Invasion dynamics of epidemic with the Allee effect

Investigating the likely success of epidemic invasion is important in the epidemic management and control. In the present study, the invasion of epidemic is initially introduced to a predator-prey system, both species of which are considered to be subject to the Allee effect. Mathematically, the invasion dynamics is described by three nonlinear diffusion-reaction equations and the spatial implicit and explicit models are designed. By means of extensive numerical simulations, the results of spatial implicit model show that the Allee effect has an opposite impact on the invasion criteria and local dynamics when that on the different species. As the intensity of the Allee effect increases, the domain of epidemic invasion reduces and the system dynamics is changed from the stable state to the limit cycle and finally becomes the chaotic state when the susceptible prey with the Allee effect, but the domain expands and the system dynamics is changed from limit cycle to a table point when the predator is subject to the Allee effect. Results from the spatial explicit model show that the strong intensity of the Allee effect can lead to the catastrophic global extinction of all species in the case of that on the susceptible prey. While the predator with the Allee effect, the increased intensity of which makes spatial species reach a stable state. Furthermore, numerical simulations reveal a certain relationship between the invasion speed and spatial patterns.     

Role of gestation delay in a plankton-fish model under stochastic fluctuations

The present paper studies a minimal prey-predator model in the context of marine plankton interaction together with predation by planktivorous fish. The time lag required for gestation of the predator is incorporated and the resulting delayed model is analyzed for stability and bifurcation phenomena. A stochastic extension of the model is considered by perturbing the growth process of phytoplankton using colored noise process known to be more appropriate for the marine environment. The stochastic models with and without gestation delay are analyzed for stability aspects and a threshold value of gestation delay is obtained; this threshold is then compared with that of the deterministic model.     

Signal transduction and amplification in a circadian oscillator: Interaction between two colored noises

The signal transduction and amplification in a Neurospora circadian clock system is studied by using the mechanism of internal signal stochastic resonance (ISSR). Two cases have been investigated: the case of no correlations between multiplicative and additive colored noises and the case of correlations between two noises. The results show that, in both cases, the noise-induced circadian oscillations can be transduced with the phenomenon of internal signal stochastic resonance (ISSR). However, the correlation time and intensity of an additive colored noise play different roles for the ISSR, driven by multiplicative colored noise, while the correlation time and intensity of multiplicative colored noise hardly influence the ISSR driven by additive colored noise. In addition, the ISSR can be amplified or suppressed at an appropriate range of the correlation intensity between two colored noises. The fundamental frequency of noise-induced circadian oscillations is hardly shifted with the increment of the intensity and correlation time of colored noises, which implies that the Neurospora system could be resistant to colored noises, exhibit strong vitality and sustain intrinsic circadian rhythms.     

Spiking regularity in a noisy small-world neuronal network

The regularity of spiking oscillations is studied in the networks with different topological structures. The network is composed of coupled Fitz-Hugh-Nagumo neurons driven by colored noise. The investigation illustrates that the spike train in both the regular and the Watts-Strogatz small-world neuronal networks can show the best regularity at a moderate noise intensity, indicating the existence of coherence resonance. Moreover, the temporal coherence of the spike train in the small-world network is superior to that in a regular network due to the increase of the randomness of the network topology. Besides the noise intensity, the spiking regularity can be optimized by tuning the randomness of the network topological structure or by tuning the correlation time of the colored noise. In particular, under the cooperation of the small-world topology and the correlation time, the spike train with good regularity could sustain a large magnitude of the local noise.     

生物钟体系中色噪音诱导的日夜节律振荡和内信号随机共振

利用脉孢菌生物钟体系,研究了色噪音对其进行诱导所产生的日夜节律振荡信号及其内信号随机共振的行为．结果表明,色噪音的相关时间对该体系内信号随机共振的强弱起较大的影响作用．当无外信号存在时,色噪音的相关时间对体系内信号随机共振强度起抑制的作用,且随相关时间的增大,抑制作用增强．当外信号加到体系中时,由于相关时间和外信号的协同作用,相关时间不仅对其内信号随机共振强度起抑制的作用,而且还影响内信号随机共振峰的数目,即随相关时间的增大,可使单峰随机共振变为随机双共振．存在最佳的外信号频率使体系的内信号随机共振强度得到最大的增强,而其他频率的外信号却起抑制作用．色内噪音和色外噪音相比,前者对该体系进行诱导所得的内信号随机共振强度比后者的更强,而且体系对前者更敏感．另外,存在极限的噪音强度使白噪音和色噪音对该体系内信号随机共振的影响差异得以消失．所得结果可为治疗生物钟紊乱综合症提供理论依据,同时可更好地理解其他节奏机理,如心脏搏动节奏、呼吸节奏以及荷尔蒙水平的波动节奏等．     

