| 21. |
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| 22. |
- Jagers, Peter, 1941, et al.
(författare)
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Dependence and interaction in branching processes
- 2013
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Ingår i: Springer Proceedings in Mathematics and Statistics. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 2194-1009 .- 2194-1017. - 9783642335488 ; 33, s. 325-333
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Konferensbidrag (refereegranskat)abstract
- Independence of reproducing individuals can be viewed as the very defining property of branching processes. It is crucial for the most famous results of the theory, the determination of the extinction probability and the dichotomy between extinction and exponential increase. In general processes, stabilisation of the age-distribution under growth follows, and indeed of the over-all population composition, and so do the many fine results of the area, like conditional stabilisation of the size of non-extinct subcritical processes. The last two decades have witnessed repeated attempts at treating branching processes with various kinds of dependence between individuals, ranging from local dependence between close relatives only to population size dependence. Of particular interest are very recent findings on processes that change from being supercritical to subcriticality at some threshold size, the carrying capacity of the habitat. We overview the development with an emphasis on these recent results.
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| 23. |
- Jagers, Peter, 1941
(författare)
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Extinction
- 2009
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Ingår i: Math. Pop Studies. ; 16:3, s. 175-176
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Tidskriftsartikel (refereegranskat)
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| 24. |
- Jagers, Peter, 1941
(författare)
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Extinction, Persistence, and Evolution
- 2011
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Ingår i: Mathematics of Darwin's Legacy, Ed. by: Chalub, FACC; Rodrigues, JF; (Book Series: Mathematics and Biosciences in Interaction); (Conference on Mathematics of Darwin's Legacy, Univ Lisbon, Lisbon, PORTUGAL, NOV 23-24, 2009). - Basel : Springer Basel. - 9783034801218 ; , s. 91-104
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Konferensbidrag (refereegranskat)abstract
- Extinction can occur for many reasons. We have a closer look at the most basic form, extinction of populations with stable but insufficient reproduction. Then we move on to competing populations and evolutionary suicide.
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| 25. |
- Jagers, Peter, 1941, et al.
(författare)
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From Size to Age and Type Structure Dependent Branching: A First Step to Sexual Reproduction in General Population Processes
- 2016
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Ingår i: Lecture Notes in Statistics: Branching Processes and Their Applications, Workshop on Branching Processes and their Applications, WBPA 2015, Badajoz, Spain, 7-10 April 2015. - Cham : Springer International Publishing. - 0930-0325 .- 2197-7186. - 9783319316390 ; 219, s. 137-148
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Classical branching processes, even the most general, share the property that individuals are supposed to multiply independently of one another, at least given some environment that in its turn is supposed to be unaffected by the population. Only more recently have birth-and-death and branching processes been considered which allow individual reproduction to be influenced by population size. The first results, due to Klebaner, deal with Galton-Watson processes. Work on general, age-structured processes and habitats with a threshold, a so called carrying capacity, came only decades later, inspired by deterministic population dynamics. Multi-type such processes have only been analysed recently. It turns out that a two-type population (males, females) where only the latter can give birth, their fecundity however influenced by the number of males present, provides an approach to sexual reproduction without mating assumptions, like random mating, which are artificial in genereral branching processes.
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| 26. |
- 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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| 27. |
- 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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| 28. |
- 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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| 29. |
- 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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| 30. |
- Jagers, Peter, 1941
(författare)
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Matematisk Statistik
- 2014
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Ingår i: Personliga tillbakablickar över ämnesområden vid Göteborgs universitet. Del 2. - 9789198142815 ; , s. 9-14
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Den matematiska statistikens historia i Göteborg skisseras.
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