THE COLORS OF FIREFLY BIOLUMINESCENCE—I. OPTIMIZATION MODEL*

Abstract— A model is developed for the optimization of signal-to-noise ratio for the detection of bioluminescence by fireflies during twilight. The relative degree of optimization is derived in terms of a dimensionless ratio, a biologically effective adaptation. The numerical values of this adaptation can be used to predict the sequence of adaptations of both visual spectral sensitivities and bioluminescence spectral emissions that result in the range of colors of bioluminescence of fireflics from green through yellow. It is shown that a narrowing of visual spectral sensitivity via a screening pigment pathway in order to discriminate against green ambient light is more efficient than a shift in visual spectral sensitivity via change in the opsin photoprotein. The model predicts that the range of wavelengths for the peak intensities of bioluminescence for North American fireflies should be between 550 and 580 nm and provides the physical basis for the observations that in general dark-active firefly species cmit green bioluminescence and twilight-active firefly species emit yellow bioluminescence.