A minimal model of predator–swarm interactions

We propose a minimal model of predator–swarm interactions which captures many of the essential dynamics observed in nature. Different outcomes are observed depending on the predator strength. For a ‘weak’ predator, the swarm is able to escape the predator completely. As the strength is increased, the predator is able to catch up with the swarm as a whole, but the individual prey is able to escape by ‘confusing’ the predator: the prey forms a ring with the predator at the centre. For higher predator strength, complex chasing dynamics are observed which can become chaotic. For even higher strength, the predator is able to successfully capture the prey. Our model is simple enough to be amenable to a full mathematical analysis, which is used to predict the shape of the swarm as well as the resulting predator–prey dynamics as a function of model parameters. We show that, as the predator strength is increased, there is a transition (owing to a Hopf bifurcation) from confusion state to chasing dynamics, and we compute the threshold analytically. Our analysis indicates that the swarming behaviour is not helpful in avoiding the predator, suggesting that there are other reasons why the species may swarm. The complex shape of the swarm in our model during the chasing dynamics is similar to the shape of a flock of sheep avoiding a shepherd.     

Ambush frequency should increase over time during optimal predator search for prey

We advance and apply the mathematical theory of search games to model the problem faced by a predator searching for prey. Two search modes are available: ambush and cruising search. Some species can adopt either mode, with their choice at a given time traditionally explained in terms of varying habitat and physiological conditions. We present an additional explanation of the observed predator alternation between these search modes, which is based on the dynamical nature of the search game they are playing: the possibility of ambush decreases the propensity of the prey to frequently change locations and thereby renders it more susceptible to the systematic cruising search portion of the strategy. This heuristic explanation is supported by showing that in a new idealized search game where the predator is allowed to ambush or search at any time, and the prey can change locations at intermittent times, optimal predator play requires an alternation (or mixture) over time of ambush and cruise search. Thus, our game is an extension of the well-studied ‘Princess and Monster’ search game. Search games are zero sum games, where the pay-off is the capture time and neither the Searcher nor the Hider knows the location of the other. We are able to determine the optimal mixture of the search modes when the predator uses a mixture which is constant over time, and also to determine how the mode mixture changes over time when dynamic strategies are allowed (the ambush probability increases over time). In particular, we establish the ‘square root law of search predation’: the optimal proportion of active search equals the square root of the fraction of the region that has not yet been explored.     

Succession of hide–seek and pursuit–evasion at heterogeneous locations

Many interactions between searching agents and their elusive targets are composed of a succession of steps, whether in the context of immune systems, predation or counterterrorism. In the simplest case, a two-step process starts with a search-and-hide phase, also called a hide-and-seek phase, followed by a round of pursuit–escape. Our aim is to link these two processes, usually analysed separately and with different models, in a single game theory context. We define a matrix game in which a searcher looks at a fixed number of discrete locations only once each searching for a hider, which can escape with varying probabilities according to its location. The value of the game is the overall probability of capture after k looks. The optimal search and hide strategies are described. If a searcher looks only once into any of the locations, an optimal hider chooses it''s hiding place so as to make all locations equally attractive. This optimal strategy remains true as long as the number of looks is below an easily calculated threshold; however, above this threshold, the optimal position for the hider is where it has the highest probability of escaping once spotted.     

Hydrodynamics of prey capture in sharks: effects of substrate

In suction feeding, a volume of water is drawn into the mouth of a predator. Previous studies of suction feeding in fishes have shown that significant fluid velocities are confined to a region within one mouth width from the mouth. Therefore, the predator must be relatively close to the prey to ensure capture success. Here, theoretical modelling is combined with empirical data to unravel the mechanism behind feeding on a substrate. First, we approached the problem theoretically by combining the stream functions of two sinks. Computational fluid dynamics modelling is then applied to make quantitative predictions regarding the effects of substrate proximity on the feeding hydrodynamics of a benthic shark. An oblique circular cylinder and a shark head model were used. To test the models, we used digital particle image velocimetry to record fluid flow around the mouth of white-spotted bamboo sharks, Chiloscyllium plagiosum, during suction feeding on the substrate and in the water column. Empirical results confirmed the modelling predictions: the length of the flow field can be doubled due to passive substrate effects during prey capture. Feeding near a substrate extends the distance over which suction is effective and a predator strike can be effective further from the prey.     

