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.

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.

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.

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.

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.

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.

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.

Multi-Location Inventory Model Considering Bidirectional and Unidirectional Transshipments Simultaneously

2013 ◽  
Vol 694-697 ◽  
pp. 2742-2745
Author(s):  
Jin Hong Zhong ◽  
Yun Zhou
Keyword(s):  
Process Model ◽  
Approximate Calculation ◽  
Inventory Model ◽  
Inventory System ◽  
Death Process ◽  
Birth And Death Process ◽  
Inventory Models ◽  
Continuous Review ◽  
Poisson Demand ◽  
Queue Theory

Abstract. A cross-regional multi-site inventory system with independent Poisson demand and continuous review (S-1,S) policy, in which there is bidirectional transshipment between the locations at the same area, and unidirectional transshipment between the locations at the different area. According to the M/G/S/S queue theory, birth and death process model and approximate calculation policy, we established inventory models respectively for the loss sales case and backorder case, and designed corresponding procedures to solve them. Finally, we verify the effectiveness of proposed models and methods by means of a lot of contrast experiments.

AN AGE-DEPENDENT BIRTH AND DEATH PROCESS

Biometrika ◽  
1955 ◽  
Vol 42 (3-4) ◽  
pp. 291-306 ◽  
Author(s):  
W. A. O'N WAUGH
Keyword(s):  
Death Process ◽  
Birth And Death Process ◽  
Age Dependent
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