biotic factors, making it both necessary and challenging to assess their combined relative importance in explaining variations across space and time. We used two congeneric butterfly species for which extensive count data and a deep understanding of their natural history is available to test three hypotheses explaining intraspecific variation in their abundance: (H1) seasonal dispersal behaviour driven by climate, (H2) resource availability and (H3) apparent competition mediated via shared parasitoids. Taxon: Gonepteryx rhamni (Brimstone) and G. cleopatra (Cleopatra). Location: NE Iberian Peninsula, where both species coexist, and a nearby archipelago (Balearic Islands), where only Cleopatra occurs. Methods: We analysed spatial abundance variations for both species in the mainland and island–mainland differences in the abundance of Cleopatra. Abiotic and biotic factors, including temperature, host plant and overwintering habitat availability, larval parasitism and density dependence, were tested to explain the observed variations. Results: H1 can explain variation in butterfly abundance between mainland regions since in warmer summers populations increased in cooler areas but decreased in warmer areas. H2 explains the variation within mainland climate regions with a strong positive relationship between resource availability and abundance but is unlikely to explain the island–mainland variation in the abundance of Cleopatra. H3 could neither explain biogeographical variation in abundance because although richer parasitoid communities were found on the mainland, larval mortality rates were similar or lower on the mainland than in the islands. Main Conclusions: Climate and resource availability jointly account for variation in butterfly abundance across the mainland, but neither these factors nor parasitism can explain island–mainland differences. Both coexisting butterfly species and their larval parasitoids may have undergone evolutionary processes, resulting in spatial segregation that promotes the coexistence of the two butterfly species on the mainland. [ABSTRACT FROM AUTHOR]

Recently, Kovács et al. considered a Mittag‐Leffler Euler integrator for a stochastic semilinear Volterra integral‐differential equation with additive noise and proved the strong convergence error estimates [see SIAM J. Numer. Anal. 58(1) 2020, pp. 66‐85]. In this article, we shall consider the Mittag‐Leffler integrators for more general models: stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise. The mild solutions of our models involve four different Mittag‐Leffler functions. We first consider the existence, uniqueness and the regularities of the solutions. We then introduce the full discretization schemes for solving the problems. The temporal discretization is based on the Mittag‐Leffler integrators and the spatial discretization is based on the spectral method. The optimal strong convergence error estimates are proved under the reasonable assumptions for the semilinear term and for the regularity of the noise. Numerical examples are given to show that the numerical results are consistent with the theoretical results. [ABSTRACT FROM AUTHOR]

This paper aims to present a novel study on the dynamics of a fractional predator–prey–pathogen model to investigate the existence of the chaos in the model. We applied the Atangana–Baleanu fractional operator to the predator–prey–pathogen model, and new results are presented. Furthermore, the stability of the equilibrium points of the proposed model is investigated. The convergence and uniqueness of the solution for the model are also studied. Few numerical simulations have been performed for both predator, and prey populations. Some interesting chaotic behaviors of predator and prey populations of the model are also obtained by using an effective numerical scheme. Furthermore, corresponding numerical simulations were achieved for the various values of the fractional derivative. [ABSTRACT FROM AUTHOR]

This paper studies a predator–prey model with a Beddington–DeAngelis type functional response under the stationary Ornstein–Uhlenback process. First, we prove the existence and uniqueness of the global positive solution for the given system for any initial datum. Second, we turn to its internal structures and establish the existence of a compact forward‐absorbing set as well as a forward attracting one. Finally, we carry out some numerical simulations to support the theoretical results. [ABSTRACT FROM AUTHOR]

