In this paper, an economic model was constructed to determine the optimal wolf population and distribution across the Northern Rocky Mountains. Both ecological and economic concepts were incorporated in an implicitly ...In this paper, an economic model was constructed to determine the optimal wolf population and distribution across the Northern Rocky Mountains. Both ecological and economic concepts were incorporated in an implicitly spatial social welfare maximization problem. This interdisciplinary model relies on multiple data sources, including current wolf population and distribution information, opportunity cost to local landowners, and contingent valuation studies to determine willingness-to-pay for wolves. Economic models tend to externalize ecological concerns and ecological models often omit the complex human dimensions of conservation policy. Accordingly, this model can serve as a guide for integrating best practices from both fields. The model presented here is sufficiently general to apply to wolves in other ecosystems and to other highly interacting species such as beavers and bison. The Northern Rocky Mountain wolf was used as an example of how this economic model works, but this model can be applied far more broadly.展开更多
The stabilization problem of a kind of prey-predator model with Holling fimctional response is investigated. By approximate linearization approach, a feedback control law stabilizing the closed- loop system is obtaine...The stabilization problem of a kind of prey-predator model with Holling fimctional response is investigated. By approximate linearization approach, a feedback control law stabilizing the closed- loop system is obtained. On the other hand, by exact linearization approach, a suitable change of coordinates in the state space and a feedback control law render the complex nonlinear system to be a linear controllable one such that the positive equilibrium point of the closed-loop system is globally asymptotically stable.展开更多
In this paper, we discuss the behavior of a predator-prey model with disease in the prey with and without stochastic perturbation, respectively. First, we briefly give the dynamic of the deterministic system, by analy...In this paper, we discuss the behavior of a predator-prey model with disease in the prey with and without stochastic perturbation, respectively. First, we briefly give the dynamic of the deterministic system, by analyzing stabilities of its four equilibria. Then, we consider the asymptotic behavior of the stochastic system. By Lyapunov analysis methods, we show the stochastic stability and its long time behavior around the equi- librium of the deterministic system. We obtain there are similar properties between the stochastic system and its corresponding deterministic system, when white noise is small. But large white noise can make a unstable deterministic system to be stable.展开更多
Das et al. [Effect of disease-selective predation on prey infected by contact and external sources, Biosystems 95(3) (2009) 188-199] proposed an eco-epidemiological model where the prey species is infected through...Das et al. [Effect of disease-selective predation on prey infected by contact and external sources, Biosystems 95(3) (2009) 188-199] proposed an eco-epidemiological model where the prey species is infected through the external source of infection and contact of the species. In this present study we have modified their model by assuming that the predator consumes both the susceptible as well as the infected prey following the modified Holling type-Ⅱ functional response. Our main focusing points of this study are the role of infection rate (both internal and external), alternative food, and half-saturation constant in the predator prey dynamics with disease in the prey population. We have shown the local stability of the boundary as well as the interior equilibrium point under certain conditions. We have Mso worked out the permanence of the system. Our simulation results show that the system enters into limit cycle oscillations from stable position for higher values of the contact rate. But it is also shown that the external infection rate, enrichment of the alternative food of the predator population and the half-saturation constant can prevent limit cycle oscillations and stabilize the system. Thus external dis- ease propagation, enrichment of the alternative food resource, and the half-saturation constant are the key factors for preventing the oscillatory behavior of the species.展开更多
The diffusive Leslie-Clower predator-prey model incorporating a prey refuge is recon- sidered here. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained, a...The diffusive Leslie-Clower predator-prey model incorporating a prey refuge is recon- sidered here. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained, and our results supplement earlier ones.展开更多
In this paper, we consider a modified Leslie-Clower predator prey model with Holling- type II schemes and mutual interference. By applying the comparison theorem of the differential equation and constructing a suitabl...In this paper, we consider a modified Leslie-Clower predator prey model with Holling- type II schemes and mutual interference. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov function, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained. Our results not only supplement but also improve some existing ones.展开更多
In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial...In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial value. Sufficient conditions for global asymptotic stability are established. Some simulation figures are introduced to support the analytical findings.展开更多
Phenotypic plasticity is often an adaptation of organisms to cope with temporally or spatially heter- ogenous landscapes. Like other adaptations, one would predict that different species, populations, or sexes might t...Phenotypic plasticity is often an adaptation of organisms to cope with temporally or spatially heter- ogenous landscapes. Like other adaptations, one would predict that different species, populations, or sexes might thus show some degree of parallel evolution of plasticity, in the form of parallel reaction norms, when exposed to analogous environmental gradients. Indeed, one might even ex- pect parallelism of plasticity to repeatedly evolve in multiple traits responding to the same gradi- ent, resulting in integrated parallelism of plasticity. In this study, we experimentally tested for paral- lel patterns of predator-mediated plasticity of size, shape, and behavior of 2 species and sexes of mosquitofish. Examination of behavioral trials indicated that the 2 species showed unique patterns of behavioral plasticity, whereas the 2 sexes in each species showed parallel responses. Fish shape showed parallel patterns of plasticity for both sexes and species, albeit males showed evidence of unique plasticity related to reproductive anatomy. Moreover, patterns of shape plasticity due to predator exposure were broadly parallel to what has been depicted for predator-mediated popula- tion divergence in other studies (slender bodies, expanded caudal regions, ventrally located eyes, and reduced male gonopodia). We did not find evidence of phenotypic plasticity in fish size for ei- ther species or sex. Hence, our findings support broadly integrated parallelism of plasticity for sexes within species and less integrated parallelism for species. We interpret these findings with respect to their potential broader implications for the interacting roles of adaptation and constraint in the evolutionary origins of parallelism of plasticity in general.展开更多
