Cellular automata for contact ecoepidemic processes in predator–prey systems

Spatial ecoepidemic models, in which diseases affect interacting populations, are often explored through reaction-diffusion equations. However, cellular automata (CA) are a widely recognized tool for modelling spatial pattern formation that are broadly analagous to reaction diffusion equations, but provide greater flexibility in defining population dynamics. In this work we present a CA defined to mimic the prey–predators interactions while a pathogen is affecting, in turn, one population. We explore system equilibria, given different initial conditions and local interaction neighborhoods. Furthermore, in the various ecoepidemic systems considered we report the formation of waves and spirals: a key summary of how diseases may spread among individuals. Some inferences on the predators and infection eradication strategies are presented and supported by simulations results.     

Forward and backward running waves in the arteries: analysis using the method of characteristics

The one-dimensional equations of flow in the elastic arteries are hyperbolic and admit nonlinear, wavelike solutions for the mean velocity, U, and the pressure, P. Neglecting dissipation, the solutions can be written in terms of wavelets defined as differences of the Riemann invariants across characteristics. This analysis shows that the product, dUdP, is positive definite for forward running wavelets and negative definite for backward running wavelets allowing the determination of the net magnitude and direction of propagating wavelets from pressure and velocity measured at a point in the artery. With the linearizing assumption that intersecting wavelets are additive, the forward and backward running wavelets can be separately calculated. This analysis, applied to measurements made in the ascending aorta of man, shows that forward running wavelets dominate during both the acceleration and deceleration phases of blood flow in the aorta. The forward and backward running waves calculated using the linearized analysis are similar to the results of an impedance analysis of the data. Unlike the impedance analysis, however, this is a time domain analysis which can be applied to nonperiodic or transient flow.     

Hypercycles versus parasites in the origin of life: model dependence in spatial hypercycle systems

Spatial hypercycle systems can be modelled by means of cellular automata or partial differential equations. In either model, two dimensional spirals or clusters can be formed. Different models give rise to slightly different spatial structures, but the response to parasites is fundamentally different: In cellular automata the hypercycle is resistant to parasites that are fatal in a partial differential equations model. In three dimensions scroll rings correspond to the two dimensional spirals. Numerical simulations on a partial differential equations model indicate that the scroll rings are unstable: The contract by a power law and disappear. Therefore, in three dimensions clusters seem to be the best candidate for the hypercycle resistant to parasites.     

Ideal phyllotaxis on general surfaces of revolution

A mathematical model is presented for botanical features growing at an arbitrary rate on an arbitrary surface of revolution. At each point on the surface a lattice is defined, describing the phyllotaxis (that is, the arrangement of the features) there. It is shown how two parameters determine on which conspicuous spirals successive features are in contact at any point, whether the numbers of intersecting spirals change from point to point, and, if so, through what values. These parameters are the divergence δ, which is assumed to be constant, and a quantity ξ, which is the reciprocal of the normalized rise, and which in general varies from point to point. Finally, it is proved that Fibonacci phyllotaxis (in which the numbers of intersecting spirals are always Fibonacci numbers) produces greater packing efficiency than any other, provided that the lattice varies over the surface.     

Motility of zooplankton: fitness, foraging and predation

The relative fitness of planktonic organisms foraging underthe risk of predation is examined in terms of their swimmingspeed, path geometry and jump frequency. Fitness is quantifiedin terms of encounter and ingestion of prey, respiration andenergy cost associated with swimming and mortality due to encounterswith predators. It is shown that a convoluted swimming pathin the form of meanders, zigzags or spirals confers greaterfitness than swimming along a straight path. Optimal path configurationis such that the length-scale of the path-meanders is commensuratewith an organism's detection radius to prey, which in turn scaleswith the size of the organism. Optimal swimming speed for acruise-feeding organism decreases with increasing prey concentrationand increasing risk due to ambush predators. For ambush feedingon motile prey, a benefit is gained by periodically moving toa new location. The time spent swimming is largely a functionof energetic costs, whereas the time spent feeding is stronglycontrolled by prey concentration and the risk posed, in turn,by ambush predators. These predictions are supported by observationsdrawn from the literature.     

