JAGERS, P. 1991. The growth and stabilization of populations. Statistical Sience 6: 269--283. Home/Search Document Not in Database Summary Related Articles Check |
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On the Formulation and Analysis of General Deterministic . . . - Diekmann, al. (1998) (Correct)
....relate to phenomena at the p level. In step 2 deterministically inclined people, such as the majority of us, use a formal law of large numbers argument to restrict to expected values, and this is exactly what we shall do in this paper. In the theory of multi type branching processes (see Jagers [20, 21] and the references given there) one takes the full probabilistic structure into account, which allows one to study, for example, fluctuations around the mean due to demographic stochasticity. For concrete examples of steps 1 2 we refer to METZ DIEKMANN [25] KOOIJMAN [23] DE ROOS, DIEKMANN ....
....follows from Lemma 2.12 by summing over k. Likewise we obtain (2.23) from Lemma 2.13 by summing over k, and (2.22) from Lemma 2.14. 3 i state development and survival So far our presentation echoes the treatment of expected behaviour in the theory of multi type branching processes (e.g. JAGERS [21] ) But now we introduce as our second ingredient u(t, x; s) #) probability that an individual which has state x at time t is alive s time units later and then has a state in # (3.1) What we have in mind is that individuals follow a Markov process with death as a hidden absorbing state. But ....
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JAGERS, P. 1991. The growth and stabilization of populations. Statistical Sience 6: 269--283.
Branching Processes - Athreya, Vidyashankar (1999) (113 citations) (Correct)
....a selection of topics. What is presented here does reflect the authors interests and preference s. Apart from the books mentioned earlier we must refer to the work of Swedish school led by Jagers on general branchging processes with greater level of dependencies. For an account of this see Jagers [44] and the references therein. We also have not dea lt with the problems of statistical inference in branching processes. Apart from the book of Guttorp [51] the work of Dion [34] with its extensive bibiliography is very helpful. We end this with an outline of the rest of the paper. The next ....
Jagers,P.(1991): The growth and stabilization of populations, Statistical Science, No. 3, 269-283.
When Does Evolution Optimise? On the relation between.. - Metz, Mylius, Diekmann (1996) (Correct)
....1986. Incidentally, although the usual definitions of r and R 0 are predicated upon all individuals being born equal, they can readily be extended to cater for variable birth states and spatial heterogeneity. The only proviso is that E should be constant in time. See e.g. Diekmann et al. 1990, Jagers, 1991, 1995, Kawecki Stearns, 1993, Koz#lowski, 1993, Diekmann Metz, 1994. Below E 0 denotes some specially chosen fixed value of E. The following proposition is an immediate corollary of proposition 3.1. 10 When Does Evolution Optimise Metz, Mylius Diekmann Proposition 4.1 r(X, E 0 ) orR 0 ....
P. Jagers. The growth and stabilization of populations. Statistical Science, 6(3): 269--283, 1991.
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