46 research outputs found
Limiting the spread of disease through altered migration patterns
We consider a model for an epidemic in a population that occupies
geographically distinct locations. The disease is spread within subpopulations
by contacts between infective and susceptible individuals, and is spread
between subpopulations by the migration of infected individuals. We show how
susceptible individuals can act collectively to limit the spread of disease
during the initial phase of an epidemic, by specifying the distribution that
minimises the growth rate of the epidemic when the infectives are migrating so
as to maximise the growth rate. We also give an explicit strategy that
minimises the basic reproduction number, which is also shown be optimal in
terms of the probability of extinction and total size of the epidemic
Local approximation of a metapopulation's equilibrium
We consider the approximation of the equilibrium of a metapopulation model,
in which a finite number of patches are randomly distributed over a bounded
subset of Euclidean space. The approximation is good when a large
number of patches contribute to the colonization pressure on any given
unoccupied patch, and when the quality of the patches varies little over the
length scale determined by the colonization radius. If this is the case, the
equilibrium probability of a patch at being occupied is shown to be close
to , the equilibrium occupation probability in Levins's model, at any
point not too close to the boundary, if the local colonization
pressure and extinction rates appropriate to are assumed. The approximation
is justified by giving explicit upper and lower bounds for the occupation
probabilities, expressed in terms of the model parameters. Since the patches
are distributed randomly, the occupation probabilities are also random, and we
complement our bounds with explicit bounds on the probability that they are
satisfied at all patches simultaneously
A metapopulation model with Markovian landscape dynamics
We study a variant of Hanski's incidence function model that allows habitat
patch characteristics to vary over time following a Markov process. The widely
studied case where patches are classified as either suitable or unsuitable is
included as a special case. For large metapopulations, we determine a recursion
for the probability that a given habitat patch is occupied. This recursion
enables us to clarify the role of landscape dynamics in the survival of a
metapopulation. In particular, we show that landscape dynamics affects the
persistence and equilibrium level of the metapopulation primarily through its
effect on the distribution of a local population's life span.Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0
license http://creativecommons.org/licenses/by-nc-nd/4.0
Connecting deterministic and stochastic metapopulation models
In this paper, we study the relationship between certain stochastic and
deterministic versions of Hanski's incidence function model and the spatially
realistic Levins model. We show that the stochastic version can be well
approximated in a certain sense by the deterministic version when the number of
habitat patches is large, provided that the presence or absence of individuals
in a given patch is influenced by a large number of other patches. Explicit
bounds on the deviation between the stochastic and deterministic models are
given.Comment: The final publication is available at Springer via
http://dx.doi.org/10.1007/s00285-015-0865-
The limiting behaviour of Hanski's incidence function metapopulation model
Hanski's incidence function model is one of the most widely used metapopulation models in ecology. It models the presence/absence of a species at spatially distinct habitat patches as a discrete-time Markov chain whose transition probabilities are determined by the physical landscape. In this analysis, the limiting behaviour of the model is studied as the number of patches increases and the size of the patches decreases. Two different limiting cases are identified depending on whether or not the metapopulation is initially near extinction. Basic properties of the limiting models are derived
Interaction between habitat quality and an Allee-like effect in metapopulations
We construct a stochastic patch occupancy metapopulation model that incorporates variation in habitat quality and an Allee-like effect. Using some basic results from stochastic ordering, we investigate the effect of habitat degradation on the persistence of the metapopulation. In particular, we show that for a metapopulation with Allee-like effect habitat degradation can cause a dramatic decrease in the level of persistence while in the absence of an Allee-like effect this decrease is more gradual
A New Calibrated Bayesian Internal Goodness-of-Fit Method: Sampled Posterior p-Values as Simple and General p-Values That Allow Double Use of the Data
Background: Recent approaches mixing frequentist principles with Bayesian inference propose internal goodness-of-fit (GOF) p-values that might be valuable for critical analysis of Bayesian statistical models. However, GOF p-values developed to date only have known probability distributions under restrictive conditions. As a result, no known GOF p-value has a known probability distribution for any discrepancy function. Methodology/Principal Findings: We show mathematically that a new GOF p-value, called the sampled posterior p-value (SPP), asymptotically has a uniform probability distribution whatever the discrepancy function. In a moderate finite sample context, simulations also showed that the SPP appears stable to relatively uninformative misspecifications of the prior distribution. Conclusions/Significance: These reasons, together with its numerical simplicity, make the SPP a better canonical GOF p-value than existing GOF p-values