The paper discusses the effects of constant prey harvesting on the dynamics of a modified Leslie–Gower predator–prey model. Prey harvesting will lead to enriched dynamics to help us realize ecological phenomena such as the extinction of some species with a positive initial density when the harvesting rate is larger than a critical level. All these may be very useful for biological management. Based on these reasons, firstly, we analyze the existence conditions and stability of different equilibrium points to predict the eventual state of the given system. In particular, the existence of cusps of Codimensions 2 and 3 is proved. Secondly, we successfully demonstrate the presence of Hopf bifurcation and saddle‐node bifurcation for specified parameter values. To prove the limit cycle stability of Hopf bifurcation, we use the first Lyapunov coefficient K$$ K $$ for illustration. As well as calculating the universal expansion near the cusp, the Bogdanov–Takens bifurcations of Codimensions 2 and 3 are investigated. If the parameters are chosen fittingly, there will be a stable or an unstable limit cycle, a homoclinic loop, two limit cycles, or both a limit cycle and a homoclinic loop simultaneously in the system. Finally, numerical simulations are performed using MATLAB to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a diffusive predator–prey model with prey‐taxis and prey‐stage structure under the homogeneous Neumann boundary condition. The stability of the unique positive constant equilibrium of the predator–prey model is derived. Hopf bifurcation and steady‐state bifurcation are also concluded. [ABSTRACT FROM AUTHOR]

In this note we continue the study of nonlocal interaction dynamics on a sequence of infinite graphs, extending the results of Esposito, Heinze and Schlichting to an arbitrary number of species. Our analysis relies on the observation that the graph dynamics form a gradient flow with respect to a non‐symmetric Finslerian gradient structure. Keeping the nonlocal interaction energy fixed, while localizing the graph structure, we are able to prove evolutionary Γ‐convergence to an Otto‐Wassertein‐type gradient flow with a tensor‐weighted, yet symmetric, inner product. As a byproduct this implies the existence of solutions to the multi‐species non‐local (cross‐)interaction system on the tensor‐weighted Euclidean space. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a fractional differential‐algebraic model with two discrete delays and double linear species harvesting. One of the delays denotes the time taken for digestion of the prey, and the other reflects the negative feedback of the predator's density. Taking into account of the economic profit, linear predator harvesting and prey harvesting have been incorporated into the proposed predator–prey system. From the biological viewpoint, we discuss the sufficient conditions for the existence of nontrivial positive equilibrium point. By jointly using the stability theory of fractional differential‐algebraic equations and the bifurcation theory, we study the delay‐induced instability and Hopf bifurcations. Finally, the correctness of the theoretical analysis is verified by numerical simulations, and the effects of delays, economic profit, and fractional exponents on the stability of the system are explored. [ABSTRACT FROM AUTHOR]

In this paper, we study a generalization of a Lotka–Volterra system with Holling type III functional response, where the Caputo fractional derivative is considered. Applying a multistage homotopy perturbation method, we obtain an analytical solution for the system. Moreover, analyzing the eigenvalues of the Jacobian matrix around the equilibria, we find sufficient conditions in order to guarantee the local stability and we present several examples to illustrate the behavior of solutions. [ABSTRACT FROM AUTHOR]

Usually, hypotheses involving cooperative interactions and continuous interplay among interacting agents may result in somewhat conservatism, drastically hurdling potential about interpretations of prevalent aggregation phenomena arising in both nature and practical application. Of interest uncovered in this article is the cooperative–competitive consensus problems for multi‐agent systems by leverage of impulsive‐based control perspective. We first discuss the possibility of quantifying interaction relation of the agents and the description of cooperative–competitive phenomena that capture massive interest recently. Specifically, the former is done by algebraic graph theory, following the same research avenue as the convention; while the cooperative–competitive information is described by some nonzero scaling parameter. We shall pursue the tie that enables to anchor the consensus of participating agents, without depending on the signed graph theory. Subsequently, a manner relying on the local information is carried out to induce the consensus error to circumvent the global information. Then, consensus condition, in connection with the features of both continuous and impulsiveߚbased dynamics, is obtained, as well as several typical circumstances are also elaborated. Both the proposed consensus algorithms and the derived results are underpinned via a numerical study eventually. [ABSTRACT FROM AUTHOR]

In this study, we present and examine a fractional integral operator with an I$$ I $$‐function in its kernel. This operator is used to solve several fractional differential equations (FDEs). FDE has a set of particular cases whose solutions represent different physical phenomena. Much mathematical physics, biology, engineering, and chemistry problems are identified and solved using FDE. We first solve the FDE and the integral operator for the incomplete I$$ I $$‐function (I I$$ I $$F) for the generalized composite fractional derivative (GCFD). This is followed by the discovery and investigation of several important exceptional cases. The significant finding of this study is a first‐order integer‐differential equation of the Volterra type that clearly describes the unsaturated nature of free‐electron lasers. [ABSTRACT FROM AUTHOR]