Local genetic adaptation generates latitude‐specific effects of warming on predator–prey interactions

Temperature effects on predator–prey interactions are fundamental to better understand the effects of global warming. Previous studies never considered local adaptation of both predators and prey at different latitudes, and ignored the novel population combinations of the same predator–prey species system that may arise because of northward dispersal. We set up a common garden warming experiment to study predator–prey interactions between Ischnura elegans damselfly predators and Daphnia magna zooplankton prey from three source latitudes spanning >1500 km. Damselfly foraging rates showed thermal plasticity and strong latitudinal differences consistent with adaptation to local time constraints. Relative survival was higher at 24 °C than at 20 °C in southern Daphnia and higher at 20 °C than at 24 °C, in northern Daphnia indicating local thermal adaptation of the Daphnia prey. Yet, this thermal advantage disappeared when they were confronted with the damselfly predators of the same latitude, reflecting also a signal of local thermal adaptation in the damselfly predators. Our results further suggest the invasion success of northward moving predators as well as prey to be latitude‐specific. We advocate the novel common garden experimental approach using predators and prey obtained from natural temperature gradients spanning the predicted temperature increase in the northern populations as a powerful approach to gain mechanistic insights into how community modules will be affected by global warming. It can be used as a space‐for‐time substitution to inform how predator–prey interaction may gradually evolve to long‐term warming.     

Aperiodic stochastic resonance in neural information processing with Gaussian colored noise

The aim of this paper is to explore the phenomenon of aperiodic stochastic resonance in neural systems with colored noise. For nonlinear dynamical systems driven by Gaussian colored noise, we prove that the stochastic sample trajectory can converge to the corresponding deterministic trajectory as noise intensity tends to zero in mean square, under global and local Lipschitz conditions, respectively. Then, following forbidden interval theorem we predict the phenomenon of aperiodic stochastic resonance in bistable and excitable neural systems. Two neuron models are further used to verify the theoretical prediction. Moreover, we disclose the phenomenon of aperiodic stochastic resonance induced by correlation time and this finding suggests that adjusting noise correlation might be a biologically more plausible mechanism in neural signal processing.     

Dynamics of a plant-herbivore-predator system with plant-toxicity

A system of ordinary differential equations is considered that models the interactions of two plant species populations, an herbivore population, and a predator population. We use a toxin-determined functional response to describe the interactions between plant species and herbivores and use a Holling Type II functional response to model the interactions between herbivores and predators. In order to study how the predators impact the succession of vegetation, we derive invasion conditions under which a plant species can invade into an environment in which another plant species is co-existing with a herbivore population with or without a predator population. These conditions provide threshold quantities for several parameters that may play a key role in the dynamics of the system. Numerical simulations are conducted to reinforce the analytical results. This model can be applied to a boreal ecosystem trophic chain to examine the possible cascading effects of predator-control actions when plant species differ in their levels of toxic defense.     

Spatiotemporal complexity of biological invasion in a space- and time-discrete predator–prey system with the strong Allee effect

Understanding dynamical complexity of alien species invasion is an important and timely issue as it is believed that identification of possible invasion scenarios may result in a more effective invasive species management and control. To address this issue, mathematical modeling is widely recognized as a convenient theoretical tool as it often helps to reveal generic tendencies in a situation when it would hardly be possible otherwise. However, although much attention has been paid to spatially continuous models of biological invasion, spatially discrete models have remained outside of the mainstream. Meanwhile, species habitat is often distinctly patchy or even fragmented, and then spatially discrete models seems to be the most appropriate modeling framework. In this paper, we consider invasion scenarios in a space- and time-discrete system described by a coupled map lattice. The alien species is assumed to be affected by the strong Allee effect and by a specialist predator. We first consider the stage of species introduction and obtain analytical conditions to distinguish between invasion success and invasion failure. We then focus on species spatial spread. By means of extensive computer simulations, we identify the main scenarios of species spread (e.g. patchy invasion and multiple traveling bands) and reveal the corresponding structure of the parameter space. Counter-intuitively, we have found that alien species can invade over the whole domain even in the case when its local persistence would not be possible.     

