Rapid evolution drives ecological dynamics in a predator-prey system

Ecological and evolutionary dynamics can occur on similar timescales. However, theoretical predictions of how rapid evolution can affect ecological dynamics are inconclusive and often depend on untested model assumptions. Here we report that rapid prey evolution in response to oscillating predator density affects predator-prey (rotifer-algal) cycles in laboratory microcosms. Our experiments tested explicit predictions from a model for our system that allows prey evolution. We verified the predicted existence of an evolutionary tradeoff between algal competitive ability and defence against consumption, and examined its effects on cycle dynamics by manipulating the evolutionary potential of the prey population. Single-clone algal cultures (lacking genetic variability) produced short cycle periods and typical quarter-period phase lags between prey and predator densities, whereas multi-clonal (genetically variable) algal cultures produced long cycles with prey and predator densities nearly out of phase, exactly as predicted. These results confirm that prey evolution can substantially alter predator-prey dynamics, and therefore that attempts to understand population oscillations in nature cannot neglect potential effects from ongoing rapid evolution.     

Invasion sequence affects predator-prey dynamics in a multi-species interaction

Ecologists seek to understand the rules that govern the assembly, coexistence and persistence of communities of interacting species. There is, however, a variety of sequences in which a multi-species community can be assembled--unlike more familiar one- and two-species systems. Ecological systems can exhibit contrasting dynamics depending on initial conditions, but studies have been focused on simple communities initiated at different densities, not on multi-species communities constructed in different sequences. Investigations of permanence and convergence in ecological communities have been concerned with the flux of whole species (presence or absence) but have not addressed the central issues concerning the dynamics exhibited by individual species in particular interactions. Here we examine data for replicated three-species systems and demonstrate that the dynamic trajectories of both a predator and its prey within the system are determined by the sequence in which it is constructed, and that for one construction-sequence alternative dynamic patterns are possible.     

一类非局部时滞捕食者-食饵扩散模型的空间动力学

考虑一类带阶段结构的扩散捕食者食饵模型,其中食饵个体经历两个生命阶段,未成熟和成熟阶段,捕食者生物量的转化有一个延迟,食饵生物量的增长遵循一般化的Beverton-Holt函数.就非局部椭圆特征问题的主特征值,建立一致持久性与全局灭绝性.利用波动方法,给出唯一正常数稳态解的全局吸引性.     

The central nervous system stabilizes unstable dynamics by learning optimal impedance.

To manipulate objects or to use tools we must compensate for any forces arising from interaction with the physical environment. Recent studies indicate that this compensation is achieved by learning an internal model of the dynamics, that is, a neural representation of the relation between motor command and movement. In these studies interaction with the physical environment was stable, but many common tasks are intrinsically unstable. For example, keeping a screwdriver in the slot of a screw is unstable because excessive force parallel to the slot can cause the screwdriver to slip and because misdirected force can cause loss of contact between the screwdriver and the screw. Stability may be dependent on the control of mechanical impedance in the human arm because mechanical impedance can generate forces which resist destabilizing motion. Here we examined arm movements in an unstable dynamic environment created by a robotic interface. Our results show that humans learn to stabilize unstable dynamics using the skillful and energy-efficient strategy of selective control of impedance geometry.     

一类带有阶段结构捕食系统

讨论一类对食饵分阶段，带有比率依赖的捕食动力学系统，论述了该系统的持久生存．通过构造李雅普诺夫函数，又分别获得了正平衡点及边界平衡点的局部和全局的渐近稳定性．     

一类捕食-食饵模型的共存性

研究了一类具有一般形式反应函数的捕食-食饵模型的正解.给出了正解的先验估计,利用不动点指标原理讨论了正解的存在性.通过计算degW′(I-F,D)、indexW′(F,(0,0))和indexW′(F,(θ,0)),得出食饵和捕食者可以共存当且仅当捕食者的死亡率c控制在下限-d2λ0和上限-λ1(d2,-efv(θ,0))之间,且食饵的固有增长率超过d1λ0.     

一类具Beddington-DeAngelis功能性反应捕食系统的持久性

研究一类具有时滞和阶段结构的Beddington-DeAngelis功能性反应食饵-捕食模型,应用微分方程比较原理得到了保证该系统持续生存的充分性条件.     

