The time value of leaf area

When a plant invests in construction of a leaf, the revenue-stream that accrues is shaped by three variables: first, the light-capture area per milligram dry mass invested, analogous to a potential rate of return on investment; second, the longevity of the leaf, analogous to the expected duration of the revenue stream; and third, a time-discount rate, quantifying the fact that light-capture area deployed in the immediate future is more valuable to the plant than the same area deployed at some later time. Recent comparative data make it possible to quantify the cross-species trade-off between the first variable and the second variable. Here we develop an approach through which the consequences of the third variable, the time-discount rate, can be related to the trade-off between the first variable and the second variable. The approach involves an equal-benefit set, the cross-species equivalent of a fitness set. A wide spread of strategies is actually observed to coexist in vegetation, from low to high light capture area per gram and, correspondingly, from high to low leaf longevity. The coexistence suggests that the different observed strategies do not have a clear cut advantage over the other. The equal-benefit set can be used to investigate what levels of time discount would make it the case that neither the highest-longevity nor the highest light-capture area per milligram strategies would have a clear advantage over the other, with regard to the time-discounted value of the revenue stream generated per milligram invested in leaf.