Future discounts and resource allocation in plants

For over 20 years ecologists have used dynamic optimization techniques in the study of plant allocation (Cohen 1966; King & Roughgarden 1982; Chiariello & Roughgarden 1984). Recently, the optimization methods of microeconomic theory have been explicitly applied to the study of plant growth and resource balance [the 'economic analogy' of Bloom, Chapin & Mooney (1985)]. The analogy, as developed by Bloom et al. (1985), applies optimization principles of microeconomic theory to plantresource interactions and derives predictions about how plant patterns of resource acquisition and allocation vary with environmental parameters, e.g. light and nutrient availability. The goal of this allocation theory as developed by economists is to predict the behaviour of firms or individuals operating in market conditions. The 'economic analogy' develops this theory considering plants as analogues to individual firms and biomass accumulation as the analogue to profit (Bloom et al. 1985; Chapin et al. 1987). The optimal plant according to the 'economic analogy' is one that allocates resources so as to maximize biomass accumulation. Implicit in this line of reasoning is the assumption that plants able to acquire and allocate resources so as to maximize biomass accumulation will have higher fitness and be selected over evolutionary time. The economic analogy contributes to our ability to calculate the costs and benefits of resource acquisition and allocation. Biologists have borrowed economic theory to develop models of acquisition costs that allow different costs to be measured in the same currency and different currencies to be interconverted. For example, Reekie & Bazzaz (1987) develop a model where all costs are figured in terms of carbon. In contrast, Koide & Elliot (1989) calculate the cost of a mycorrhizal symbiosis in both carbon and phosphorus currencies. By using these formal notions (exchange ratios in economic theory) it is possible to compare resource costs in a site where several resources are simultaneously limiting (Chapin et al. 1987). In addition to improving calculations of acquisition costs, the economic analogy adds to our understanding of the benefits of allocation decisions. For example, the principle of equalizing marginal revenue and marginal cost states that expenditures should continue until the return on a unit of expenditure equals its cost; this has been demonstrated for crop plants where allocation to leaf production stops when the cost of producing the next leaf exceeds the carbon return that leaf will bring through photosynthesis (Monteith & Elston 1983). Similarly, patterns of allocation to storage in annual herbs have been explained using mathematical models originally developed for economics (Chiariello & Roughgarden 1984; Bloom 1986). Despite the success of the economic analogy in calculating the costs of acquisition and the benefits of allocations to different tissues, it has proved difficult to use the economic principles developed by Bloom et al. (1985) to predict the timing of optimal resource allocation, i.e. whether it is better to allocate immediately to a certain tissue type or to allocate first to another type (Lubbers & Lechowicz 1989). Analysis of temporal allocation decisions (I recognize and ask indulgence for the anthropocentric terminology, but to avoid tortuous sentence construction, I will continue, recognizing that plants do not think about their decisions) requires a comparison of future vs present costs and benefits. Attempts have been made to model the impact of present and future allocation to defence or photosynthetic apparatus, but these efforts have not formally considered the comparison between present and future costs and benefits (Coley, Bryant & Chapin 1985; Gulmon & Mooney 1986). Microeconomic theory provides a method to make such comparisons, the principle of Future Discounts (Samuelson & Nordhaus 1989). Future discounting allows calculation of future costs and benefits in terms of their present values; the principle is based on the idea that both benefits and costs have a higher absolute value in the present than in the future. Applying future discounting to plant resource allocation helps predict patterns of resource allocation and the effect of risk on these patterns. In this paper the concept of future discounting is used to help understand the controls over the timing of resource allocation. Future discounting, as economists use it, is defined and this concept adapted for calculations of plant resource investment to show how changes in the environment can affect a plant's discount rate and allocation pattern. Future discounts are then explicitly used in a cost-benefit model of plant allocation to show the advantages of this approach. Finally, some of the complications in using discount rates in the study of plant allocation are discussed.