Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

What can ecosystems learn? Expanding evolutionary ecology with learning theory.

BACKGROUND: The structure and organisation of ecological interactions within an ecosystem is modified by the evolution and coevolution of the individual species it contains. Understanding how historical conditions have shaped this architecture is vital for understanding system responses to change at scales from the microbial upwards. However, in the absence of a group selection process, the collective behaviours and ecosystem functions exhibited by the whole community cannot be organised or adapted in a Darwinian sense. A long-standing open question thus persists: Are there alternative organising principles that enable us to understand and predict how the coevolution of the component species creates and maintains complex collective behaviours exhibited by the ecosystem as a whole? RESULTS: Here we answer this question by incorporating principles from connectionist learning, a previously unrelated discipline already using well-developed theories on how emergent behaviours arise in simple networks. Specifically, we show conditions where natural selection on ecological interactions is functionally equivalent to a simple type of connectionist learning, 'unsupervised learning', well-known in neural-network models of cognitive systems to produce many non-trivial collective behaviours. Accordingly, we find that a community can self-organise in a well-defined and non-trivial sense without selection at the community level; its organisation can be conditioned by past experience in the same sense as connectionist learning models habituate to stimuli. This conditioning drives the community to form a distributed ecological memory of multiple past states, causing the community to: a) converge to these states from any random initial composition; b) accurately restore historical compositions from small fragments; c) recover a state composition following disturbance; and d) to correctly classify ambiguous initial compositions according to their similarity to learned compositions. We examine how the formation of alternative stable states alters the community's response to changing environmental forcing, and we identify conditions under which the ecosystem exhibits hysteresis with potential for catastrophic regime shifts. CONCLUSIONS: This work highlights the potential of connectionist theory to expand our understanding of evo-eco dynamics and collective ecological behaviours. Within this framework we find that, despite not being a Darwinian unit, ecological communities can behave like connectionist learning systems, creating internal conditions that habituate to past environmental conditions and actively recalling those conditions. REVIEWERS: This article was reviewed by Prof. Ricard V Solé, Universitat Pompeu Fabra, Barcelona and Prof. Rob Knight, University of Colorado, Boulder.

RTOS Framework for Real-Time Control System

This thesis is done as a complementary part for the active magnet bearing (AMB) control software development project in Lappeenranta University of Technology. The main focus of the thesis is to examine an idea of a real-time operating system (RTOS) framework that operates in a dedicated digital signal processor (DSP) environment. General use real-time operating systems do not necessarily provide sufficient platform for periodic control algorithm utilisation. In addition, application program interfaces found in real-time operating systems are commonly non-existent or provided as chip-support libraries, thus hindering platform independent software development. Hence, two divergent real-time operating systems and additional periodic extension software with the framework design are examined to find solutions for the research problems. The research is discharged by; tracing the selected real-time operating system, formulating requirements for the system, and designing the real-time operating system framework (OSFW). The OSFW is formed by programming the framework and conjoining the outcome with the RTOS and the periodic extension. The system is tested and functionality of the software is evaluated in theoretical context of the Rate Monotonic Scheduling (RMS) theory. The performance of the OSFW and substance of the approach are discussed in contrast to the research theme. The findings of the thesis demonstrates that the forged real-time operating system framework is a viable groundwork solution for periodic control applications.

The efficacy of anti-predator behaviour in the wood fog tadpole (Rana sylvatica) /