Age-structured predator–prey model with habitat complexity: oscillations and control

In this article, we study a predator–prey interaction in a homogeneously complex habitat where predator takes a fixed time to develop from immature to its mature stage. The age-structure of the predator and its interaction with the prey is framed in a system of delay differential equations. The objective is to study the role of habitat complexity and the maturation delay of the predator on the overall dynamics of the model system. Different interesting dynamical behaviours can be obtained by regulating two key parameters, namely the degree of habitat complexity and the maturation delay. It is observed that the system becomes unstable from its stable condition when the maturation delay crosses some critical value. The periodic solutions bifurcated from the interior equilibrium is found to be supercritical and stable. Synchronization of population fluctuations is, however, possible by increasing the strength of habitat complexity. The predator population goes to extinction and the prey population reaches to its maximum, irrespective of the length of maturation delay, when the habitat complexity crosses some upper critical value. The qualitative dynamical behaviours of the model system are verified with the data of Paramecium aurelia (prey) and Didinium nasutum (predator) interaction.     

具有时滞和脉冲捕获、污染物脉冲输入的捕食-食饵-环境模型

本文建立了污染环境中,捕食者具有阶段结构、食饵具有脉冲收获、污染物具有脉冲输入的时滞捕食-食饵-环境模型,利用离散动力系统的频闪映射和比较原理,得到了捕食者灭绝周期解的全局吸引性和系统持久性的充分条件．通过数值仿真,研究了食饵的捕获、污染物的脉冲输入和脉冲作用周期对捕食者灭绝和持续生存的影响,同时也验证了理论结果．对生物资源的开发、种群数量的收获及环境的控制提供了宝贵的理论依据．     

Deterministic and Stochastic Fractional-Order Hastings-Powell Food Chain Model

In this paper, a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed. The interaction between prey, middle predator and top predator population is investigated. In order to clarify the characteristics of the proposed model, the analysis of existence, uniqueness, non-negativity and boundedness of the solutions of the proposed model are examined. Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained. By using stability analysis of the fractional-order system, it is proved that if the basic reproduction number , the predator free equilibrium point is globally asymptotically stable. The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem. Some numerical examples are given to illustrate the theoretical findings. The impact of harvesting on prey and the middle predator is studied. We conclude that harvesting parameters can control the dynamics of the middle predator. A numerical approximation method is developed for the proposed stochastic fractional-order model.     

Volumetric quantification of fluid flow reveals fish's use of hydrodynamic stealth to capture evasive prey

In aquatic ecosystems, predation on zooplankton by fish provides a major pathway for the transfer of energy to higher trophic levels. Copepods are an abundant zooplankton group that sense hydromechanical disturbances produced by approaching predators and respond with rapid escapes. Despite this capability, fish capture copepods with high success. Previous studies have focused on the predatory strike to elucidate details of this interaction. However, these raptorial strikes and resulting suction are only effective at short range. Thus, small fish must closely approach highly sensitive prey without triggering an escape in order for a strike to be successful. We use a new method, high-speed, infrared, tomographic particle image velocimetry, to investigate three-dimensional fluid patterns around predator and prey during approaches. Our results show that at least one planktivorous fish (Danio rerio) can control the bow wave in front of the head during the approach and consumption of prey (copepod). This alters hydrodynamic profiles at the location of the copepod such that it is below the threshold required to elicit an escape response. We find this behaviour to be mediated by the generation of suction within the buccopharyngeal cavity, where the velocity into the mouth roughly matches the forward speed of the fish. These results provide insight into how animals modulate aspects of fluid motion around their bodies to overcome escape responses and enhance prey capture.     

