An evolutionary attractor model for sapwood cross section in relation to leaf area

Sapwood cross-sectional area per unit leaf area (SA:LA) is an influential trait that plants coordinate with physical environment and with other traits. We develop theory for SA:LA and also for root surface area per leaf area (RA:LA) on the premise that plants maximizing the surplus of revenue over costs should have competitive advantage. SA:LA is predicted to increase in water-relations environments that reduce photosynthetic revenue, including low soil water potential, high water vapor pressure deficit (VPD), and low atmospheric CO₂. Because sapwood has costs, SA:LA adjustment does not completely offset difficult water relations. Where sapwood costs are large, as in tall plants, optimal SA:LA may actually decline with (say) high VPD. Large soil-to-root resistance caps the benefits that can be obtained from increasing SA:LA. Where a plant can adjust water-absorbing surface area of root per leaf area (RA:LA) as well as SA:LA, optimal RA:SA is not affected by VPD, CO₂ or plant height. If selection favours increased height more so than increased revenue-minus-cost, then height is predicted to rise substantially under improved water-relations environments such as high-CO₂ atmospheres. Evolutionary-attractor theory for SA:LA and RA:LA complements models that take whole-plant conductivity per leaf area as a parameter.