Extinction in relation to demographic and environmental stochasticity in age-structured models.

The demographic variance of an age-structured population is defined. This parameter is further split into components generated by demographic stochasticity in each vital rate. The applicability of these parameters are investigated by checking how an age-structured population process can be approximated by a diffusion with only three parameters. These are the deterministic growth rate computed from the expected projection matrix and the environmental and demographic variances. We also consider age-structured populations where the fecundity at any stage is either zero or one, and there is neither environmental stochasticity nor dependence between individual fecundity and survival. In this case the demographic variance is uniquely determined by the vital rates defining the projection matrix. The demographic variance for a long-lived bird species, the wandering albatross in the southwestern part of the Indian Ocean, is estimated. We also compute estimates of the age-specific contributions to the total demographic variance from survival, fecundity and the covariance between survival and fecundity.

[1]  J. E. Cohen,et al.  Comparative statics and stochastic dynamics of age-structured populations. , 1979, Theoretical population biology.

[2]  P. Holgate,et al.  Matrix Population Models. , 1990 .

[3]  Pierre Jouventin,et al.  Population dynamics of wandering albatross Diomedea exulans and Amsterdam albatross D. amsterdamensis in the Indian Ocean and their relationships with long-line fisheries: Conservation implications , 1997 .

[4]  Steinar Engen,et al.  Analyzing Spatial Structure of Communities Using the Two‐Dimensional Poisson Lognormal Species Abundance Model , 2002, The American Naturalist.

[5]  S. Karlin,et al.  A second course in stochastic processes , 1981 .

[6]  P. A. Prince,et al.  Reproductive performance, recruitment and survival of wandering albatrosses Diomedea exulans at Bird Island, South Georgia , 1990 .

[7]  R. Lande,et al.  Stochastic Population Dynamics in Ecology and Conservation , 2003 .

[8]  David R. Cox,et al.  The Theory of Stochastic Processes , 1967, The Mathematical Gazette.

[9]  Bruce E. Kendall,et al.  Demographic stochasticity and the variance reduction effect , 2002 .

[10]  C. Pfister,et al.  Patterns of variance in stage-structured populations: evolutionary predictions and ecological implications. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Joel E. Cohen,et al.  Ergodicity of age structure in populations with Markovian vital rates, III: Finite-state moments and growth rate; an illustration , 1977, Advances in Applied Probability.

[12]  REPRODUCTIVE EFFORT IN VARIABLE ENVIRONMENTS, OR ENVIRONMENTAL VARIATION IS FOR THE BIRDS , 2001 .

[13]  David R. Cox,et al.  The Theory of Stochastic Processes , 1967, The Mathematical Gazette.

[14]  B. Sæther,et al.  AVIAN LIFE HISTORY VARIATION AND CONTRIBUTION OF DEMOGRAPHIC TRAITS TO THE POPULATION GROWTH RATE , 2000 .

[15]  B. Sæther,et al.  Life History Variation, Population Processes and Priorities in Species Conservation: Towards a Reunion of Research Paradigms , 1996 .

[16]  S. Engen,et al.  ASSESSING THE VIABILITY OF SCANDINAVIAN BROWN BEAR, URSUS ARCTOS, POPULATIONS : THE EFFECTS OF UNCERTAIN PARAMETER ESTIMATES , 1998 .

[17]  S. Tuljapurkar,et al.  An uncertain life: demography in random environments. , 1989, Theoretical population biology.

[18]  B. Sæther.  Pattern of covariation between life-history traits of European birds , 1988, Nature.

[19]  Shripad Tuljapurkar,et al.  Population dynamics in variable environments I. Long-run growth rates and extinction , 1980 .

[20]  Erik Matthysen,et al.  Demographic Characteristics and Population Dynamical Patterns of Solitary Birds , 2002, Science.

[21]  Robin McCleery,et al.  Environmental Stochasticity and Extinction Risk in a Population of a Small Songbird, the Great Tit , 1998, The American Naturalist.

[22]  Shripad Tuljapurkar,et al.  Population dynamics in variable environments. III. Evolutionary dynamics of r-selection , 1982 .

[23]  R. Lande,et al.  Extinction dynamics of age-structured populations in a fluctuating environment. , 1988, Proceedings of the National Academy of Sciences of the United States of America.

[24]  A. Grant,et al.  How to Keep Fit in the Real World: Elasticity Analyses and Selection Pressures on Life Histories in a Variable Environment , 1996, The American Naturalist.

[25]  B. Kendall,et al.  Variation among Individuals and Reduced Demographic Stochasticity , 2002, Conservation biology : the journal of the Society for Conservation Biology.

[26]  M. Bulmer.  On Fitting the Poisson Lognormal Distribution to Species-Abundance Data , 1974 .

[27]  Shripad Tuljapurkar,et al.  Population Dynamics in Variable Environments , 1990 .

[28]  Øyvind Bakke,et al.  Demographic and Environmental Stochasticity Concepts and Definitions , 1998 .

[29]  J. H. Pollard,et al.  On the use of the direct matrix product in analysing certain stochastic population models , 1966 .

[30]  T. Markow,et al.  Life history variation , 2006 .

[31]  ERGODICITY OF AGE STRUCTURE IN POPULATIONS WITH MARKOVIAN VITAL RATES , 111 : FINITE-STATE MOMENTS AND GROWTH RATE , 2005 .

[32]  W. Mare,et al.  Population dynamics of the wandering albatross (Diomedea exulans) on Macquarie Island and the effects of mortality from longline fishing , 1994, Polar Biology.

[33]  L. A. Goodman.  The probabilities of extenction for birth-and-death processes that are age-dependent or phase-dependent. , 1967, Biometrika.

[34]  Bernt-Erik Sæther,et al.  DEMOGRAPHIC STOCHASTICITY AND ALLEE EFFECTS IN POPULATIONS WITH TWO SEXES , 2003 .

[35]  S. Engen,et al.  STOCHASTIC POPULATION MODELS : SOME CONCEPTS, DEFINITIONS AND RESULTS , 1998 .

[36]  R. Lande,et al.  Demographic stochasticity and Allee effect on a scale with isotropic noise , 1998 .

[37]  P. A. Prince,et al.  Population changes in albatrosses at South Georgia , 1998 .

[38]  Bernt-Erik Sæther,et al.  Stochastic population dynamics and time to extinction of a declining population of barn swallows , 2001 .

[39]  J. Clobert,et al.  Survival in five southern albatrosses and its relationship with their life history , 1987 .

[40]  P. H. Leslie.  SOME FURTHER NOTES ON THE USE OF MATRICES IN POPULATION MATHEMATICS , 1948 .

[41]  H. Weimerskirch,et al.  Population Dynamics of the Wandering Albatross, Diomedea exulans, of the Crozet Islands: Causes and Consequences of the Population Decline , 1987 .

[42]  J N Smith,et al.  Estimating the time to extinction in an island population of song sparrows , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.