Spatial dynamics of specialist seed predators on synchronized and intermittent seed production of host plants

Masting, the synchronized and intermittent seed production by plant populations, provides highly variable food resources for specialist seed predators. Such a reproductive mode helps minimize seed losses through predator satiation and extinction of seed predator populations. The seed predators can buffer the resource variation through dispersal or extended diapause. We developed a spatially explicit resource-consumer model to understand the effect of masting on specialist seed predators. The masting dynamics were assumed to follow a resource-based model for plant reproduction, and the population dynamics of the predator were represented by a spatially extended Nicholson-Bailey model. The resultant model demonstrated that when host plants reproduce intermittently, seed predator populations go locally extinct, but global persistence of the predator is facilitated by dispersal or extended diapause. Global extinction of the predator resulted when the intermittent reproduction is highly synchronized among plants. An approximate invasion criterion for the predators showed that negative lag-1 autocorrelation in seeding reduces invasibility, and positive lag-1 cross-correlation enhances invasibility. Spatial synchronization in seeding at local scale caused by pollen coupling (or climate forcing) further prevented invasion of the predators. If the predators employed extended diapause, extremely high temporal variability in reproduction was required for plants to evade the predators.     

Invasion Waves in Populations with Excitable Dynamics

Whilst the most obvious mechanism for a biological invasion is the occupation of a new territory as a result of direct ingress by individuals of the invading population, a more subtle “invasion” may occur without significant motion of invading individuals if the population dynamics in a predator prey scenario has an “excitable” character. Here, “excitable” means that a local equilibrium state, either of coexistence of predator and prey, or of prey only, may, when disturbed by a small perturbation, switch to a new, essentially invaded state. In an invasion of this type little spatial movement of individuals occurs, but a wave of rapid change of population level nevertheless travels through the invaded territory. In this article we summarise and review recent modelling research which shows that the macroscopic features of these invasion waves depend strongly on the detailed spatial dynamics of the predator–prey relationship; the models assume simple (linear) diffusion and pursuit-evasion, represented by (non-linear) cross-diffusion, as examples. In the context of plankton population dynamics, such waves may be produced by sudden injections of nutrient and consequent rapid increase in plankton populations, brought about, for example, by the upwelling caused by a passing atmospheric low pressure system.     

Patterns of Patchy Spread in Deterministic and Stochastic Models of Biological Invasion and Biological Control

A few spatiotemporal models of population dynamics are considered in relation to biological invasion and biological control. The patterns of spread in one and two spatial dimensions are studied by means of extensive numerical simulations. We show that, in the case that population multiplication is damped by the strong Allee effect (when the population growth rate becomes negative for small population density), in a certain parameter range the spread can take place not via the intuitively expected circular expanding population front but via motion and interaction of separate patches. Alternatively, the patchy spread can take place in a system without Allee effect as a result of strong environmental noise. We then show that the phenomenon of deterministic patchy invasion takes place ‘at the edge of extinction’ so that a small change of controlling parameters either brings the species to extinction or restores the travelling population fronts. Moreover, we show that the regime of patchy invasion in two spatial dimensions actually takes place when the species go extinct in the corresponding 1-D system.     

Inhibition of rhythmic spiking by colored noise in neural systems

We study the effect of colored noise on the rhythmic spiking activity of neural systems in this paper. The phenomenon of the so-called inverse stochastic resonance , that is, noise with appropriate intensity suppresses the spiking activity in neural systems, is clearly observed in a special parameter regime. We find that the inhibition effect of colored noise is stronger than that of Gaussian white noise. Furthermore, our simulation results show that the inhibition effect of colored noise provides a useful mechanism for the generation of synchronized burst in type-2 mixed-feed-forward-feedback loop neuronal network motif, which indicates that such inhibition effect might have some biological implications.     

The Interplay of Intrinsic and Extrinsic Bounded Noises in Biomolecular Networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a biomolecular network. The influence of intrinsic and extrinsic noises on biomolecular networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, a model of enzymatic futile cycle and a genetic toggle switch. In and we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possible functional role of bounded noises.     

萼花臂尾轮虫对晶囊轮虫反捕食行为及形态响应的母体效应

为研究轮虫通过母体效应诱导能否产生行为响应, 以萼花臂尾轮虫(Brachionus calyciflorus)为例, 研究其反捕食漂浮行为响应的母体效应。通过控制轮虫母体在捕食者诱导液中的暴露时间及带卵状态, 收集母体产生的后代, 再将这些后代再次用捕食者诱导液处理, 观察后代的漂浮行为及形态特征。研究发现: 暴露于捕食者诱导液诱导较长时间的母体产生的后代个体, 当再次暴露于捕食者诱导液时, 其产生的行为响应强于没有母体暴露经历的后代; 母体暴露时间越长, 后代形态和行为响应均更加强烈。研究显示萼花臂尾轮虫可通过母体效应产生漂浮行为响应。     

Eating the competition speeds up invasions

Many introduced species engage in intraguild predation (IGP), the consumption of species with which they compete for shared resources. While the factors influencing local persistence of IG predator and prey species are well-understood, using these factors to predict the invasion speed of an introduced IG predator has received less attention. Existing theory predicts that native competitors slow invasions via depletion of shared resources, but this fails to account for additional resources acquired when an invader consumes competitors. Here, I outline a general framework for understanding the effect of IGP on invasion speeds. I find that invaders that consume native competitors may be able to spread where invasion by pure competitors would fail, and that invasion speed increases with increasing levels of IGP. Notably, if the benefit from consuming competitors outweighs the loss of shared resources to competitors, invasion proceeds faster than invasion in the absence of competitors. This may explain empirical observations of rapid spread rates of invaders that feed at multiple trophic levels.     