Predator confusion is sufficient to evolve swarming behaviour

Swarming behaviours in animals have been extensively studied owing to their implications for the evolution of cooperation, social cognition and predator–prey dynamics. An important goal of these studies is discerning which evolutionary pressures favour the formation of swarms. One hypothesis is that swarms arise because the presence of multiple moving prey in swarms causes confusion for attacking predators, but it remains unclear how important this selective force is. Using an evolutionary model of a predator–prey system, we show that predator confusion provides a sufficient selection pressure to evolve swarming behaviour in prey. Furthermore, we demonstrate that the evolutionary effect of predator confusion on prey could in turn exert pressure on the structure of the predator''s visual field, favouring the frontally oriented, high-resolution visual systems commonly observed in predators that feed on swarming animals. Finally, we provide evidence that when prey evolve swarming in response to predator confusion, there is a change in the shape of the functional response curve describing the predator''s consumption rate as prey density increases. Thus, we show that a relatively simple perceptual constraint—predator confusion—could have pervasive evolutionary effects on prey behaviour, predator sensory mechanisms and the ecological interactions between predators and prey.     

Relative importance of growth and behaviour to elasmobranch suction-feeding performance over early ontogeny.

Development of the ability to capture prey is crucial to predator survival. Trends in food-capture performance over early ontogeny were quantified for leopard sharks Triakis semifasciata and whitespotted bamboosharks Chiloscyllium plagiosum by measuring suction pressure and flow in front of the mouth during feeding. At any size, C. plagiosum produce greater subambient pressure and ingest more rounded water parcels. Maximum subambient pressure scaled with negative allometry in T. semifasciata and was accompanied by an increase in the time to reach maximum gape. Despite a similar trend in buccal expansion timing, maximum pressure in C. plagiosum scaled with isometry and was accompanied by an earlier onset of hyoid depression and a positive allometric increase in buccal reserve volume. Growth was the primary factor responsible for developmental trends in both species, with size-independent behavioural changes contributing little to overall performance variability. Ontogenetic dietary shifts are predicted for both species as a consequence of size-dependent changes in performance. Chiloscyllium plagiosum becomes anatomically and behaviourally canalized towards suction feeding, limiting the effective range of prey capture and possibly necessitating stalking. Triakis semifasciata, by contrast, retains the flexibility to employ both ram and suction and therefore captures more elusive prey with age.     

Biomagnification of cadmium selenide quantum dots in a simple experimental microbial food chain

Previous studies have shown that engineered nanomaterials can be transferred from prey to predator, but the ecological impacts of this are mostly unknown. In particular, it is not known if these materials can be biomagnified-a process in which higher concentrations of materials accumulate in organisms higher up in the food chain. Here, we show that bare CdSe quantum dots that have accumulated in Pseudomonas aeruginosa bacteria can be transferred to and biomagnified in the Tetrahymena thermophila protozoa that prey on the bacteria. Cadmium concentrations in the protozoa predator were approximately five times higher than their bacterial prey. Quantum-dot-treated bacteria were differentially toxic to the protozoa, in that they inhibited their own digestion in the protozoan food vacuoles. Because the protozoa did not lyse, largely intact quantum dots remain available to higher trophic levels. The observed biomagnification from bacterial prey is significant because bacteria are at the base of environmental food webs. Our findings illustrate the potential for biomagnification as an ecological impact of nanomaterials.     