Competing predators for a prey in a chemostat model with periodic nutrient input

A system of ordinary differential equations is used to model the interactions of n competing predators on a single prey population in a chemostat environment with a periodic nutrient input. In the case of one or no predators, criteria for the existence of periodic solutions are given. In the general case, conditions for all populations to persist are derived.Research is in part based on a Ph.D. thesis submitted to the Faculty of Graduate Studies, University of AlbertaResearch is partly supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A4823     

Conformational studies of the copolymer poly(L-lysine,L-tyrosine) 1:1 in aqueous solution

The absorption and circular dichroism spectra of the 1:1 copolymer (L -Lys, L -Tyr)_n have been investigated in aqueous solutions at pH ranging from 3 to 13. The spectral patterns indicate that the fully charged polympholyte assumes a nonperiodic conformation on the acid and basic sides of the isoelectric point. At pH ranging from 9.2 to 11.6, the polymer is largely ordered and takes mostly an antiparallel β-structure as is shown by the infrared spectra in D₂O solutions. Moreover, the rotational strength of the L_a transition of tyrosyl is independent of the polymer conformation, whereas that of the L_b transition is strongly sensitive to it.     

Collision-Based Spiral Acceleration in Cardiac Media: Roles of Wavefront Curvature and Excitable Gap

We have previously shown in experimental cardiac cell monolayers that rapid point pacing can convert basic functional reentry (single spiral) into a stable multiwave spiral that activates the tissue at an accelerated rate. Here, our goal is to further elucidate the biophysical mechanisms of this rate acceleration without the potential confounding effects of microscopic tissue heterogeneities inherent to experimental preparations. We use computer simulations to show that, similar to experimental observations, single spirals can be converted by point stimuli into stable multiwave spirals. In multiwave spirals, individual waves collide, yielding regions with negative wavefront curvature. When a sufficient excitable gap is present and the negative-curvature regions are close to spiral tips, an electrotonic spread of excitatory currents from these regions propels each colliding spiral to rotate faster than the single spiral, causing an overall rate acceleration. As observed experimentally, the degree of rate acceleration increases with the number of colliding spiral waves. Conversely, if collision sites are far from spiral tips, excitatory currents have no effect on spiral rotation and multiple spirals rotate independently, without rate acceleration. Understanding the mechanisms of spiral rate acceleration may yield new strategies for preventing the transition from monomorphic tachycardia to polymorphic tachycardia and fibrillation.     

Dynamical behavior of two predators competing over a single prey

Dynamical behavior of a food web comprising two predators competing over a single prey has been investigated. The analysis of the food web model shows that the persistence is not possible for two competing predators sharing a single prey species in the cases when any one of the boundary prey–predator planes has a stable equilibrium point. The principle of competitive exclusion holds in such cases. However, numerical simulations exhibit persistence in the presence of periodic solutions in the boundary planes. The system exhibits quasi-periodic behavior in the positive octant. The co-existence in the form of a limit cycle is also possible in some cases.     

Dynamical behavior of two predators competing over a single prey

Dynamical behavior of a food web comprising two predators competing over a single prey has been investigated. The analysis of the food web model shows that the persistence is not possible for two competing predators sharing a single prey species in the cases when any one of the boundary prey–predator planes has a stable equilibrium point. The principle of competitive exclusion holds in such cases. However, numerical simulations exhibit persistence in the presence of periodic solutions in the boundary planes. The system exhibits quasi-periodic behavior in the positive octant. The co-existence in the form of a limit cycle is also possible in some cases.     

Predator-prey models in periodically fluctuating environments

A class of ordinary or integrodifferential equations describing predator-prey dynamics is considered under the assumption that the coefficients are periodic functions of time. This class is characterized by the logistic behaviour of the prey in the absence of predators and it includes the Leslie model. We show that there exists a periodic solution provided that the average of the predator's intrinsic rate of increase is greater than a critical value. We use well-known results in bifurcation theory for nonlinear eigenvalue problems, as well as an extension to the case of non-globally defined operators of some recent results on the global nature of branches of solutions.     