In this paper, a collocation method based on shifted second‐order Chebyshev polynomials is implemented to obtain the approximate solution of the stochastic Itô–Volterra integral equation of Abel type with weakly singular kernel. In this method, operational matrices are used to convert the stochastic Itô–Volterra integral equation to algebraic equations that are linear. The algorithm of the proposed numerical scheme has been presented in this paper. Also, the error bound and convergence of the proposed method are well established. Consequently, two illustrative examples are provided to demonstrate the efficiency, plausibility, reliability, and consistency of the current methodology. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the intrinsic impact of the predator‐taxis coefficient on the formation of spatial patterns in a predator–prey system with prey social behavior subject to Neumann boundary conditions. By treating the predator‐taxis coefficient as a potential critical parameter for Turing bifurcation, we observe that the Turing pattern is fully captured by three distinct critical thresholds. Meanwhile, utilizing weakly nonlinear analysis and the amplitude equation, we establish the direction of Turing bifurcation. Our mathematical analysis reveals that the inclusion of the predator‐taxis coefficient in the predator–prey system may lead to the emergence of either subcritical or supercritical Turing bifurcation. Our numerical experiments confirm the theoretical findings and exhibit various spatial patterns with different values of predator‐taxis coefficients. [ABSTRACT FROM AUTHOR]

The Stress Gradient Hypothesis predicts facilitation will become more important than competition where abiotic stress is high, and the framework successfully predicts positive interactions between species in many systems. Fewer studies have focused on intraspecific facilitation, and to our knowledge none examine intraspecific interactions in Pacific Coast salt marshes of North America. We used two species that tend to occur in large, monospecific patches to test for intraspecific facilitation in a restored California marsh, where tides and evaporation during summer create moisture and salinity gradients across elevation. We tested performance of Frankenia salina or Jaumea carnosa in restoration plots using two treatments: clustered plantings to promote facilitation, and widely spaced plantings to limit interaction between individuals. We characterized the soil water potential gradient and measured plant survival, cover, physiology, and susceptibility to herbivory across elevation and planting treatments. Soil water potential declined sharply with elevation, suggesting plant stress should be higher upslope. However, tissue water potential was unaffected by elevation, and survival was high—suggesting growing conditions remained benign. A seawater addition treatment did not alter the response of plants or plant interactions to the abiotic gradient. At 19 months, intraspecific competition prevailed across the entire elevation gradient for both species, with less transplant cover in clustered plantings. However, clustered Frankenia fared better during a transient period of heavy rabbit herbivory. Aside from this temporary benefit, clustering did not reduce stress and strongly suppressed growth—suggesting that restoration designs for the high marsh should minimize competition. [ABSTRACT FROM AUTHOR]

Populations along geographical range limits are often exposed to unsuitable climate and low resource availability relative to core populations. As such, there has been a renewed focus on understanding the factors that determine range limits to better predict how species will respond to global change. Using recent theory on range limits and classical understanding of density dependence, we evaluated the influence of resource availability on the snowshoe hare Lepus americanus along its trailing range edge. We estimated variation in population density, habitat use, survival, and parasite loads to test the Great Escape Hypothesis (GEH), i.e. that density dependence determines, in part, a species' persistence along trailing edges. We found that variability in resource availability affected density and population fluctuations and led to trade‐offs in survival for snowshoe hare populations in the northeastern USA. Hares living in resource‐limited environments had lower and less variable population density, yet higher survival and lower parasitism compared to populations living in resource‐rich environments. We suggest that density‐dependent dynamics, elicited by resource availability, provide hares a unique survival advantage and partly explain persistence along their trailing edge. We hypothesize that this low‐density escape from predation and parasitism occurs for other prey species along trailing edges, but the extent to which it occurs is likely conditional on the quality of matrix habitat. Our work indicates that biotic factors play an important role in shaping species' trailing edges and more detailed examination of non‐climatic factors is warranted to better inform conservation and management decisions. [ABSTRACT FROM AUTHOR]

