On the use of time series representations of population models

1986 ◽  
Vol 23 (A) ◽  
pp. 345-353 ◽  
Author(s):  
C. C. Heyde
Keyword(s):  
Time Series ◽  
Population Models ◽  
Stationary Time Series ◽  
Time Series Models ◽  
Vital Rates ◽  
Use Of Time ◽  
Structured Population ◽  
Series Representations ◽  
The Matrix ◽  
Age Structured

Many population models which are far from stationarity can nevertheless be written in autoregressive format, perhaps with random coefficient. It is the thesis of this paper that procedures developed for stationary time series models are a useful guide to inferential results for population processes and may indeed be directly applicable. The illustrations concentrate on estimation of the matrix of mean vital rates in an age-structured population.

On the use of time series representations of population models

1986 ◽  
Vol 23 (A) ◽  
pp. 345-353 ◽  
Author(s):  
C. C. Heyde
Keyword(s):  
Time Series ◽  
Population Models ◽  
Stationary Time Series ◽  
Time Series Models ◽  
Vital Rates ◽  
Use Of Time ◽  
Structured Population ◽  
Series Representations ◽  
The Matrix ◽  
Age Structured

Many population models which are far from stationarity can nevertheless be written in autoregressive format, perhaps with random coefficient. It is the thesis of this paper that procedures developed for stationary time series models are a useful guide to inferential results for population processes and may indeed be directly applicable. The illustrations concentrate on estimation of the matrix of mean vital rates in an age-structured population.

Age-structured models in a random environment

2019 ◽  
pp. 194-213
Author(s):  
Louis W. Botsford ◽  
J. Wilson White ◽  
Alan Hastings
Keyword(s):  
Time Series ◽  
Environmental Variability ◽  
Extinction Risk ◽  
Population Viability Analysis ◽  
Leslie Matrix ◽  
Vital Rates ◽  
Viability Analysis ◽  
Practical Concern ◽  
Probability Of Extinction ◽  
Age Structured

Most ecological populations exist in a randomly fluctuating environment, and these fluctuations influence vital rates, thus changing population dynamics. These changes are the focus of this chapter. The primary practical concern about environmental variability is the possibility that it could cause a population to go extinct, so the chapter describes several approaches to estimating the probability of extinction. The first is the small fluctuations approximation (SFA) to describe the growth of a population with a randomly varying Leslie matrix. The results reveal that randomly varying populations grow more slowly on average than the equivalent deterministic population. Further applications of the SFA examine how correlated variation in different vital rates affects the probability of extinction, when variability is too large to use the SFA, and how it has been applied to population time series. Finally, several other approaches to estimating extinction risk—also known as population viability analysis—are compared.

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