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.
Keywords
- Density Dependence
- Random Environment
- White Stork
- Demographic Stochasticity
- Population Viability Analysis
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Deterministic theory in population ecology thus seems to be of little help in providing a framework for probability theory. We had better not adhere too much to our deterministic concepts and ideas, but start afresh. —J. Reddingius (1971)
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Literature Cited
Asmussen S, Hering H (1983) Branching processes. Birkhäuser, 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
Burkey TV (1989) Extinction in nature reserves: the effect of fragmentation and the importance of migration between reserve fragments. Oikos 55:75–81
Caswell H (1989) Matrix population models. Sinauer, Sunderland, MA
Chesson P (1978) Predator-prey theory and variability. Annual Review of Ecology and Systematics 9:323–347
Cohen JE (1969) Natural primate troops and a stochastic population model. American Naturalist 103:455–477
Day JR, Possingham HP (1995) A stochastic metapopulation model with variability in patch size and position. Theoretical Population Biology 48:333–360
DeAngelis DL (1976) Application of stochastic models to a wildlife population. Mathematical Biosciences 31:227–236
Dennis B, Munholland PL, Scott JM (1991) Estimation of growth and extinction parameters for endangered species. Ecological Monographs 61:115–143
Durrett R, Levin S (1994) The importance of being discrete (and spatial). Theoretical Population Biology 46:363–394
Eberhardt LL (1985) Assessing the dynamics of wild populations. Journal of Wildlife Management 49:997–1012
Facelli JM, Pickett STA (1990) Markovian chains and the role of history in succession. TREE 5:27–30
Gabriel W, Bürger R (1992) Survival of small populations under demographic stochasticity. Theoretical Population Biology 41:44–71
Galton F (1873) Problem 4001. Educational Times 17
Gilpin ME (1987) Spatial structure and population variability. In: Soulé ME (ed) Viable populations for conservation. Cambridge University Press, Cambridge, UK, pp 125–140
Gilpin ME, Soulé ME (1986) Minimum viable populations: the processes of species extinctions. In: Soulé ME (ed) Conservation biology: science of scarcity and diversity. Sinauer, Sunderland, MA, pp 13–34
Ginzburg LR, Slobodkin LB, Johnson K, Bindman AG (1982) Quasiextinction probabilities as a measure of impact on population growth. Risk Analysis 2:171–181
Goodman D (1987) The demography of chance extinction. In: Soulé ME (ed) Viable populations for conservation. Cambridge University Press, Cambridge, UK, pp 11–34
Gosselin F (1996) Extinction in a simple source/sink system: application of new mathematical results. Acta Oecologica 17:563–584
Gosselin F (1997) Modèles stochastiques d’extinction de population: propriétés mathématiques et leurs applications. Unpublished PhD thesis, Paris 6 University, Paris
Gosselin F (1998a) Asymptotic behaviour of some discrete-time Markov chains conditional on non-extinction. I-Theory. Mimeographed research report 98-04. Biometrics Unit, INRA/ENSAM/University Montpellier II, France
Gosselin F (1998b) Asymptotic behaviour of some discrete-time Markov chains conditional on non-extinction. II-Applications. Mimeographed research report 98-05, Biometrics Unit, INRA/ENSAM/University Montpellier II, France
Gosselin F (1998c) Reconciling theoretical approaches to stochastic patch-occupancy metapopulation models. Bulletin of Mathematical Biology 60:955–971
Gosselin F (1998d) Asymptotic behavior of some discrete time Markov chains conditional on non-extinction. I-Theory; II-Applications. Technical Reports 98-04, 98-05. Groupe de Biostatistique et d’Analyse des Systèms. Université de Montpellier II, France
Gyllenberg M, Silvestrov DS (1994) Quasi-stationary distributions of a stochastic metapopulation model. Journal of Mathematical Biology 33:35–70
Hanski I (1994) A practical model of metapopulation dynamics. Journal of Animal Ecology 63:151–162
Hanski I, Woiwod IP (1993) Spatial synchrony in the dynamics of moth and aphid populations. Journal of Animal Ecology 62:656–668
Heathcote CR, Seneta E, Vere-Jones D (1967) A refinement of two theorems in the theory of branching processes. Theory of Probability and Its Applications 12:342–346
Jagers P (1975) Branching processes with biological applications. Wiley, London
Joffe A, Spitzer F (1967) On multitype branching processes with ρ ≤ 1. Journal of Mathematical Analysis and Applications 19:409–430
Kanyamibwa S (1991) Dynamique des populations de Cigogne Blanche (Ciconia Ciconia L) en Europe Occidentale: contribution à la conservation des populations naturelles. Unpublished thesis, Montpellier II University, Montpellier, France
Kanyamibwa S, Lebreton JD (1992) Variation des effectifs de Cigogne Blanche et facteurs du milieu: un modèle démographique. In: Mériaux JL, Schierer A, Tombal C, Tombal JC (eds) Les cigognes d’Europe. Institut Européen d’Ecologie, Metz, France, pp 259–264
Kanyamibwa S, Schierer A, Pradel R, Lebreton J-D (1990) Changes in adult survival rates in a western European population of the White Stork Ciconia ciconia. Ibis 132:27–35
Kanyamibwa S, Bairlein F, Schierer A (1993) Comparison of survival rates between populations of the White Stork Ciconia ciconia in central Europe. Ornis Scandinavica 24:297–302
Lande R (1988) Genetics and demography in biological conservation. Science 241:1455–1460
Lande R (1993) Risks of population extinction from demographic and environmental stochasticity and random catastrophes. American Naturalist 142:911–927
