5,108 research outputs found
Moving forward in circles: challenges and opportunities in modelling population cycles
Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research
Evolution of predator dispersal in relation to spatio-temporal prey dynamics : how not to get stuck in the wrong place!
Peer reviewedPublisher PD
Robust permanence for interacting structured populations
The dynamics of interacting structured populations can be modeled by
where , , and
are matrices with non-negative off-diagonal entries. These models are
permanent if there exists a positive global attractor and are robustly
permanent if they remain permanent following perturbations of .
Necessary and sufficient conditions for robust permanence are derived using
dominant Lyapunov exponents of the with respect to
invariant measures . The necessary condition requires for all ergodic measures with support in the boundary of the
non-negative cone. The sufficient condition requires that the boundary admits a
Morse decomposition such that for all invariant
measures supported by a component of the Morse decomposition. When the
Morse components are Axiom A, uniquely ergodic, or support all but one
population, the necessary and sufficient conditions are equivalent.
Applications to spatial ecology, epidemiology, and gene networks are given
Theoretical Study of Pest Control Using Stage Structured Natural Enemies with Maturation Delay: A Crop-Pest-Natural Enemy Model
In the natural world, there are many insect species whose individual members
have a life history that takes them through two stages, immature and mature.
Moreover, the rates of survival, development, and reproduction almost always
depend on age, size, or development stage. Keeping this in mind, in this paper,
a three species crop-pest-natural enemy food chain model with two stages for
natural enemies is investigated. Using characteristic equations, a set of
sufficient conditions for local asymptotic stability of all the feasible
equilibria is obtained. Moreover, using approach as in (Beretta and Kuang,
2002), the possibility of the existence of a Hopf bifurcation for the interior
equilibrium with respect to maturation delay is explored, which shows that the
maturation delay plays an important role in the dynamical behavior of three
species system. Also obtain some threshold values of maturation delay for the
stability-switching of the particular system. In succession, using the normal
form theory and center manifold argument, we derive the explicit formulas which
determine the stability and direction of bifurcating periodic solutions.
Finally, a numerical simulation for supporting the theoretical analysis is
given.Comment: 28 pages, 9 figure
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
Permanence and periodicity of a delayed ratio-dependent predator–prey model with Holling type functional response and stage structure
AbstractA periodic and delayed ratio-dependent predator–prey system with Holling type III functional response and stage structure for both prey and predator is investigated. It is assumed that immature predator and mature individuals of each species are divided by a fixed age, and immature predator do not have the ability to attack prey. Sufficient conditions are derived for the permanence and existence of positive periodic solution of the model. Numerical simulations are presented to illustrate the feasibility of our main results
Studying Both Direct and Indirect Effects in Predator-Prey Interaction
Studying and modelling the interaction between predators and prey have been one of the central topics in ecology and evolutionary biology. In this thesis, we study two different aspects of predator-prey interaction: direct effect and indirect effect.
Firstly, we study the direct predation between predators and prey in a patchy landscape.
Secondly, we study indirect effects between predators and prey.
Thirdly, we extend our previous model by incorporating a stage-structure into prey.
Finally, we further extend our previous model by incorporating spatial structures into modelling
On the interplay of speciation and dispersal: An evolutionary food web model in space
We introduce an evolutionary metacommunity of multitrophic food webs on
several habitats coupled by migration. In contrast to previous studies that
focus either on evolutionary or on spatial aspects, we include both and
investigate the interplay between them. Locally, the species emerge, interact
and go extinct according to the rules of the well-known evolutionary food web
model proposed by Loeuille and Loreau in 2005. Additionally, species are able
to migrate between the habitats. With random migration, we are able to
reproduce common trends in diversity-dispersal relationships: Regional
diversity decreases with increasing migration rates, whereas local diversity
can increase in case of a low level of dispersal. Moreover, we find that the
total biomasses in the different patches become similar even when species
composition remains different. With adaptive migration, we observe species
compositions that differ considerably between patches and contain species that
are descendant from ancestors on both patches. This result indicates that the
combination of spatial aspects and evolutionary processes affects the structure
of food webs in different ways than each of them alone.Comment: under review at JT
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