We formulate a system of integro-differential equations to model the dynamics of competition in a two-species community,in which the mortality,fertility and growth are sizedependent.Existence and uniqueness of nonnega...We formulate a system of integro-differential equations to model the dynamics of competition in a two-species community,in which the mortality,fertility and growth are sizedependent.Existence and uniqueness of nonnegative solutions to the system are analyzed.The existence of the stationary size distributions is discussed,and the linear stability is investigated by means of the semigroup theory of operators and the characteristic equation technique.Some sufficient conditions for asymptotical stability/instability of steady states are obtained.The resulting conclusion extends some existing results involving age-independent and age-dependent population models.展开更多
In this paper,we consider a nonlinear size-structured population model with functional response,which describes the dynamics of a predator-prey system living in a common habitat.We present a kind of functional respons...In this paper,we consider a nonlinear size-structured population model with functional response,which describes the dynamics of a predator-prey system living in a common habitat.We present a kind of functional response for the prey being a plant or algae,and explain its biological meanings.When the vital rates depend both on the individual's size and on the total population or only depend on the former,we obtain the existence of equilibrium solutions.展开更多
Background: The Chapman-Richards distribution is developed as a special case of the equilibrium solution to the McKendrick-Von Foerster equation. The Chapman-Richards distribution incorporates the vital rate assumptio...Background: The Chapman-Richards distribution is developed as a special case of the equilibrium solution to the McKendrick-Von Foerster equation. The Chapman-Richards distribution incorporates the vital rate assumptions of the Chapman-Richards growth function, constant mortality and recruitment into the mathematical form of the distribution. Therefore, unlike 'assumed' distribution models, it is intrinsically linked with the underlying vital rates for the forest area under consideration. Methods: It is shown that the Chapman-Richards distribution can be recast as a subset of the generalized beta distribution of the first kind, a rich family of assumed probability distribution models with known properties. These known properties for the generalized beta are then immediately available for the Chapman-Richards distribution, such as the form of the compatible basal area-size distribution. A simple two-stage procedure is proposed for the estimation of the model parameters and simulation experiments are conducted to validate the procedure for four different possible distribution shapes. Results: The simulations explore the efficacy of the two-stage estimation procedure;these cover the estimation of the growth equation and mortality-recruitment derives from the equilibrium assumption. The parameter estimates are shown to depend on both the sample size and the amount of noise imparted to the synthetic measurements. The results vary somewhat by distribution shape, with the smaller, noisier samples providing less reliable estimates of the vital rates and final distribution forms. Conclusions: The Chapman-Richards distribution in its original form, or recast as a generalized beta form, presents a potentially useful model integrating vital rates and stand diameters into a flexible family of resultant distributions shapes. The data requirements are modest, and parameter estimation is straightforward provided the minimal recommended sample sizes are obtained.展开更多
In this paper,we propose a size-stage-structured cooperation model which has two distinct life stages in facultative cooperator.The primary feature of this model is to consider size structure,stage structure and oblig...In this paper,we propose a size-stage-structured cooperation model which has two distinct life stages in facultative cooperator.The primary feature of this model is to consider size structure,stage structure and obligate and facultative symbiosis at the same time in a cooperation system.We use the method of characteristic to show that this new model can be reduced to a threshold delay equations(TDEs)model,which can be further transformed into a functional differential equations(FDEs)model by a simple change of variables.Such simplification allows us to apply the classical theory of FDEs and establish a set of sufficient conditions to investigate the qualitative analysis of solutions of the FDEs model,including the global existence and uniqueness,positivity and boundedness.What's more,we use the geometric criteria to get the conclusions about stability and Hopf bifurcation of positive equilibrium because the coefficients of the characteristic equation depend on the bifurcation parameter.Finally,numerical simulations are carried out as supporting evidences of our analytical results.Our results show that the presence of size structure and stage structure plays an important role in the dynamic behavior of the model.展开更多
Cannibalism is widespread in size-structured populations. If cannibals and victims are in different life stages, dominant cohorts of cannibals can regulate recruitment. Arizona Tiger Salamanders, Ambystoma tigrinum ne...Cannibalism is widespread in size-structured populations. If cannibals and victims are in different life stages, dominant cohorts of cannibals can regulate recruitment. Arizona Tiger Salamanders, Ambystoma tigrinum nebulosum, exhibit facultative paedomorphosis in which salamander larvae either metamorphose into terrestrial adults or become sexually mature while still in their larval form. Although many salamanders exhibit cannibalism of larvae, the Arizona Tiger Salamander also exhibits cannibalism of young by the aquatic adults. We formulate a differential equations model of this system under the assumption that the terrestrial adults do not impact the system beyond their contribution to the birth of young larvae. We establish non-negativity, boundedness and persistence of the salamander population under certain assumptions. We consider the equilibrium states of the system in the presence or absence of a birth contribution from the terrestrial or metamorph adults. Constant per capita paedomorphosis leads to asymptotically stable equilibria. The per capita paedomorphosis rate of the larvae must be density dependent in order for periodic solutions to exist. Furthermore, the stage transition rate must be sufficiently decreasing in order to guarantee the existence of an unstable equilibrium. Periodic solutions are only possible in the presence of a unique non-trivial unstable equilibrium. Our results conform to previous theory on paedomorphosis which suggests general applicability of our results to similar systems.展开更多
In this paper the existence and stability of the positive equilibrium of the size-structured population model are proved by Rabinowitz's theorem and the local linearization method.The result here shows that near t...In this paper the existence and stability of the positive equilibrium of the size-structured population model are proved by Rabinowitz's theorem and the local linearization method.The result here shows that near the bifurcation point where a branch of positive equilibria appears,the stability of the positive equilibrium on the branch is dcpendent on the direction of the bifurcation.The argument for the model of age-structured population is generalized in this paper.展开更多
基金the National Natural Science Foundation of China(11871185,11401549)and Zhejiang Provin-cial Natural Science Foundation of China(LY18A010010).
