Harmless delays and global attractivity for nonautonomous predator-prey system with dispersion

AbstractIn this paper, we consider a nonautonomous predator-prey model with dispersion and a finite number of discrete delays. The system consists of two Lotka-Volterra patches and has two species: one can disperse between two patches, but the other is confined to one patch and cannot disperse. Our purpose is to demonstrate that the time delays are harmless for uniform persistence of the solutions of the system. Furthermore, we establish conditions under which the system admits a positive periodic solution which attracts all solutions

The effect of rate, frequency, and form of migration on host parasite population dynamics

Thesis (M.S.) University of Alaska Fairbanks, 2019What is the effect of migration on host-parasite population dynamics? Animals live in a landscape where they move between patches. They are also locked in host-parasite conflicts. Host-parasite interactions are modeled with consumer resource functions. I constructed models using two different consumer resource functions (the Lotka Volterra system and the Saturating Type II system). The first model was a conservative system. The second was dissipative and more biologically realistic. I examined the effect of rate of migration, time between migration events, and form of migration. I found that the time between migration events had the largest effect on the synchronization in host-parasites population dynamics between the patches. Decreased time between migration events increased the fraction of simulation to completely synchronize and decreased the time it took to do so. In the first model, I observed simulations with a low rate of migration took a long time to synchronization and with a high rate of migration took a short time to synchronize. There was a phase transition between these two amounts of time it took to synchronize. In the second model, simulations done at low rates of migration did not synchronize while with increased migration rates the fraction of simulations to synchronize increased. I found in some simulations of parasite only migration that the patches synchronized faster. My results imply that parasite only migration to islands could have a greater impact on the extinction risk on islands further from the mainland than other forms of migration.National Institute of General Medical Sciences of the National Institutes of Health under Award Numbers UL1GM118991, TL4GM118992, or RL5GM118990, Institutional Development Award (IDeA) from the National Institute of General Medical Sciences of the National Institutes of Health under grant number P20GM10339

Interacting populations : hosts and pathogens, prey and predators

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 June 2007The interactions between populations can be positive, neutral or negative. Predation and parasitism are both relationships where one species benefits from the interaction at the expense of the other. Predators kill their prey instantly and use it only for food, whereas parasites use their hosts both as their habitat and their food. I am particularly interested in microbial parasites (including bacteria, fungi, viri, and some protozoans) since they cause many infectious diseases. This thesis considers two different points in the population-interaction spectrum and focuses on modeling host-pathogen and predator-prey interactions. The first part focuses on epidemiology, i. e., the dynamics of infectious diseases, and the estimation of parameters using the epidemiological data from two different diseases, phocine distemper virus that affects harbor seals in Europe, and the outbreak of HIV/AIDS in Cuba. The second part analyzes the stability of the predator-prey populations that are spatially organized into discrete units or patches. Patches are connected by dispersing individuals that may, or may not differ in the duration of their trip. This travel time is incorporated via a dispersal delay in the interpatch migration term, and has a stabilizing effect on predator-prey dynamics.This work has been supported by the US National Science Foundation (DEB-0235692), the US Environmental Protection Agency (R-82908901), the Ocean Ventures Fund, and the Academic Programs Office

Stability of Ecological Systems: A Theoretical Review

The stability of ecological systems is a fundamental concept in ecology, which offers profound insights into species coexistence, biodiversity, and community persistence. In this article, we provide a systematic and comprehensive review on the theoretical frameworks for analyzing the stability of ecological systems. Notably, we survey various stability notions, including linear stability, sign stability, diagonal stability, D-stability, total stability, sector stability, structural stability, and higher-order stability. For each of these stability notions, we examine necessary or sufficient conditions for achieving such stability and demonstrate the intricate interplay of these conditions on the network structures of ecological systems. Finally, we explore the future prospects of these stability notions

Aggregation methods in dynamical systems and applications in population and community dynamics

Approximate aggregation techniques allow one to transform a complex system involving many coupled variables into a simpler reduced model with a lesser number of global variables in such a way that the dynamics of the former can be approximated by that of the latter. In ecology, as a paradigmatic example, we are faced with modelling complex systems involving many variables corresponding to various interacting organization levels. This review is devoted to approximate aggregation methods that are based on the existence of different time scales, which is the case in many real systems as ecological ones where the different organization levels (individual, population, community and ecosystem) possess a different characteristic time scale. Two main goals of variables aggregation are dealt with in this work. The first one is to reduce the dimension of the mathematical model to be handled analytically and the second one is to understand how different organization levels interact and which properties of a given level emerge at other levels. The review is organized in three sections devoted to aggregation methods associated to different mathematical formalisms: ordinary differential equations, infinite-dimensional evolution equations and difference equations

Interacting populations : hosts and pathogens, prey and predators

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Biology, 2007.Includes bibliographical references.The interactions between populations can be positive, neutral or negative. Predation and parasitism are both relationships where one species benefits from the interaction at the expense of the other. Predators kill their prey instantly and use it only for food, whereas parasites use their hosts both as their habitat and their food. I am particularly interested in microbial parasites (including bacteria, fungi, viri, and some protozoans) since they cause many infectious diseases. This thesis considers two different points in the population-interaction spectrum and focuses on modeling host-pathogen and predator-prey interactions. The first part focuses on epidemiology, i. e., the dynamics of infectious diseases, and the estimation of parameters using the epidemiological data from two different diseases, phocine distemper virus that affects harbor seals in Europe, and the outbreak of HIV/AIDS in Cuba. The second part analyzes the stability of the predator-prey populations that are spatially organized into discrete units or patches. Patches are connected by dispersing individuals that may, or may not differ in the duration of their trip. This travel time is incorporated via a dispersal delay in the interpatch migration term, and has a stabilizing effect on predator-prey dynamics.by Petra Klepac.Ph.D