The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the ...The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator-prey system conforms to the realistically biological environment. We firstly introduce a sufficient condition for the permanence of the system and then use a specific set to obtain a weaker sufficient condition. Afterward, we provide corresponding conditions for the extinction of the system and the existence of boundary periodical solutions, respectively. ~rther, we get a sufficient condition for global attractiveness of the boundary periodic solution by constructing a Lyapunov function, arriving at the uniqueness of boundary periodic solutions since the uniqueness of boundary periodic solutions can be ensured by global attractiveness. Finally, based on the existence of positive periodic solutions, which can be ensured by the Brouwer fixed- point theorem, we provide a sufficient condition for the uniqueness of positive periodic solutions.展开更多
to biological and chemical control strategy for pest control, a Holling II func- tional response predator-prey system concerning state-dependent impulsive control is investigated. We define the successor functions of ...to biological and chemical control strategy for pest control, a Holling II func- tional response predator-prey system concerning state-dependent impulsive control is investigated. We define the successor functions of semi-continuous dynamic system and give an existence theorem of order 1 periodic solution of such a system. By means of sequence convergence rules and quMitative analysis, we successfully get the conditions of existence and attractiveness of order 1 periodic solution. Our results show that our method used in this paper is more efficient and easier than the existing methods to prove the existence and attractiveness of order 1 periodic solution.展开更多
The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria: a zero equilibr...The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria: a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.展开更多
Predation is thought to be one of the main structuring forces in animal communities. However, se- lective predation is often measured on isolated traits in response to a single predatory species, but only rarely are s...Predation is thought to be one of the main structuring forces in animal communities. However, se- lective predation is often measured on isolated traits in response to a single predatory species, but only rarely are selective forces on several traits quantified or even compared between different predators naturally occurring in the same system. In the present study, we therefore measured be- havioral and morphological traits in young-of-the-year Eurasian perch Perca fluviatilis and com- pared their selective values in response to the 2 most common predators, adult perch and pike Esox lucius. Using mixed effects models and model averaging to analyze our data, we quantified and compared the selectivity of the 2 predators on the different morphological and behavioral traits. We found that selection on the behavioral traits was higher than on morphological traits and perch predators preyed overall more selectively than pike predators. Pike tended to positively se- lect shallow bodied and nonvigilant individuals (i.e. individuals not performing predator inspec- tion). In contrast, perch predators selected mainly for bolder juvenile perch (i.e. individuals spend- ing more time in the open, more active), which was most important. Our results are to the best of our knowledge the first that analyzed behavioral and morphological adaptations of juvenile perch facing 2 different predation strategies. We found that relative specific predation intensity for the di- vergent traits differed between the predators, providing some additional ideas why juvenile perch display such a high degree of phenotypic plasticity.展开更多
Correlations among behavioral traits can generate trade-offs and constrain phenotypic evolution. Interspecific hybridization has the potential to alter behavioral trait correlations, but the effect of hybridization on...Correlations among behavioral traits can generate trade-offs and constrain phenotypic evolution. Interspecific hybridization has the potential to alter behavioral trait correlations, but the effect of hybridization on suites of behavioral traits has received relatively little attention. We evaluated how natural hybridization changes the relationship between boldness (time of emergence and proportion of time out of shelter) and response to a simulated predator threat in swordtails (Teleostei: Xiphophorus). In poeciliid fishes, bold individuals have increased survival in the presence of predators. This non-intuitive observation may arise as a result of bold individuals being more likely to engage in anti-predator behaviors. Contrary to our prediction, bold indi- viduals were less likely to perform a fast-start response to a predator threat. This correlation was consistent among populations and species but was only significant in hybrids. The observed correlation between boldness and anti-predator behavior could im- pact hybrid fitness and the evolvability of hybrid lineages. More generally, our findings suggest that hybridization could influence the integration of behavioral phenotypes, as has been amply documented for morphology. Animal personality and behavioral syndromes could therefore play an important role in the evolutionary fate of natural hybrids [Current Zoology 61 (4): 596-603, 2015].展开更多
文摘In this paper, an economic model was constructed to determine the optimal wolf population and distribution across the Northern Rocky Mountains. Both ecological and economic concepts were incorporated in an implicitly spatial social welfare maximization problem. This interdisciplinary model relies on multiple data sources, including current wolf population and distribution information, opportunity cost to local landowners, and contingent valuation studies to determine willingness-to-pay for wolves. Economic models tend to externalize ecological concerns and ecological models often omit the complex human dimensions of conservation policy. Accordingly, this model can serve as a guide for integrating best practices from both fields. The model presented here is sufficiently general to apply to wolves in other ecosystems and to other highly interacting species such as beavers and bison. The Northern Rocky Mountain wolf was used as an example of how this economic model works, but this model can be applied far more broadly.
