A simple method for finding explicit analytic transition densities of diffusion processes with general diploid selection.

نویسندگان

  • Yun S Song
  • Matthias Steinrücken
چکیده

The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An explicit transition density expansion for a multi-allelic Wright-Fisher diffusion with general diploid selection.

Characterizing time-evolution of allele frequencies in a population is a fundamental problem in population genetics. In the Wright-Fisher diffusion, such dynamics is captured by the transition density function, which satisfies well-known partial differential equations. For a multi-allelic model with general diploid selection, various theoretical results exist on representations of the transitio...

متن کامل

SpectralTDF: transition densities of diffusion processes with time-varying selection parameters, mutation rates and effective population sizes

MOTIVATION In the Wright-Fisher diffusion, the transition density function describes the time evolution of the population-wide frequency of an allele. This function has several practical applications in population genetics and computing it for biologically realistic scenarios with selection and demography is an important problem. RESULTS We develop an efficient method for finding a spectral r...

متن کامل

Exact simulation of the Wright-Fisher diffusion

The Wright-Fisher family of diffusion processes is a class of evolutionary models widely used in population genetics, with applications also in finance and Bayesian statistics. Simulation and inference from these diffusions is therefore of widespread interest. However, simulating a Wright-Fisher diffusion is difficult because there is no known closed-form formula for its transition function. In...

متن کامل

Numerical Study of Entropy Generation for Natural Convection in Cylindrical Cavities

In this paper, an enhanced computational code was developed using finite-volume method for solving the incompressible natural convection flow within the cylindrical cavities. Grids were generated by an easy method with a view to computer program providing. An explicit integration algorithm was applied to find the steady state condition. Also instead of the conventional algorithms of SIMPLE, SIM...

متن کامل

Pricing the smile in a forward LIBOR market model

We introduce two general classes of analytically-tractable diffusions for modeling forward LIBOR rates under their canonical measure. The first class is based on the assumption of forward-rate densities given by the mixture of known basic densities. We consider two fundamental examples: i) a mixture of lognormal densities, and ii) a mixture of densities associated to “hyperbolic-sine” processes...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Genetics

دوره 190 3  شماره 

صفحات  -

تاریخ انتشار 2012