The study of mutualistic plant and animal networks is an emerging field of ecological research. We reviewed progress in this field over the past 30 years. While earlier studies mostly focused on network structure, sta...The study of mutualistic plant and animal networks is an emerging field of ecological research. We reviewed progress in this field over the past 30 years. While earlier studies mostly focused on network structure, stability, and biodiversity maintenance, recent studies have investigated the conservation implications of mutualistic networks, specifically the influence of invasive species and how networks respond to habitat loss. Current research has also focused on evolutionary questions including phylogenetic signal in networks, impact of networks on the coevolution of interacting partners, and network influences on the evolution of interacting species. We outline some directions for future research, particularly the evolution of specialization in mutualistic networks, and provide concrete recommendations for environmental managers.展开更多
This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by ...This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by discussing its Jacobian matrix, we give two priori estimates and prove that the model is permanent when ε1 ＋ε2≠ 0. Moreover sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the model are obtained. Nonexistence of nonconstant positive steady states of the model is also given. When ε1 ＋ε2 = 0, grow up property is derived if the geometric mean of the interaction coefficients is greater than I （a1a2 〉 1）, while if the geometric mean of the interaction coefficients is less than I （a1a2 〈 1）, there exists a global solution. Finally, numerical simulations are given.展开更多
In this paper,a fractional Laplacian mutualistic system under Neumann boundary conditions is studied.Using the method of upper and lower solutions,it is proven that the solutions of the fractional Laplacian strong mut...In this paper,a fractional Laplacian mutualistic system under Neumann boundary conditions is studied.Using the method of upper and lower solutions,it is proven that the solutions of the fractional Laplacian strong mutualistic model with Neumann boundary conditions will blow up when the intrinsic growth rates of species are large.展开更多
Sharks and sharksuckers maintain a mutualistic symbiotic relationship;thus, it is surprising to observe a lemon shark, Negaprion brevirostris, killing a sharksucker, Echeneis lucrates, which has been recorded during a...Sharks and sharksuckers maintain a mutualistic symbiotic relationship;thus, it is surprising to observe a lemon shark, Negaprion brevirostris, killing a sharksucker, Echeneis lucrates, which has been recorded during a dive with lemon sharks. Does this observation indicate that the symbiosis between the two species may shift occasionally? The awkwardness of the recorded kill, combined with its comparatively long duration, suggests this bout be a freak incident, rather than a common occurrence;thus, the mutualistic relationship needs not be questioned. What triggered the bout, however, can only be speculated. Although the caloric value of the killed sharksucker is not known, a feeding-oriented behavior can likely be rejected as the potential cause based on the teleost’s rather small size, and an irritation related issue is more likely to have triggered this bout.展开更多
Plants have both fought and cooperated with microbes for as long as they have existed,so their ability to distinguish friends from foes is an important evolutionary adaptation(Delaux and Schornack,2021).The soil micro...Plants have both fought and cooperated with microbes for as long as they have existed,so their ability to distinguish friends from foes is an important evolutionary adaptation(Delaux and Schornack,2021).The soil microbiome includes both pathogens and mutualistic symbiotic partners like rhizobia and arbuscular mycorrhizal fungi(AMFs).How do plants fine-tune their molecular responses to accommodate beneficial microbes while defending against invaders?Three recent publications have begun to unravel this complex puzzle(Zhang et al.,2024;Tan et al.,2025;Wang et al.,2025).Collectively,these studies present a molecular framework involving the lysin-motifreceptor-like kinases(LysM-RLKs)and cytoplasmic kinases that allow plants to precisely decode microbial messages(Figure 1).展开更多
To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environ- ment. Semi-coexistence states have been ...To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environ- ment. Semi-coexistence states have been studied by using the corresponding eigenvalue problems, and sufficient conditions for the existence and non-existence of coexistence states are given. Our results show that the model possesses at least one coexistence solution if the intrinsic populations growth rates are big or free-diffusion and cross-diffusion coefficients are weak. Otherwise, the model have no coexistence solution. The true solutions are obtained by utilizing the monotone iterative schemes. In order to illustrate our analytical results, some numerical simulations are given.展开更多
In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species,we study a mutualistic model on a periodically evolving domain.To overcome the difficulty caused by the ad...In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species,we study a mutualistic model on a periodically evolving domain.To overcome the difficulty caused by the advection and dilution terms,we transform the model to a reaction-difusion problem in a fixed domain.By means of eigenvalue problems,the threshold parameters are introduced.The asymptotic profiles of the solutions on an evolving domain are studied by using the threshold parameters and the upper and lower solutions method.The impact of the domain evolution rate on the persistence or extinction of species is analyzed.Numerical simulations are performed to illustrate our analytical results.展开更多
