A Cost-Benefit Analysis of Leaf Habit and Leaf Longevity of Trees and Their Geographical Pattern

-To maximize net gain of a tree, leaves must be replaced when net gain of a leaf per unit time over the leaf's life span is maximum. A model in which leaf longevity is determined to maximize the net gain of a leaf per unit time is constructed. The model predicts that leaf longevity is short when initial net photosynthetic rate of the leaf is large, long when the construction cost of the leaf is large, and short when the decrease in net photosynthetic rate with time is large. The model describes leaf habit (deciduousness and evergreenness) with the length of the favorable period for photosynthesis within a year and simulates distributional pattern of leaf habit along latitudes. The percentages of evergreenness decrease with decreasing favorableperiod length and reach the minimum at an intermediate length of the favorable period but increase again with a decrease in the length of the favorable period. A bimodal distributional pattern with two peaks, one at lower and the other at higher latitudes, is observed for the percentages of evergreenness. Percentages of deciduousness show a unimodal distribution pattern with a peak at midlatitude. Leaf longevity is a property of individual leaves, while leaf habit (i.e., evergreenness and deciduousness) is a property of a population of leaves. A tree is considered evergreen if it retains leaves throughout a year, whereas a deciduous tree sheds all of its leaves and spends a portion of the year without foliage. It is generally thought that evergreen trees have leaves that live longer than those of deciduous trees, but this is not always true. An evergreen tree can replace leaves several times a year, although at any one time the tree has green leaves. In such a case, though leaf longevity is shorter than a year, the tree is still a functional evergreen. Leaf longevity and leaf habit, however, have not always been distinguished. In many cases evergreenness has been used as a surrogate for a long leaf life span (Monk 1966; Chabot and Hicks 1982). Where environmental conditions are less variable and trees can conduct photosynthesis throughout he year as in the mesic tropics, trees are assumed to be functionally evergreen regardless of their leaf longevity. The deciduous habit is considered to be accompanied by seasonality of climatic conditions. Evergreen broad-leaved species that predominate in tropical regions usually decrease in abundance with increasing latitude, accompanied by a corresponding increase of deciduous broad-leaved species. However, at higher latitudes, evergreen conifers Am. Nat. 1991. Vol. 138, pp. 1250-1263. ? 1991 by The University of Chicago. 0003-0147/91/3805-0012$02.00. All rights reserved. LEAF HABIT AND LEAF LONGEVITY 1251 predominate. Therefore, evergreen tree species show a peculiar biogeographical distributional pattern with two distributional maxima, one at lower latitudes and another at higher latitudes. This bimodal distributional pattern has been called puzzling and is not readily explained by a cost-benefit analysis alone (Chabot and Hicks 1982). Since leaves are a resource-gaining organ, I believe to the contrary that this pattern must and can be explained on a cost-benefit basis. I develop a model in which a tree replaces its leaves to maximize its net carbon gain. The model is a simple equation consisting of a few parameters: photosynthetic rates, construction costs, and maintenance costs of a leaf. By applying the model to seasonal environments where favorable and unfavorable periods for photosynthesis alternate within a year, I explain the biogeographical pattern of leaf longevity and leaf habit. In this article, I will (1) analyze leaf longevity from a cost-benefit point of view for resource acquisition by a tree, (2) clarify the distinction between leaf longevity and leaf habit, and (3) explain the biogeographical distributional pattern of evergreen and deciduous tree species.