Modelled three-dimensional suction accuracy predicts prey capture success in three species of centrarchid fishes

Prey capture is critical for survival, and differences in correctly positioning and timing a strike (accuracy) are likely related to variation in capture success. However, an ability to quantify accuracy under natural conditions, particularly for fishes, is lacking. We developed a predictive model of suction hydrodynamics and applied it to natural behaviours using three-dimensional kinematics of three centrarchid fishes capturing evasive and non-evasive prey. A spheroid ingested volume of water (IVW) with dimensions predicted by peak gape and ram speed was verified with known hydrodynamics for two species. Differences in capture success occurred primarily with evasive prey (64–96% success). Micropterus salmoides had the greatest ram and gape when capturing evasive prey, resulting in the largest and most elongate IVW. Accuracy predicted capture success, although other factors may also be important. The lower accuracy previously observed in M. salmoides was not replicated, but this is likely due to more natural conditions in our study. Additionally, we discuss the role of modulation and integrated behaviours in shaping the IVW and determining accuracy. With our model, accuracy is a more accessible performance measure for suction-feeding fishes, which can be used to explore macroevolutionary patterns of prey capture evolution.     

A Two-Patch Predator-Prey Metapopulation Model

A minimal model for predator-prey interaction in a composite environment is presented and analysed. We first consider free migrations between two patches for both interacting populations, and then the particular cases where only one-directional migration is allowed and where only one of the two populations can migrate. Our findings indicate that in all cases the ecosystem can never disappear entirely, under the model assumptions. The predator-free equilibrium and the coexistence of all populations are found to be the only feasible stable equilibria. When there are only one-directional migrations, the abandoned patch cannot be repopulated. Other equilibria then arise, with only prey in the second patch, coexistence in the second patch, or prey in both patches but predators only in the second one. For the case of sedentary prey, with predator migration, the prey cannot thrive alone in either of the two environments. However, predators can survive in a prey-free patch due to their ability to migrate into the other patch, provided prey is present there. If only the prey can migrate, the predators may be eliminated from one patch or from both. In the first case, the patch where there are no predators acts as a refuge for the survival of the prey.     

Identification of Factors Governing Mechanical Properties of TRIP-Aided Steel Using Genetic Algorithms and Neural Networks

Mechanical properties of transformation induced plasticity (TRIP)-aided multiphase steels are modeled by neural networks using two methods of reducing the network connectivity, viz. a pruning algorithm and a predator prey algorithm, to gain understanding on the impact of steel composition and treatment. The pruning algorithm gradually reduces the complexity of the lower layer of connections, removing less significant connections. In the predator prey algorithm, a genetic algorithm based multi-objective optimization technique evolves neural networks on a Pareto front, simultaneously minimizing training error and network size. The results show that the techniques find parsimonious models and, furthermore, extract useful knowledge from the data.     

On Grey Relation Projection Model Based On Projection Pursuit

Multidimensional grey relation projection value can be synthesized as one-dimensional projection value by using projection pursuit model. The larger the projection value is, the better the model. Thus, according to the projection value, the best one can be chosen from the model aggregation. Because projection pursuit modeling based on accelerating genetic algorithm can simplify the implementation procedure of the projection pursuit technique and overcome its complex calculation as well as the difficulty in implementing its program, a new method can be obtained for choosing the best grey relation projection model based on the projection pursuit technique.     

The smaller your mouth, the longer your snout: predicting the snout length of Syngnathus acus, Centriscus scutatus and other pipette feeders

Like most ray-finned fishes (Actinopterygii), pipefishes (Syngnathoidei) feed by suction. Most pipefishes reach their prey by a rapid dorso-rotation of the head. In the present study, we analysed the feeding kinematics of the razor fish, Centriscus scutatus, and of the greater pipefish, Syngnathus acus in detail. We found capture times of as little as 4-6ms for C. scutatus and 6-8ms for S. acus. We then hypothesized that the long snout of pipefishes is optimal for such fast feeding. To test this, we implemented in a mathematical model the following considerations. To reach the prey as fast as possible, a low moment of inertia increases the head's angular speed, whereas a long snout decreases the angle over which the head must be turned. The model accurately predicted the snout lengths of a number of pipefishes. We found that the optimal snout length, with which a prey will be reached fastest, is inversely related to its cross-section. In spite of the small cross-section, the development of a long snout can be an evolutionary advantage because this reduces the time to approach the prey.     

