Quasi-cycles in a spatial predator-prey model

We show that spatial models of simple predator-prey interactions predict that predator and prey numbers oscillate in time and space. These oscillations are not seen in the deterministic versions of the models, but are due to stochastic fluctuations about the time-independent solutions of the deterministic equations which are amplified due to the existence of a resonance. We calculate the power spectra of the fluctuations analytically and show that they agree well with results obtained from stochastic simulations. This work extends the analysis of these quasi-cycles from that previously developed for well-mixed systems to spatial systems, and shows that the ideas and methods used for non-spatial models naturally generalize to the spatial case.Comment: 18 pages, 4 figure

Multi-Species Prey-Predator Dynamics During a Multi-Strain Pandemic

Small and large scale pandemics are a natural phenomenon repeatably appearing throughout history, causing ecological and biological shifts in ecosystems and a wide range of their habitats. These pandemics usually start with a single strain but shortly become multi-strain due to a mutation process of the pathogen causing the epidemic. In this study, we propose a novel eco-epidemiological model that captures multi-species prey-predator dynamics with a multi-strain pandemic. The proposed model extends and combines the Lotka-Volterra prey-predator model and the Susceptible-Infectious-Recovered (SIR) epidemiological model. We investigate the ecosystem's sensitivity and stability during such a multi-strain pandemic through extensive simulation relying on both synthetic cases as well as two real-world configurations. Our results are aligned with known ecological and epidemiological findings, thus supporting the adequacy of the proposed model in realistically capturing the complex eco-epidemiological properties of the multi-species multi-strain pandemic dynamics

Analytical detection of stationary and dynamic patterns in a prey-predator model with reproductive Allee effect in prey growth

Allee effect in population dynamics has a major impact in suppressing the paradox of enrichment through global bifurcation, and it can generate highly complex dynamics. The influence of the reproductive Allee effect, incorporated in the prey's growth rate of a prey-predator model with Beddington-DeAngelis functional response, is investigated here. Preliminary local and global bifurcations are identified of the temporal model. Existence and non-existence of heterogeneous steady-state solutions of the spatio-temporal system are established for suitable ranges of parameter values. The spatio-temporal model satisfies Turing instability conditions, but numerical investigation reveals that the heterogeneous patterns corresponding to unstable Turing eigen modes acts as a transitory pattern. Inclusion of the reproductive Allee effect in the prey population has a destabilising effect on the coexistence equilibrium. For a range of parameter values, various branches of stationary solutions including mode-dependent Turing solutions and localized pattern solutions are identified using numerical bifurcation technique. The model is also capable to produce some complex dynamic patterns such as travelling wave, moving pulse solution, and spatio-temporal chaos for certain range of parameters and diffusivity along with appropriate choice of initial conditions Judicious choices of parametrization for the Beddington-DeAngelis functional response help us to infer about the resulting patterns for similar prey-predator models with Holling type-II functional response and ratio-dependent functional response

Dynamics of marine zooplankton : social behavior ecological interactions, and physically-induced variability

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2008Marine ecosystems reflect the physical structure of their environment and the biological processes they carry out. This leads to spatial heterogeneity and temporal variability, some of which is imposed externally and some of which emerges from the ecological mechanisms themselves. The main focus of this thesis is on the formation of spatial patterns in the distribution of zooplankton arising from social interactions between individuals. In the Southern Ocean, krill often assemble in swarms and schools, the dynamics of which have important ecological consequences. Mathematical and numerical models are employed to study the interplay of biological and physical processes that contribute to the observed patchiness. The evolution of social behavior is simulated in a theoretical framework that includes zooplankton population dynamics, swimming behavior, and some aspects of the variability inherent to fluid environments. First, I formulate a model of resource utilization by a stage-structured predator population with density-dependent reproduction. Second, I incorporate the predator-prey dynamics into a spatially-explicit model, in which aggregations develop spontaneously as a result of linear instability of the uniform distribution. In this idealized ecosystem, benefits related to the local abundance of mates are offset by the cost of having to share resources with other group members. Third, I derive a weakly nonlinear approximation for the steady-state distributions of predator and prey biomass that captures the spatial patterns driven by social tendencies. Fourth, I simulate the schooling behavior of zooplankton in a variable environment; when turbulent flows generate patchiness in the resource field, schools can forage more efficiently than individuals. Taken together, these chapters demonstrate that aggregation/ schooling can indeed be the favored behavior when (i) reproduction (or other survival measures) increases with density in part of the range and (ii) mixing of prey into patches is rapid enough to offset the depletion. In the final two chapters, I consider sources of temporal variability in marine ecosystems. External perturbations amplified by nonlinear ecological interactions induce transient excursions away from equilibrium; in predator-prey dynamics the amplitude and duration of these transients are controlled by biological processes such as growth and mortality. In the Southern Ocean, large-scale winds associated with ENSO and the Southern Annular Mode cause convective mixing, which in turn drives air-sea fluxes of carbon dioxide and oxygen. Whether driven by stochastic fluctuations or by climatic phenomena, variability of the biogeochemical/physical environment has implications for ecosystem dynamics.Funding was provided by the Academic Programs Office of the MIT-WHOI Joint Program, an Ocean Ventures Fund Award, an Anonymous Ys Endowed Science Fellowship, and by NSF grants OCE-0221369 and OCE-336839