The purpose of this work is to investigate the existence and stability of traveling wavefronts for a three‐species competitive‐cooperative system with nonlocal dispersal. By applying monotone iteration method combining with a pair of suitable super‐ and sub‐solutions, we establish the existence of traveling wavefronts. The nonexistence of traveling wavefronts is obtained by a contradiction argument. Finally, by using the weighted energy method together with the comparison principle, we prove that the traveling wavefronts with relatively large speeds are exponentially stable as perturbation in some exponentially weighted spaces, when the difference between initial data and traveling wavefronts decays exponentially at negative infinity, but in other locations, the initial data can be very large. [ABSTRACT FROM AUTHOR]

In this paper, the numerical solution of a two‐dimensional partial Volterra integro‐differential equation (2D‐PVIDE) is provided by extending the Taylor collocation scheme of one‐dimensional Volterra integral equations. The method is based on the use of Taylor polynomials in two‐dimensional, while the approximate solution is given by using explicit schemes. The method is proved to be high‐order convergent with respect to the maximum norm. Some numerical examples are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the decoding problem for multiple Bose–Chaudhuri–Hocquenghem (BCH)‐Goppa codes over the same finite field is investigated. A new iterative decoding algorithm is proposed based on the quotient difference (qd)‐type discrete hungry Lotka–Volterra equation over finite fields. Compared with certain existing algorithms, the proposed algorithm manifests its advantage in computational complexity. A few of examples are presented to demonstrate its efficiency. [ABSTRACT FROM AUTHOR]

Through compelling examples from various continents, Reidinger effectively illustrates the far-reaching consequences of invasive species on native ecosystems and local communities, and the complexities of mitigating damage. In Chapter 6, Communities, Ecosystems, and Landscapes, Reidinger equates ecosystems to communities - all organisms living in an area at a given time interacting with their abiotic components. Russell Reidinger's revised book, I Human-Wildlife Conflict Management: Prevention and Problem Solving i , provides a comprehensive and practical guide to understanding human-wildlife conflict, and offers a variety of effective strategies in prevention and resolution. [Extracted from the article]

The aim of this paper is to establish some sufficient conditions ensuring the existence and uniqueness of positive (Bohr) almost periodic solutions to a class of semilinear evolution equations of the form: u′(t)=A(t)u(t)+f(t,u(t)),t∈ℝ$$ {u}^{\prime }(t)=A(t)u(t)+f\left(t,u(t)\right),t\in \mathbb{R} $$. We assume that the family of closed linear operators (A(t))t∈ℝ$$ {\left(A(t)\right)}_{t\in \mathbb{R}} $$ on a Banach lattice X$$ X $$ satisfies the "Acquistapace–Terreni" conditions, so that the associated evolution family is positive and has an exponential dichotomy on ℝ$$ \mathbb{R} $$. The nonlinear term f$$ f $$, acting on certain real interpolation spaces, is assumed to be almost periodic only in a weaker sense (i.e., in Stepanov's sense) with respect to t$$ t $$, and Lipschitzian in bounded sets with respect to the second variable. Moreover, we prove a new composition result for Stepanov almost periodic functions by assuming only continuity of f$$ f $$ with respect to the second variable (see the condition Lemma 1‐(ii)). Finally, we provide an application to a system of Lotka–Volterra predator–prey type model with diffusion and time–dependent parameters in a generalized almost periodic environment. [ABSTRACT FROM AUTHOR]

Physical laws governing population dynamics are generally expressed as differential equations. Research in recent decades has incorporated fractional‐order (non‐integer) derivatives into differential models of natural phenomena, such as reaction–diffusion systems. In this paper, we develop a method to numerically solve a multi‐component and multi‐dimensional space‐fractional system. For space discretization, we apply a Fourier spectral method that is suited for multidimensional partial differential equation systems. Efficient approximation of time‐stepping is accomplished with a locally one dimensional exponential time differencing approach. We show the effect of different fractional parameters on growth models and consider the convergence, stability, and uniqueness of solutions, as well as the biological interpretation of parameters and boundary conditions. [ABSTRACT FROM AUTHOR]

