The spatial distribution of Tribolium confusum

1980 ◽  
Vol 17 (4) ◽  
pp. 895-911 ◽  
Author(s):  
Eric Renshaw
Keyword(s):  
Spatial Distribution ◽  
Diffusion Process ◽  
Tribolium Confusum ◽  
Lattice Points ◽  
Closed Container ◽  
Migration Model ◽  
Birth Death

Neyman, Park and Scott (1956) describe an experiment which they performed to determine the spatial distribution of Tribolium confusum developing within a closed container. To explain the concentration of beetles at the boundary a birth–death–migration model is developed in which the beetles may migrate over a set of lattice points, and this is shown to produce a distribution of the required shape. Not only is this distribution independent of the number of lattice points, but it is also indistinguishable from the associated diffusion process.

The spatial distribution of Tribolium confusum

1980 ◽  
Vol 17 (04) ◽  
pp. 895-911 ◽  
Author(s):  
Eric Renshaw
Keyword(s):  
Spatial Distribution ◽  
Diffusion Process ◽  
Tribolium Confusum ◽  
Lattice Points ◽  
Closed Container ◽  
Migration Model ◽  
Birth Death

Neyman, Park and Scott (1956) describe an experiment which they performed to determine the spatial distribution ofTribolium confusumdeveloping within a closed container. To explain the concentration of beetles at the boundary a birth–death–migration model is developed in which the beetles may migrate over a set of lattice points, and this is shown to produce a distribution of the required shape. Not only is this distribution independent of the number of lattice points, but it is also indistinguishable from the associated diffusion process.

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.

A Multilevel birth-death particle system and its continuous diffusion

1993 ◽  
Vol 25 (03) ◽  
pp. 549-569 ◽  
Author(s):  
Yadong Wu
Keyword(s):  
Diffusion Process ◽  
Unique Solution ◽  
Diffusion Approximation ◽  
Particle System ◽  
Martingale Problem ◽  
The Moment ◽  
Birth Death

In this paper we introduce a multilevel birth-death particle system and consider its diffusion approximation which can be characterized as aM([R+)-valued process. The tightness of rescaled processes is proved and we show that the limitingM(R+)-valued process is the unique solution of theM([R+)-valued martingale problem for the limiting generator. We also study the moment structures of the limiting diffusion process.

The Numic Spread: A Computer Simulation

1992 ◽  
Vol 57 (1) ◽  
pp. 85-99 ◽  
Author(s):  
David A. Young ◽  
Robert L. Bettinger
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Spatial Distribution ◽  
Differential Equations ◽  
Diffusion Process ◽  
Great Basin ◽  
Demographic Variables ◽  
Migration Rates ◽  
Ethnographic Data ◽  
Competing Populations

We develop a mathematical model for the spread of Numic-speaking peoples across the Great Basin in the second millennium A.D., in accord with the ideas of Bettinger and Baumhoff (1982), who suggested a competitive interaction between the Numic and Prenumic peoples of the region. We construct differential equations representing two competing populations that spread by a diffusion process across an area representing the Great Basin. The demographic variables are fixed to agree with ethnographic data, while the migration rates are fitted to the estimated time for the completion of the spread. The model predicts a spatial distribution of the Numic languages in satisfactory agreement with observations and suggests new avenues of investigation.

Study on Pseudolarix amabilis Population Spatial Distribution Pattern

2012 ◽  
Vol 485 ◽  
pp. 221-224 ◽  
Author(s):  
Ren Yan Duan ◽  
Min Yi Huang ◽  
Fei Lin ◽  
Yue Zhang
Keyword(s):  
Spatial Distribution ◽  
Diffusion Process ◽  
Distribution Pattern ◽  
Spatial Patterns ◽  
Field Data ◽  
Spatial Distribution Pattern ◽  
Morisita Index ◽  
Pattern Scale ◽  
Population Spatial Distribution ◽  
Peak Value

Field data were sampled by the method of contiguous grid quadrate. The spatial patterns of Pseudolarix amabilis populations were studied by the following methods: DispItalic textersal index (C), David moores index (I), Lloyd index (m*/m), Morisita index (Iδ), Parameter of negative index (K) and Cassie index (1/K). The quadrate variance analysis, Greig-Smith and Kershaw methods were used to study the spatial distribution pattern, pattern scale and pattern intensity of Pinus armandi population at different sizes. The result showed that P. amabilis population is most clumped. The result indicated the pattern intensity was decreasing with the size increasing and a single peak value appeared in the curve with the area increasing. There was a slow change in the pattern intensity of population, which means a smaller variation in environment and a bigger difference in the relative density of population patches during diffusion process.

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.

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