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Journal Article

On two conjectures about perturbations of the stochastic growth rate

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Giaimo,  Stefano       
Department Evolutionary Theory (Traulsen), Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Supplementary Material (public)

anzs12382-sup-0001-supinfo.pdf
(Supplementary material), 326KB

Citation

Giaimo, S. (2023). On two conjectures about perturbations of the stochastic growth rate. Australian & New Zealand Journal of Statistics, 65(1), 1-13. doi:10.1111/anzs.12382.


Cite as: https://hdl.handle.net/21.11116/0000-000C-E712-B
Abstract
The stochastic growth rate describes long-run growth of a population that lives in a fluctuating environment. Perturbation analysis of the stochastic growth rate provides crucial information for population managers, ecologists and evolutionary biologists. This analysis quantifies the response of the stochastic growth rate to changes in demographic parameters. A form of this analysis deals with changes that only occur in some environmental states. Caswell put forth two conjectures about environment-specific perturbations of the stochastic growth rate. The conjectures link the stationary distribution of the stochastic environmental process with the magnitude of some environment-specific perturbations. This note disproves one conjecture and proves the other.