Inspired by the increasing development of theories subordinate to the topic of stability in the sense of Ulam–Hyers and Ulam–Hyers–Rassias, we present in this paper new sufficient conditions for concluding the stability of classes of integral equations with kernels depending on sine and cosine functions. This will be done by taking the profit of fixed‐point arguments in the framework of spaces of continuous functions endowed with a generalization of the Bielecki metric. After presenting the main theorems, some examples are provided to verify the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Understanding the mechanisms underlying species distributions and coexistence is both a priority and a challenge for biodiversity hotspots such as the Neotropics. Here, we highlight that Müllerian mimicry, where defended prey species display similar warning signals, is key to the maintenance of biodiversity in the c. 400 species of the Neotropical butterfly tribe Ithomiini (Nymphalidae: Danainae). We show that mimicry drives large‐scale spatial association among phenotypically similar species, providing new empirical evidence for the validity of Müller's model at a macroecological scale. Additionally, we show that mimetic interactions drive the evolutionary convergence of species climatic niche, thereby strengthening the co‐occurrence of co‐mimetic species. This study provides new insights into the importance of mutualistic interactions in shaping both niche evolution and species assemblages at large spatial scales. Critically, in the context of climate change, our results highlight the vulnerability to extinction cascades of such adaptively assembled communities tied by positive interactions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate pattern dynamics in a reaction‐diffusion‐chemotaxis food chain model with predator‐taxis, which extends previous studies of reaction‐diffusion food chain model. By virtue of diffusion semigroup theory, we first prove global classical solvability and boundedness for the considered model over a bounded domain Ω⊂ℝn(n≥1)$$ \Omega \subset {\mathbb{R}}^n\kern0.1em \left(n\ge 1\right) $$ with smooth boundary for arbitrary predator‐taxis sensitivity coefficient. Then the linear stability analysis for the considered model shows that chemotaxis can induce the losing of stability of the unique positive spatially homogeneous steady state via Turing bifurcation and Turing‐spatiotemporal Hopf bifurcation. These bifurcations results in the formation of two kinds of important spatiotemporal patterns: stationary Turing pattern and oscillatory pattern. Simultaneously, the threshold values for Turing bifurcation and Turing‐spatiotemporal Hopf bifurcation are given explicitly. Finally, numerical simulations are performed to illustrate and support our theoretical findings, and some interesting non‐Turing patterns are found in temporal Hopf parameter space by numerical simulation. [ABSTRACT FROM AUTHOR]

We perform the mathematical analysis of a model describing the interaction of two species in a chemostat, involving competition and mutualism, simultaneously. The model is a five‐dimensional system of differential equations with nonlinear growth functions. We give a comprehensive description of the dynamics of the system by determining analytically the existence and the local stability conditions of all steady‐states, considering a large class of growth rates. We prove that there exists a unique stable coexistence steady‐state and give the conditions under which bistability can occur. We give bifurcation diagrams and operating diagrams showing the rich behavior of the system. [ABSTRACT FROM AUTHOR]

The evolutionary dynamics of cross‐reaction–diffusion equations of predator–prey type are investigated in the sense of fractional operator. In the models, we replace the classical time and spatial derivatives with the Caputo–Fabrizio and Riesz fractional derivatives, respectively. The nature of the resulting problem (is nonlinear, nonlocal, and nonsingular) do not either admit a closed form solution, while in most cases the analytical solution is too involved to be useful. As a result, there is need to provide a reliable numerical scheme that can approximate these derivatives in time and space. Hence, we formulate an approximation scheme with second‐order convergence rate for the time‐Caputo–Fabrizio fractional operator of order 0 < α ≤ 1 and L1 formula for the Riesz fractional derivative of order 1 < β ≤ 2 in space. As a case study, we consider two examples of strongly coupled cross fractional reaction–diffusion systems describing the interaction between two individual species that prey on the other one. We examine the system for stability analysis and establish the condition for the occurrence of Turing instability. The complexity of the dynamics of time–space cross fractional reaction–diffusion systems is theoretically studied and numerically in one and two dimensions for some instances of fractional orders. [ABSTRACT FROM AUTHOR]

