117 research outputs found
Single-crossover dynamics: finite versus infinite populations
Populations evolving under the joint influence of recombination and
resampling (traditionally known as genetic drift) are investigated. First, we
summarise and adapt a deterministic approach, as valid for infinite
populations, which assumes continuous time and single crossover events. The
corresponding nonlinear system of differential equations permits a closed
solution, both in terms of the type frequencies and via linkage disequilibria
of all orders. To include stochastic effects, we then consider the
corresponding finite-population model, the Moran model with single crossovers,
and examine it both analytically and by means of simulations. Particular
emphasis is on the connection with the deterministic solution. If there is only
recombination and every pair of recombined offspring replaces their pair of
parents (i.e., there is no resampling), then the {\em expected} type
frequencies in the finite population, of arbitrary size, equal the type
frequencies in the infinite population. If resampling is included, the
stochastic process converges, in the infinite-population limit, to the
deterministic dynamics, which turns out to be a good approximation already for
populations of moderate size.Comment: 21 pages, 4 figure
How Gaussian competition leads to lumpy or uniform species distributions
A central model in theoretical ecology considers the competition of a range
of species for a broad spectrum of resources. Recent studies have shown that
essentially two different outcomes are possible. Either the species surviving
competition are more or less uniformly distributed over the resource spectrum,
or their distribution is 'lumped' (or 'clumped'), consisting of clusters of
species with similar resource use that are separated by gaps in resource space.
Which of these outcomes will occur crucially depends on the competition kernel,
which reflects the shape of the resource utilization pattern of the competing
species. Most models considered in the literature assume a Gaussian competition
kernel. This is unfortunate, since predictions based on such a Gaussian
assumption are not robust. In fact, Gaussian kernels are a border case
scenario, and slight deviations from this function can lead to either uniform
or lumped species distributions. Here we illustrate the non-robustness of the
Gaussian assumption by simulating different implementations of the standard
competition model with constant carrying capacity. In this scenario, lumped
species distributions can come about by secondary ecological or evolutionary
mechanisms or by details of the numerical implementation of the model. We
analyze the origin of this sensitivity and discuss it in the context of recent
applications of the model.Comment: 11 pages, 3 figures, revised versio
Qualitative Multi-Objective Reachability for Ordered Branching MDPs
We study qualitative multi-objective reachability problems for Ordered
Branching Markov Decision Processes (OBMDPs), or equivalently context-free
MDPs, building on prior results for single-target reachability on Branching
Markov Decision Processes (BMDPs).
We provide two separate algorithms for "almost-sure" and "limit-sure"
multi-target reachability for OBMDPs. Specifically, given an OBMDP,
, given a starting non-terminal, and given a set of target
non-terminals of size , our first algorithm decides whether the
supremum probability, of generating a tree that contains every target
non-terminal in set , is . Our second algorithm decides whether there is
a strategy for the player to almost-surely (with probability ) generate a
tree that contains every target non-terminal in set .
The two separate algorithms are needed: we show that indeed, in this context,
"almost-sure" "limit-sure" for multi-target reachability, meaning that
there are OBMDPs for which the player may not have any strategy to achieve
probability exactly of reaching all targets in set in the same
generated tree, but may have a sequence of strategies that achieve probability
arbitrarily close to . Both algorithms run in time , where is the total bit encoding length
of the given OBMDP, . Hence they run in polynomial time when
is fixed, and are fixed-parameter tractable with respect to . Moreover, we
show that even the qualitative almost-sure (and limit-sure) multi-target
reachability decision problem is in general NP-hard, when the size of the
set of target non-terminals is not fixed.Comment: 47 page
Superprocesses as models for information dissemination in the Future Internet
Future Internet will be composed by a tremendous number of potentially
interconnected people and devices, offering a variety of services, applications
and communication opportunities. In particular, short-range wireless
communications, which are available on almost all portable devices, will enable
the formation of the largest cloud of interconnected, smart computing devices
mankind has ever dreamed about: the Proximate Internet. In this paper, we
consider superprocesses, more specifically super Brownian motion, as a suitable
mathematical model to analyse a basic problem of information dissemination
arising in the context of Proximate Internet. The proposed model provides a
promising analytical framework to both study theoretical properties related to
the information dissemination process and to devise efficient and reliable
simulation schemes for very large systems
A rotation test for behavioural point-process data
Author Posting. © Elsevier B.V., 2008. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Animal Behaviour 76 (2008): 1429-1434, doi:10.1016/j.anbehav.2008.06.016.A common problem in animal behavior is determining whether the rate at which a certain behavioural event occurs is affected by an environmental or other factor. In the example considered later in this paper, the event is a vocalization by an individual sperm whale and the factor is the operation or non-operation of an underwater sound source. A typical experiment to test for such effects involves observing animals during control and treatment periods and recording the times of the events that occur in each. In statistical terminology, the data arising from such an experiment – the times at which events of a specified type occur – represent a point process (Cox & Lewis 1978). Events in a point process are treated as having no duration. Although this is not strictly correct for behavioural events, the approximation is reasonable when the duration of events is small in relation to the interval between them.Funding for the sperm whale experiments was provided by the Office of Naval Research, the U.S. Department of the Interior Minerals Management Service Cooperative Agreements Nos. 1435-01-02-CA-321 85186 and NA87RJ0445, and the Industry Research Funding Coalition
Computational Cancer Biology: An Evolutionary Perspective
ISSN:1553-734XISSN:1553-735
Critical patch size generated by Allee effect in gypsy moth, Lymantria dispar (L.)
