Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-28T14:34:49.372Z Has data issue: false hasContentIssue false

12 - A Lagrangian stochastic model for the dynamics of a stage structured population. Application to a copepod population

Published online by Cambridge University Press:  07 September 2009

By
Giuseppe Buffoni ,
Maria Grazia Mazzocchi  and
Sara Pasquali
Edited by
Annalisa Griffa ,
A. D. Kirwan, Jr. ,
Arthur J. Mariano ,
Tamay Özgökmen  and
H. Thomas Rossby
Giuseppe Buffoni
Affiliation:
ENEA, La Spezia, Italy
Maria Grazia Mazzocchi
Affiliation:
Stazione Zoologica A. Dohrn, Napoli, Italy
Sara Pasquali
Affiliation:
CNR-IMATI, Milano, Italy
Annalisa Griffa
Affiliation:
University of Miami
A. D. Kirwan, Jr.
Affiliation:
University of Delaware
Arthur J. Mariano
Affiliation:
University of Miami
Tamay Özgökmen
Affiliation:
University of Miami
H. Thomas Rossby
Affiliation:
University of Rhode Island
Get access

Summary

Introduction

We produce the population dynamics of a stage structured population, where the stages are defined by sharp biological events (egg hatching, molt, adult emergence, beginning and end of oviposition, death), by means of a stochastic individual-based model that simulates the life histories of its individuals (Judson, 1994; Berec, 2002; Buffoni et al., 2002; Buffoni et al., 2004). Aspects of the life history of an individual, such as survival probabilities, development rates and egg production, depend on its “status,” on the population size, and on external factors such as the environmental conditions (e.g. physical factors, food availability). In general, the status of an individual can be identified by means of a number of physiological variables or biometric descriptors, which describe the behavior of an individual in a given situation, and define its physiological age. The physiological age of an individual is generally described only by a variable. Here the status of an individual is individuated by its stage and its physiological age in the stage. The physiological age is defined as the percentage of development for non-reproductive individuals, and as the percentage of the potential reproductive effort for an adult female. The life history is obtained by the time evolution of the status of an individual, from birth to death, following its development and, when the individual is an adult female, the production of eggs.