Considering the media coverage and age‐dependent education, a deterministic and a stochastic class‐age‐structured rumor propagation models are studied, respectively. First, the deterministic rumor propagation model is characterized by a coupled system of ordinary and partial differential equations. The positivity and boundness of solutions are proved, and the basic reproduction number is derived. Second, the stochastic rumor propagation model is formulated by stochastic differential equations. The existence of global positive solutions in model is discussed with the Itô's formula and stochastic Lyapunov function. Additionally, by utilizing comparison principle of stochastic differential equations and the strong law of large numbers, several sufficient conditions for extinction and persistence of the rumor are derived. Finally, numerical simulations are carried out for illustrating the results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of singular prey‐taxis models in a smooth bounded domain under homogeneous Neumann boundary conditions. The main challenge of analysis is the possible singularity as the prey density vanishes. Employing the technique of a priori assumption, the comparison principle of differential equations and semigroup estimates, we show that the singularity can be precluded if the intrinsic growth rate of prey is suitably large and hence obtain the existence of global classical bounded solutions. Moreover, the global stability of co‐existence and prey‐only steady states with convergence rates is established by the method of Lyapunov functionals. [ABSTRACT FROM AUTHOR]

Aim: Understanding cetacean species' distributions and population structure over space and time is necessary for effective conservation and management. Geographic differences in acoustic signals may provide a line of evidence for population‐level discrimination in some cetacean species. We use acoustic recordings collected over broad spatial and temporal scales to investigate whether global variability in echolocation click peak frequency could elucidate population structure in Blainville's beaked whale (Mesoplodon densirostris), a cryptic species well‐studied acoustically. Location: North Pacific, Western North Atlantic and Gulf of Mexico. Time period: 2004–2021. Major taxa studied: Blainville's beaked whale. Methods: Passive acoustic data were collected at 76 sites and 150 cumulative years of data were analysed to extract beaked whale echolocation clicks. Using an automated detector and subsequent weighted network clustering on spectral content and interclick interval of clicks, we determined the properties of a primary cluster of clicks with similar characteristics per site. These were compared within regions and across ocean basins and evaluated for suitability as population‐level indicators. Results: Spectral averages obtained from primary clusters of echolocation clicks identified at each site were similar in overall shape but varied in peak frequency by up to 8 kHz. We identified a latitudinal cline, with higher peak frequencies occurring in lower latitudes. Main conclusions: It may be possible to acoustically delineate populations of Blainville's beaked whales. The documented negative correlation between signal peak frequency and latitude could relate to body size. Body size has been shown to influence signal frequency, with lower frequencies produced by larger animals, which are subsequently more common in higher latitudes for some species, although data are lacking to adequately investigate this for beaked whales. Prey size and depth may shape frequency content of echolocation signals, and larger prey items may occur in higher latitudes, resulting in lower signal frequencies of their predators. [ABSTRACT FROM AUTHOR]

Aim: Linking local population dynamics and species distributions is crucial to predicting the impacts of climate change. Although many studies focus on the mean fitness of populations, theory shows that species distributions can be shaped by demographic stochasticity or population resilience. Here, we examine how mean fitness (measured by invasion rate), demographic stochasticity and resilience (measured by the ability to recover from disturbance) constrain populations at the edges compared with the climatic centre. Location: Europe: Spain, France, Germany, Finland and Sweden. Period: Forest inventory data used for fitting the models cover the period from 1985 to 2013. Major taxa Dominant European tree species; angiosperms and gymnosperms. Methods: We developed dynamic population models covering the entire life cycle of 25 European tree species with climatically dependent recruitment models fitted to forest inventory data. We then ran simulations using integral projection and individual‐based models to test how invasion rates, risk of stochastic extinction and ability to recover from stochastic disturbances differ between the centre and edges of the climatic niches of species. Results: Results varied among species, but in general, demographic constraints were stronger at warm edges and for species in harsher climates. Conversely, recovery was more limiting at cold edges. In addition, we found that for several species, constraints at the edges were attributable to demographic stochasticity and capacity for recovery rather than mean fitness. Main conclusions Our results highlight that mean fitness is not the only mechanism at play at the edges; demographic stochasticity and population capacity to recover also matter for European tree species. To understand how climate change will drive species range shifts, future studies will need to analyse the interplay between population mean growth rate and stochastic demographic processes in addition to disturbances. [ABSTRACT FROM AUTHOR]

