Weak convergence to the coalescent in neutral population models

1999 ◽  
Vol 36 (2) ◽  
pp. 446-460 ◽  
Author(s):  
M. Möhle
Keyword(s):  
Weak Convergence ◽  
Population Size ◽  
Large Class ◽  
Total Population ◽  
Population Models ◽  
Total Population Size ◽  
Hitting Probabilities ◽  
Time Scaling ◽  
Convergence Behaviour ◽  
Or Genes

For a large class of neutral population models the asymptotics of the ancestral structure of a sample of n individuals (or genes) is studied, if the total population size becomes large. Under certain conditions and under a well-known time-scaling, which can be expressed in terms of the coalescence probabilities, weak convergence in DE([0,∞)) to the coalescent holds. Further the convergence behaviour of the jump chain of the ancestral process is studied. The results are used to approximate probabilities which are of certain interest in applications, for example hitting probabilities.

Weak convergence to the coalescent in neutral population models

1999 ◽  
Vol 36 (02) ◽  
pp. 446-460 ◽  
Author(s):  
M. Möhle
Keyword(s):  
Weak Convergence ◽  
Population Size ◽  
Large Class ◽  
Total Population ◽  
Population Models ◽  
Total Population Size ◽  
Hitting Probabilities ◽  
Time Scaling ◽  
Convergence Behaviour ◽  
Or Genes

For a large class of neutral population models the asymptotics of the ancestral structure of a sample of n individuals (or genes) is studied, if the total population size becomes large. Under certain conditions and under a well-known time-scaling, which can be expressed in terms of the coalescence probabilities, weak convergence in D E ([0,∞)) to the coalescent holds. Further the convergence behaviour of the jump chain of the ancestral process is studied. The results are used to approximate probabilities which are of certain interest in applications, for example hitting probabilities.

scholarly journals Carrying Capacity of a Population Diffusing in a Heterogeneous Environment

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 49 ◽  
Author(s):  
D.L. DeAngelis ◽  
Bo Zhang ◽  
Wei-Ming Ni ◽  
Yuanshi Wang
Keyword(s):  
Population Size ◽  
Carrying Capacity ◽  
Heterogeneous System ◽  
Total Population ◽  
Reaction Diffusion ◽  
Maximum Growth ◽  
Reaction Diffusion Equations ◽  
Logistic Growth ◽  
Chemostat Model ◽  
Total Population Size

The carrying capacity of the environment for a population is one of the key concepts in ecology and it is incorporated in the growth term of reaction-diffusion equations describing populations in space. Analysis of reaction-diffusion models of populations in heterogeneous space have shown that, when the maximum growth rate and carrying capacity in a logistic growth function vary in space, conditions exist for which the total population size at equilibrium (i) exceeds the total population that which would occur in the absence of diffusion and (ii) exceeds that which would occur if the system were homogeneous and the total carrying capacity, computed as the integral over the local carrying capacities, was the same in the heterogeneous and homogeneous cases. We review here work over the past few years that has explained these apparently counter-intuitive results in terms of the way input of energy or another limiting resource (e.g., a nutrient) varies across the system. We report on both mathematical analysis and laboratory experiments confirming that total population size in a heterogeneous system with diffusion can exceed that in the system without diffusion. We further report, however, that when the resource of the population in question is explicitly modeled as a coupled variable, as in a reaction-diffusion chemostat model rather than a model with logistic growth, the total population in the heterogeneous system with diffusion cannot exceed the total population size in the corresponding homogeneous system in which the total carrying capacities are the same.

