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- Jagers, Peter, 1941, et al.
(author)
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Convergence to the coalescent in populations of substantially varying size.
- 2004
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In: J. Appl. Probab.. - 0021-9002. ; 41:2, s. 368-378
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Journal article (peer-reviewed)abstract
- Kingman's classical coalescent uncovers the basic pattern of genealogical trees of random samples of individuals in large but time-constant populations. Time is viewed as discrete and identified with non-overlapping generations. Reproduction can be very generally taken as exchangeable (meaning that the labelling of individuals in each generation carries no significance). Recent generalisations have dealt with population sizes exhibiting given deterministic or (minor) random fluctuations. We consider population sizes which constitute a stationary Markov chain, explicitly allowing large fluctuations in short times. Convergence of the genealogical tree, as population size tends to infinity, towards the (time-scaled) coalescent is simply proved under minimal conditions. As a result, a formula for effective population size obtains, generalising the well-knownharmonic mean expression for effective size.
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| 3. |
- Jagers, Peter, 1941, et al.
(author)
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General branching processes in discrete time as random trees.
- 2008
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In: Bernoulli. - 1350-7265. ; 14:4, s. 949-962
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Journal article (peer-reviewed)abstract
- The simple Galton-Watson process describes populations where individuals live one season and are then replaced by a random number of children. It can also be viewed as a way of generating random trees, each vertex being an individual of the family tree. This viewpoint has led to new insights and a revival of classical theory. We show how a similar reinterpretation can shed new light on the more interesting forms of branching processes that allow repeated bearings and, thus, overlapping generations. In particular, we use the stable pedigree law to give a transparent description of a size-biased version of general branching processes in discrete time. This allows us to analyse the xlog x condition for exponential growth of supercritical general processes, and also the relation between simple Galton-Watson and more general branching processes.
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| 6. |
- Jagers, Peter, 1941, et al.
(author)
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Stochasticity in the adaptive dynamics of evolution: the bare bones
- 2011
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In: Journal of Biological Dynamics. - : Informa UK Limited. - 1751-3758 .- 1751-3766. ; 5:2, s. 147-162
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Journal article (peer-reviewed)abstract
- First a population model with one single type of individuals is considered. Individuals reproduce asexually by splitting into two, with a population size dependent probability. Population extinction, growth and persistence are studied. Subsequently results are extended to such a population with two competing morphs.Results are applied to a simple model, where morphs arise through mutation. The movement in trait space of a monomorphic population and its possible branching into polymorphism are discussed. This is a first report.It purports to display the basic conceptual structure of a simple exact probabilistic formulation of adaptive dynamics.
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| 8. |
- Sagitov, Serik, 1956, et al.
(author)
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Coalescent approximation for structured populations in a stationary random environment
- 2010
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In: Theoretical Population Biology. - : Elsevier BV. - 0040-5809 .- 1096-0325. ; 78:3, s. 192-199
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Journal article (peer-reviewed)abstract
- We establish convergence to the Kingman coalescent for the genealogy of a geographically - or otherwise - structured version of the Wright-Fisher population model with fast migration. The new feature is that migration probabilities may change in a random fashion. This brings a novel formula for the coalescent effective population size (EPS). We call it a quenched EPS to emphasize the key feature of our model - random environment. The quenched EPS is compared with an annealed (mean-field) EPS which describes the case of constant migration probabilities obtained by averaging the random migration probabilities over possible environments.
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| 9. |
- Sagitov, Serik, 1956, et al.
(author)
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Evolutionary branching in a stochastic population model with discrete mutational steps
- 2013
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In: Theoretical Population Biology. - : Elsevier BV. - 0040-5809 .- 1096-0325. ; 83, s. 145-154
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Journal article (peer-reviewed)abstract
- Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a trait, and also by population sizes, and that mutations lead to small changes ϵ in trait value. Then, traditionally, the evolutionary dynamics is studied in the limit ϵ→0. In the present approach, small but non-negligible mutational steps are considered. By means of theoretical analysis in the limit of infinitely large populations, as well as computer simulations, we demonstrate how discrete mutational steps affect the patterns of evolutionary branching. We also argue that the average time to the first branching depends in a sensitive way on both mutational step size and population size.
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