1,274 research outputs found
Impact of climate change on insect pests of trees
There are many interactions and it is exetremely difficult to predict the impact of climate change on insect pests in the future, but we may expect an increase of certain primary pests as well as secondary pests and invasive specie
The coalescent effective size of age-structured populations
We establish convergence to the Kingman coalescent for a class of
age-structured population models with time-constant population size. Time is
discrete with unit called a year. Offspring numbers in a year may depend on
mother's age.Comment: Published at http://dx.doi.org/10.1214/105051605000000223 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Rank-dependent Galton-Watson processes and their pathwise duals
We introduce a modified Galton-Watson process using the framework of an
infinite system of particles labeled by , where is the rank of the
particle born at time . The key assumption concerning the offspring numbers
of different particles is that they are independent, but their distributions
may depend on the particle label . For the associated system of coupled
monotone Markov chains, we address the issue of pathwise duality elucidated by
a remarkable graphical representation, with the trajectories of the primary
Markov chains and their duals coalescing together to form forest graphs on a
two-dimensional grid
Splitting trees with neutral Poissonian mutations II: Largest and Oldest families
We consider a supercritical branching population, where individuals have
i.i.d. lifetime durations (which are not necessarily exponentially distributed)
and give birth (singly) at constant rate. We assume that individuals
independently experience neutral mutations, at constant rate during
their lifetimes, under the infinite-alleles assumption: each mutation
instantaneously confers a brand new type, called allele or haplotype, to its
carrier. The type carried by a mother at the time when she gives birth is
transmitted to the newborn. We are interested in the sizes and ages at time
of the clonal families carrying the most abundant alleles or the oldest ones,
as , on the survival event. Intuitively, the results must depend on
how the mutation rate and the Malthusian parameter compare.
Hereafter, is the population size at time , constants
are scaling constants, whereas are explicit positive constants which
depend on the parameters of the model. When , the most abundant
families are also the oldest ones, they have size and
age . When , the oldest families have age and tight sizes; the most abundant families have sizes
and all have age . When
, the oldest families have age and tight sizes;
the most abundant families have sizes and all
have age . Those informal results can be stated rigorously in expectation.
Relying heavily on the theory of coalescent point processes, we are also able,
when , to show convergence in distribution of the joint,
properly scaled ages and sizes of the most abundant/oldest families and to
specify the limits as some explicit Cox processes
On the continued Erlang loss function
We prove two fundamental results in teletraffic theory. The first is the frequently conjectured convexity of the analytic continuation B(x, a) of the classical Erlang loss function as a function of x, x 0. The second is the uniqueness of the solution of the basic set of equations associated with the ‘equivalent random method’
Coalescent approximation for structured populations in a stationary random environment
We establish convergence to the Kingman coalescent for the genealogy of a
geographically - or otherwise - structured version of the Wright-Fisher
population model with fast migration. The new feature is that migration
probabilities may change in a random fashion. This brings a novel formula for
the coalescent effective population size (EPS). We call it a quenched EPS to
emphasize the key feature of our model - random environment. The quenched EPS
is compared with an annealed (mean-field) EPS which describes the case of
constant migration probabilities obtained by averaging the random migration
probabilities over possible environments
Populations with interaction and environmental dependence: from few, (almost) independent, members into deterministic evolution of high densities
Many populations, e.g. of cells, bacteria, viruses, or replicating DNA
molecules, start small, from a few individuals, and grow large into a
noticeable fraction of the environmental carrying capacity . Typically, the
elements of the initiating, sparse set will not be hampering each other and
their number will grow from in a branching process or Malthusian
like, roughly exponential fashion, , where is the size at
discrete time , is the offspring mean per individual (at the
low starting density of elements, and large ), and a sum of i.i.d.
random variables. It will, thus, become detectable (i.e. of the same order as
) only after around generations, when its density will
tend to be strictly positive. Typically, this entity will be random, even if
the very beginning was not at all stochastic, as indicated by lower case ,
due to variations during the early development. However, from that time
onwards, law of large numbers effects will render the process deterministic,
though initiated by the random density at time log , expressed through the
variable . Thus, acts both as a random veil concealing the start and a
stochastic initial value for later, deterministic population density
development. We make such arguments precise, studying general density and also
system-size dependent, processes, as . As an intrinsic size
parameter, may also be chosen to be the time unit. The fundamental ideas
are to couple the initial system to a branching process and to show that late
densities develop very much like iterates of a conditional expectation
operator.Comment: presented at IV Workshop on Branching Processes and their
Applications at Badajoz, Spain, 10-13 April, 201
Information criteria determine the number of active sources
With the neuroelectromagnetic inverse problem, the optimal choice of the number of sources is a difficult problem, especially in the presence of correlated noise. In this paper we present a number of information criteria that help to solve this problem. They are based on the probability density function of the measurements or their eigenvalues. Make use of the Akaike or MDL (minimum description length) correction term and all employ some sort of noise information. By extensive simulations we investigated the conditions under which these criteria yield reliable estimations. We were able to quantify two major factors of influence: (1) the precision of the noise information and (2) the signal-to-noise ratio (SNR). Here defined as the ratio of the smallest signal eigenvalues and the average of the noise eigenvalues. Furthermore, we found that the Akaike correction term tends to overestimate, due to its greater sensibility to the precision of the noise informatio
Convergence of the age structure of general schemes of population processes
We consider a family of general branching processes with reproduction
parameters depending on the age of the individual as well as the population age
structure and a parameter , which may represent the carrying capacity. These
processes are Markovian in the age structure. In a previous paper the Law of
Large Numbers as was derived. Here we prove the Central Limit
Theorem, namely the weak convergence of the fluctuation processes in an
appropriate Skorokhod space. We also show that the limit is driven by a
stochastic partial differential equation
Limit theorems for multi-type general branching processes with population dependence
A general multi-type population model is considered, where individuals live
and reproduce according to their age and type, but also under the influence of
the size and composition of the entire population. We describe the dynamics of
the population density as a measure-valued process and obtain its asymptotics,
as the population grows with the environmental carrying capacity. "Density" in
this paper generally refers to the population size as compared to the carrying
capacity. Thus, a deterministic approximation is given, in the form of a Law of
Large Numbers, as well as a Central Limit Theorem. Migration can also be
incorporated. This general framework is then adapted to model sexual
reproduction, with a special section on serial monogamic mating systems
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