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| 2. |
- Jagers, Peter, 1941, et al.
(författare)
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General branching processes conditioned on extinction are still branching processes
- 2008
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Ingår i: Electronic Communications in Probability. - 1083-589X. ; 13, s. 540-547
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Tidskriftsartikel (refereegranskat)abstract
- It is well known that a simple, supercritical Bienaymé-Galton-Watson process turns into a subcritical such process, if conditioned to die out. We prove that the corresponding holds true for general, multi-type branching, where child-bearing may occur at different ages, life span may depend upon reproduction, and the whole course of events is thus affected by conditioning upon extinction.
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| 3. |
- Jagers, Peter, 1941, et al.
(författare)
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General branching processes in discrete time as random trees.
- 2008
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Ingår i: Bernoulli. - 1350-7265. ; 14:4, s. 949-962
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Tidskriftsartikel (refereegranskat)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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| 4. |
- Jagers, Peter, 1941, et al.
(författare)
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Markovian Paths to Extinction
- 2007
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Ingår i: Adv. Appl. Prob.. ; 39, s. 569-587
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Tidskriftsartikel (refereegranskat)
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| 5. |
- Jagers, Peter, 1941
(författare)
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Matematikens ord
- 2009
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Ingår i: LexicoNordica. ; 16, s. 315-318
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Tidskriftsartikel (refereegranskat)
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| 6. |
- Jagers, Peter, 1941, et al.
(författare)
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On the Path to Extinction
- 2007
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Ingår i: PNAS. ; 104
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Tidskriftsartikel (refereegranskat)
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| 7. |
- Jagers, Peter, 1941
(författare)
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Opinionsmätningar tar över
- 2009
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Ingår i: Dagens Nyheter. ; 2009-04-07
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 8. |
- Jagers, Peter, 1941, et al.
(författare)
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Politiken hotar matematiken
- 2009
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Ingår i: Svenska Dagbladet. ; 2009-09-02
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 9. |
- Jagers, Peter, 1941, et al.
(författare)
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The mixing advantage is less than 2
- 2009
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Ingår i: Extremes. - : Springer Science and Business Media LLC. - 1386-1999 .- 1572-915X. ; 12:1, s. 19-31
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Tidskriftsartikel (refereegranskat)abstract
- Corresponding to n independent non-negative random variables X_1,...,X_n , are values M_1,...,M_n , where each M_i is the expected value of the maximum of n independent copies of X_i. We obtain an upper bound for the expected value of the maximum of X_1,...,X_n in terms of M_1,...,M_n . This inequality is sharp in the sense that the random variables can be chosen so that the bound is approached arbitrarily closely. We also present related comparison results.
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| 10. |
- 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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