| 31. |
- Jagers, Peter, 1941, et al.
(författare)
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Viability of small populations experiencing recurring catastrophes
- 2009
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Ingår i: Mathematical Population Studies. - 0889-8480. ; 16:3, s. 177-198
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Tidskriftsartikel (refereegranskat)abstract
- Some small populations are characterized by periods of exponential growth, interrupted by sudden declines in population number. These declines may be linked to the population size itself, for example through overexploitation of local resources. We estimate the longterm population extinction risk and the time to extinction for thistype of repeatedly collapsing populations. Our method is based on general branching processes, allowing realistic modelling of reproduction patterns, litter (or brood or clutch) sizes, and life span distributions, as long as individuals reproduce freely and density effects are absent. But as the population grows, two extrinsic factors enter: habitat carrying capacity and severity of decline after hitting the carrying capacity. The reproductive behaviour of individuals during periods when the population is not experiencing any density effects also has a fundamental impact on the development. In particular, this concerns the population's potentialfor recovery, as mirrored by the intrinsic rate of increase as well as the extinction probability of separate family lines of unhampered populations. Thus, the details of life history which shape demographic stochasticity and determine both rate of increase and extinction probability of freely growing populations,can have a strong effect on overall population extinction risk. We are interested in consequences for evolution of life history strategies inthis type of systems. We compare time to extinction of asingle large system (high carrying capacity) with that of a population distributed over several small patches, andfind that for non-migrating systems a single large ispreferable to several small habitats.
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| 32. |
- Lalam, Nadia, 1976, et al.
(författare)
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Estimation of the PCR efficiency based on a size-dependent modelling of the amplification process
- 2005
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Ingår i: Comptes Rendus Mathematique. - : Elsevier BV. - 1631-073X. ; 341:10, s. 631-634
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Tidskriftsartikel (refereegranskat)abstract
- We propose a stochastic modelling of the PCR amplification process by a size-dependent branching process starting as a supercritical Bienaymé-Galton-Watson transient phase and then having a saturation near-critical size-dependent phase. This model based on the concept of saturation allows one to estimate the probability of replication of a DNA molecule at each cycle of a single PCR trajectory with a very good accuracy.
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| 33. |
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| 34. |
- Sagitov, Serik, 1956, et al.
(författare)
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Coalescent approximation for structured populations in a stationary random environment
- 2010
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Ingår i: Theoretical Population Biology. - : Elsevier BV. - 0040-5809 .- 1096-0325. ; 78:3, s. 192-199
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Tidskriftsartikel (refereegranskat)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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| 35. |
- Sagitov, Serik, 1956, et al.
(författare)
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Evolutionary branching in a stochastic population model with discrete mutational steps
- 2013
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Ingår i: Theoretical Population Biology. - : Elsevier BV. - 0040-5809 .- 1096-0325. ; 83, s. 145-154
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Tidskriftsartikel (refereegranskat)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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| 36. |
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| 37. |
- Vatutin, V.A., et al.
(författare)
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A Decomposable Branching Process in a Markovian Environment
- 2012
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Ingår i: International Journal of Stochastic Analysis. - : Hindawi Limited. - 2090-3332 .- 2090-3340. ; :Article ID 694285
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Tidskriftsartikel (refereegranskat)abstract
- A population has two types of individuals, with each occupying an island. One of those, where individuals of type 1 live, offers a variable environment. Type 2 individuals dwell on the other island, in a constant environment. Only one-way migration is possible. We study then asymptotics of the survival probability in critical and subcritical cases.
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| 38. |
- Yen Fan, Jie, 1988, et al.
(författare)
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LIMIT THEOREMS FOR MULTI-TYPE GENERAL BRANCHING PROCESSES WITH POPULATION DEPENDENCE
- 2020
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Ingår i: Advances in Applied Probability. - : Cambridge University Press (CUP). - 0001-8678 .- 1475-6064. ; 52:4, s. 1127-1163
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Tidskriftsartikel (refereegranskat)abstract
- A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the population as a measure-valued process and obtain its asymptotics as the population grows with the environmental carrying capacity. Thus, a deterministic approximation is given, in the form of a law of large numbers, as well as a central limit theorem. This general framework is then adapted to model sexual reproduction, with a special section on serial monogamic mating systems.
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