Lande R, Orzack SH (1988) Extinction dynamics of age-structured populations in a fluctuating environment. Proceedings of the National Academy of Sciences of the USA 85:7418–7421
Lebreton J-D (1978) Un modèle probabiliste de la dynamique des populations de la Cigogne Blanche (Ciconia ciconia L) en Europe Occidentale. In: Legay JM, Tomassone R (eds) Biométrie et Ecologie. Société de Biométrie, Paris, pp 277–343
Lebreton J-D (1981) Contribution á la dynamique des populations d’oiseaux. Modèles mathématiques en temps discret. Unpublished thesis, Lyon I University, Villeurbanne, France
Lebreton J-D (1982) Applications of discrete time branching processes to bird population dynamics modelling. In: ANAIS da 10 a conferência Internacional de Biometria. EMBRAPA-DID/DMQ/Sociedade Internacional de Biometria, Brasil, pp 115–133
Lebreton J-D (1990) Modelling density dependence environmental variability and demographic stochasticity from population counts: an example using Wytham Wood Great Tits. In: Blondel J, Gosler A, Lebreton J-D, McCleery R (eds) Population biology of passerine birds: an integrated approach. NATO ASI series. Series G: Ecological sciences, vol 24. Springer Verlag, Berlin, pp 89–102
Lebreton J-D, Clobert J (1991) Bird population dynamics management and conservation: the role of mathematical modeling. In: Perrins CM, Lebreton J-D, Hirons GJM (eds) Bird population studies: relevance to conservation and management. Oxford University Press, Oxford, UK, pp 105–125
Legendre S, Clobert J (1995) ULM: a software for conservation and evolutionary biologists. Journal of Applied Statistics 22:817–834
Lindenmayer DB, Burgman MA, Akçakaya HR, Lacy RC, Possingham HR (1995) A review of the generic computer programs ALEX RAMAS/space and VORTEX for modelling the viability of wildlife metapopulations. Ecological Modelling 82:161–174
Malthus TR (1798) An essay on the principle of population, as it affects the future improvements of society, with remarks on the speculations of Mr. Godwin, M. Condorcet, and other writers. John Murray, London
Mangle M, Tier C (1993) Dynamics of metapopulations with demographic stochasticity and environmental catastrophes. Theoretical Population Biology 44:1–31
McCarthy MA, Franklin DC, Burgman MA (1994) The importance of demographic uncertainty: an example from the Helmeted Honeyeater. Biological Conservation 67:135–142
Mode CJ, Jacobson ME (1987a) A study of the impact of environmental stochasticity on extinction probabilities by Monte Carlo integration. Mathematical Biosciences 83:105–125
Mode CJ, Jacobson ME (1987b) On estimating population size for an endangered species in the presence of environmental stochasticity. Mathematical Biosciences 85:185–209
Mode CJ, Pickens GT (1986) Demographic stochasticity and uncertainty in population projections—a study by computer simulation. Mathematical Biosciences 79:55–72
North PM, Boddy AW, Forrester DR (1988) A computer simulation study of stochastic models to investigate the population dynamics of the Screech Owl (Otus asio) under increased mortality. Ecological Modelling 40:233–263
Nunney L, Campbell KA (1993) Assessing minimum viable population size: demography meets population genetics. TREE 8:234–239
Pollard JH (1966) On the use of the direct matrix product in analysing certain stochastic population models. Biometrika 53:397–415
Reddingius J (1971) Gambling for existence. Acta Biotheoretica 20 Suppl:1–208
Schneider RR, Yodzis P (1994) Extinction dynamics in the American Marten (Martes americana). Conservation Biology 8:1058–1068
Seneta E, Vere-Jones D (1966) On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states. Journal of Applied Probability 3:403–434
Shaffer M (1987) Minimum viable populations: coping with uncertainty. In: Soulé ME (eds) Viable populations for conservation. Cambridge University Press, Cambridge, UK, pp 69–86
Shaffer ML (1981) Minimum population sizes for species conservation. Bioscience 31:131–134
Smith WL, Wilkinson WE (1969) On branching processes in random environments. Annals of Mathematical Statistics 40:814–827
Stacey PB, Taper M (1992) Environmental variation and the persistence of small populations. Ecological Applications 2:18–29
Tuljapurkar S (1990) Population dynamics in variable environments. Lecture Notes in Biomathematics 85. Springer-Verlag, New York
Verboom J, Lankester K, Metz JAJ (1991) Linking local and regional dynamics in stochastic metapopulation models. Biological Journal of the Linnean Society 42:39–55
Wissel C (1989) Metastability a consequence of stochastics in multiple stable population dynamics. Theoretical Population Biology 36:296–310
Wissel C, Stöcker S (1991) Extinction of populations by random influences. Theoretical Population Biology 39:315–328
Wissel C, Zaschke S-H (1994) Stochastic birth and death processes describing minimum viable populations. Ecological Modelling 75/76:193–201
Woolfenden GE, Fitzpatrick JW (1991) Florida Scrub Jay ecology and conservation. In: Perrins CM, Lebreton J-D, Hirons GJM (eds) Bird population studies: relevance to conservation and management. Oxford University Press, Oxford, UK, pp 542–565
Rights and permissions
Copyright information
© 2000 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Gosselin, F., Lebreton, JD. (2000). Potential of Branching Processes as a Modeling Tool for Conservation Biology. In: Quantitative Methods for Conservation Biology. Springer, New York, NY. https://doi.org/10.1007/0-387-22648-6_13
Download citation
DOI: https://doi.org/10.1007/0-387-22648-6_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95486-8
Online ISBN: 978-0-387-22648-4
eBook Packages: Springer Book Archive