On an Ecological Model of Mutualisim Between Two Species With a Mortal Predator

In this paper, we study an ecological model of a three-space food chain consists of two logically growing mutual species and third species acts as a predator to second mutual species with Holling type II functional response. This model is constituted by a system of nonlinear decoupled ordinary differential equations. By using perturbed method, we identify the nature of the system at each equilibrium point and also global stability is investigated for this model using Lypanov function at the possible equilibrium points

Mathematical Models in Population Dynamics

(Statement of Responsibility) by Alexander Salisbury(Thesis) Thesis (B.A.) -- New College of Florida, 2011RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE(Bibliography) Includes bibliographical references.This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.Faculty Sponsor: Yildirim, Necmetti

Reconciling cooperation, biodiversity and stability in complex ecological communities

Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular displaying cooperative behaviors. However, standard modeling of population dynamics based on Lotka-Volterra type of equations predicts that ecosystem stability should decrease as the number of species in the community increases and that cooperative systems are less stable than communities with only competitive and/or exploitative interactions. Here we propose a stochastic model of population dynamics, which includes exploitative interactions as well as cooperative interactions induced by cross-feeding. The model is exactly solved and we obtain results for relevant macro-ecological patterns, such as species abundance distributions and correlation functions. In the large system size limit, any number of species can coexist for a very general class of interaction networks and stability increases as the number of species grows. For pure mutualistic/commensalistic interactions we determine the topological properties of the network that guarantee species coexistence. We also show that the stationary state is globally stable and that inferring species interactions through species abundance correlation analysis may be misleading. Our theoretical approach thus show that appropriate models of cooperation naturally leads to a solution of the long-standing question about complexity-stability paradox and on how highly biodiverse communities can coexist.Comment: 25 pages, 10 figure

Comparison of dynamic behavior between continuous- and discrete-time models of intraguild predation

Intraguild predation is a common ecological phenomenon that manifests itself by the aggression of one predator by another to obtain a shared prey species. In this paper, we develop a discrete analog of a stoichiometric continuous-time intraguild predation model. We analyze the dynamics of the discrete-time model, such as boundedness and invariance, stability of equilibria, and features of ecological matrices. The dynamic behavior of the two models is compared and analyzed through numerical analysis. We observe the same coexistence region of populations and stoichiometric effects of food quality of the shared prey in both models. Obvious differences between the discrete- and continuous-time models can be observed with intermediate and high levels of light intensity. The multistability characteristics and the existence interval of chaos differ among the different time scale models. This study provides evidence of the importance of time scales on intraguild predation

Modeling and analysis of a three-species food web with facilitated and intraguild predation

Biotic interactions are known to shape natural community assemblages and biodiversity. Positive interactions such as facilitation have recently received attention in ecological food webs. Mechanistic models have improved our understanding of these complex food web interactions. Here, focus is given to a three-species food web system with a beach dune natural community in mind. In the last decade, there has been a series of studies investigating intraguild predation between two major loggerhead sea turtle nest predators, North American raccoons and Atlantic ghost crabs. Studies have also highlighted that ghost crab predation assists raccoons in finding nests (i.e., facilitated predation). However, the combined effects of these two intraguild interactions and their consequences on nests have not been examined explicitly. The aims of this study were to (i) develop a three-species, ordinary differential equation model (ii) implement a sensitivity analysis to understand the influence of facilitation and other factors in driving species richness and abundance and (iii) characterize the dynamic interactions between intraguild predators and their effects on a shared resource. Interactions between ghost crabs and sea turtle eggs and facilitation can yield a wide variety of species abundance responses and were influential factors in the model. I found that high secondary sea turtle egg depredation and low facilitated predation by raccoons led to three species co-existence regions in the model. Controlling for nest predators at higher abundance levels showed that ghost crabs had a larger negative effect on sea turtle egg abundance responses when compared to raccoons. This suggests that interactions between sea turtle eggs and ghost crabs appear to be important and potential sea turtle nest management implications are discussed such as the use of ghost crab exclusion devices

Computational and mathematical modelling of plant species interactions in a harsh climate

This thesis will consider the following assumptions which are based on a few insights about the artic climate: (1)the artic climate can be characterised by a growing season called summer and a dormat season called winter (2)in the summer season growing conditions are reasonably favourable and species are more likely to compete for plentiful resources (3)in the winter season there would be no further growth and the plant populations would instead by subjected to fierce weather events such as storms which is more likely to lead to the destruction of some or all of the biomass. Under these assumptions, is it possible to find those change in the environment that might cause mutualism (see section 1.9.2) from competition (see section 1.9.1) to change? The primary aim of this thesis to to provide a prototype simulation of growth of two plant species in the artic that: (1)take account of different models for summer and winter seasons (2)permits the effects of changing climate to be seen on each type of plant species interaction

Predicting the stability, equilibrium response, and nonequilibrium dynamics of ecological systems

In this dissertation, new theory and its applications are developed to predict three properties of complex ecological communities: stability, equilibrium response, and non-equilibrium dynamics. First, a graph-theoretic analysis identifies the interconnections in a complex ecosystem that promote or diminish stability (Chapter 2). The hierarchy of interactions that influences stability and feedback processes can guide resource allocation for environmental monitoring, investigate alternative management strategies, and help formulate novel research hypotheses. Second, a combined graph-theoretic and probabilistic approach evaluates the potential for long-term changes in equilibrium (Chapter 3). Conditional probabilities of long-term increase and decrease in variables are transferred from the graph-theoretic models into a Bayesian network. The Bayesian network allows researchers both to predict how an ecosystem might change given a perturbation and to diagnose which model structure best matches empirical observations. Third, a threshold index predicts whether or not largemagnitude short-term transitory changes in disease prevalence can occur (Chapter 4). The concept of reactivity is used to derive a threshold index for epidemicity, E0, which gives the maximum number of new infections produced by an infective individual at a disease free equilibrium. This index provides a threshold that determines whether or not major epidemics are possible. The relative importance of parameters differs between control strategies that seek to reduce endemicity and those that seek to reduce epidemicity. The index E0 therefore is an important measure of epidemic potential that may assist efforts to control epidemics. Together these approaches provide new theory that help bridge the gap between our need to understand complex ecological systems and the empirical data available for their characterization

Linking anthropogenic resources to wildlife-pathogen dynamics: a review and meta-analysis

Urbanisation and agriculture cause declines for many wildlife, but some species benefit from novelresources, especially food, provided in human-dominated habitats. Resulting shifts in wildlife ecol-ogy can alter infectious disease dynamics and create opportunities for cross-species transmission,yet predicting host–pathogen responses to resource provisioning is challenging. Factors enhancingtransmission, such as increased aggregation, could be offset by better host immunity due toimproved nutrition. Here, we conduct a review and meta-analysis to show that food provisioningresults in highly heterogeneous infection outcomes that depend on pathogen type and anthropo-genic food source. We also find empirical support for behavioural and immune mechanismsthrough which human-provided resources alter host exposure and tolerance to pathogens. Areview of recent theoretical models of resource provisioning and infection dynamics shows thatchanges in host contact rates and immunity produce strong non-linear responses in pathogen inva-sion and prevalence. By integrating results of our meta-analysis back into a theoretical frame-work, we find provisioning amplifies pathogen invasion under increased host aggregation andtolerance, but reduces transmission if provisioned food decreases dietary exposure to parasites.These results carry implications for wildlife disease management and highlight areas for futurework, such as how resource shifts might affect virulence evolution