文摘The stabilization problem of a kind of prey-predator model with Holling fimctional response is investigated. By approximate linearization approach, a feedback control law stabilizing the closed- loop system is obtained. On the other hand, by exact linearization approach, a suitable change of coordinates in the state space and a feedback control law render the complex nonlinear system to be a linear controllable one such that the positive equilibrium point of the closed-loop system is globally asymptotically stable.
文摘In this paper, we discuss the behavior of a predator-prey model with disease in the prey with and without stochastic perturbation, respectively. First, we briefly give the dynamic of the deterministic system, by analyzing stabilities of its four equilibria. Then, we consider the asymptotic behavior of the stochastic system. By Lyapunov analysis methods, we show the stochastic stability and its long time behavior around the equi- librium of the deterministic system. We obtain there are similar properties between the stochastic system and its corresponding deterministic system, when white noise is small. But large white noise can make a unstable deterministic system to be stable.
文摘Das et al. [Effect of disease-selective predation on prey infected by contact and external sources, Biosystems 95(3) (2009) 188-199] proposed an eco-epidemiological model where the prey species is infected through the external source of infection and contact of the species. In this present study we have modified their model by assuming that the predator consumes both the susceptible as well as the infected prey following the modified Holling type-Ⅱ functional response. Our main focusing points of this study are the role of infection rate (both internal and external), alternative food, and half-saturation constant in the predator prey dynamics with disease in the prey population. We have shown the local stability of the boundary as well as the interior equilibrium point under certain conditions. We have Mso worked out the permanence of the system. Our simulation results show that the system enters into limit cycle oscillations from stable position for higher values of the contact rate. But it is also shown that the external infection rate, enrichment of the alternative food of the predator population and the half-saturation constant can prevent limit cycle oscillations and stabilize the system. Thus external dis- ease propagation, enrichment of the alternative food resource, and the half-saturation constant are the key factors for preventing the oscillatory behavior of the species.
基金This work is supported by the Natural Science Foundation of China (11102041, 11201072, 10831005), the Natural Science Foundation of Fujian Province (2011J01002, 2012J01002), and the Foundation of Fujian Education Bureau (Jm2030).
文摘The diffusive Leslie-Clower predator-prey model incorporating a prey refuge is recon- sidered here. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained, and our results supplement earlier ones.
文摘In this paper, we consider a modified Leslie-Clower predator prey model with Holling- type II schemes and mutual interference. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov function, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained. Our results not only supplement but also improve some existing ones.
基金Acknowledgments The authors thank the editor and referees for their valuable comments and suggestions. This work is supported by the National Basic Research Program of China (2010CB732501) and the National Natural Science Foundation of China (61273015), the NSFC Tianyuan Foundation (Grant No. 11226256) and the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY13A010010), Zhejiang Provincial Natural Science Foundation of China LQ13A010023).
文摘In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial value. Sufficient conditions for global asymptotic stability are established. Some simulation figures are introduced to support the analytical findings.
文摘Phenotypic plasticity is often an adaptation of organisms to cope with temporally or spatially heter- ogenous landscapes. Like other adaptations, one would predict that different species, populations, or sexes might thus show some degree of parallel evolution of plasticity, in the form of parallel reaction norms, when exposed to analogous environmental gradients. Indeed, one might even ex- pect parallelism of plasticity to repeatedly evolve in multiple traits responding to the same gradi- ent, resulting in integrated parallelism of plasticity. In this study, we experimentally tested for paral- lel patterns of predator-mediated plasticity of size, shape, and behavior of 2 species and sexes of mosquitofish. Examination of behavioral trials indicated that the 2 species showed unique patterns of behavioral plasticity, whereas the 2 sexes in each species showed parallel responses. Fish shape showed parallel patterns of plasticity for both sexes and species, albeit males showed evidence of unique plasticity related to reproductive anatomy. Moreover, patterns of shape plasticity due to predator exposure were broadly parallel to what has been depicted for predator-mediated popula- tion divergence in other studies (slender bodies, expanded caudal regions, ventrally located eyes, and reduced male gonopodia). We did not find evidence of phenotypic plasticity in fish size for ei- ther species or sex. Hence, our findings support broadly integrated parallelism of plasticity for sexes within species and less integrated parallelism for species. We interpret these findings with respect to their potential broader implications for the interacting roles of adaptation and constraint in the evolutionary origins of parallelism of plasticity in general.
