Curvature in models of the photosynthesis-irradiance response

An equation for the rate of photosynthesis as a function of irradiance introduced by T. T. Bannister included an empirical parameter b to account for observed variations in curvature between the initial slope and the maximum rate of photosynthesis. Yet researchers have generally favored equations with fixed curvature, possibly because b was viewed as having no physiological meaning. We developed an analytic photosynthesis-irradiance equation relating variations in curvature to changes in the degree of connectivity between photosystems, and also considered a recently published alternative, based on changes in the size of the plastoquinone pool. When fitted to a set of 185 observed photosynthesis-irradiance curves, it was found that the Bannister equation provided the best fit more frequently compared to either of the analytic equations. While Bannister's curvature parameter engendered negligible improvement in the statistical fit to the study data, we argued that the parameter is nevertheless quite useful because it allows for consistent estimates of initial slope and saturation irradiance for observations exhibiting a range of curvatures, which would otherwise have to be fitted to different fixed-curvature equations. Using theoretical models, we also found that intra- and intercellular self-shading can result in biased estimates of both curvature and the saturation irradiance parameter. We concluded that Bannister's is the best currently available equation accounting for variations in curvature precisely because it does not assign inappropriate physiological meaning to its curvature parameter, and we proposed that b should be thought of as the expression of the integration of all factors impacting curvature.