275 research outputs found
Models of genetic drift as limiting forms of the Lotka-Volterra competition model
The relationship between the Moran model and stochastic Lotka-Volterra
competition (SLVC) model is explored via timescale separation arguments. For
neutral systems the two are found to be equivalent at long times. For systems
with selective pressure, their behavior differs. It is argued that the SLVC is
preferable to the Moran model since in the SLVC population size is regulated by
competition, rather than arbitrarily fixed as in the Moran model. As a
consequence, ambiguities found in the Moran model associated with the
introduction of more complex processes, such as selection, are avoided.Comment: 5 pages, 4 figure
Dynamical description of vesicle growth and shape change
We systematize and extend the description of vesicle growth and shape change
using linear nonequilibrium thermodynamics. By restricting the study to shape
changes from spheres to axisymmetric ellipsoids, we are able to give a
consistent formulation which includes the lateral tension of the vesicle
membrane. This allows us to generalize and correct a previous calculation. Our
present calculations suggest that, for small growing vesicles, a prolate
ellipsoidal shape should be favored over oblate ellipsoids, whereas for large
growing vesicles oblates should be favored over prolates. The validity of this
prediction is examined in the light of the various assumptions made in its
derivation.Comment: 6 page
Intrinsic noise and discrete-time processes
A general formalism is developed to construct a Markov chain model that
converges to a one-dimensional map in the infinite population limit. Stochastic
fluctuations are therefore internal to the system and not externally specified.
For finite populations an approximate Gaussian scheme is devised to describe
the stochastic fluctuations in the non-chaotic regime. More generally, the
stochastic dynamics can be captured using a stochastic difference equation,
derived through an approximation to the Markov chain. The scheme is
demonstrated using the logistic map as a case study.Comment: Modified version accepted for publication in Phys. Rev. E Rapid
Communications. New figures adde
Reduction of a metapopulation genetic model to an effective one island model
We explore a model of metapopulation genetics which is based on a more
ecologically motivated approach than is frequently used in population genetics.
The size of the population is regulated by competition between individuals,
rather than by artificially imposing a fixed population size. The increased
complexity of the model is managed by employing techniques often used in the
physical sciences, namely exploiting time-scale separation to eliminate fast
variables and then constructing an effective model from the slow modes.
Remarkably, an initial model with 2 variables, where
is the number of islands in the metapopulation, can be reduced to a model with
a single variable. We analyze this effective model and show that the
predictions for the probability of fixation of the alleles and the mean time to
fixation agree well with those found from numerical simulations of the original
model.Comment: 16 pages, 4 figures. Supplementary material: 22 pages, 3 figure
Fixation and consensus times on a network: a unified approach
We investigate a set of stochastic models of biodiversity, population
genetics, language evolution and opinion dynamics on a network within a common
framework. Each node has a state, 0 < x_i < 1, with interactions specified by
strengths m_{ij}. For any set of m_{ij} we derive an approximate expression for
the mean time to reach fixation or consensus (all x_i=0 or 1). Remarkably in a
case relevant to language change this time is independent of the network
structure.Comment: 4+epsilon pages, two-column, RevTeX4, 3 eps figures; version accepted
by Phys. Rev. Let
Renormalization group and perfect operators for stochastic differential equations
We develop renormalization group methods for solving partial and stochastic
differential equations on coarse meshes. Renormalization group transformations
are used to calculate the precise effect of small scale dynamics on the
dynamics at the mesh size. The fixed point of these transformations yields a
perfect operator: an exact representation of physical observables on the mesh
scale with minimal lattice artifacts. We apply the formalism to simple
nonlinear models of critical dynamics, and show how the method leads to an
improvement in the computational performance of Monte Carlo methods.Comment: 35 pages, 16 figure
A spatial model of autocatalytic reactions
Biological cells with all of their surface structure and complex interior
stripped away are essentially vesicles - membranes composed of lipid bilayers
which form closed sacs. Vesicles are thought to be relevant as models of
primitive protocells, and they could have provided the ideal environment for
pre-biotic reactions to occur. In this paper, we investigate the stochastic
dynamics of a set of autocatalytic reactions, within a spatially bounded
domain, so as to mimic a primordial cell. The discreteness of the constituents
of the autocatalytic reactions gives rise to large sustained oscillations, even
when the number of constituents is quite large. These oscillations are
spatio-temporal in nature, unlike those found in previous studies, which
consisted only of temporal oscillations. We speculate that these oscillations
may have a role in seeding membrane instabilities which lead to vesicle
division. In this way synchronization could be achieved between protocell
growth and the reproduction rate of the constituents (the protogenetic
material) in simple protocells.Comment: Submitted to Phys. Rev.
- …