Bionomics of Dytiscus alaskanus J. Balfour-Browne (Coleoptera: Dytiscidae) in a central Alberta lake

1985 ◽  
Vol 63 (6) ◽  
pp. 1316-1323 ◽  
Author(s):  
R. B. Aiken ◽  
C. W. Wilkinson
Keyword(s):  
Life History ◽  
Life Cycle ◽  
North America ◽  
Population Growth ◽  
Population Size ◽  
Total Population ◽  
Eutrophic Lake ◽  
North Central ◽  
Total Population Size

There are few studies of life history and population growth of large dytiscid beetles in North America. We sampled populations of Dytiscus alaskanus in a eutrophic lake in north central Alberta weekly in the summers of 1982 and 1983. Like many other temperate zone dytiscids, D. alaskanus has a univoltine life cycle. Dytiscus alaskanus prefers the area at the limit of emergent vegetation in the lake and is most often associated with shoreline vegetation of cattail and sedge. Populations of adult D. alaskanus are at a peak in the late spring and decline throughout the summer. Mark–recapture experiments allowed determination of total population size and monitoring of movement patterns in the lake. Data are discussed with reference to the relatively short summer with which these beetles must cope.

Estimation of the parameters of a branching process from migrating binomial observations

1998 ◽  
Vol 30 (4) ◽  
pp. 948-967 ◽  
Author(s):  
C. Jacob ◽  
J. Peccoud
Keyword(s):  
Confidence Interval ◽  
Asymptotic Behaviour ◽  
Population Size ◽  
Branching Process ◽  
Total Population ◽  
Initial Population ◽  
Asymptotic Confidence Interval ◽  
Total Population Size ◽  
Initial Population Size ◽  
Watson Process

This paper considers a branching process generated by an offspring distribution F with mean m < ∞ and variance σ2 < ∞ and such that, at each generation n, there is an observed δ-migration, according to a binomial law Bpvn*Nnbef which depends on the total population size Nnbef. The δ-migration is defined as an emigration, an immigration or a null migration, depending on the value of δ, which is assumed constant throughout the different generations. The process with δ-migration is a generation-dependent Galton-Watson process, whereas the observed process is not in general a martingale. Under the assumption that the process with δ-migration is supercritical, we generalize for the observed migrating process the results relative to the Galton-Watson supercritical case that concern the asymptotic behaviour of the process and the estimation of m and σ2, as n → ∞. Moreover, an asymptotic confidence interval of the initial population size is given.

scholarly journals The influence of QTL allelic diversity on QTL detection in multi-parent populations: a simulation study in sugar beet

2020 ◽  
Author(s):  
Vincent Garin ◽  
Valentin Wimmer ◽  
Dietrich Borchardt ◽  
Marcos Malosetti ◽  
Fred van Eeuwijk
Keyword(s):  
Genetic Diversity ◽  
Population Size ◽  
Confidence Intervals ◽  
Total Population ◽  
Allelic Diversity ◽  
Qtl Detection ◽  
Phenotypic Effect ◽  
Detection Power ◽  
Total Population Size ◽  
Qtl Effects

AbstractMulti-parent populations (MPPs) are important resources for studying plant genetic architecture and detecting quantitative trait loci (QTLs). In MPPs, the QTL effects can show various levels of allelic diversity, which is an important factor influencing the detection of QTLs. In MPPs, the allelic effects can be more or less specific. They can depend on an ancestor, a parent or the combination of parents in a cross. In this paper, we evaluated the effect of QTL allelic diversity on the QTL detection power in MPPs.We simulated: a) cross-specific QTLs; b) parental and ancestral QTLs; and c) bi-allelic QTLs. Inspired by a real application, we tested different MPP designs (diallel, chessboard, factorial, and NAM) derived from five or nine parents to explore the ability to sample genetic diversity and detect QTLs. Using a fixed total population size, the QTL detection power was larger in MPPs with fewer but larger crosses derived from a reduced number of parents. The use of a larger set of parents was useful to detect rare alleles with a large phenotypic effect. The benefit of using a larger set of parents was however conditioned on an increase of the total population size. We also determined empirical confidence intervals for QTL location to compare the resolution of different designs. For QTLs representing 6% of the phenotypic variation, using 1600 offspring individuals, we found 95% empirical confidence intervals of 50 and 26 cM for cross-specific and bi-allelic QTLs, respectively.MPPs derived from less parents with few but large crosses generally increased the QTL detection power. Using a larger set of parents to cover a wider genetic diversity can be useful to detect QTLs with a reduced minor allele frequency when the QTL effect is large and when the total population size is increased.

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