Publication Abstract

Population extinction and optimalresource management

P. Whittle and J.W. Horwood

Theoptimal exploitation of a population is considered for three stochastic population models;these allow both demographic and environmental variability and the possibility ofextinction. The dynamics are linear in the harvest rate; the optimal policy thenrecommends harvesting at the maximal rate above a critical level (the `threshold') and atzero rate below. However, in all cases the optimal threshold differs radically accordingas to whether one maximizes the total return before extinction or the rate of return perunit time over the period before extinction. In the former case the optimal threshold isat the deterministic equilibrium level of the unexploited population, in the latter caseit is approximately at the level of maximal sustainable production. Part of theexplanation is that maximization of total yield turns out to be almost equivalent tomaximization of time to extinction. Both average yield rate and the expected time toextinction vary with the policy, but the second much more powerfully. Both the criteriaabove are extreme: one obtains a balanced criterion (and an intermediate threshold) if onemaximizes rate of return (before extinction) subject to the conservation requirement of alower bound on the expected time to extinction. In the case when extinction is excludedbecause of a potential `rescue effect' one comes to the same view by taking account of therelative time needed to restart an obliterated population. The practical implication isthat more attention should be paid to extinction and restart times. For vulnerablepopulations it is likely that maximal utilization before an inevitable extinction will beachieved at low harvest rates. For large populations or metapopulations, with large timesto extinction or quick recovery from a temporary extinction, classical resource models areappropriate.

Reference:

P. Whittle and J.W. Horwood, 1995. Population extinction and optimal resource management.Phil. Transactions of the Royal Society London, B, 350: 179-188.