In this paper, we study a predator–prey system with the simplified Holling IV functional response and antipredator behavior such that the adult prey can attack vulnerable predators. The model has been investigated by Tang and Xiao, and the existence and stability of all possible equilibria are determined. In addition, they performed a bifurcation analysis and showed that the system undergoes a Codimension 2 Bogdanov–Takens bifurcation. In this paper, for the same model, we further show that the cusp‐type Bogdanov–Takens bifurcation can be of Codimension 3, which acts as an organizing center for the whole bifurcation set. In addition, we propose the existence of Hopf bifurcation of Codimension 2 and the coexistence of stable limit cycle and unstable limit cycle. In particular, we show that the antipredator behavior has great effect on the dynamics of the model, it may cause the predator population to extinct while the prey population will increase up to the carrying capacity. Numerical simulations including bifurcation diagrams and phase portraits are performed to illustrate and confirm the theoretical results. These results may enrich the dynamics of predator–prey systems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate bifurcations of stationary solutions of a cross‐diffusion prey–predator system with Ivlev functional response and Neumann boundary conditions. First, we analyze the local stability and existence of a Hopf bifurcation at a coexistence stationary solution. We show that the bifurcating periodic solutions are asymptotically orbitally stable and the bifurcation direction is supercritical when the ratio of the conversion of prey captured by predator to the death rate of predator is in the interval (1,2]$$ \left(1,2\right] $$. Next, we derive sufficient conditions for the existence of a steady‐state bifurcation from a simple eigenvalue. We establish the existence of two intersecting C1$$ {C}^1 $$ curves of steady‐state solutions near the coexistence stationary solution. To illustrate our theoretical results, we give some numerical examples. From numerical simulations we observe that the coexistence stationary solution loses its stability via the Hopf bifurcation and a periodic solution emerges after a short time. Also by taking the bifurcation parameter value in the stable region, the effect of the initial condition disappears over time and the solution returns to the coexistence stationary solution. [ABSTRACT FROM AUTHOR]

We consider a predator‐prey model with dissimilar functional and numerical responses that induce an Allee effect. There is a time lag between consumption and digestion of prey biomass by predator. Hence, a time delay has been incorporated in the numerical response function. The system consists of two interior equilibria. Taking time delay as the bifurcation parameter, four different dynamic behaviors appear, viz., (R1) system undergoes no change in its stability for all time delay, (R2) system undergoes stability change, (R3) system undergoes stability switching, and (R4) system undergoes instability switching. Here, finding four distinct dynamics in a single population model with only one delay is a novelty in this contribution. This variation in dynamics emerges due to asymmetricity in functional and numerical responses. All the relevant theorems in establishing stability are provided, and these are verified numerically. We analytically prove that if an interior equilibrium is a saddle point in absence of time delay, then the equilibrium cannot be stabilized by varying the time delay. It is popularly believed that existence of two distinct pair of purely imaginary roots of the characteristic function leads to stability switching. However, we provide examples where the system remains unstable, stability changes, and instability switching occurs. This is another new and interesting observation in our work. The numerical examples are furnished with phase portraits, time series plots, bifurcation diagrams, and eigenvalues evaluation with delay, for better understanding. Our model with a single delay exhibits variety of dynamics, which were not explored before. [ABSTRACT FROM AUTHOR]

