scholarly journals One-dimensional stepping stone models, sardine genetics and Brownian local time

2008 ◽  
Vol 18 (1) ◽  
pp. 334-358 ◽  
Author(s):  
Richard Durrett ◽  
Mateo Restrepo
Keyword(s):  
Local Time ◽  
One Dimensional ◽  
Stepping Stone ◽  
Brownian Local Time ◽  
Stepping Stone Models

Stepping stone models of finite length

1970 ◽  
Vol 2 (02) ◽  
pp. 229-258 ◽  
Author(s):  
Takeo Maruyama
Keyword(s):  
Monte Carlo ◽  
Population Structure ◽  
Finite Length ◽  
Correlation Coefficients ◽  
Gene Frequencies ◽  
Explicit Formulas ◽  
Stepping Stone ◽  
Monte Carlo Experiments ◽  
Stepping Stone Models ◽  
Stepping Stone Model

The stepping stone model of population structure, of finite length, is analysed with special reference to the variance, and correlation coefficients of gene frequencies. Explicit formulas for these quantities are obtained. The model is also analysed for the genetic variability maintained in the population. In order to check the validity of the analytical results, several numerical computations were carried out using two different methods: iterations and Monte Carlo experiments. The values obtained by these numerical methods agree well with the theoretical values obtained by formulas derived analytically.

Increment sizes of the principal value of Brownian local time

2000 ◽  
Vol 117 (4) ◽  
pp. 515-531 ◽  
Author(s):  
Endre Csáki ◽  
Miklós Csörgő ◽  
Antónia Földes ◽  
Zhan Shi
Keyword(s):  
Local Time ◽  
Brownian Local Time ◽  
Principal Value

A survey of stepping-stone models in population dynamics

1986 ◽  
Vol 18 (03) ◽  
pp. 581-627 ◽  
Author(s):  
Eric Renshaw
Keyword(s):  
Population Dynamics ◽  
Final Section ◽  
Main Body ◽  
Nearest Neighbour ◽  
General Applicability ◽  
Transfer Rates ◽  
Predator Prey ◽  
Stepping Stone ◽  
Vector Process ◽  
Stepping Stone Models

A survey is presented of stochastic and deterministic developments in the study of the effects of nearest-neighbour ‘migration’ between spatially separated ‘colonies’. Such processes are of general applicability, and are relevant to any vector processX(t) = (X1(t), · ··,XN(t)) in which the arrival, departure and transfer rates for the states {X(t) = n} may be written in the formαi(ni), βi(ni) andγij(ni,nj), respectively, wheren =(n1,· ··, nN). Whilst the main body of results are described in terms of birth-death, genetic and epidemic situations, the final section examines within colony interaction in the context of spatial predator-prey processes.

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