# Approximate Aggregation Methods in Discrete Time Stochastic Population Models

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 6, page 38-69
- ISSN: 0973-5348

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topSanz, L., and Alonso, J. A.. "Approximate Aggregation Methods in Discrete Time Stochastic Population Models." Mathematical Modelling of Natural Phenomena 5.6 (2010): 38-69. <http://eudml.org/doc/197641>.

@article{Sanz2010,

abstract = {Approximate aggregation techniques consist of introducing certain approximations that
allow one to reduce a complex system involving many coupled variables obtaining a simpler
ʽʽaggregated systemʼʼ governed by a few variables. Moreover, they give results that allow
one to extract information about the complex original system in terms of the behavior of
the reduced one. Often, the feature that allows one to carry out such a reduction is the
presence of different time scales in the system under consideration. In this work we deal
with aggregation techniques in stochastic discrete time models and their application to
the study of multiregional models, i.e., of models for an age structured population
distributed amongst different spatial patches and in which migration between the patches
is usually fast with respect to the demography (reproduction-survival) in each patch.
Stochasticity in population models can be of two kinds: environmental and demographic. We
review the formulation and the main properties of the dynamics of the different models for
populations evolving in discrete time and subjected to the effects of environmental and
demographic stochasticity. Then we present different stochastic multiregional models with
two time scales in which migration is fast with respect to demography and we review the
main relationships between the dynamics of the original complex system and the aggregated
simpler one. Finally, and within the context of models with environmental stochasticity in
which the environmental variation is Markovian, we make use these techniques to analyze
qualitatively the behavior of two multiregional models in which the original complex
system is intractable. In particular we study conditions under which the population goes
extinct or grows exponentially.},

author = {Sanz, L., Alonso, J. A.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {approximate aggregation; environmental stochasticity; demographic stochasticity; time scales; multiregional models; lognormal distribution},

language = {eng},

month = {4},

number = {6},

pages = {38-69},

publisher = {EDP Sciences},

title = {Approximate Aggregation Methods in Discrete Time Stochastic Population Models},

url = {http://eudml.org/doc/197641},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Sanz, L.

AU - Alonso, J. A.

TI - Approximate Aggregation Methods in Discrete Time Stochastic Population Models

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/4//

PB - EDP Sciences

VL - 5

IS - 6

SP - 38

EP - 69

AB - Approximate aggregation techniques consist of introducing certain approximations that
allow one to reduce a complex system involving many coupled variables obtaining a simpler
ʽʽaggregated systemʼʼ governed by a few variables. Moreover, they give results that allow
one to extract information about the complex original system in terms of the behavior of
the reduced one. Often, the feature that allows one to carry out such a reduction is the
presence of different time scales in the system under consideration. In this work we deal
with aggregation techniques in stochastic discrete time models and their application to
the study of multiregional models, i.e., of models for an age structured population
distributed amongst different spatial patches and in which migration between the patches
is usually fast with respect to the demography (reproduction-survival) in each patch.
Stochasticity in population models can be of two kinds: environmental and demographic. We
review the formulation and the main properties of the dynamics of the different models for
populations evolving in discrete time and subjected to the effects of environmental and
demographic stochasticity. Then we present different stochastic multiregional models with
two time scales in which migration is fast with respect to demography and we review the
main relationships between the dynamics of the original complex system and the aggregated
simpler one. Finally, and within the context of models with environmental stochasticity in
which the environmental variation is Markovian, we make use these techniques to analyze
qualitatively the behavior of two multiregional models in which the original complex
system is intractable. In particular we study conditions under which the population goes
extinct or grows exponentially.

LA - eng

KW - approximate aggregation; environmental stochasticity; demographic stochasticity; time scales; multiregional models; lognormal distribution

UR - http://eudml.org/doc/197641

ER -

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