272 research outputs found
Ergodic behavior of locally regulated branching populations
For a class of processes modeling the evolution of a spatially structured
population with migration and a logistic local regulation of the reproduction
dynamics, we show convergence to an upper invariant measure from a suitable
class of initial distributions. It follows from recent work of Alison Etheridge
that this upper invariant measure is nontrivial for sufficiently large
super-criticality in the reproduction. For sufficiently small
super-criticality, we prove local extinction by comparison with a mean field
model. This latter result extends also to more general local reproduction
regulations.Comment: Published at http://dx.doi.org/10.1214/105051606000000745 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
The process of most recent common ancestors in an evolving coalescent
Consider a haploid population which has evolved through an exchangeable
reproduction dynamics, and in which all individuals alive at time have a
most recent common ancestor (MRCA) who lived at time , say. As time goes
on, not only the population but also its genealogy evolves: some families will
get lost from the population and eventually a new MRCA will be established. For
a time-stationary situation and in the limit of infinite population size
with time measured in generations, i.e. in the scaling of population
genetics which leads to Fisher-Wright diffusions and Kingman's coalescent, we
study the process whose jumps form the point process of
time pairs when new MRCAs are established and when they lived. By
representing these pairs as the entrance and exit time of particles whose
trajectories are embedded in the look-down graph of Donnelly and Kurtz (1999)
we can show by exchangeability arguments that the times as well as the
times from a Poisson process. Furthermore, the particle representation
helps to compute various features of the MRCA process, such as the distribution
of the coalescent at the instant when a new MRCA is established, and the
distribution of the number of MRCAs to come that live in today's past
A path-valued Markov process indexed by the ancestral mass
A family of Feller branching diffusions , , with nonlinear
drift and initial value can, with a suitable coupling over the {\em
ancestral masses} , be viewed as a path-valued process indexed by . For a
coupling due to Dawson and Li, which in case of a linear drift describes the
corresponding Feller branching diffusion, and in our case makes the path-valued
process Markovian, we find an SDE solved by , which is driven by a random
point measure on excursion space. In this way we are able to identify the
infinitesimal generator of the path-valued process. We also establish path
properties of using various couplings of with classical
Feller branching diffusions.Comment: 23 pages, 1 figure. This version will appear in ALEA. Compared to v1,
it contains amendmends mainly in Sec. 2 and in the proof of Proposition 4.
Wage Subsidies, Work Incentives, and the Reform of the Austrian Welfare System
We analyze the labor supply and income effects of a needs-based minimum benefit system ("Bedarfsorientierte Mindestsicherung") to be introduced in Austria by the end of this/beginning of next year. The aim of this reform is to reduce poverty as well as increasing employment rates of recipients of social assistance. On the basis of a behavioral microsimulation model we show that this new system will slightly increase incomes for the poorest households and slightly reduce labor supply due to the generous allowances for marginal employment under the current and the planned regulations of unemployment assistance. As an alternative, we analyze a reform proposal which reduces financial incentives for marginal employment not covered by social security, and rewards working longer hours by a wage subsidy. Although this alternative reform would yield modest positive labor supply effects, a relatively large number of households would suffer income losses.work incentives, labor supply, social safety system, microsimulation
Trees under attack: a Ray-Knight representation of Feller's branching diffusion with logistic growth
We obtain a representation of Feller's branching diffusion with logistic
growth in terms of the local times of a reflected Brownian motion with a
drift that is affine linear in the local time accumulated by at its current
level. As in the classical Ray-Knight representation, the excursions of are
the exploration paths of the trees of descendants of the ancestors at time
, and the local time of at height measures the population size at
time (see e.g. \cite{LG4}). We cope with the dependence in the reproduction
by introducing a pecking order of individuals: an individual explored at time
and living at time is prone to be killed by any of its
contemporaneans that have been explored so far. The proof of our main result
relies on approximating with a sequence of Harris paths which figure
in a Ray-Knight representation of the total mass of a branching particle
system. We obtain a suitable joint convergence of together with its local
times {\em and} with the Girsanov densities that introduce the dependence in
the reproduction
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