Optimization theory of stomatal behaviour - I. A critical evaluation of five methods of calculation

There are two principal aims in this first manuscript, first, to compare five methods for calculating the marginal unit water cost of plant carbon gain (partial derivative E/partial derivative A) of leaves of two Australian tropical tree species, and second, to test the hypothesis that partial derivative E/partial derivative A of tropical tree leaves is constant when leaf to-air vapour pressure difference (D) varies. Few differences in the absolute values of partial derivative E/partial derivative A or the form of the response were found between species. However differences did exist between methods of calculation. Importantly, partial derivative E/partial derivative A was rarely constant with changing D. Stomatal limitations of net photosynthesis caused by a reduction in internal carbon dioxide concentration as stomatal conductance declined caused partial derivative E/partial derivative A to increase when D was increased. Some methods are applicable to canopy scale field measurements whilst others could only be used in laboratory settings where sufficient control of the environment is possible. The best method of calculation of partial derivative E/partial derivative A varied according to the criteria used to judge best. However, overall, despite the large numbers of independent data sets required, Method 1 was judged best for calculating partial derivative E/partial derivative A for individual leaves as, although it relies on the largest number of independently derived relationships, it has the fewest assumptions. Methods 2 and 3 were applicable to the field when a number of simplifying assumptions were made.