Some generalizations of Bailey's birth death and migration model

1970 ◽  
Vol 2 (1) ◽  
pp. 83-109 ◽  
Author(s):  
A. W. Davis
Keyword(s):  
Diffusion Process ◽  
Hypergeometric Functions ◽  
Spatial Location ◽  
Death Process ◽  
Birth And Death Process ◽  
Limiting Distributions ◽  
Migration Model ◽  
Branching Diffusion ◽  
And Migration ◽  
Natural Measures

Some results for a general Markov branching-diffusion process are presented, and applied to a model recently considered by Bailey. Moments of the limiting distributions of certain natural measures of the spatial location and dispersion of the population are shown to be expressible in terms of the Lauricella FD-type hypergeometric functions, when the population multiplies according to the simple birth and death process with λ > μ.

Some generalizations of Bailey's birth death and migration model

1970 ◽  
Vol 2 (01) ◽  
pp. 83-109 ◽  
Author(s):  
A. W. Davis
Keyword(s):  
Diffusion Process ◽  
Hypergeometric Functions ◽  
Spatial Location ◽  
Death Process ◽  
Birth And Death Process ◽  
Limiting Distributions ◽  
Migration Model ◽  
Branching Diffusion ◽  
And Migration ◽  
Natural Measures

Some results for a general Markov branching-diffusion process are presented, and applied to a model recently considered by Bailey. Moments of the limiting distributions of certain natural measures of the spatial location and dispersion of the population are shown to be expressible in terms of the LauricellaFD-type hypergeometric functions, when the population multiplies according to the simple birth and death process with λ > μ.

Velocities of propagation for stepping-stone models of population growth

1977 ◽  
Vol 14 (03) ◽  
pp. 591-597 ◽  
Author(s):  
Eric Renshaw
Keyword(s):  
Wave Profile ◽  
Death Process ◽  
Birth And Death Process ◽  
Integer Points ◽  
Ordinate Axis ◽  
Nearest Neighbours ◽  
Saddle Point Approximations ◽  
Velocity Of Propagation ◽  
Stepping Stone Models ◽  
And Migration

A population is composed of an infinite number of colonies situated at the integer points of a single co-ordinate axis. Each colony develops according to a simple birth and death process and migration is allowed between nearest neighbours only. Exact expressions are derived for both the asymptotic velocity of propagation and the shape of the wave profile as the population spreads along the axis, and it is shown that they are identical with the saddle point approximations developed by Daniels.

Velocities of propagation for stepping-stone models of population growth

1977 ◽  
Vol 14 (3) ◽  
pp. 591-597 ◽  
Author(s):  
Eric Renshaw
Keyword(s):  
Wave Profile ◽  
Death Process ◽  
Birth And Death Process ◽  
Integer Points ◽  
Ordinate Axis ◽  
Nearest Neighbours ◽  
Saddle Point Approximations ◽  
Velocity Of Propagation ◽  
Stepping Stone Models ◽  
And Migration

A population is composed of an infinite number of colonies situated at the integer points of a single co-ordinate axis. Each colony develops according to a simple birth and death process and migration is allowed between nearest neighbours only. Exact expressions are derived for both the asymptotic velocity of propagation and the shape of the wave profile as the population spreads along the axis, and it is shown that they are identical with the saddle point approximations developed by Daniels.

Stepping stone models for population growth

1974 ◽  
Vol 11 (1) ◽  
pp. 16-31 ◽  
Author(s):  
E. Renshaw
Keyword(s):  
Death Process ◽  
Exact Results ◽  
Birth And Death Process ◽  
Integer Points ◽  
Ordinate Axis ◽  
Single Colony ◽  
Probability Structure ◽  
Nearest Neighbours ◽  
Stepping Stone Models ◽  
And Migration

A population is composed of an infinite number of colonies situated at the integer points of a single co-ordinate axis. Each colony develops according to a simple birth and death process and migration is allowed between nearest neighbours. An approximate solution is obtained for the probability structure of the population size, and exact results are derived for the process when immigration is introduced into a single colony from outside the system.

