| Titre : | Potential of branching processes as a modeling tool for conservation biology |
| Auteurs : | F. Gosselin ; J. Lebreton ; CEMAGREF NOGENT SUR VERNISSON EFNO ; CNRS MONTPELLIER CEFE |
| Type de document : | article/chapitre/communication |
| Année de publication : | 2000 |
| Format : | p. 199-225 |
| Note générale : |
Il s'agit du chap.13 de l'ouvrage Sigle : EFNO Sigle : CEMAGREF Sigle : CEFE Diffusion tous publics |
| Langues: | = Anglais |
| Catégories : | |
| Mots-clés: | ESPECE MENACEE ; ESTIMATION ; DYNAMIQUE DE POPULATION ; MODELISATION ; MODELE MATHEMATIQUE ; DENSITE DE POPULATION |
| Résumé : | The aim of this chapter is to introduce a class of extinction models, called Discrete Time Branching Processes (BP), and to present mathematical results about them that are useful in the context of population extinction. In particular, we emphasize a paradoxical form of stability when ultimate extinction is certain, called quasi-stationarity, which provides a clear conceptual background to the interplay of persistence and extinction. Quasi-stationarity is often implicit in many PVAs, especially in relation to a geometric probability distribution of time to extinction (Goodman 1987, Woolfenden and Fitzpatrick 1991, Gabriel and Bürger 1992). Although quasi-stationarity has already been explicitly used in some stochastic finite state population models (e.g., Verboom et al. 1991, Day and Possingham 1995), BPs are among the simplest individual-based, infinite state models in which quasi-stationarity can be studied formally. We hope, in turn, to convince the reader that BPs are suitable for playing a theoretical and practical role in the study of population extinction similar to that of matrix models (e.g., Caswell 1989) in the study of population growth. Our chapter is organized as follows: after having first recalled the general features of BPs (section 2), we consider in section 3 the simplest case of density-independent growth, and introduce the key notion of quasi-stationarity. In section 4, we investigate BP that account for an age structure and apply such a BP to a population of White Storks. We then introduce density dependence and random environment to a BP, first separately, then simultaneously, together with an age structure (5). Finally, we discuss the relevance of BPs as extinction models. |
| Source : | Quantitative methods for conservation biology, FERSON S., BURGMAN M. |
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