Stage, age and individual stochasticity in demography
Demography is the study of the population consequences of the fates of individuals. Individuals are differentiated on the basis of age or, in general, life cycle stages. The movement of an individual through its life cycle is a random process, and although the eventual destination (death) is certain...
Published in: | Oikos |
---|---|
Main Author: | |
Format: | Article in Journal/Newspaper |
Language: | English |
Published: |
Wiley
2009
|
Subjects: | |
Online Access: | http://dx.doi.org/10.1111/j.1600-0706.2009.17620.x https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2Fj.1600-0706.2009.17620.x https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1600-0706.2009.17620.x |
id |
crwiley:10.1111/j.1600-0706.2009.17620.x |
---|---|
record_format |
openpolar |
spelling |
crwiley:10.1111/j.1600-0706.2009.17620.x 2024-06-23T07:55:14+00:00 Stage, age and individual stochasticity in demography Caswell, Hal 2009 http://dx.doi.org/10.1111/j.1600-0706.2009.17620.x https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2Fj.1600-0706.2009.17620.x https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1600-0706.2009.17620.x en eng Wiley http://onlinelibrary.wiley.com/termsAndConditions#vor Oikos volume 118, issue 12, page 1763-1782 ISSN 0030-1299 1600-0706 journal-article 2009 crwiley https://doi.org/10.1111/j.1600-0706.2009.17620.x 2024-06-13T04:24:32Z Demography is the study of the population consequences of the fates of individuals. Individuals are differentiated on the basis of age or, in general, life cycle stages. The movement of an individual through its life cycle is a random process, and although the eventual destination (death) is certain, the pathways taken to that destination are stochastic and will differ even between identical individuals; this is individual stochasticity. A stage‐classified demographic model contains implicit age‐specific information, which can be analyzed using Markov chain methods. The living stages in the life cycles are transient states in an absorbing Markov chain; death is an absorbing state. This paper presents Markov chain methods for computing the mean and variance of the lifetime number of visits to any transient state, the mean and variance of longevity, the net reproductive rate R 0 , and the cohort generation time. It presents the matrix calculus methods needed to calculate the sensitivity and elasticity of all these indices to any life history parameters. These sensitivities have many uses, including calculation of selection gradients. It is shown that the use of R 0 as a measure of fitness or an invasion exponent gives erroneous results except when R 0 =λ=1. The Markov chain approach is then generalized to variable environments (deterministic environmental sequences, periodic environments, iid random environments, Markovian environments). Variable environments are analyzed using the vec‐permutation method to create a model that classifies individuals jointly by the stage and environmental condition. Throughout, examples are presented using the North Atlantic right whale ( Eubaleana glacialis ) and an endangered prairie plant ( Lomatium bradshawii ) in a stochastic fire environment. Article in Journal/Newspaper North Atlantic North Atlantic right whale Wiley Online Library Oikos 118 12 1763 1782 |
institution |
Open Polar |
collection |
Wiley Online Library |
op_collection_id |
crwiley |
language |
English |
description |
Demography is the study of the population consequences of the fates of individuals. Individuals are differentiated on the basis of age or, in general, life cycle stages. The movement of an individual through its life cycle is a random process, and although the eventual destination (death) is certain, the pathways taken to that destination are stochastic and will differ even between identical individuals; this is individual stochasticity. A stage‐classified demographic model contains implicit age‐specific information, which can be analyzed using Markov chain methods. The living stages in the life cycles are transient states in an absorbing Markov chain; death is an absorbing state. This paper presents Markov chain methods for computing the mean and variance of the lifetime number of visits to any transient state, the mean and variance of longevity, the net reproductive rate R 0 , and the cohort generation time. It presents the matrix calculus methods needed to calculate the sensitivity and elasticity of all these indices to any life history parameters. These sensitivities have many uses, including calculation of selection gradients. It is shown that the use of R 0 as a measure of fitness or an invasion exponent gives erroneous results except when R 0 =λ=1. The Markov chain approach is then generalized to variable environments (deterministic environmental sequences, periodic environments, iid random environments, Markovian environments). Variable environments are analyzed using the vec‐permutation method to create a model that classifies individuals jointly by the stage and environmental condition. Throughout, examples are presented using the North Atlantic right whale ( Eubaleana glacialis ) and an endangered prairie plant ( Lomatium bradshawii ) in a stochastic fire environment. |
format |
Article in Journal/Newspaper |
author |
Caswell, Hal |
spellingShingle |
Caswell, Hal Stage, age and individual stochasticity in demography |
author_facet |
Caswell, Hal |
author_sort |
Caswell, Hal |
title |
Stage, age and individual stochasticity in demography |
title_short |
Stage, age and individual stochasticity in demography |
title_full |
Stage, age and individual stochasticity in demography |
title_fullStr |
Stage, age and individual stochasticity in demography |
title_full_unstemmed |
Stage, age and individual stochasticity in demography |
title_sort |
stage, age and individual stochasticity in demography |
publisher |
Wiley |
publishDate |
2009 |
url |
http://dx.doi.org/10.1111/j.1600-0706.2009.17620.x https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2Fj.1600-0706.2009.17620.x https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1600-0706.2009.17620.x |
genre |
North Atlantic North Atlantic right whale |
genre_facet |
North Atlantic North Atlantic right whale |
op_source |
Oikos volume 118, issue 12, page 1763-1782 ISSN 0030-1299 1600-0706 |
op_rights |
http://onlinelibrary.wiley.com/termsAndConditions#vor |
op_doi |
https://doi.org/10.1111/j.1600-0706.2009.17620.x |
container_title |
Oikos |
container_volume |
118 |
container_issue |
12 |
container_start_page |
1763 |
op_container_end_page |
1782 |
_version_ |
1802647729483022336 |