scholarly journals Probability of Identity by Descent in Metapopulations

Genetics ◽  
1999 ◽  
Vol 152 (3) ◽  
pp. 1217-1228
Author(s):  
Ingemar Kaj ◽  
Martin Lascoux
Keyword(s):  
Population Size ◽  
Colony Size ◽  
Continuous Time ◽  
Identity By Descent ◽  
Moran Model ◽  
Metapopulation Models ◽  
Size Model ◽  
Varying Population ◽  
F Statistics ◽  
Birth Death

Abstract Equilibrium probabilities of identity by descent (IBD), for pairs of genes within individuals, for genes between individuals within subpopulations, and for genes between subpopulations are calculated in metapopulation models with fixed or varying colony sizes. A continuous-time analog to the Moran model was used in either case. For fixed-colony size both propagule and migrant pool models were considered. The varying population size model is based on a birth-death-immigration (BDI) process, to which migration between colonies is added. Wright's F statistics are calculated and compared to previous results. Adding between-island migration to the BDI model can have an important effect on the equilibrium probabilities of IBD and on Wright's index.

scholarly journals A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

2021 ◽  
Author(s):  
Michel Mandjes ◽  
Birgit Sollie
Keyword(s):  
Continuous Time ◽  
Real Life ◽  
Numerical Approach ◽  
Time Dependent ◽  
Death Process ◽  
Continuous Time Markov Chain ◽  
Likelihood Estimator ◽  
Real Life Data ◽  
The Matrix ◽  
Birth Death

AbstractThis paper considers a continuous-time quasi birth-death (qbd) process, which informally can be seen as a birth-death process of which the parameters are modulated by an external continuous-time Markov chain. The aim is to numerically approximate the time-dependent distribution of the resulting bivariate Markov process in an accurate and efficient way. An approach based on the Erlangization principle is proposed and formally justified. Its performance is investigated and compared with two existing approaches: one based on numerical evaluation of the matrix exponential underlying the qbd process, and one based on the uniformization technique. It is shown that in many settings the approach based on Erlangization is faster than the other approaches, while still being highly accurate. In the last part of the paper, we demonstrate the use of the developed technique in the context of the evaluation of the likelihood pertaining to a time series, which can then be optimized over its parameters to obtain the maximum likelihood estimator. More specifically, through a series of examples with simulated and real-life data, we show how it can be deployed in model selection problems that involve the choice between a qbd and its non-modulated counterpart.

The eastern horseshoe bat, Rhinolophus megaphyllus, in south-east Queensland, Australia: colony demography and dynamics, activity levels, seasonal weight changes, and capture-recapture analyses

2001 ◽  
Vol 28 (4) ◽  
pp. 425 ◽  
Author(s):  
R. A. Young
Keyword(s):  
Population Size ◽  
Colony Size ◽  
Activity Levels ◽  
Adult Males ◽  
Weight Changes ◽  
Adult Females ◽  
Colony Demography ◽  
Capture Recapture ◽  
Horseshoe Bat ◽  
Size Estimates

During this study, 634 eastern hoseshoe bats, Rhinolophus megaphyllus, were captured at three colonies in south-east Queensland, with most data coming from two colonies (Anjuramba mine and Ravensbourne cave). Colony size, sex ratios, age structure, and colony function varied between colonies and with season. Capture–recapture data of banded bats was used to monitor movement patterns, seasonal weight changes, colony-size estimates at Anjuramba (JOLLY model), and the recapture frequency according to sex and age. The JOLLY estimator of the population size over-estimated the actual population at Anjuramba on most occasions but paralleled changes in population size. Of the 319 bats banded, 21.9% were recaptured, with only one recovery involving a movement between roosts. Adult males have a high roost-site fidelity and are more sedentary than adult females. The recapture rate and recapture frequency for adult males was significantly higher than for adult females. R. megaphyllus is active throughout the year but may enter torpor for short periods, with more females than males observed in torpor. There was no significant association between torpor and season. Longevity records of 7 years and 1 month were recorded for a sub-adult female and 7 years and 7 months for a juvenile female.

A branching model by population size dependence

1975 ◽  
Vol 7 (03) ◽  
pp. 495-510
Author(s):  
Carla Lipow
Keyword(s):  
Limit Theorem ◽  
Population Size ◽  
Generating Function ◽  
Continuous Time ◽  
Branching Process ◽  
Size Dependence ◽  
Stationary Measure ◽  
Markov Branching Process ◽  
Branching Model

A continuous-time Markov branching process is modified to allow some dependence of offspring generating function on population size. The model involves a given population size M, below which the offspring generating function is supercritical and above which it is subcritical. Immigration is allowed when the population size is 0. The process has a stationary measure, and an expression for its generating function is found. A limit theorem for the stationary measure as M tends to ∞ is then obtained.

The Wright–Fisher model with varying selection

1986 ◽  
Vol 23 (02) ◽  
pp. 504-508
Author(s):  
N. C. Weber
Keyword(s):  
Population Growth ◽  
Population Size ◽  
Sufficient Conditions ◽  
Selective Advantage ◽  
Fisher Model ◽  
Ultimate Homozygosity ◽  
Varying Population

The Wright–Fisher model with varying population size is examined in the case where the selective advantage varies from generation to generation. Models are considered where the selective advantage is not always in favour of a particular genotype. Sufficient conditions in terms of the selection coefficients and the population growth are given to ensure ultimate homozygosity.

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