167 research outputs found
Polymorphic evolution sequence and evolutionary branching
We are interested in the study of models describing the evolution of a
polymorphic population with mutation and selection in the specific scales of
the biological framework of adaptive dynamics. The population size is assumed
to be large and the mutation rate small. We prove that under a good combination
of these two scales, the population process is approximated in the long time
scale of mutations by a Markov pure jump process describing the successive
trait equilibria of the population. This process, which generalizes the
so-called trait substitution sequence, is called polymorphic evolution
sequence. Then we introduce a scaling of the size of mutations and we study the
polymorphic evolution sequence in the limit of small mutations. From this study
in the neighborhood of evolutionary singularities, we obtain a full
mathematical justification of a heuristic criterion for the phenomenon of
evolutionary branching. To this end we finely analyze the asymptotic behavior
of 3-dimensional competitive Lotka-Volterra systems
Direct competition results from strong competiton for limited resource
We study a model of competition for resource through a chemostat-type model
where species consume the common resource that is constantly supplied. We
assume that the species and resources are characterized by a continuous trait.
As already proved, this model, although more complicated than the usual
Lotka-Volterra direct competition model, describes competitive interactions
leading to concentrated distributions of species in continuous trait space.
Here we assume a very fast dynamics for the supply of the resource and a fast
dynamics for death and uptake rates. In this regime we show that factors that
are independent of the resource competition become as important as the
competition efficiency and that the direct competition model is a good
approximation of the chemostat. Assuming these two timescales allows us to
establish a mathematically rigorous proof showing that our resource-competition
model with continuous traits converges to a direct competition model. We also
show that the two timescales assumption is required to mathematically justify
the corresponding classic result on a model consisting of only finite number of
species and resources (MacArthur, R. Theor. Popul. Biol. 1970:1, 1-11). This is
performed through asymptotic analysis, introducing different scales for the
resource renewal rate and the uptake rate. The mathematical difficulty relies
in a possible initial layer for the resource dynamics. The chemostat model
comes with a global convex Lyapunov functional. We show that the particular
form of the competition kernel derived from the uptake kernel, satisfies a
positivity property which is known to be necessary for the direct competition
model to enjoy the related Lyapunov functional
Croissance du patudo (Thunnus obesus) de l'Océan Atlantique intertropical oriental
The growth of big eye tuna (Thunnus obesus) in the Eastern Tropical Atlantic Ocean was studied using Petersen's method, by the analysis of the length frequency data of the F.I.S. (French-Ivorian-Senegalese) surface tuna fleet from 1969 to 1977. The results are in agreement with a previous study by Champagnat and Pianet (1973) and with observations made in the Pacific Ocean
A simple mathematical model of gradual Darwinian evolution: Emergence of a Gaussian trait distribution in adaptation along a fitness gradient
We consider a simple mathematical model of gradual Darwinian evolution in
continuous time and continuous trait space, due to intraspecific competition
for common resource in an asexually reproducing population in constant
environment, while far from evolutionary stable equilibrium. The model admits
exact analytical solution. In particular, Gaussian distribution of the trait
emerges from generic initial conditions.Comment: 21 pages, 2 figures, as accepted to J Math Biol 2013/03/1
The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields
We consider an "elastic" version of the statistical mechanical monomer-dimer
problem on the n-dimensional integer lattice. Our setting includes the
classical "rigid" formulation as a special case and extends it by allowing each
dimer to consist of particles at arbitrarily distant sites of the lattice, with
the energy of interaction between the particles in a dimer depending on their
relative position. We reduce the free energy of the elastic dimer-monomer (EDM)
system per lattice site in the thermodynamic limit to the moment Lyapunov
exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value
and covariance function are the Boltzmann factors associated with the monomer
energy and dimer potential. In particular, the classical monomer-dimer problem
becomes related to the MLE of a moving average GRF. We outline an approach to
recursive computation of the partition function for "Manhattan" EDM systems
where the dimer potential is a weighted l1-distance and the auxiliary GRF is a
Markov random field of Pickard type which behaves in space like autoregressive
processes do in time. For one-dimensional Manhattan EDM systems, we compute the
MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a
compact transfer operator on a Hilbert space which is related to the
annihilation and creation operators of the quantum harmonic oscillator and also
recast it as the eigenvalue problem for a pantograph functional-differential
equation.Comment: 24 pages, 4 figures, submitted on 14 October 2011 to a special issue
of DCDS-
Stochasticity in the adaptive dynamics of evolution: The bare bones
First a population model with one single type of individuals is considered. Individuals reproduce asexually by splitting into two, with a population-size-dependent probability. Population extinction, growth and persistence are studied. Subsequently the results are extended to such a population with two competing morphs and are applied to a simple model, where morphs arise through mutation. The movement in the trait space of a monomorphic population and its possible branching into polymorphism are discussed. This is a first report. It purports to display the basic conceptual structure of a simple exact probabilistic formulation of adaptive dynamics
The frequency-dependent Wright-Fisher model: diffusive and non-diffusive approximations
We study a class of processes that are akin to the Wright-Fisher model, with
transition probabilities weighted in terms of the frequency-dependent fitness
of the population types. By considering an approximate weak formulation of the
discrete problem, we are able to derive a corresponding continuous weak
formulation for the probability density. Therefore, we obtain a family of
partial differential equations (PDE) for the evolution of the probability
density, and which will be an approximation of the discrete process in the
joint large population, small time-steps and weak selection limit. If the
fitness functions are sufficiently regular, we can recast the weak formulation
in a more standard formulation, without any boundary conditions, but
supplemented by a number of conservation laws. The equations in this family can
be purely diffusive, purely hyperbolic or of convection-diffusion type, with
frequency dependent convection. The particular outcome will depend on the
assumed scalings. The diffusive equations are of the degenerate type; using a
duality approach, we also obtain a frequency dependent version of the Kimura
equation without any further assumptions. We also show that the convective
approximation is related to the replicator dynamics and provide some estimate
of how accurate is the convective approximation, with respect to the
convective-diffusion approximation. In particular, we show that the mode, but
not the expected value, of the probability distribution is modelled by the
replicator dynamics. Some numerical simulations that illustrate the results are
also presented
Patient/family views on data sharing in rare diseases: study in the European LeukoTreat project.: Survey assessing data sharing in leukodystrophies
International audienceThe purpose of this study was to explore patient and family views on the sharing of their medical data in the context of compiling a European leukodystrophies database. A survey questionnaire was delivered with help from referral centers and the European Leukodystrophies Association, and the questionnaires returned were both quantitatively and qualitatively analyzed. This study found that patients/families were strongly in favor of participating. Patients/families hold great hope and trust in the development of this type of research. They have a strong need for information and transparency on database governance, the conditions framing access to data, all research conducted, partnerships with the pharmaceutical industry, and they also need access to results. Our findings bring ethics-driven arguments for a process combining initial broad consent with ongoing information. On both, we propose key item-deliverables to database participants
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