The paradox of enrichment in predator-prey systems

>Magister Scientiae - MScIn principle, an enrichment of resources in predator-prey systems show prompts destabilisation of a framework, accordingly, falling trophic communication, a phenomenon known to as the \Paradox of Enrichment" [54]. After it was rst genius postured by Rosenzweig [48], various resulting examines, including recently those of Mougi-Nishimura [43] as well as that of Bohannan-Lenski [8], were completed on this problem over numerous decades. Nonetheless, there has been a universal none acceptance of the \paradox" word within an ecological eld due to diverse interpretations [51]. In this dissertation, some theoretical exploratory works are being surveyed in line with giving a concise outline proposed responses to the paradox. Consequently, a quantity of di usion-driven models in mathematical ecology are evaluated and analysed. Accordingly, piloting the way for the spatial structured pattern (we denote it by SSP) formation in nonlinear systems of partial di erential equations [36, 40]. The central point of attention is on enrichment consequences which results toward a paradoxical state. For this purpose, evaluating a number of compartmental models in ecology similar to those of [48] will be of great assistance. Such displays have greater in uence in pattern formations due to diversity in meta-population. Studying the outcomes of initiating an enrichment into [9] of Braverman's model, with a nutrient density (denoted by n) and bacteria compactness (denoted by b) respectively, suits the purpose. The main objective behind being able to transform [9]'s system (2.16) into a new model as a result of enrichment. Accordingly, n has a logistic- type growth with linear di usion, while b poses a Holling Type II and nonlinear di usion r2 nb2 [9, 40]. Five fundamental questions are imposed in order to address and guide the study in accordance with the following sequence: (a) What will be the outcomes of introducing enrichment into [9]'s model? (b) How will such a process in (i) be done in order to change the system (2.16)'s stability state [50]? (c) Whether the paradox does exist in a particular situation or not [51]? Lastly, (d) If an absurdity in (d) does exist, is it reversible [8, 16, 54]? Based on the problem statement above, the investigation will include various matlab simulations. Therefore, being able to give analysis on a local asymptotic stability state when a small perturbation has been introduced [40]. It is for this reason that a bifurcation relevance comes into e ect [58]. There are principal de nitions that are undertaken as the research evolves around them. A study of quantitative response is presented in predator-prey systems in order to establish its stability properties. Due to tradeo s, there is a great likelihood that the growth rate, attack abilities and defense capacities of species have to be examined in line with reviewing parameters which favor stability conditions. Accordingly, an investigation must also re ect chances that leads to extinction or coexistence [7]. Nature is much more complex than scienti c models and laboratories [39]. Therefore, di erent mechanisms have to be integrated in order to establish stability even when a system has been under enrichment [51]. As a result, SSP system is modeled by way of reaction-di usion di erential equations simulated both spatially and temporally. The outcomes of such a system will be best suitable for real-world life situations which control similar behaviors in the future. Comparable models are used in the main compilation phase of dissertation and truly re ected in the literature. The SSP model can be regarded as between (2018-2011), with a stability control study which is of an original

