On the evolution of protandry and the distinction between preference and rank order in pollinator visitation

Question: How can protandry of hermaphrodite flowers be an adaptive strategy? Does this differ for plant species with vertical (Digitalis purpurea) and non-vertical (Echium vulgare) inflorescences? Mathematical methods: We develop a measure for quantifying rank order of visitation to flowers in the male and female stage. Key assumptions: Protandry is adaptive when it leads to female flowers being visited before male flowers. Conclusions: In D. purpurea, female flowers were visited first; for a bumblebee visiting 10 flowers on the plant, the average rank of the female flowers visited was 2 rank numbers below that of the male flowers, while the maximum rank difference (all female flowers visited before male flowers) was 5. In E. vulgare, there was no consistent difference in rank of visitation, despite a strong preference of bumblebees for visiting high-rewarding male-phase flowers. While results for Digitalis are in line with expectation, those for Echium are not.