文摘We formulate a system of integro-differential equations to model the dynamics of competition in a two-species community,in which the mortality,fertility and growth are sizedependent.Existence and uniqueness of nonnegative solutions to the system are analyzed.The existence of the stationary size distributions is discussed,and the linear stability is investigated by means of the semigroup theory of operators and the characteristic equation technique.Some sufficient conditions for asymptotical stability/instability of steady states are obtained.The resulting conclusion extends some existing results involving age-independent and age-dependent population models.
基金Supported by the National Natural Science Foundation of China(10471108)
文摘In this paper,we consider a nonlinear size-structured population model with functional response,which describes the dynamics of a predator-prey system living in a common habitat.We present a kind of functional response for the prey being a plant or algae,and explain its biological meanings.When the vital rates depend both on the individual's size and on the total population or only depend on the former,we obtain the existence of equilibrium solutions.
基金partially supported by the USDA National Institute of Food and Agriculture,Mc Intire Stennis Project OKL0 3063the Division of Agricultural Sciences and Natural Resources at Oklahoma State Universityprovided by the USDA Forest Service,Research Joint Venture 17-JV-11242306045,Old-Growth Forest Dynamics and Structure,to Mark Ducey
文摘Background: The Chapman-Richards distribution is developed as a special case of the equilibrium solution to the McKendrick-Von Foerster equation. The Chapman-Richards distribution incorporates the vital rate assumptions of the Chapman-Richards growth function, constant mortality and recruitment into the mathematical form of the distribution. Therefore, unlike 'assumed' distribution models, it is intrinsically linked with the underlying vital rates for the forest area under consideration. Methods: It is shown that the Chapman-Richards distribution can be recast as a subset of the generalized beta distribution of the first kind, a rich family of assumed probability distribution models with known properties. These known properties for the generalized beta are then immediately available for the Chapman-Richards distribution, such as the form of the compatible basal area-size distribution. A simple two-stage procedure is proposed for the estimation of the model parameters and simulation experiments are conducted to validate the procedure for four different possible distribution shapes. Results: The simulations explore the efficacy of the two-stage estimation procedure;these cover the estimation of the growth equation and mortality-recruitment derives from the equilibrium assumption. The parameter estimates are shown to depend on both the sample size and the amount of noise imparted to the synthetic measurements. The results vary somewhat by distribution shape, with the smaller, noisier samples providing less reliable estimates of the vital rates and final distribution forms. Conclusions: The Chapman-Richards distribution in its original form, or recast as a generalized beta form, presents a potentially useful model integrating vital rates and stand diameters into a flexible family of resultant distributions shapes. The data requirements are modest, and parameter estimation is straightforward provided the minimal recommended sample sizes are obtained.
基金supported by the National Natural Science Foundation of China(Grant Nos.:11871007,11811530272 and 12071297)the Fundamental Research Funds for the Central Universities.
文摘In this paper,we propose a size-stage-structured cooperation model which has two distinct life stages in facultative cooperator.The primary feature of this model is to consider size structure,stage structure and obligate and facultative symbiosis at the same time in a cooperation system.We use the method of characteristic to show that this new model can be reduced to a threshold delay equations(TDEs)model,which can be further transformed into a functional differential equations(FDEs)model by a simple change of variables.Such simplification allows us to apply the classical theory of FDEs and establish a set of sufficient conditions to investigate the qualitative analysis of solutions of the FDEs model,including the global existence and uniqueness,positivity and boundedness.What's more,we use the geometric criteria to get the conclusions about stability and Hopf bifurcation of positive equilibrium because the coefficients of the characteristic equation depend on the bifurcation parameter.Finally,numerical simulations are carried out as supporting evidences of our analytical results.Our results show that the presence of size structure and stage structure plays an important role in the dynamic behavior of the model.
基金We acknowledge that part of this research has been made possible by support from the Murray State University Center for Institutional Studies and Research and the National Science Foundation （DEB 0109436 and DUE-1028125）.
文摘Cannibalism is widespread in size-structured populations. If cannibals and victims are in different life stages, dominant cohorts of cannibals can regulate recruitment. Arizona Tiger Salamanders, Ambystoma tigrinum nebulosum, exhibit facultative paedomorphosis in which salamander larvae either metamorphose into terrestrial adults or become sexually mature while still in their larval form. Although many salamanders exhibit cannibalism of larvae, the Arizona Tiger Salamander also exhibits cannibalism of young by the aquatic adults. We formulate a differential equations model of this system under the assumption that the terrestrial adults do not impact the system beyond their contribution to the birth of young larvae. We establish non-negativity, boundedness and persistence of the salamander population under certain assumptions. We consider the equilibrium states of the system in the presence or absence of a birth contribution from the terrestrial or metamorph adults. Constant per capita paedomorphosis leads to asymptotically stable equilibria. The per capita paedomorphosis rate of the larvae must be density dependent in order for periodic solutions to exist. Furthermore, the stage transition rate must be sufficiently decreasing in order to guarantee the existence of an unstable equilibrium. Periodic solutions are only possible in the presence of a unique non-trivial unstable equilibrium. Our results conform to previous theory on paedomorphosis which suggests general applicability of our results to similar systems.
文摘In this paper the existence and stability of the positive equilibrium of the size-structured population model are proved by Rabinowitz's theorem and the local linearization method.The result here shows that near the bifurcation point where a branch of positive equilibria appears,the stability of the positive equilibrium on the branch is dcpendent on the direction of the bifurcation.The argument for the model of age-structured population is generalized in this paper.
