60,987 research outputs found
GillespieSSA: Implementing the Gillespie Stochastic Simulation Algorithm in R
The deterministic dynamics of populations in continuous time are traditionally described using coupled, first-order ordinary differential equations. While this approach is accurate for large systems, it is often inadequate for small systems where key species may be present in small numbers or where key reactions occur at a low rate. The Gillespie stochastic simulation algorithm (SSA) is a procedure for generating time-evolution trajectories of finite populations in continuous time and has become the standard algorithm for these types of stochastic models. This article presents a simple-to-use and flexible framework for implementing the SSA using the high-level statistical computing language R and the package GillespieSSA. Using three ecological models as examples (logistic growth, Rosenzweig-MacArthur predator-prey model, and Kermack-McKendrick SIRS metapopulation model), this paper shows how a deterministic model can be formulated as a finite-population stochastic model within the framework of SSA theory and how it can be implemented in R. Simulations of the stochastic models are performed using four different SSA Monte Carlo methods: one exact method (Gillespie's direct method); and three approximate methods (explicit, binomial, and optimized tau-leap methods). Comparison of simulation results confirms that while the time-evolution trajectories obtained from the different SSA methods are indistinguishable, the approximate methods are up to four orders of magnitude faster than the exact methods.
Structural Drift: The Population Dynamics of Sequential Learning
We introduce a theory of sequential causal inference in which learners in a
chain estimate a structural model from their upstream teacher and then pass
samples from the model to their downstream student. It extends the population
dynamics of genetic drift, recasting Kimura's selectively neutral theory as a
special case of a generalized drift process using structured populations with
memory. We examine the diffusion and fixation properties of several drift
processes and propose applications to learning, inference, and evolution. We
also demonstrate how the organization of drift process space controls fidelity,
facilitates innovations, and leads to information loss in sequential learning
with and without memory.Comment: 15 pages, 9 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/sdrift.ht
Dynamics in atomic signaling games
We study an atomic signaling game under stochastic evolutionary dynamics.
There is a finite number of players who repeatedly update from a finite number
of available languages/signaling strategies. Players imitate the most fit
agents with high probability or mutate with low probability. We analyze the
long-run distribution of states and show that, for sufficiently small mutation
probability, its support is limited to efficient communication systems. We find
that this behavior is insensitive to the particular choice of evolutionary
dynamic, a property that is due to the game having a potential structure with a
potential function corresponding to average fitness. Consequently, the model
supports conclusions similar to those found in the literature on language
competition. That is, we show that efficient languages eventually predominate
the society while reproducing the empirical phenomenon of linguistic drift. The
emergence of efficiency in the atomic case can be contrasted with results for
non-atomic signaling games that establish the non-negligible possibility of
convergence, under replicator dynamics, to states of unbounded efficiency loss
The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population
We study fixation probabilities and times as a consequence of neutral genetic
drift in subdivided populations, motivated by a model of the cultural
evolutionary process of language change that is described by the same
mathematics as the biological process. We focus on the growth of fixation times
with the number of subpopulations, and variation of fixation probabilities and
times with initial distributions of mutants. A general formula for the fixation
probability for arbitrary initial condition is derived by extending a duality
relation between forwards- and backwards-time properties of the model from a
panmictic to a subdivided population. From this we obtain new formulae,
formally exact in the limit of extremely weak migration, for the mean fixation
time from an arbitrary initial condition for Wright's island model, presenting
two cases as examples. For more general models of population subdivision,
formulae are introduced for an arbitrary number of mutants that are randomly
located, and a single mutant whose position is known. These formulae contain
parameters that typically have to be obtained numerically, a procedure we
follow for two contrasting clustered models. These data suggest that variation
of fixation time with the initial condition is slight, but depends strongly on
the nature of subdivision. In particular, we demonstrate conditions under which
the fixation time remains finite even in the limit of an infinite number of
demes. In many cases - except this last where fixation in a finite time is seen
- the time to fixation is shown to be in precise agreement with predictions
from formulae for the asymptotic effective population size.Comment: 17 pages, 8 figures, requires elsart5p.cls; substantially revised and
improved version; accepted for publication in Theoretical Population Biolog
Modeling the emergence of a new language: Naming Game with hybridization
In recent times, the research field of language dynamics has focused on the
investigation of language evolution, dividing the work in three evolutive
steps, according to the level of complexity: lexicon, categories and grammar.
The Naming Game is a simple model capable of accounting for the emergence of a
lexicon, intended as the set of words through which objects are named. We
introduce a stochastic modification of the Naming Game model with the aim of
characterizing the emergence of a new language as the result of the interaction
of agents. We fix the initial phase by splitting the population in two sets
speaking either language A or B. Whenever the result of the interaction of two
individuals results in an agent able to speak both A and B, we introduce a
finite probability that this state turns into a new idiom C, so to mimic a sort
of hybridization process. We study the system in the space of parameters
defining the interaction, and show that the proposed model displays a rich
variety of behaviours, despite the simple mean field topology of interactions.Comment: 12 pages, 10 figures, presented at IWSOS 2013 Palma de Mallorca, the
final publication will be available at LNCS http://www.springer.com/lnc
Influence of geography on language competition
Competition between languages or cultural traits diffusing in the same
geographical area is studied combining the language competition model of Abrams
and Strogatz and a human dispersal model on an inhomogeneous substrate. Also,
the effect of population growth is discussed. It is shown through numerical
experiments that the final configuration of the surviving language can be
strongly affected by geographical and historical factors. These factors are not
related to the dynamics of culture transmission, but rather to initial
population distributions as well as geographical boundaries and
inhomogeneities, which modulate the diffusion process.Comment: typos in contact information have been corrected - text/figures not
change
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