We study the internal stabilization of steady-state solutions to a 2-species mutualistic reaction diffusion system via finite-dimensional feedback controllers. Our main idea is to use different internal controllers to...We study the internal stabilization of steady-state solutions to a 2-species mutualistic reaction diffusion system via finite-dimensional feedback controllers. Our main idea is to use different internal controllers to stabilize different steady-state solutions. The controllers axe provided by considering LQ problems associated with the lineaxized systems at steady-state solutions.展开更多
In this paper we deal with the positive steady states of a Competitor-Competitor-Mutualist modelwith diffusion and homogeneous Dirichlet boundary conditions.We first give the necessary conditions,and thenestablish the...In this paper we deal with the positive steady states of a Competitor-Competitor-Mutualist modelwith diffusion and homogeneous Dirichlet boundary conditions.We first give the necessary conditions,and thenestablish the sufficient conditions for the existence of positive steady states.展开更多
This paper is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic eco- logical model. The local existence and uni...This paper is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic eco- logical model. The local existence and uniqueness of a classical solution are obtained and the asymptotic behavior of the free boundary problem is studied. Our results indi- cate that two free boundaries tend monotonically to finite or infinite limits at the same time, and the free boundary problem admits a global slow solution with unbounded free boundaries if the intra-specific competitions are strong, while if the intra-specific competitions are weak, there exist the blowup solution and global fast solution.展开更多
In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient condi- tions which guarantee the uniform persistence and the global attractiv...In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient condi- tions which guarantee the uniform persistence and the global attractivity of the system are obtained. For the almost periodic case, by constructing a suit- able Lyapunov function, sufficient conditions which guarantee the existence of a unique globally attractive positive almost periodic solution of the system are obtained. An example together with its numerical simulations shows the feasibility of the main results.展开更多
Plantshave evolvedvariousmechanismsto interact withmicroorganisms,which help them acquire nutrients from the soil and enhance their tolerance to environmental stresses.One of the most widespread mutualistic interactio...Plantshave evolvedvariousmechanismsto interact withmicroorganisms,which help them acquire nutrients from the soil and enhance their tolerance to environmental stresses.One of the most widespread mutualistic interactions is arbuscular mycorrhizal(AM)symbiosis,which is formed by 80%-90%of terrestrial plants in association with AM fungi.In AM symbiosis,plants acquire mineral nutrients from the fungi in exchange for fatty acids and sugars that are produced during photosynthesis(Jiang et al.,2017).展开更多
文摘The study of mutualistic plant and animal networks is an emerging field of ecological research. We reviewed progress in this field over the past 30 years. While earlier studies mostly focused on network structure, stability, and biodiversity maintenance, recent studies have investigated the conservation implications of mutualistic networks, specifically the influence of invasive species and how networks respond to habitat loss. Current research has also focused on evolutionary questions including phylogenetic signal in networks, impact of networks on the coevolution of interacting partners, and network influences on the evolution of interacting species. We outline some directions for future research, particularly the evolution of specialization in mutualistic networks, and provide concrete recommendations for environmental managers.
基金supported by the NSFC Grant(No.11171158)Project of Graduate Education Innovation of Jiangsu Province(No.KYLX 0719)Project of Natural Science Research of Higher Education Institutions of Jiangsu Province(No.15KJB110008)
文摘This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by discussing its Jacobian matrix, we give two priori estimates and prove that the model is permanent when ε1 ＋ε2≠ 0. Moreover sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the model are obtained. Nonexistence of nonconstant positive steady states of the model is also given. When ε1 ＋ε2 = 0, grow up property is derived if the geometric mean of the interaction coefficients is greater than I （a1a2 〉 1）, while if the geometric mean of the interaction coefficients is less than I （a1a2 〈 1）, there exists a global solution. Finally, numerical simulations are given.
基金partially supported by National Natural Science Foundation of China(11771380)Natural Science Foundation of Jiangsu Province(BK20191436).
文摘In this paper,a fractional Laplacian mutualistic system under Neumann boundary conditions is studied.Using the method of upper and lower solutions,it is proven that the solutions of the fractional Laplacian strong mutualistic model with Neumann boundary conditions will blow up when the intrinsic growth rates of species are large.