Type
Chapter
Information
Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics , pp. 401 - 422
Publisher: Cambridge University Press
Print publication year: 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abbiati, M., Buffoni, G., Caforio, G., Cola, G. Di, and Santangelo, G., 1992. Harvesting, predation and competition effects on a red coral population. Netherlands J. Sea Res., 30, 219–28.CrossRefGoogle Scholar
Asknes, D. L. and Ohman, M. D., 1996. A vertical life table approach to zooplankton mortality estimation. Limnol. Oceanogr., 41, 1461–9.Google Scholar
Berec, L., 2002. Techniques of spatially explicit individual-based models: construction, simulation, and mean-field analysis. Ecol. Model., 150 (2002), 55–81.CrossRefGoogle Scholar
Bergh, M. O. and Getz, W. M., 1988. Stability of discrete age-structured and aggregated delay-difference population models. J. Math. Biol., 26, 551–81.CrossRefGoogle Scholar
Buffoni, G. and Cappelletti, A., 2000. Size structured populations: dispersion effects due to stochastic variability of the individual growth rate. Mathematical and Computer Modelling, 31, 27–34.CrossRefGoogle Scholar
Buffoni, G., G. Gilioli, and S. Pasquali, 2002. Population Dynamics: a Stochastic Model Based on Individual Life History Data. IAMI Technical Report, 07–02.
Buffoni, G. and S. Pasquali, 2003. Structured population dynamics: Eulerian and Lagrangian approachs. In Proceedings of the Fourth International Conference “Tools for Mathematical Modelling”, Saint Petersburg, June 23–28, 2003, ed. G. S. Osipeuko. Electronic Journal “Differential Equations and Control Processes”, 9, 74–86.
Buffoni, G., Pasquali, S., and Gilioli, G., 2004. A stochastic model for the dynamics of a structured population. Discrete and Continuous Dynamical Systems Series B, 4(3) (2004), 517–25.CrossRefGoogle Scholar
Buffoni, G. and S. Pasquali. Structured population dynamics: continuous size and discontinuous stage structure. Submitted to J. Math. Biol.
Carotenuto, Y., Ianora, A., Buttino, I., Romano, G., and Miralto, A., 2002. Is postembryonic development in the copepod Temora stylifera negatively affected by diatom diets?J. Exp. Mar. Biol. Ecol., 276, 49–66.CrossRefGoogle Scholar
Carpi, M. and Di Cola, G., 1988. Un modello stocastico della dinamica di una popolazione con struttura di età. Quaderno del Dipartimento di Matematica dell'Università di Parma, n. 31.Google Scholar
Curry, G. L. and Feldman, R. M., 1987. Mathematical Foundations of Population Dynamics. College Station, Texas: Texas AM University Press.Google Scholar
Estrada, M., F. Vives, and M. Alcaraz, 1985. Life and productivity of the open sea. In Western Mediterranean, ed. Margalef, R.. Oxford: Pergamon Press, 148–97.Google Scholar
Feller, W., 1957. An Introduction to Probability Theory and Its Applications, Volume I. New York: J. Wiley.Google Scholar
Gardiner, C. W., 1994. Handbook of Stochastic Methods. Berlin: Springer-Verlag.Google Scholar
Hoppensteadt, F., 1975. Mathematical Theories of Populations: Demographics, Genetics and Epidemics. Philadelphia: Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
Huys, R. and Boxshall, G. A., 1991. Copepod Evolution. London: The Ray Society.Google Scholar
Ianora, A., 1998. Copepod life history traits in subtemperate regions. J. Mar. Sys., 15, 337–49.CrossRefGoogle Scholar
Ianora, A. and Poulet, S. A., 1993. Egg viability in the copepod Temora stylifera. Limnol. Oceanogr., 38, 1615–26.CrossRefGoogle Scholar
Judson, O. P., 1994. The rise of the individual-based model in ecology. Tree, 9, 9–14.Google ScholarPubMed
Karlin, S. and Taylor, H. M., 1981. A Second Course in Stochastic Processes. New York: Academic Press.Google Scholar
Mauchline, J., 1998. The biology of calanoid copepods. Adv. Mar. Biol., 33, 1–710.Google Scholar
Mazzocchi, M. G. and d'Alcalà, M. Ribera, 1995. Recurrent patterns in zooplankton structure and succession in a variable coastal environment. ICES J. Mar. Sci., 52, 679–91.CrossRefGoogle Scholar
Munholland, P. L. and Dennis, B., 1992. Biological aspects of a stochastic model for insect life history data. Environ. Entomol., 21(6), 1229–38.CrossRefGoogle Scholar
Ohman, M. D. and Hirche, H. J., 2001. Density dependent mortality in an oceanic copepod population. Nature, 412, 638–41.CrossRefGoogle Scholar
Ohman, M. D. and Wood, S. N., 1996. Mortality estimation for planktonic copepods: Pseudocalanus newmani in a temperate fjord. Limnol. Oceanogr., 41, 126–35.CrossRefGoogle Scholar
d'Alcalà, Ribera M., Conversano, F., Corato, F., Licandro, P., Mangoni, O., Marino, D., Mazzocchi, M. G., Modigh, M., Montresor, M., Nardella, M., Saggiomo, V., Sarno, D., and Zingone, A., 2004. Seasonal patterns in plankton communities in a pluriannual time series at a coastal Mediterranean site (Gulf of Naples): an attempt to discern recurrences and trends. Sci. Mar., 67(Suppl. 1), 65–83.CrossRefGoogle Scholar
Roff, D. A., 1992. The Evolution of Life Histories. New York: Chapman and Hall.Google Scholar
Thomson, D. J., 1987. Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech., 180, 529–56.CrossRefGoogle Scholar
Zambianchi, E. and Griffa, A., 1994. Effects of finite scales of turbulence on dispersion estimates, J. Mar. Res., 52, 129–48.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×