Activity has been suggested as an important behaviour that is tightly linked with predator avoidance in tadpoles. In this thesis I examine predator-prey relationships using wood frog tadpoles {Rana sylvaticd) as prey and dragonfly larvae {AnaxJunius) and backswimmers {Notonecta undulatd) as predators. I explore the role of prey activity in predator attack rates, prey response to single and multiple predator introductions, and prey survivorship. The data suggest that Anax is the more successful predator, able to capture both active and inactive tadpoles. In contrast, Notonecta strike at inactive prey less frequently and are seldom successftil when they do. A mesocosm study revealed that the presence of any predator resulted in reduced activity level of tadpoles. Each predator species alone had similar effects on tadpole activity, as did the combined predator treatment. Tadpole survivorship, however, differed significantly among both predator treatments and prey populations. Tadpwles in the combined predator treatment had enhanced risk; survivorship was lower than that expected if the two predators had additive effects. Differences in survivorship among wood frog populations showed that tadpoles from a lake habitat had the lowest survivorship, those from a shallow pond habitat had an intermediate survivorship, and tadpoles from a marsh habitat had the highest survivorship. The frequency of interactions with predators in the native habitat may be driving the population differences observed. In conclusion, results from this study show that complex interactions exist between predators, prey, and the environment, with activity playing a key role in the survival of tadpoles.

Développement d’un modèle centré sur l’individu des déplacements du caribou, du loup et de l’orignal, et de leurs interactions, en forêt boréale aménagée

Le caribou forestier est une espèce menacée au Canada, la principale hypothèse au déclin des populations étant l’intensification de la prédation provoquée par les perturbations anthropiques du paysage. Afin de faire face à cette situation, il est nécessaire d’étudier et comprendre l’impact de l’environnement sur les interactions prédateur-proies entre le caribou et le loup, ainsi qu’avec l’orignal, qui est sa principale proie alternative. Pour cela, cette thèse présente la conception d’un modèle centré sur l’individu des déplacements de ces trois espèces en fonction de leur environnement, dont résulteront les interactions prédateur-proies. Afin de permettre l’application de ce modèle sur de longues périodes, et donc pour un environnement changeant, une méthodologie a été développée, qui s’articule atour de deux aspects principaux. Tout d’abord, la notion de niveaux d’émergence est introduite, permettant d’ordonner les comportements observables du système selon leurs interdépendances, afin de choisir comme trait du modèle un com- portement correspondant au domaine d’applicabilité visé. Ordonner les comportements selon leurs niveaux d’émergence permet également d’identifier la redondance entre les patrons, qui peut être à l’origine d’un phénomène de sur-apprentissage lorsqu’ils sont utilisés lors de la calibration. Dans un second temps, un nouveau protocole pour la calibration et la validation du ou des traits choisis à l’aide des niveaux d’émergence, nommé réplication de système basé sur l’individu (Individual Based System Replication - IBSRtion) est également présenté. Ce protocole met l’emphase sur la modélisation directe, contrairement au principal protocole existant, la modélisation orientée patrons (Pattern Oriented Modelling - POM), et permet une approche empirique en générant artificiellement des données non disponibles ou ne pouvant être récoltées par des études de terrains. IBSRtion a également l’avantage de pouvoir être intégrée dans POM, afin de contribuer à la création d’une méthodologie universelle pour la conception de modèles centrés sur l’individu. Le processus de conception de ce modèle aura entre autre permis de faire une synthèse des connaissances et d’identifier certaines lacunes. Une étude visant à palier le manque de connaissances satisfaisantes sur les réponses comportementales à court-terme des proies face au risque de prédation a notamment permis d’observer que celles-ci sont une combinaison de comportements chroniques et éphémères, et que les mécanismes qui en sont à l’origine sont complexes et non-linéaires. Le résultat de ce travail est un modèle complexe utilisant de nombreux sous-modèles, et calibré de façon empirique, applicable à une grande variété d’environnements. Ce modèle a permis de tester l’impact de l’enfeuillement sur les relations prédateur-proies. Des simulations ont été effectuées pour différentes quantités d’enfeuillement, suivant deux configurations spatiales différentes. Les résultats de simulation suggèrent que des plans d’aménagement considérant également l’habitat de l’orignal pourraient être bénéfiques pour le caribou forestier, car ils permettraient d’améliorer la ségrégation spatiale entre les deux espèces, et donc entre le caribou et le loup. En le couplant avec un module de naissances et de morts naturelles ainsi qu’un modèle d’évolution du paysage, ce modèle permettra par la suite d’évaluer l’impact de plans d’aménagement forestier sur la viabilité des populations de caribou forestier.