Allee effects are important dynamical mechanisms in small-density populations in which per capita population growth rate increases with density. When positive density dependence is sufficiently severe (a ‘strong’ Allee effect), a critical density arises below which populations do not persist. For spatially distributed populations subject to dispersal, theory predicts that the occupied area also exhibits a critical threshold for population persistence, but this result has not been confirmed in nature. We tested this prediction in patterns of population persistence across the invasion front of the European gypsy moth (Lymantria dispar) in the United States in data collected between 1996 and 2008. Our analysis consistently provided evidence for effects of both population area and density on persistence, as predicted by the general theory, and confirmed here using a mechanistic model developed for the gypsy moth system. We believe this study to be the first empirical documentation of critical patch size induced by an Allee effect
The early phase of a bacterial insertion sequence infection
Bacterial insertion sequences are the simplest form of autonomous mobile DNA. It is unknown whether they need to have beneficial effects to infect and persist in bacterial populations, or whether horizontal gene transfer suffices for their persistence. We address this question by using branching process models to investigate the critical, early phase of an insertion sequence infection. We find that the probability of a successful infection is low and depends linearly on the difference between the rate of horizontal gene transfer and the fitness cost of the insertion sequences. Our models show that the median time to extinction of an insertion sequence that dies out is very short, while the median time for a successful infection to reach a modest population size is very long. We conclude that horizontal gene transfer is strong enough to allow the persistence of insertion sequences, although infection is an erratic and slow process
Evaluation of vaccination strategies for SIR epidemics on random networks incorporating household structure
This paper is concerned with the analysis of vaccination strategies in a stochastic SIR (susceptible → infected → removed) model for the spread of an epidemic amongst a population of individuals with a random network of social contacts that is also partitioned into households. Under various vaccine action models, we consider both household-based vaccination schemes, in which the way in which individuals are chosen for vaccination depends on the size of the households in which they reside, and acquaintance vaccination, which targets individuals of high degree in the social network. For both types of vaccination scheme, assuming a large population with few initial infectives, we derive a threshold parameter which determines whether or not a large outbreak can occur and also the probability and fraction of the population infected by such an outbreak. The performance of these schemes is studied numerically, focusing on the influence of the household size distribution and the degree distribution of the social network. We find that acquaintance vaccination can significantly outperform the best household-based scheme if the degree distribution of the social network is heavy-tailed. For household-based schemes, when the vaccine coverage is insufficient to prevent a major outbreak and the vaccine is imperfect, we find situations in which both the probability and size of a major outbreak under the scheme which minimises the threshold parameter are \emph{larger} than in the scheme which maximises the threshold parameter
Examining Landscape Factors Influencing Relative Distribution of Mosquito Genera and Frequency of Virus Infection
Mosquito-borne infections cause some of the most debilitating human diseases, including yellow fever and malaria, yet we lack an understanding of how disease risk scales with human-driven habitat changes. We present an approach to study variation in mosquito distribution and concomitant viral infections on the landscape level. In a pilot study we analyzed mosquito distribution along a 10-km transect of a West African rainforest area, which included primary forest, secondary forest, plantations, and human settlements. Variation was observed in the abundance of Anopheles, Aedes,Culex, and Uranotaenia mosquitoes between the different habitat types. Screening of trapped mosquitoes from the different habitats led to the isolation of five uncharacterized viruses of the families Bunyaviridae, Coronaviridae, Flaviviridae, and Rhabdoviridae, as well as an unclassified virus. Polymerase chain reaction screening for these five viruses in individual mosquitoes indicated a trend toward infection with specific viruses in specific mosquito genera that differed by habitat. Based on these initial analyses, we believe that further work is indicated to investigate the impact of anthropogenic landscape changes on mosquito distribution and accompanying arbovirus infection
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