We present a well-resolved, highly inclusive phylogeny for monocots, based on ndhF sequence variation, and use it to test a priori hypotheses that net venation and vertebrate-dispersed fleshy fruits should undergo concerted convergence, representing independent but often concurrent adaptations to shaded conditions. Our data demonstrate that net venation arose at least 26 times and was lost eight times over the past 90 million years; fleshy fruits arose at least 21 times and disappeared 11 times. Both traits show a highly significant pattern of concerted convergence (p<10(-9)), arising 16 times and disappearing four times in tandem. This phenomenon appears driven by even stronger tendencies for both traits to evolve in shade and be lost in open habitats (p<10(-13)-10(-29)). These patterns are among the strongest ever demonstrated for evolutionary convergence in individual traits and the predictability of evolution, and the strongest evidence yet uncovered for concerted convergence. The rate of adaptive shifts per taxon has declined exponentially over the past 90 million years, as expected when large-scale radiations fill adaptive zones.