Owls and rabbits: predation against substandard individuals of an easy prey

The interactions among the multiple factors regulating predator-prey relationships make predation a more complex process than previously thought. The degree to which substandard individuals are captured disproportionately seems to be better a function of the difficulty of prey capture than of the hunting techniques (coursing vs. ambushing predators). That is, when the capture and killing of a prey species is easy, substandard individuals will be predated in proportion to their occurrence in the prey population. In the present study, we made use of eagle owls Bubo bubo and their main prey, the rabbit Oryctolagus cuniculus: (a) the brightness of the white tails of rabbits seems to be correlated with the physical condition of individuals, (b) by using the tails of predated rabbits as an index of individual condition, we found that eagle owls seem to prefer substandard individuals (characterized by duller tails), and (c) by using information from continuous radiotracking of 14 individuals, we suggest that the difficulty of rabbit capture could be low. Although the relative benefits of preying on substandard individuals should considerably decrease when a predator is attacking an easy prey, we hypothesise that the eagle owl preference for substandard individuals could be due to the easy detection of poor individuals by a visual cue, the brightness of the rabbit tail. Several elements allow us to believe that this form of visual communication between a prey and one of its main predators could be more widespread than previously thought. In fact: (a) visual signalling plays a relevant role in intraspecific communication in eagle owls and, consequently, visual signals could also play a role in interspecific interactions, and (b) empirical studies showed that signals may inform the predator that it has been perceived, or that the prey is in a sufficiently healthy state to elude the predator.

The stability of ecosystems: a brief overview of the paradox of enrichment

In theory, enrichment of resource in a predator-prey model leads to destabilization of the system, thereby collapsing the trophic interaction, a phenomenon referred to as "the paradox of enrichment". After it was first proposed by Rosenzweig (1971), a number of subsequent studies were carried out on this dilemma over many decades. In this article, we review these theoretical and experimental works and give a brief overview of the proposed solutions to the paradox. The mechanisms that have been discussed are modifications of simple predator-prey models in the presence of prey that is inedible, invulnerable, unpalatable and toxic. Another class of mechanisms includes an incorporation of a ratio-dependent functional form, inducible defence of prey and density-dependent mortality of the predator. Moreover, we find a third set of explanations based on complex population dynamics including chaos in space and time. We conclude that, although any one of the various mechanisms proposed so far might potentially prevent destabilization of the predator-prey dynamics following enrichment, in nature different mechanisms may combine to cause stability, even when a system is enriched. The exact mechanisms, which may differ among systems, need to be disentangled through extensive field studies and laboratory experiments coupled with realistic theoretical models.

Predator Survival Tactics and Use of Habitat Cover in Rana Catesbeiana.

Predator-prey relationships are an important aspect of the natural world, and, because of its relevance to survival and natural selection, is an interesting relationship to study. In amphibian larvae, level of activity and landscape use are often what determines the survival as prey. I studied the anti-predator behavior of the North American bullfrog (Rana catesbeiana) tadpoles when presented with dragonfly (Aeshna) larvae, a known predator of tadpoles. Tadpoles were acclimated to four different habitats with varying degrees of habitat cover, and were transferred to a new habitat with a degree of cover equal to one of the acclimation tanks. A restrained predator, and thus its chemical cue, was introduced, and the behavior, particularly the use of the habitat cover to hide from the perceived risk of predation was observed. A significantly higher frequency of inactivity was found in tank I than in II and III, and inactivity followed a general trend of decreasing with increasing habitat cover. Difference in tank cover was not found to have a significant effect on swimming behavior, but did have a significant effect on hiding behavior, which increased with higher availability. Foraging decreased significantly with the addition of a predator, but did not vary significantly with different levels of cover. Hiding behavior and reducing conspicuous behaviors (like foraging) are probably the behaviors that afford the tadpole the most success at eluding a predator in their natural environment.