Spatial Heterogeneity in Ecology

This project predominantly investigated the implications of spatial heterogeneity in the ecological processes of competition and infection. Empirical analysis of spatial heterogeneity was carried out using the lepidopteran species Plodia interpunctella. Using differently viscous food media, it was possible to alter the movement rate of larvae. Soft Foods allow the movement rate of larvae to be high, so that individuals can disperse through the environment and avoid physical encounters with conspecifics. Harder foods lower the movement rate of larvae, restricting the ability of individuals to disperse away from birth sites and avoid conspecifics encounters. Increasing food viscosity and lowering movement rate therefore has the effect of making uniform distributed larval populations more aggregated and patchy. Different spatial structures changed the nature of intraspecific competition, with patchy populations characterised by individuals experiencing lower growth rates and greater mortality because of the reduced food and space available within densely packed aggregations. At the population scale, the increased competition for food individuals experience in aggregations emerges as longer generational cycles and reduced population densities. Aggregating individuals also altered the outcome of interspecific competition between Plodia and Ephestia cautella. In food media that allowed high movement rates, Plodia had a greater survival rate than Ephestia because the larger movement rate of Plodia allowed it to more effectively avoid intraspecific competition. Also the faster growth rate, and so larger size, of Plodia allowed it to dominate interspecific encounters by either predating or interfering with the feeding of Ephestia. In food that restricts movement, the resulting aggregations cause Plodia to experience more intraspecific encounters relative to interspecific, reducing its competitive advantage and levelling the survival of the two species. Spatial structure also affected the dynamics of a Plodia-granulosis virus interaction and the evolution of virus infectivity. Larval aggregation forced transmission to become limited to within host patches, making the overall prevalence of the virus low. However potentially high rates of cannibalism and multiple infections within overcrowded host aggregations caused virus-induced mortality to be high, as indicated by the low host population density when virus is presented. Also aggregated host populations cause the evolution of lower virus infectivity, where less infective virus strains maintain more susceptible hosts within the aggregation and so possess a greater transmission rate. The pattern of variation in resistance of Plodia interpunctella towards its granulosis virus was found using two forms of graphical analysis. There was a bimodal pattern of variation, with most individuals exhibiting either low or high levels of resistance. This pattern was related to a resistance mechanism that is decreasingly costly to host fitness

2012 Conference Abstracts: Annual Undergraduate Research Conference at the Interface of Biology and Mathematics

URC Schedule and Abstract Book for the Fourth Annual Undergraduate Research Conference at the Interface of Biology and Mathematics Date: November 17-18, 2012Plenary speaker: Christine E. Heitsch, Associate Professor of Mathematics at Georgia Institute of TechnologyFeatured speaker: John W. Glasser, Center for Disease Contro

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

The influence of seasonal forcing on the population dynamics of ecological systems

Seasonal forcing represents a pervasive source of environmental variability and it has been shown to be important in generating the cycles observed in many ecological and epidemiological systems. We use a combination of bifurcation analysis and simulation to understand the impact of seasonality on population dynamics, with a focus on predator-prey and host-macroparasite systems. Multi-year cycles with a wide range of periods, quasi-periodicity and chaos are found. We consider the importance of the unforced dynamics in a predator-prey system by contrasting the e ect of seasonality when the underlying behaviour is oscillatory decay to the equilibrium or limit cycles. The limit cycles case shows a wider range of dynamics and multiple solutions. The e ect of variations in the seasonal forcing term are analysed in a predator-prey model by changing the breeding season length, using the vole system in Fennoscandia as a case study. It is found that the period of the multi-year cycles increases as the breeding season length decreases. By studying a general host-macroparasite system, in which the e ect of seasonality has not previously been explored in detail, we nd a larger potential for multiple solution behaviour compared to predator-prey systems. Overall, we show the critical role that seasonality can play in ecological systems

Integrated Stress and Community Perceptions: Toward an Understanding of Human-Cougar Tolerance

Evidence suggests that cougars (Puma concolor) are beginning to recolonize their traditional range in the Midwestern and Eastern US, returning to a landscape and a social environment that have changed drastically in a century of absence. Any hope of the cougar’s persistence depends on both human tolerance of their presence and on cougar tolerance of disrupted habitat. In this thesis, we took advantage of diverse cougar policy in place in the Western US to explore variation in human attitudes and acceptability of cougars and in the cougar stress response. We validated a process to identify and extract cortisol from cougar hair and examined relationships between cougar stress and intrinsic, environmental, and anthropogenic variables. We also validated a definition of human tolerance adapted from the sociological literature – “putting up with wildlife and wildlife behaviors you don’t like” – and tested its fit on data gathered from a social survey of rural communities in the West. After operationalizing tolerance, we explored whether permitting cougar hunting was likely to improve tolerance among the general public. In Chapter 2, we found that age class, season, precipitation, human population density, and hunting all significantly influenced cougar hair cortisol content, with cougars demonstrating higher cortisol when hunted and when inhabiting areas of lower human density. In Chapter 3, we identified four distinct typologies characterized by attitudes toward and acceptability of cougars among the general public – the “enthusiastic,” the “pragmatic,” the “intolerant,” and the “tolerant.” Finally, in Chapter 4, we found that while the general public had high attitudes and acceptability of cougars, hunters in California, where cougar hunting is banned, were intolerant of cougars compared to hunters elsewhere. Wildlife managers in eastern states should be aware that cougars do physiologically respond to anthropogenic disturbance and that hunters may chafe under restrictive cougar hunting regulations