| 31. |
|
|
| 32. |
- Jagers, Peter, 1941
(author)
-
On the Complete Life Career of Populations in Environments with a Finite Carrying Capacity
- 2015
-
In: Pliska Studia Mathematica. - 0204-9805. ; 24, s. 55-60
-
Journal article (peer-reviewed)abstract
- If a general branching process evolves in a habitat with a finite carrying capacity, i. e. a number such that reproduction turns subcritical as soon as population size exceeds that number, then the population may either die out quickly, or else grow up to arround the carrying capacity, where it will linger for a long time, until it starts decaying exponentially to extinction.
|
|
| 33. |
|
|
| 34. |
- Jagers, Peter, 1941
(author)
-
Opinionsmätningar tar över
- 2009
-
In: Dagens Nyheter. ; 2009-04-07
-
Journal article (other academic/artistic)
|
|
| 35. |
- Jagers, Peter, 1941, et al.
(author)
-
Politiken hotar matematiken
- 2009
-
In: Svenska Dagbladet. ; 2009-09-02
-
Journal article (other academic/artistic)
|
|
| 36. |
- Jagers, Peter, 1941
(author)
-
Population Dynamics: Probabilistic Extinction, Stability, and Explosion Theorems.
- 2015
-
In: International Encyclopedia of the Social & Behavioral Sciences, 2nd edition, Vol. 18. - 9780080970868 ; , s. 579-580
-
Book chapter (other academic/artistic)abstract
- The relation between individual reproduction and the probability that populations die out is given. Populations that decrease on average will, of course, always die out, but populations whose expected sizes grow can also have a high probability of extinction. Malthus's law of exponential growth of populations, i.e., not dying out, holds in general, not only for populations of independently reproducing individuals, but also under some types of interaction. The stable age distribution and general stable composition, appearing as a consequence of exponential growth, are described. Finally, populations whose size and composition may influence individual reproduction are described.
|
|
| 37. |
- Jagers, Peter, 1941, et al.
(author)
-
Population-size-dependent, age-structured branching processes linger around their carrying capacity
- 2011
-
In: Journal of Applied Probability. - 0021-9002. ; 48A, s. 249-260
-
Journal article (peer-reviewed)abstract
- Dependence of individual reproduction upon the size of the whole population is studied in a general branching process context. The particular feature under scrutiny is that of reproduction changing from supercritical in small populations to subcritical in large ones. The transition occurs when population size passes a critical threshold, known in ecology as the carrying capacity. We show that populations either die out directly, never coming close to the carrying capacity, or else they grow quickly towards the latter, subsequently lingering around it for a time that is expected to be exponentially long in terms of a carrying capacity tending to infinity.
|
|
| 38. |
|
|
| 39. |
- Jagers, Peter, 1941, et al.
(author)
-
Populations in environments with a soft carrying capacity are eventually extinct
- 2020
-
In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 81:3, s. 845-851
-
Journal article (peer-reviewed)abstract
- Consider a population whose size changes stepwise by its members reproducing or dying (disappearing), but is otherwise quite general. Denote the initial (non-random) size by Z(0) and the size of the nth change by C-n, n = 1, 2, .... Population sizes hence develop successively as Z(1) = Z(0) + C-1, Z(2) = Z(1)+ C-2 and so on, indefinitely or until there are no further size changes, due to extinction. Extinction is thus assumed final, so that Z(n) = 0 implies that Z(n+1) = 0, without there being any other finite absorbing class of population sizes. We make no assumptions about the time durations between the successive changes. In the real world, or more specific models, those may be of varying length, depending upon individual life span distributions and their interdependencies, the age-distribution at hand and intervening circumstances. We could consider toy models of Galton-Watson type generation counting or of the birth-and-death type, with one individual acting per change, until extinction, or the most general multitype CMJ branching processes with, say, population size dependence of reproduction. Changes may have quite varying distributions. The basic assumption is that there is a carrying capacity, i.e. a non-negative number K such that the conditional expectation of the change, given the complete past history, is non-positive whenever the population exceeds the carrying capacity. Further, to avoid unnecessary technicalities, we assume that the change C-n equals -1 (one individual dying) with a conditional (given the past) probability uniformly bounded away from 0. It is a simple and not very restrictive way to avoid parity phenomena, it is related to irreducibility in Markov settings. The straightforward, but in contents and implications far-reaching, consequence is that all such populations must die out. Mathematically, it follows by a supermartingale convergence property and positive probability of reaching the absorbing extinction state.
|
|
| 40. |
- Jagers, Peter, 1941, et al.
(author)
-
Random variation and concentration effects in PCR
- 2003
-
In: J. Theoret. Biol. 224, 299-304 (2003). - 0022-5193 .- 1095-8541. ; 224, s. 299-304
-
Journal article (peer-reviewed)abstract
- Even though the efficiency of the PCR reaction decreases, analyses are made in terms of Galton-Watson processes, or simple deterministic models with constant replication probability (efficiency).Recently Schnell and Mendoza have suggested that the form of the efficiency can be derived from enzyme kinetics. This results in the sequence of molecules numbers forming a stochastic process with the properties of a branching process with population size dependence, which is supercritical, but has a mean reproductionnumber that approaches one. Such processes display ultimate linear growth, after an initial exponential phase, as is the case in PCR. It is also shown that the resulting stochastic process for a large Michaelis Menten constant behaves like the deterministic sequence x_n arising by iterations of the function f(x) = x+x/(1+x).
|
|