文摘Sharks and sharksuckers maintain a mutualistic symbiotic relationship;thus, it is surprising to observe a lemon shark, Negaprion brevirostris, killing a sharksucker, Echeneis lucrates, which has been recorded during a dive with lemon sharks. Does this observation indicate that the symbiosis between the two species may shift occasionally? The awkwardness of the recorded kill, combined with its comparatively long duration, suggests this bout be a freak incident, rather than a common occurrence;thus, the mutualistic relationship needs not be questioned. What triggered the bout, however, can only be speculated. Although the caloric value of the killed sharksucker is not known, a feeding-oriented behavior can likely be rejected as the potential cause based on the teleost’s rather small size, and an irritation related issue is more likely to have triggered this bout.
基金support to J.D.M.from Shanghai Science and Technology Commission grant 22JC1410800.
文摘Plants have both fought and cooperated with microbes for as long as they have existed,so their ability to distinguish friends from foes is an important evolutionary adaptation(Delaux and Schornack,2021).The soil microbiome includes both pathogens and mutualistic symbiotic partners like rhizobia and arbuscular mycorrhizal fungi(AMFs).How do plants fine-tune their molecular responses to accommodate beneficial microbes while defending against invaders?Three recent publications have begun to unravel this complex puzzle(Zhang et al.,2024;Tan et al.,2025;Wang et al.,2025).Collectively,these studies present a molecular framework involving the lysin-motifreceptor-like kinases(LysM-RLKs)and cytoplasmic kinases that allow plants to precisely decode microbial messages(Figure 1).
基金This work was partially supported by the National Natural Science Foundation of China （11771381） and Project funded by China Postdoctoral Science Foundation.
文摘To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environ- ment. Semi-coexistence states have been studied by using the corresponding eigenvalue problems, and sufficient conditions for the existence and non-existence of coexistence states are given. Our results show that the model possesses at least one coexistence solution if the intrinsic populations growth rates are big or free-diffusion and cross-diffusion coefficients are weak. Otherwise, the model have no coexistence solution. The true solutions are obtained by utilizing the monotone iterative schemes. In order to illustrate our analytical results, some numerical simulations are given.
基金This work was partially supported by the National Natural Science Foundation of China(11771381 and 11911540464).
文摘In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species,we study a mutualistic model on a periodically evolving domain.To overcome the difficulty caused by the advection and dilution terms,we transform the model to a reaction-difusion problem in a fixed domain.By means of eigenvalue problems,the threshold parameters are introduced.The asymptotic profiles of the solutions on an evolving domain are studied by using the threshold parameters and the upper and lower solutions method.The impact of the domain evolution rate on the persistence or extinction of species is analyzed.Numerical simulations are performed to illustrate our analytical results.
基金supported by the Chinese NSF under grant 10671079
文摘We study the internal stabilization of steady-state solutions to a 2-species mutualistic reaction diffusion system via finite-dimensional feedback controllers. Our main idea is to use different internal controllers to stabilize different steady-state solutions. The controllers axe provided by considering LQ problems associated with the lineaxized systems at steady-state solutions.
基金Supported by the National Natural Science Foundation of China (No.19831060)the"333"Project of JiangSu Province
文摘In this paper we deal with the positive steady states of a Competitor-Competitor-Mutualist modelwith diffusion and homogeneous Dirichlet boundary conditions.We first give the necessary conditions,and thenestablish the sufficient conditions for the existence of positive steady states.
文摘This paper is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic eco- logical model. The local existence and uniqueness of a classical solution are obtained and the asymptotic behavior of the free boundary problem is studied. Our results indi- cate that two free boundaries tend monotonically to finite or infinite limits at the same time, and the free boundary problem admits a global slow solution with unbounded free boundaries if the intra-specific competitions are strong, while if the intra-specific competitions are weak, there exist the blowup solution and global fast solution.
基金supported by the Natural Science Foundation of Fujian Province(2015J01012,2015J01019)
文摘In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient condi- tions which guarantee the uniform persistence and the global attractivity of the system are obtained. For the almost periodic case, by constructing a suit- able Lyapunov function, sufficient conditions which guarantee the existence of a unique globally attractive positive almost periodic solution of the system are obtained. An example together with its numerical simulations shows the feasibility of the main results.
基金supported by the National Key R&D Program of China(2022YFF1001800)the National Natural Science Foundation of China(32088102)the Strategic Priority Research Program of the Chinese Academy of Sciences(XDB0630103).
文摘Plantshave evolvedvariousmechanismsto interact withmicroorganisms,which help them acquire nutrients from the soil and enhance their tolerance to environmental stresses.One of the most widespread mutualistic interactions is arbuscular mycorrhizal(AM)symbiosis,which is formed by 80%-90%of terrestrial plants in association with AM fungi.In AM symbiosis,plants acquire mineral nutrients from the fungi in exchange for fatty acids and sugars that are produced during photosynthesis(Jiang et al.,2017).
