13. Potential of Branching Processes as a Modeling Tool
219
Conclusion
The canonical structure of BPs and the theoretical results available allow us to
handle, within the same conceptual framework, PVA models with a variety of
demographic features. The reader interested in applying BPs structures and results
to a specific PVA has the choice between developing his or her own model and
using a generic extinction simulation tool (for a review of some of these models,
see Lindenmayer et al. 1995). Among generic simulation tools, the latest version
of the software ULM (Legendre and Clobert 1995) takes explicitly into account
the theoretical results presented here.
Last, the tuning of a BP model to a specific population-environment system
based on empirical data will meet problems of parameter estimation in small
populations and of detection and assessment of a specific functional form of
density dependence. These questions, which depend critically on the quality of the
data available, are, however, not specific to BPs. Classically, the range of strategies thus spreads from a detailed PVA model, relying on extensive data (as in,
e.g., Woolfenden and Fitzpatrick 1991), to a series of different scenarios corresponding to varying assumptions and parameter values, when data are not
sufficient.
Acknowledgments. This chapter is partly based on a talk at the Second European
Congress of Mathematics Applied to Biology and Medicine (Lyon, France,
December 1993). We thank Claude Millier (Scientific Director, ENGREF) and
Jean Jacod (Probability Lab, Paris VI University) for their cooperation in this
project and for comments on a former version of the manuscript.
Literature Cited
Asmussen S, Hering H (1983) Branching processes. Birkh¨ auser, Boston, MA
Athreya KB, Karlin S (1971) Branching processes with random environments. I Annals of
Mathematical Statistics 42:1499–1520; II Annals of Mathematical Statistics 42:1843–
1858
Athreya KB, Ney PE (1972) Branching processes. Springer Verlag, New York
Bagley JH (1982) Asymptotic properties of subcritical Galton-Watson processes. Journal of
Applied Probability 19:510–517
Bairlein F (1991) Population studies of White Storks Ciconia ciconia in Europe. In: Perrins
CM, Lebreton J-D, Hirons GJM (eds) Bird population studies: relevance to conservation
and management. Oxford University Press, Oxford, UK, pp 207–229
Bart J (1995) Evaluation of population trend estimates calculated using capture recapture
and population projection methods. Ecological Applications 5:662–671
Beissinger SR (1995) Modeling extinction in periodic environments: Everglades water
levels and Snail Kite population viability. Ecological Applications 5:618–631
Box GEP, Jenkins GM (1970) Time series analysis forecasting and control. Holden-Day,
San Francisco, CA
Boyce MS (1992) Population viability analysis. Annual Review of Ecology and Systematics 23:481–506
219
Conclusion
The canonical structure of BPs and the theoretical results available allow us to
handle, within the same conceptual framework, PVA models with a variety of
demographic features. The reader interested in applying BPs structures and results
to a specific PVA has the choice between developing his or her own model and
using a generic extinction simulation tool (for a review of some of these models,
see Lindenmayer et al. 1995). Among generic simulation tools, the latest version
of the software ULM (Legendre and Clobert 1995) takes explicitly into account
the theoretical results presented here.
Last, the tuning of a BP model to a specific population-environment system
based on empirical data will meet problems of parameter estimation in small
populations and of detection and assessment of a specific functional form of
density dependence. These questions, which depend critically on the quality of the
data available, are, however, not specific to BPs. Classically, the range of strategies thus spreads from a detailed PVA model, relying on extensive data (as in,
e.g., Woolfenden and Fitzpatrick 1991), to a series of different scenarios corresponding to varying assumptions and parameter values, when data are not
sufficient.
Acknowledgments. This chapter is partly based on a talk at the Second European
Congress of Mathematics Applied to Biology and Medicine (Lyon, France,
December 1993). We thank Claude Millier (Scientific Director, ENGREF) and
Jean Jacod (Probability Lab, Paris VI University) for their cooperation in this
project and for comments on a former version of the manuscript.
Literature Cited
Asmussen S, Hering H (1983) Branching processes. Birkh¨ auser, Boston, MA
Athreya KB, Karlin S (1971) Branching processes with random environments. I Annals of
Mathematical Statistics 42:1499–1520; II Annals of Mathematical Statistics 42:1843–
1858
Athreya KB, Ney PE (1972) Branching processes. Springer Verlag, New York
Bagley JH (1982) Asymptotic properties of subcritical Galton-Watson processes. Journal of
Applied Probability 19:510–517
Bairlein F (1991) Population studies of White Storks Ciconia ciconia in Europe. In: Perrins
CM, Lebreton J-D, Hirons GJM (eds) Bird population studies: relevance to conservation
and management. Oxford University Press, Oxford, UK, pp 207–229
Bart J (1995) Evaluation of population trend estimates calculated using capture recapture
and population projection methods. Ecological Applications 5:662–671
Beissinger SR (1995) Modeling extinction in periodic environments: Everglades water
levels and Snail Kite population viability. Ecological Applications 5:618–631
Box GEP, Jenkins GM (1970) Time series analysis forecasting and control. Holden-Day,
San Francisco, CA
Boyce MS (1992) Population viability analysis. Annual Review of Ecology and Systematics 23:481–506