Tension directly stabilizes reconstituted kinetochore-microtubule attachments

Kinetochores are macromolecular machines that couple chromosomes to dynamic microtubule tips during cell division, thereby generating force to segregate the chromosomes. Accurate segregation depends on selective stabilization of correct 'bi-oriented' kinetochore-microtubule attachments, which come under tension as the result of opposing forces exerted by microtubules. Tension is thought to stabilize these bi-oriented attachments indirectly, by suppressing the destabilizing activity of a kinase, Aurora B. However, a complete mechanistic understanding of the role of tension requires reconstitution of kinetochore-microtubule attachments for biochemical and biophysical analyses in vitro. Here we show that native kinetochore particles retaining the majority of kinetochore proteins can be purified from budding yeast and used to reconstitute dynamic microtubule attachments. Individual kinetochore particles maintain load-bearing associations with assembling and disassembling ends of single microtubules for >30?min, providing a close match to the persistent coupling seen in vivo between budding yeast kinetochores and single microtubules. Moreover, tension increases the lifetimes of the reconstituted attachments directly, through a catch bond-like mechanism that does not require Aurora B. On the basis of these findings, we propose that tension selectively stabilizes proper kinetochore-microtubule attachments in vivo through a combination of direct mechanical stabilization and tension-dependent phosphoregulation.     

一类捕食-被捕食系统的鞍结点分支

文章讨论了一类捕食种群和被捕食种群都有密度制约和Holling 型功能性反应的捕食-被捕食系统。给出了系统的奇点个数及其稳定性的变化情况,证明了该系统在给定条件下在第一象限内可能由一个奇点变为两个奇点或奇点消失,即存在鞍结点分支。     

一类中立型捕食系统的Hopf分支

对一类中立型的捕食与被捕食系统,通过讨论线性近似系统的特征方程根的分布,得到了正平衡点的稳定性及Hopf分支的存在性.     

一类三次捕食者-食饵扩散系统的稳定性

引进一类三次捕食者一食饵模型,该模型是两种群Lotka-Volterra扩散系统的推广．应用线性化方法和Lyapunov泛函方法讨论该模型非负平衡点的稳定性．     

一类被开发的两种群捕食模型的定性分析

讨论了一类食饵种群被开发的两种群捕食系统.运用定性分析和分支方法给出了该系统极限环的不存在性、存在性和惟一性等结论,并对相应的生态学意义作了说明.     

具有时滞的食饵-捕食者模型的分支分析(英文)

研究一类具有时滞和比率依赖型功能反应函数的食饵-捕食者模型,通过局部和Hopf分支分析考察其动力学特性,分析其对应的特征方程,研究模型的线性稳定性和Hopf分支.同时得到了系统正平衡点稳定的时滞范围,给出数值模拟验证了所得结果的正确性.最后给出主要结论.     

一类具有扩散的捕食系统的持久性

研究了一类具有Michaclis-menten型反应函数的扩散系统的持久性问题,利用比较原理,得到了系统一致持久的充分条件.     

一类捕食-食饵模型解的存在性

研究了一类具有避难所的两物种间的捕食-食饵模型在齐次Direchlet边界条件下的平衡态正解的存在性,其功能反应函数为Holling Ⅱ型.利用不动点指标理论得到系统正解存在的充分条件α/d1>λ1,-r/d2>λ1((-cβmθ)/(d2(1+amθ))).     

非自治捕食-食饵扩散系统的渐近性质

讨论了一个非自治具有第Ⅱ类功能性反应函数的两种群捕食食饵系统,一个种群可以在两个斑块间扩散,另一种群限制在一个斑块上．证明了在适当条件下,系统是永久持续生存的;若系统是周期系统,则在适当条件下,该系统存在惟一的全局吸引的正周期解．     

Transmitter-evoked local calcium release stabilizes developing dendrites

In the central nervous system, dendritic arborizations of neurons undergo dynamic structural remodelling during development. Processes are elaborated, maintained or eliminated to attain the adult pattern of synaptic connections. Although neuronal activity influences this remodelling, it is not known how activity exerts its effects. Here we show that neurotransmission-evoked calcium (Ca(2+)) release from intracellular stores stabilizes dendrites during the period of synapse formation. Using a ballistic labelling method to load cells with Ca(2+) indicator dyes, we simultaneously monitored dendritic activity and structure in the intact retina. Two distinct patterns of spontaneous Ca(2+) increases occurred in developing retinal ganglion cells--global increases throughout the arborization, and local 'flashes' of activity restricted to small dendritic segments. Blockade of local, but not global, activity caused rapid retraction of dendrites. This retraction was prevented locally by focal uncaging of caged Ca(2+) that triggered Ca(2+) release from internal stores. Thus, local Ca(2+) release is a mechanism by which afferent activity can selectively and differentially regulate dendritic structure across the developing arborization.     

非自治比率依赖型捕食-食饵系统的定性分析

对一类具有HollingⅢ类功能性反应的非自治比率依赖型捕食-食饵系统进行了定性分析.详细考察了系统的正不变性、最终有界性、非持续生存、持久性、灭绝性及全局渐近稳定性.     

具有阶段结构的捕食——食饵模型

构造了一个具有阶段结构的捕食-食饵模型,并研究了庇护所效应对于该系统平衡点的稳定性、平衡密度及其种群长期续存的影响.结果表明庇护所效应不仅能够增加猎物种群的密度,并且在一定条件下也能增加捕食者种群的平衡密度,还会增加系统的稳定性.