Population Extinction and Optimal Resource Management

• Published in: Philosophical transactions of the Royal Society of London. Series B. Biological sciences Vol. 350; no. 1332; pp. 179 - 188
• Main Authors: Whittle, Peter, Horwood, Joseph
• Format: Journal Article
• Language: English
• Published: London The Royal Society 29-11-1995; Royal Society of London
• Subjects: Commercial extinction; Demography; Determinism; Mathematics; Population size; Recommendations; Species extinction; Stochastic models; Sustainable fisheries management; Yield
• ISSN: 0962-8436; 1471-2970
• DOI: 10.1098/rstb.1995.0151

The optimal exploitation of a population is considered for three stochastic population models; these allow both demographic and environmental variability and the possibility of extinction. The dynamics are linear in the harvest rate; the optimal policy then recommends harvesting at the maximal rate above a critical level (the ‘threshold’) and at zero rate below. However, in all cases the optimal threshold differs radically according as to whether one maximizes the total return before extinction or the rate of return per unit time over the period before extinction. In the former case the optimal threshold is at the deterministic equilibrium level of the unexploited population, in the latter case it is approximately at the level of maximal sustainable production. Part of the explanation is that maximization of total yield turns out to be almost equivalent to maximization of time to extinction. Both average yield rate and the expected time to extinction vary with the policy, but the second much more powerfully. Both the criteria above are extreme: one obtains a balanced criterion (and an intermediate threshold) if one maximizes rate of return (before extinction) subject to the conservation requirement of a lower bound on the expected time to extinction. In the case when extinction is excluded because of a potential ‘rescue effect’ one comes to the same view by taking account of the relative time needed to restart an obliterated population. The practical implication is that more attention should be paid to extinction and restart times. For vulnerable populations it is likely that maximal utilization before an inevitable extinction will be achieved at low harvest rates. For large populations or metapopulations, with large times to extinction or quick recovery from a temporary extinction, classical resource models are appropriate.