Comparison of pheromone application rates, point source densities, and dispensing methods for mating disruption of tufted apple bud moth (Lepidoptera: Tortricidae)

Small-plot (approximately 0.1 ha) studies were used to evaluate different pheromone dispensing systems, application rates, and point-source densities for mating disruption of the tufted apple bud moth, Platynota idaeusalis (Walker). Using polyvinyl chloride spirals impregnated with tufted apple bud moth pheromone (1:1 ratio of E11-tetradecenyl alcohol/E11-tetradecenyl acetate), pheromone rates of > or = 1,482 spirals per hectare (74.1 g pheromone per hectare) were superior to a rate of 988 spirals per hectare (49.4 g pheromone per hectare) in decreasing male response to pheromone traps in 1995, whereas no differences were detected among rates of 988, 1,482 and 1,975 spirals per hectare in 1996. Within a range of 370-988 pheromone dispensers per hectare, point source densities were equally effective in suppressing male response to pheromone traps. Pheromone-impregnated paraffin disks were equally effective at inhibiting male response to pheromone traps compared with polyvinyl chloride spirals. However, a paraffin emulsion formulation of pheromone applied with a hand-held grease gun provided longer residual communication disruption effects than polyvinyl chloride spirals. Dilution of paraffin emulsion pheromone formulations in water for application with a backpack sprayer and airblast sprayer rendered them ineffective in reducing male response to pheromone traps. The releases of pheromone from polyvinyl chloride spirals and paraffin disks aged in the field were described by a linear and negative logarithmic curve, respectively, indicating that dispenser life time should be longer for spirals. The ratio of acetate to alcohol components of pheromone released from spirals increased over time, whereas the release ratio remained more constant for paraffin disks. This suggests that the disruption efficacy of spirals may be prematurely reduced because of imbalance of the released components.     

An integral method for the analysis of blood flow

The existing methods to solve the problems of pulsatile flow in the cardiovascular system are based on either linear axisymmetric equations or non-linear one-dimensional equations. The solutions thus obtained give only a mediocre comparison with measurements. In this paper, a non-linear axisymmetric theory is proposed. The starting point of the present theory is a third degree polynomial representation of the velocity profile. Integral methods are then applied to obtain the governing equations. To ascertain the accuracy of the theory proposed above, the calculations for a simple case involving pulsatile flow in a long rigid tube were performed. The results are: (a) the average velocities compare very well with exact solutions and (b) the velocity profiles for a given frequency agree very well with exact solutions for flow in small tubes, but tend to differ as tube size is increased.     

具有年龄结构的食蚜蝇-蚜虫捕食模型

现有的具有年龄结构的捕食-食饵模型总是假设只有成年捕食者捕食猎物,这与实际情况不符。建立了一个幼年捕食者捕食食饵的具有年龄结构的食蚜蝇-蚜虫模型,应用微分方程定性理论,讨论了系统平衡点及其稳定性:其中平衡点E1(0,0,0)为不稳定的;满足一定条件时,边界平衡点E2(K,0,0)及正平衡点E3(x*,y1*,y2*)为局部渐近稳定的;且应用一致持续生存理论得到了系统永久持续生存的条件,为有害生物综合治理提供了理论依据。     

A solution to the accelerated-predator-satiety Lotka-Volterra predator-prey problem using Boubaker polynomial expansion scheme

In this study, an analytical method is introduced for the identification of predator-prey populations time-dependent evolution in a Lotka-Volterra predator-prey model which takes into account the concept of accelerated-predator-satiety.Oppositely to most of the predator-prey problem models, the actual model does not suppose that the predation is strictly proportional to the prey density. In reference to some recent experimental results and particularly to the conclusions of May (1973) about predators which are ‘never not hungry’, an accelerated satiety function is matched with the initial conventional equations. Solutions are plotted and compared to some relevant ones. The obtained trends are in good agreement with many standard Lotka-Volterra solutions except for the asymptotic behaviour.     