Stomach fullness modulates prey size choice in the frillfin goby, Bathygobius soporator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Foraging behaviour by an intraguild predator blowfly, Chrysomya albiceps (Diptera : Calliphoridae)

Optimal foraging theory assumes that predators use different prey types to maximize their rate of energetic gain. Studies focusing on prey preference are important sources of information to understand the foraging dynamics of Chrysomya albiceps. The purpose of this investigation is to determine the influence of larval starvation in C. albiceps on the predation rate of different prey blowfly species and instars under laboratory conditions. Our results suggest that C. albiceps prefers Cochliomyia macellaria larvae to Chrysomya megacephala under non-starvation and starvation conditions. Nevertheless, predators gained more weight consuming C. macellaria. This result suggests that C. albiceps profit more in consuming C. macellaria rather than C. megacephala. The foraging behaviour displayed by C. abiceps on their prey and the consequences for the blowfly community are also discussed.

Chemical cues related to conspecific size in pintado catfish, Pseudoplatystoma coruscans

The pintado (Pseudoplatystoma coruscans) is a ferocious carnivorous catfish with evident cannibalistic behaviour; its nocturnal habits are related to its ability to use predominately chemical sensorial modalities. This study investigated whether the pintado distinguishes conspecifics of different body sizes using chemical cues, which may reflect different physiological conditions such as hunger or stress. Pintados were observed when receiving water conditioned by either larger or similar-size conspecifics. A control group consisted of pintados receiving unconditioned water. Twelve repetitions were used for each condition. Feeding-like behaviours were investigated in the receiver fish and showed that they responded only to the conditioned water. Furthermore, a higher frequency of responses occurred when the water was conditioned by a similar-size conspecific. Thus, it is concluded that pintados are able to recognize conspecific size by chemical cues related to size and that this ability contributes to the individual's decision making on whether to approach or to avoid the conspecific.

Anurans as prey: an exploratory analysis and size relationships between predators and their prey

The vertebrate predators of post-metamorphic anurans were quantified and the predator-prey relationship was investigated by analysing the relative size of invertebrate predators and anurans. More than 100 vertebrate predators were identified (in more than 200 reports) and classified as opportunistic, convenience, temporary specialized and specialized predators. Invertebrate predators were classified as solitary non-venomous, venomous and social foragers according to 333 reviewed reports. Each of these categories of invertebrate predators was compared with the relative size of the anurans, showing an increase in the relative size of the prey when predators used special predatory tactics. The number of species and the number of families of anurans that were preyed upon did not vary with the size of the predator, suggesting that prey selection was not arbitrary and that energetic constraints must be involved in this choice. The relatively low predation pressure upon brachycephalids was related to the presence of some defensive strategies of its species. This compounding review can be used as the foundation for future advances in vertebrate predator-prey interactions.

Management of vomplex systems: Modeling the biological pest control

The aim of this paper is to study the cropping system as complex one, applying methods from theory of dynamic systems and from the control theory to the mathematical modeling of the biological pest control. The complex system can be described by different mathematical models. Based on three models of the pest control, the various scenarios have been simulated in order to obtain the pest control strategy only through natural enemies' introduction. © 2008 World Scientific Publishing Company.

Aplicações do modelo presa-predador ao estudo da influência da dinâmica populacional de espécies de sardinha, cavala e atum e sobre o processo de eutrofização marinha

A discussion concerning marine eutrophication, possible generated from an imbalance of fish population is presented. Simulations through a code in FORCE 2.0 considering a predator-prey model have been made and the numerical results for a three different fish species were plot in ORIGIN code. The populations considered in this study were: Sardines being prey and both mackerel and tuna being the sardine’s predators. Some hipotheses concerning to the marine eutrophication have being made according to the stages of the dynamics of the system. For situations were the prey’s populationis very low, the quality of the water experiences a strong depreciation leading to a possible eutrophication of the water.