Accounting for Management Costs in Sensitivity Analyses of Matrix Population Models
PETER W.J. BAXTER,1,2,3 MICHAEL A. McCARTHY,1,2 HUGH P POSSINGHAM,3 PETER W MENKHORST,4 AND NATASHA McLEAN1,4
1School of Botany, University of Melbourne, Parkville VIC 3010, Australia
2Australian Research Centre for Urban Ecology, Royal Botanic Gardens, Melbourne, c/- School of Botany, University of Melbourne, Parkville VIC 3010, Australia
3The Ecology Centre, Departments of Zoology and Mathematics, The University of Queensland, Brisbane, QLD 4072, Australia
4Department of Sustainability and Environment, PO Box 500, East Melbourne, VIC 3002, Australia
5Department of Zoology, University of Melbourne, Parkville VIC 3010, Australia
Traditional sensitivity and elasticity analyses of matrix population models have been used to inform management decisions, but they ignore the economic costs of manipulating vital rates. For example, the growth rate of a population is often most sensitive to changes in adult survival rate, but this does not mean that increasing that rate is the best option for managing the population because it may be much more expensive than other options. To explore how managers should optimize their manipulation of vital rates, we incorporated the cost of changing those rates into matrix population models. We derived analytic expressions for locations in parameter space where managers should shift between management offecundity and survival, for the balance between fecundity and survival management at those boundaries, and for the allocation of management resources to sustain that optimal balance. For simple matrices, the optimal budget allocation can often be expressed as simple functions of vital rates and the relative costs of changing them. We applied our method to management of the Helmeted Honeyeater (Lichenostomus melanops cassidix, an endangered Australian bird) and the koala (Phascolarctos cinereus) as examples. Our method showed that cost-efficient management of the Helmeted Honeyeater should focus on increasing fecundity via nest protection, whereas optimal koala management should focus on manipulating both fecundity and survival simultaneously. These findings are contrary to the cost-negligent recommendations of elasticity analysis, which would suggestfocusing on managing survival in both cases. A further investigation of Helmeted Honeyeater management options, based on an individual-based model incorporating density dependence, spatial structure, and environmental stochasticity, confirmed thatfecundity management was the most cost-effective strategy. Our results demonstrate that decisions that ignore economic factors will reduce management efficiency.