Invest conflicts of adult predators

Parental care is incorporated into a prey-predator model in which immature predators are taken care of by their parents. It is assumed that adult predators confront the problem to stay home to protect offspring or to go out to forage. The global dynamics of the mathematical model is analyzed by means of analytical methods and numerical simulations. Conditions for the extinction of predator populations are established and the manners in which predators become extinct are revealed. Bifurcation analysis shows that the model admits changes from the extinction of predators to stable coexistence at a positive equilibrium point, and then to stage-structure induced oscillations. It is shown that optimal invest of adult predators can be achieved.     

Spatial reconstruction of the human motion based on images of a single camera

The inverse dynamic analysis procedures used in the study of the human gait require that the kinematics of the supporting biomechanical model is known beforehand. The first step to obtain the kinematic data is the reconstruction of human spatial motion, i.e., the evaluation of the anatomic points positions that enables to uniquely define the position of all anatomical segments. In photogrammetry, the projection of each anatomical point is described by two linear equations relating its three spatial coordinates with the two coordinates of the projected point. The need for the image of two cameras arises from the fact that three equations are necessary to find the original spatial position of the anatomical point. It is shown here that the kinematic constraint equations associated with a biomechanical model can be used as the extra set of equations required for the reconstruction process, instead of the equations associated with the second camera. With this methodology, the system of equations arising from the point projections and biomechanical model kinematic constraints are solved simultaneously. Since the system of equations has multiple solutions for each image, a strategy based on the minimization of the cost function associated to the smoothness of the reconstructed motion is devised, leading to an automated computer procedure enabling a unique reconstruction.     

Co-evolution and ecosystem based problem solving

Emergent cooperative relations in ecosystems are ill understood, but have the potential to strongly improve evolutionary computing. On the other hand, eco-evolutionary computation has the potential to provide new insights in the structuring and functioning of ecosystems. Here we study ecosystem based problem solving in a co-evolutionary framework of predators (solvers) and prey (problems), extended with a population of scavengers, which can eat the remains of prey (that is, cooperate with the predators in solving the problems). We show that such an artificial ecosystem of predators, prey and scavengers, with a selection and fitness regime favoring specialization, self-organizes in space and time such that (1) problems are automatically decomposed in easier to solve parts, (2) the predator, prey and scavenger populations differentiate in sub-populations according to this decomposition, and (3) predators and scavengers automatically co-localize in space such that the problems are indeed solved by predator–scavenger combinations which together correctly approximate the target function. That is, the use of a spatial co-evolutionary ecosystem as information processing unit for evolutionary computation gives rise to an emergent structure of niches, each consisting of complementary partial solutions. As a result, ecosystem based solutions are preferred over individual-based solutions in solving the studied function approximation task.     

The struggle for life—IV two predators sharing a prey

Some of the properties of the equations describing two predators competing for the same prey are analyzed. In particular it is found that, under certain conditions, both predators can curvive, with or without oscillations in the prey population.     

A single spiral artefact in Arthropod cuticle

Spirals are often seen in sections transverse to the axes of bumped structures in arthropod cuticle. (Sections through arthropod cornea or exocones yield excellent examples.) As arthropod cuticle has a helicoidal architecture (Bouligand, 1965), it might be expected that the spirals are a simple consequence of that structure. According to a symmetry argument, the spirals thus predicted must be double spirals. In contrast, the observed spirals are usually single. We propose that the single spirals result from an interaction between the microtome knife and the cuticle architecture. The direction of knife travel defines an orientation within the cuticle, subverting the symmetry arguments that require double spirals. Bouligand (1972) presented a model for the interaction of the knife with the cuticle. However, we offer arguments and observations which show that Bouligand's model is incorrect. We argue from detailed observations of the single spiral that it is indeed a knifing artifact and that its explanation probably lies within a certain class of models. Two related models based on relative movements of cuticle components are examined via computer techniques.