Stepping stone models for population growth

1974 ◽  
Vol 11 (01) ◽  
pp. 16-31 ◽  
Author(s):  
E. Renshaw
Keyword(s):  
Death Process ◽  
Exact Results ◽  
Birth And Death Process ◽  
Integer Points ◽  
Ordinate Axis ◽  
Single Colony ◽  
Probability Structure ◽  
Nearest Neighbours ◽  
Stepping Stone Models ◽  
And Migration

A population is composed of an infinite number of colonies situated at the integer points of a single co-ordinate axis. Each colony develops according to a simple birth and death process and migration is allowed between nearest neighbours. An approximate solution is obtained for the probability structure of the population size, and exact results are derived for the process when immigration is introduced into a single colony from outside the system.

Two Families of Associated Wilson Polynomials

1990 ◽  
Vol 42 (4) ◽  
pp. 659-695 ◽  
Author(s):  
M. E. H. Ismail ◽  
J. Letessier ◽  
G. Valent ◽  
J. Wimp
Keyword(s):  
Hypergeometric Functions ◽  
Initial Conditions ◽  
Death Process ◽  
Birth And Death Process ◽  
Absolutely Continuous ◽  
Generalized Hypergeometric Functions ◽  
Continuous Components ◽  
Explicit Representations ◽  
Contiguous Relations ◽  
Wilson Polynomials

AbstractTwo families of associated Wilson polynomials are introduced. Both families are birth and death process polynomials, satisfying the same recurrence relation but having different initial conditions. Contiguous relations for generalized hypergeometric functions of the type 7F6 are derived and used to find explicit representations for the polynomials and to compute the corresponding continued fractions. The absolutely continuous components of the orthogonality measures of both families are computed. Generating functions are also given.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

scholarly journals The application of137Cs and210Pbexmethods in soil erosion research of Titel loess plateau, Vojvodina, Northern Serbia

2020 ◽  
Vol 12 (1) ◽  
pp. 11-24
Author(s):  
Kristina S. Kalkan ◽  
Sofija Forkapić ◽  
Slobodan B. Marković ◽  
Kristina Bikit ◽  
Milivoj B. Gavrilov ◽  
...  
Keyword(s):  
Soil Erosion ◽  
Loess Plateau ◽  
Alternative Methods ◽  
Delivery Ratio ◽  
Undisturbed Soil ◽  
Migration Model ◽  
Erosion Rates ◽  
Soil Erosion Rates ◽  
Profile Distribution ◽  
And Migration

AbstractSoil erosion is one of the largest global problems of environmental protection and sustainable development, causing serious land degradation and environmental deterioration. The need for fast and accurate soil rate assessment of erosion and deposition favors the application of alternative methods based on the radionuclide measurement technique contrary to long-term conventional methods. In this paper, we used gamma spectrometry measurements of 137Cs and unsupported 210Pbex in order to quantify the erosion on the Titel Loess Plateau near the Tisa (Tisza) River in the Vojvodina province of Serbia. Along the slope of the study area and in the immediate vicinity eight representative soil depth profiles were taken and the radioactivity content in 1 cm thick soil layers was analyzed. Soil erosion rates were estimated according to the profile distribution model and the diffusion and migration model for undisturbed soil. The net soil erosion rates, estimated by 137Cs method range from −2.3 t ha−1 yr−1 to −2.7 t ha−1 yr−1, related to the used conversion model which is comparable to published results of similar studies of soil erosion in the region. Vertical distribution of natural radionuclides in soil profiles was also discussed and compared with the profile distribution of unsupported 210Pbex measurements. The use of diffusion and migration model to convert the results of 210Pbex activities to soil redistribution rates indicates a slightly higher net erosion of −3.7 t ha−1 yr−1 with 98% of the sediment delivery ratio.

A stochastic process related to language change

1970 ◽  
Vol 7 (01) ◽  
pp. 69-78 ◽  
Author(s):  
Barron Brainerd
Keyword(s):  
Stochastic Process ◽  
Language Change ◽  
Death Process ◽  
Birth And Death Process ◽  
Standard Methods

The purpose of this note is two-fold. First, to introduce the mathematical reader to a group of problems in the study of language change which has received little attention from mathematicians and probabilists. Secondly, to introduce a birth and death process, arising naturally out of this group of problems, which has received little attention in the literature. This process can be solved using the standard methods and the solution is exhibited here.

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