The forces exerted by aquatic suction feeders on their prey

Successful prey capture by aquatic suction feeders depends on the ability of the predator to generate a flow of water external to the mouth that overcomes any movements and forces that the prey uses to resist the suction flow. Elucidating the nature and magnitude of these forces is a key to understanding what limits suction feeding performance. We identify three potential forces produced by the suction flow field: drag, acceleration reaction and the fluid pressure gradient. Using a mathematical model parametrized with empirical data from feeding bluegill, Lepomis macrochirus, we explore the relative magnitude of these forces under three encounter scenarios with a 5mm diameter, spherical prey: an immobile mid-water prey; a similar prey that executes an escape response; and a prey item that grips a substratum. Contrary to the almost exclusive emphasis on drag in the suction feeding literature, it made a minor contribution to the total forces in all three cases. In all three scenarios, the pressure gradient is the largest of the three forces. These results are important because previous researchers have emphasized drag and have not explicitly recognized a role for the pressure gradient force in suction feeding. The simulations suggest previously unrecognized mechanisms that suction feeders can use to enhance the forces that they exert, by increasing the steepness of the pressure gradient that the prey item is exposed to. This can be accomplished either by increasing the rate of increase in fluid velocity or by restricting the size of the mouth aperture, which creates a steeper spatial gradient in pressure.     

Extremely fast prey capture in pipefish is powered by elastic recoil.

The exceptionally high speed at which syngnathid fishes are able to rotate their snout towards prey and capture it by suction is potentially caused by a catapult mechanism in which the energy previously stored in deformed elastic elements is suddenly released. According to this hypothesis, tension is built up in tendons of the post-cranial muscles before prey capture is initiated. Next, an abrupt elastic recoil generates high-speed dorsal rotation of the head and snout, rapidly bringing the mouth close to the prey, thus enabling the pipefish to be close enough to engulf the prey by suction. However, no experimental evidence exists for such a mechanism of mechanical power amplification during feeding in these fishes. To test this hypothesis, inverse dynamical modelling based upon kinematic data from high-speed videos of prey capture in bay pipefish Syngnathus leptorhynchus, as well as electromyography of the muscle responsible for head rotation (the epaxial muscle) was performed. The remarkably high instantaneous muscle-mass-specific power requirement calculated for the initial phase of head rotation (up to 5795 W kg(-1)), as well as the early onset times of epaxial muscle activity (often observed more than 300 ms before the first externally discernible prey capture motion), support the elastic power enhancement hypothesis.     

Optimal memoryless strategies of a two‐rate communication link

Abstract

Game theory has been applied to study the performance of a communication system in a hostile environment. By appropriately choosing the payoff, a communication system in the presence of a hostile jammer can be modeled as a finite two‐person zero‐sum game. In this paper, we model a two‐rate communication link interfered by an on‐off jammer as a two‐person zero‐sum game and derive the optimal memoryless communication and jamming strategies. The ensemble mean of the time average throughput is considered as the payoff to the communicator. It is found that, under average jamming power constraints, the optimal memoryless jamming strategy is, in general, to allocate as much jamming power as possible to one direction. We study both symmetric and asymmetric communication strategy cases. The performance of the communication system is better if an asymmetric communication strategy is adopted. However, the system resulting from an optimal asymmetric communication strategy may become non‐ergodic.     

Dynamics of Particle Confined Between Oscillating and Fixed Walls

In this paper, we investigate the motion of a particle confined between the oscillating and fixed walls. As the particle collides with the moving wall in the phase of oscillations, when the wall velocity grows, the wall after collision catches up with the particle. This process can be repeated many times until in finite time interval the particle is found lying on the wall and continues its motion together with the wall. When the sign of the wall acceleration changes the particle detaches from the wall with zero velocity, so that it looks as if the particle “sticks” to the wall. It has been found that if the collision is inelastic, “sticking” leads to convergence of close trajectories except for the case of weak decay. On the contrary, in the case of elastic collision “sticking” of the particle causes even a more rapid divergence of theses trajectories.