The solutions of weakly singular fractional Volterra integro‐differential equations involving the Caputo derivative typically have solutions whose derivatives are unbounded at the left end‐point of the interval of integration. In this paper, we design an algorithm to prevail on this non‐smooth behavior of solutions of the nonlinear fractional Volterra integro‐differential equations with a weakly singular kernel. The convergence of the proposed method is investigated. The proposed scheme is employed to solve four numerical examples in order to test its efficiency and accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we formulate and investigate a stochastic one‐prey and two‐predator model with Holling II functional response and disease in the prey, in which the predators only feed on infected prey. The existence and uniqueness of global positive solution is proved by using conventional methods. The corresponding deterministic model has a disease‐free equilibrium point if the basic reproduction number R0<1$$ {R}_0<1 $$, and it has three boundary equilibrium points and one positive equilibrium point if R0>1$$ {R}_0>1 $$. For the stochastic model, we investigate the asymptotic behavior around all of the five equilibrium points and prove that there is a unique ergodic stationary distribution under certain conditions. Moreover, we obtain the condition on which the population of the infected prey and the two predators will die out in the time mean sense. Finally, numerical simulations are conducted to illustrate our analysis results. [ABSTRACT FROM AUTHOR]

Abiotic factors are usually considered key drivers of species distribution at macro scales, while biotic interactions are mostly used at local scales. A few studies have explored the role of biotic interactions at macro scales, but all considered a limited number of species and obligate interactions. We examine the role of biotic interactions in large‐scale SDMs by testing two main hypotheses: (1) biotic factors in SDMs can have an important role at continental scale; (2) the inclusion of biotic factors in large‐scale SDMs is important also for generalist species. We used a maximum entropy algorithm to model the distribution of 177 bat species in Africa calibrating two SDMs for each species: one considering only abiotic variables (noBIO‐SDMs) and the other (BIO‐SDMs) including also biotic variables (trophic resource richness). We focused the interpretation of our results on variable importance and response curves. For each species, we also compared the potential distribution measuring the percentage of change between the two models in each pixel of the study area. All models gave AUC >0.7, with values on average higher in BIO‐SDMs compared to noBIO‐SDMs. Trophic resources showed an importance overall higher level than all abiotic predictors in most of the species (~68%), including generalist species. Response curves were highly interpretable in all models, confirming the ecological reliability of our models. Model comparison between the two models showed a change in potential distribution for more than 80% of the species, particularly in tropical forests and shrublands. Our results highlight the importance of considering biotic interactions in SDMs at macro scales. We demonstrated that a generic biotic proxy can be important for modeling species distribution when species‐specific data are not available, but we envision that a multi‐scale analysis combined with a better knowledge of the species might provide a better understanding of the role of biotic interactions. [ABSTRACT FROM AUTHOR]

In this paper, a spectral method is implemented to solve a nonlinear multidimensional Volterra integral equation. Under some condition, the spectral convergence analysis of the solution u$$ u $$ is investigated in both L∞$$ {L}^{\infty } $$ norm and Lωα,β2$$ {L}_{\omega^{\alpha, \beta}}^2 $$ norm. The results of a numerical example confirm the theoretical prediction. [ABSTRACT FROM AUTHOR]

This paper is in concern with the study of differential problems involving the ψ$$ \psi $$‐shifted fractional derivatives, where ψ$$ \psi $$ is a scaling function. Such operators can be thought of as a generalization of several fractional derivatives such as the classical Riemann–Liouville and Caputo operators, the Hadamard operators, the generalized fractional operators, and the Erdélyi–Kober operators, among others. Two types of boundary conditions are considered: the Cauchy problems and the integral boundary conditions. [ABSTRACT FROM AUTHOR]

A diffusive predator–prey system with the network connection and harvesting policy is investigated in the present paper. The global existence and boundedness of the positive solutions to the parabolic equations are analyzed. Hereafter, a priori estimates and non‐existence of the non‐constant steady states are investigated for the corresponding elliptic equation. Next, we focus on the network connect model. The stability of the positive equilibrium, the Hopf bifurcation, and the Turing instability of networked system are explored. By using the multiple time scale (MTS), the direction of the Hopf bifurcation is determined. It is found that the networked system may admit a supercritical or subcritical Hopf bifurcation. For the Turing instability, the positive equilibrium will change its stability from an unstable state to a stable one with the change of the connecting probability. That is not the case in the model without network structure. Theoretical results also show that the model can create rich dynamical behaviors and numerical simulations well verify the validity of the theoretical analysis. [ABSTRACT FROM AUTHOR]