文摘The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator-prey system conforms to the realistically biological environment. We firstly introduce a sufficient condition for the permanence of the system and then use a specific set to obtain a weaker sufficient condition. Afterward, we provide corresponding conditions for the extinction of the system and the existence of boundary periodical solutions, respectively. ~rther, we get a sufficient condition for global attractiveness of the boundary periodic solution by constructing a Lyapunov function, arriving at the uniqueness of boundary periodic solutions since the uniqueness of boundary periodic solutions can be ensured by global attractiveness. Finally, based on the existence of positive periodic solutions, which can be ensured by the Brouwer fixed- point theorem, we provide a sufficient condition for the uniqueness of positive periodic solutions.
文摘to biological and chemical control strategy for pest control, a Holling II func- tional response predator-prey system concerning state-dependent impulsive control is investigated. We define the successor functions of semi-continuous dynamic system and give an existence theorem of order 1 periodic solution of such a system. By means of sequence convergence rules and quMitative analysis, we successfully get the conditions of existence and attractiveness of order 1 periodic solution. Our results show that our method used in this paper is more efficient and easier than the existing methods to prove the existence and attractiveness of order 1 periodic solution.
文摘The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria: a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.
文摘Predation is thought to be one of the main structuring forces in animal communities. However, se- lective predation is often measured on isolated traits in response to a single predatory species, but only rarely are selective forces on several traits quantified or even compared between different predators naturally occurring in the same system. In the present study, we therefore measured be- havioral and morphological traits in young-of-the-year Eurasian perch Perca fluviatilis and com- pared their selective values in response to the 2 most common predators, adult perch and pike Esox lucius. Using mixed effects models and model averaging to analyze our data, we quantified and compared the selectivity of the 2 predators on the different morphological and behavioral traits. We found that selection on the behavioral traits was higher than on morphological traits and perch predators preyed overall more selectively than pike predators. Pike tended to positively se- lect shallow bodied and nonvigilant individuals (i.e. individuals not performing predator inspec- tion). In contrast, perch predators selected mainly for bolder juvenile perch (i.e. individuals spend- ing more time in the open, more active), which was most important. Our results are to the best of our knowledge the first that analyzed behavioral and morphological adaptations of juvenile perch facing 2 different predation strategies. We found that relative specific predation intensity for the di- vergent traits differed between the predators, providing some additional ideas why juvenile perch display such a high degree of phenotypic plasticity.
基金We would like to thank the Mexican federal government and the state of Hidalgo for providing permits to collect fish and Nick Ratterman, Kirk Winemiller and Lee Fitzgerald for helpful comments on early versions of this manuscript. This work was supported by funding provided by a National Science Foundation grant (I0S-0923825) award- ed to G.G.R.R.E. was supported by an Undergraduate Program in Biological and Mathematical Sciences (UBM National Science Foundation grant (DBI-1029401) directed by Dr. Jay Walton. All experiments conducted in this study complied with current state, federal, and local laws in the United States and Mexico.
文摘Correlations among behavioral traits can generate trade-offs and constrain phenotypic evolution. Interspecific hybridization has the potential to alter behavioral trait correlations, but the effect of hybridization on suites of behavioral traits has received relatively little attention. We evaluated how natural hybridization changes the relationship between boldness (time of emergence and proportion of time out of shelter) and response to a simulated predator threat in swordtails (Teleostei: Xiphophorus). In poeciliid fishes, bold individuals have increased survival in the presence of predators. This non-intuitive observation may arise as a result of bold individuals being more likely to engage in anti-predator behaviors. Contrary to our prediction, bold indi- viduals were less likely to perform a fast-start response to a predator threat. This correlation was consistent among populations and species but was only significant in hybrids. The observed correlation between boldness and anti-predator behavior could im- pact hybrid fitness and the evolvability of hybrid lineages. More generally, our findings suggest that hybridization could influence the integration of behavioral phenotypes, as has been amply documented for morphology. Animal personality and behavioral syndromes could therefore play an important role in the evolutionary fate of natural hybrids [Current Zoology 61 (4): 596-603, 2015].