A mathematical analysis of leaf longevity of trees under seasonally varying temperatures, based on a cost-benefit model

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Questions: Under what climatic conditions is long leaf longevity, or evergreen-ness, favoured? Under what physiological conditions of leaves is long leaf longevity, or evergreen-ness, favoured? Why is evergreen-ness favoured in both tropical and frigid regions? What is the difference in biological meaning of evergreen-ness between tropical and frigid regions? Mathematical method: Optimization with two variables, expansion and shedding times of leaves. The objective function for optimality is the amount of assimilating product per unit time of an individual leaf. We obtained the optimal expansion and shedding times of leaves by numerical calculation. Key assumptions: (1) Air temperature varies seasonally with average temperature and the amplitude (climatic condition). (2) The key parameters of a leaf are construction cost, photosynthetic rate, and ageing rate (physiological condition). (3) A leaf adopts the optimal strategies of expansion and shedding times both under various climatic conditions and physiological conditions. Predictions: (1) There are two climatic conditions in which evergreen-ness is optimal. The first is where average temperature is over 30°C and the amplitude is very small, as in the tropics. The other is in cold regions, such as a frigid area. (2) Low maximum photosynthetic rate and high construction cost are likely to select for evergreen leaves.
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