Invasive plants may promote predator‐mediated feedback that inhibits further invasion

Understanding the impacts of invasive species requires placing invasion within a full community context. Plant invaders are often considered in the context of herbivores that may drive invasion by avoiding invaders while consuming natives (enemy escape), or inhibit invasion by consuming invaders (biotic resistance). However, predators that attack those herbivores are rarely considered as major players in invasion. Invasive plants often promote predators, generally by providing improved habitat. Here, we show that predator‐promoting invaders may initiate a negative feedback loop that inhibits invasion. By enabling top‐down control of herbivores, predator‐promoting invaders lose any advantage gained through enemy escape, indirectly favoring natives. In cases where palatable invaders encounter biotic resistance, predator promotion may allow an invader to persist, but not dominate. Overall, results indicate that placing invaders in a full community context may reveal reduced impacts of invaders compared to expectations based on simple plant–plant or plant–herbivore subsystems.     

Regimes of biological invasion in a predator-prey system with the Allee effect

Spatiotemporal dynamics of a predator-prey system is considered under the assumption that prey growth is damped by the strong Allee effect. Mathematically, the model consists of two coupled diffusion-reaction equations. The initial conditions are described by functions of finite support which corresponds to invasion of exotic species. By means of extensive numerical simulations, we identify the main scenarios of the system dynamics as related to biological invasion. We construct the maps in the parameter space of the system with different domains corresponding to different invasion regimes and show that the impact of the Allee effect essentially increases the system spatiotemporal complexity. In particular, we show that, as a result of the interplay between the Allee effect and predation, successful establishment of exotic species may not necessarily lead to geographical spread and geographical spread does not always enhance regional persistence of invading species.     

Multiple Roles of Tail Display by the Curly-Tailed Lizard Leiocephalus carinatus: Pursuit Deterrent and Deflective Roles of a Social Signal

The same display may be used in different contexts to convey different messages, or may have other, non-signaling functions. Several lines of evidence suggest that vertical tail curling, a previously documented social display in the lizard Leiocephalus carinatus , has antipredatory functions that may include pursuit deterrence and deflection of attacks from the body to the tail, which can be autotomized. An antipredatory role of tail curling is suggested by its more frequent occurrence when a predator is approaching than moving away, its greater frequency and intensity when a lizard is approached by a predator than when it moves spontaneously, and its greater frequency when the predator approaches directly rather than on a path bypassing the lizard. Evidence is presented contradicting use of tail curling for flash concealment or as an alarm signal to conspecifics. A pursuit-deterrent function of tail curling is suggested by its (1) more frequent use by lizards close to a refuge than those further from a refuge, (2) greater frequency during direct approaches by predators, and (3) much greater frequency when a predator is far enough away for pursuit to be deterred than when the predator is close enough to pose a high risk of capture. Lizards fled into a refuge without tail curling when the predator was very close, but often stopped outside a refuge while displaying the curled tail when the predator was farther away. Tail curling also may deflect attacks to the autotomizable tail, as suggested by its occurrence during spontaneous movements when no predator is approaching and by the high frequency of completely uncurled tails among individuals under bushes. The role of the tail in autotomy may facilitate evolution of pursuit-deterrent signals involving the tail.     

Generating conservation kernels to select areas to control red fox (Vulpes vulpes): Potential implications for pest management practice in state forests

Summary In Australia, controlling introduced predators across large areas is unlikely to be successful without careful consideration of the predator's ecology, the economics of the control exercise and the distribution of the taxa to be protected from the predator. Inadequate strategic planning in pest control is commonplace and there is a need for better methods for determining where, when and how to control predators. The present paper describes a method (currently being introduced into planning programmes) of using areas of high prey species integrity (conservation kernels) to identify strategically optimal areas for predator control (particularly Red Fox, Vulpes vulpes ), across broad landscapes. These landscapes are selected using a geographical information system and a combination of predictive habitat models and records of threatened species at risk of predation by the Red Fox, to identify sites of biological wealth. We propose this method as a first step in developing a strategic predator control plan.