Abstract
Despite considerable interest in the dynamics of populations subject to temporally varying environments, alternate population growth rates and their sensitivities remain incompletely understood. For a Markovian environment, we compare and contrast the meanings of the stochastic growth rate (λ 5), the growth rate of average population (λM), the growth rate for average transition rates (λA), and the growth rate of an aggregate represented by a megamatrix (shown here to equal λ M). We distinguish these growth rates by the averages that define them. We illustrate our results using data on an understory shrub in a hurricane-disturbed landscape, employing a range of hurricane frequencies. We demonstrate important differences among growth rates: λS < λM, but λA can be < or > λ M. We show that stochastic elasticity, EijS, and megamatrix elasticity, EijM, describe a complex perturbation of both means and variances of rates by the same proportion. Megamatrix elasticities respond slightly and stochastic elasticities respond strongly to changing the frequency of disturbance in the habitat (in our example, the frequency of hurricanes). The elasticity Eij A of λA does not predict changes in the other elasticities. Because ES, although commonly utilized, is difficult to interpret, we introduce elasticities with a more direct interpretation: ESμ for perturbations of means and ESσ for variances. We argue that a fundamental tool for studying selection pressures in varying environments is the response of growth rate to vital rates in all habitat states.
| Original language | English |
|---|---|
| Pages (from-to) | 489-502 |
| Number of pages | 14 |
| Journal | American Naturalist |
| Volume | 162 |
| Issue number | 4 |
| DOIs | |
| State | Published - Oct 1 2003 |
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Keywords
- Ardisia escallonioides
- Canopy-gap forest dynamics
- Elasticity
- Hurricanes
- Norm of response
- Plant population biology
- Sensitivity
- Stochastic demography
- Temporal variation in demography
ASJC Scopus subject areas
- Ecology
Cite this
The Many Growth Rates and Elasticities of Populations in Random Environments. / Tuljapurkar, Shripad; Horvitz, Carol C; Pascarella, John B.
In: American Naturalist, Vol. 162, No. 4, 01.10.2003, p. 489-502.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The Many Growth Rates and Elasticities of Populations in Random Environments
AU - Tuljapurkar, Shripad
AU - Horvitz, Carol C
AU - Pascarella, John B.
PY - 2003/10/1
Y1 - 2003/10/1
N2 - Despite considerable interest in the dynamics of populations subject to temporally varying environments, alternate population growth rates and their sensitivities remain incompletely understood. For a Markovian environment, we compare and contrast the meanings of the stochastic growth rate (λ 5), the growth rate of average population (λM), the growth rate for average transition rates (λA), and the growth rate of an aggregate represented by a megamatrix (shown here to equal λ M). We distinguish these growth rates by the averages that define them. We illustrate our results using data on an understory shrub in a hurricane-disturbed landscape, employing a range of hurricane frequencies. We demonstrate important differences among growth rates: λS < λM, but λA can be < or > λ M. We show that stochastic elasticity, EijS, and megamatrix elasticity, EijM, describe a complex perturbation of both means and variances of rates by the same proportion. Megamatrix elasticities respond slightly and stochastic elasticities respond strongly to changing the frequency of disturbance in the habitat (in our example, the frequency of hurricanes). The elasticity Eij A of λA does not predict changes in the other elasticities. Because ES, although commonly utilized, is difficult to interpret, we introduce elasticities with a more direct interpretation: ESμ for perturbations of means and ESσ for variances. We argue that a fundamental tool for studying selection pressures in varying environments is the response of growth rate to vital rates in all habitat states.
AB - Despite considerable interest in the dynamics of populations subject to temporally varying environments, alternate population growth rates and their sensitivities remain incompletely understood. For a Markovian environment, we compare and contrast the meanings of the stochastic growth rate (λ 5), the growth rate of average population (λM), the growth rate for average transition rates (λA), and the growth rate of an aggregate represented by a megamatrix (shown here to equal λ M). We distinguish these growth rates by the averages that define them. We illustrate our results using data on an understory shrub in a hurricane-disturbed landscape, employing a range of hurricane frequencies. We demonstrate important differences among growth rates: λS < λM, but λA can be < or > λ M. We show that stochastic elasticity, EijS, and megamatrix elasticity, EijM, describe a complex perturbation of both means and variances of rates by the same proportion. Megamatrix elasticities respond slightly and stochastic elasticities respond strongly to changing the frequency of disturbance in the habitat (in our example, the frequency of hurricanes). The elasticity Eij A of λA does not predict changes in the other elasticities. Because ES, although commonly utilized, is difficult to interpret, we introduce elasticities with a more direct interpretation: ESμ for perturbations of means and ESσ for variances. We argue that a fundamental tool for studying selection pressures in varying environments is the response of growth rate to vital rates in all habitat states.
KW - Ardisia escallonioides
KW - Canopy-gap forest dynamics
KW - Elasticity
KW - Hurricanes
KW - Norm of response
KW - Plant population biology
KW - Sensitivity
KW - Stochastic demography
KW - Temporal variation in demography
UR - http://www.scopus.com/inward/record.url?scp=0242709325&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0242709325&partnerID=8YFLogxK
U2 - 10.1086/378648
DO - 10.1086/378648
M3 - Article
C2 - 14582010
AN - SCOPUS:0242709325
VL - 162
SP - 489
EP - 502
JO - American Naturalist
JF - American Naturalist
SN - 0003-0147
IS - 4
ER -