Four species with different flower colors were chosen: the white campion Silene latifolia (ssp. alba) Poir. (Caryophyllaceae), the Chilean bellflower Nolana paradoxa Lindl. (Solanaceae), the Missouri evening primrose Oenothera macrocarpa Nutt. (also known as O. missouriensis, Onagraceae) and the common poppy Papaver rhoeas L. (Papaveraceae) (Figure 2). Together these species span the spectrum of flower colors that are common in nature. S. latifolia and O. macrocarpa are pollinated by nocturnal moths (e.g., Young, 2002; Krakos and Austin, 2020), and P. rhoeas in Europe is pollinated by bees (van der Kooi and Stavenga, 2019). For N. paradoxa I could not find reliable data on the pollinating species. For N. paradoxa and P. rhoeas, we previously applied the optical model to study the optical properties (particularly the backscattering) of these flowers (Stavenga and van der Kooi, 2016; van der Kooi and Stavenga, 2019).

Reflectance spectra of the four species were measured with an integrating sphere (AvaSphere-50-Refl) and a deuterium-halogen lamp [AvaLight-D(H)-S] and the spectrometer an AvaSpec-2048 (Avantes, Netherlands). A piece of flower was directionally and about perpendicularly illuminated from within the sphere at an area with diameter ∼5 mm. A white diffuse tile (Avantes WS-2) was used as a reference. For transmittance measurements, the sample was illuminated from outside the sphere with a fiber, with an illumination spot size of ∼1 mm. To model the spectra, it is necessary to have the (absolute) amounts of transmittance and reflectance, which can be obtained with an integrating sphere and not with a reflection probe. For T. pratense (Figure 1A) the reflectance spectra were obtained with a bifurcated reflection probe, because the flowers were too small to be measured with the sphere. Petal absorbance spectra (Figure 1B) were obtained using a microspectrophotometer equipped with a xenon arc light source (for details, see Stavenga and van der Kooi, 2016).

To obtain reflectance spectra of similar shape but with different degrees of modulation, I applied our previously developed optical model (Stavenga and van der Kooi, 2016). That model combines the Kubelka-Munk theory for scattering and absorbing media (Kubelka and Munk, 1931; Allen et al., 1969) with a layer-stack model (Stavenga et al., 2006). Two key aspects of the model are the scattering and absorption parameters, S^∗ and K^∗, which can be derived from the measured reflectance (R) and transmittance (T) (Yamada and Fujimura, 1991; Stavenga and van der Kooi, 2016):

with

S^∗ and K^∗ are proportional to the amount of scattering and absorption, respectively. After the scattering and absorption parameters of a flower have been calculated using measured spectra (Figures 3A,B), modeled reflectance spectra can be obtained using a series of matrix calculations (see the appendix of Stavenga and van der Kooi, 2016; also see the R script). Spectra of similar shape but with different modulation were obtained by systematically varying K^∗ but leaving S^∗ unchanged, because K^∗ is the main factor that determines the modulation. The contribution of K^∗ in the model was set to be 0.2, 0.4, 0.6 … 4 (Figure 3C). The chosen parameter range yields spectra that are similar to those that can be found in real flowers and enables modeling cases of extreme amounts of pigment. What follows is a series of reflectance spectra, which are similar to those of flowers with different amounts of the same pigment (Figure 3D). S^∗ was kept identical to the value obtained for real flowers, so the modulation of the reflectance spectrum varied independently from the total amount of reflectance (see the convergence in the long wavelength range, Figure 3D).

Different optical processes determine the modulation of the reflected light and the applied optical model can be used to quantitatively investigate that, but the approach used here is not to study these factors. The aim of this study is to investigate the consequences of variation in absorption by pigments, but not via which anatomical ways this is achieved, because that requires detailed species-specific anatomical information. For example, increases in modulation of the reflected light can be obtained by increasing the total amount of pigment as well as by concentrating a smaller amount of pigment in the outer layer at the side of viewing (see Figure 5 in van der Kooi et al., 2016). To standardize the degree of modulation among the four different species, I used fractions and multiples of the empirical K^∗ (Figure 3). The different cases are classified by a “pigment index,” with pigment index = 5 being identical to the measured spectra (Figure 3) and lower and higher indices being the more weakly and strongly modulated cases, respectively.

It is important to point out that scattering and absorption, and so S^∗ and K^∗, are not strictly separated, because presence of pigments (slightly) influences the refractive index of a medium, and thereby the medium’s scattering. Nevertheless, the obtained spectra are highly similar to those found in nature, so the chosen approach is sufficient to study the effect of modulation for visibility to pollinators.

To interpret the different reflectance spectra with a pollinator subjective view, I deployed two commonly used insect vision models, i.e., the hexagon and the receptor noise-limited model (Chittka, 1992; Vorobyev and Osorio, 1998), using honeybee (Apis mellifera) and hawk moth (Deilephila elpenor) spectral sensitivities (van der Kooi et al., 2021a) and an average green leaf background under D65 ambient illumination. Both models yield a color contrast value, which is broadly considered a good proxy for visibility to a wide range of animals (Giurfa et al., 1996; Spaethe et al., 2001; Kelber et al., 2003; Dyer and Chittka, 2004).

When color contrast is modeled as a function of the amount of pigment, for all four cases there is a non-linear relationship. At low levels (i.e., for pale flowers), an increase in the amount of pigment enhances the flower’s contrast to the background. However, at a certain (species-specific) point, the color contrast curve plateaus, and further increases in the amount of pigment will not increase or even decrease color contrast (Figure 4)—indicating a pattern of diminishing return. The relationship of the color contrast and the amount of pigment depends on the type of pigment, but at least for the modeled white, blue and yellow colors the overall effect is similar. For the (ultraviolet reflecting) red P. rhoeas flowers the amount of pigment does not drastically change the flower’s contrast, meaning that within the current set of parameters changing the amount of pigment has a comparatively small effect on the visibility. Nevertheless, also for this species, the overall observation of diminishing returns in contrast with the amount of pigment is supported.

The results are largely vision model-independent, that is, within one color category, color contrast as a function of the amount of pigment is similar regardless of whether the hexagon or the receptor noise-limited model was applied (compare columns 2 and 3 in Figure 4). The effect of the amount of pigment on color contrast is also similar for bees and hawk moths (compare black and green in column 2, Figure 4), though there is one interesting exception. For moth-pollinated S. latifolia, color contrast increases more for moths than for bees (Figure 4A), suggesting that increasing the amount of pigment would disproportionally improve visibility to pollinators. However, in the other moth-pollinated species, O. macrocarpa, the effect may be opposite with (slightly) larger increases for bees than for moths.

Intriguingly, for almost all species, empirical contrast values (pigment index = 5) are not the highest that are theoretically possible. For the (ultraviolet reflecting) red poppy flower, the empirical color contrast is very close to the theoretical optimum, but for white, blue and yellow flowers, more wavelength-specific absorption by pigment would increase visibility. On the other hand, the empirical color contrast values are (well) above the detection threshold for bees, which are ∼0.10 for the hexagon model (Dyer and Chittka, 2004) and ∼2 for the RNL model (Vorobyev et al., 2001).

The observation that, in addition to the type of pigment, the amount of pigment is important for flower visibility is relatively overlooked in studies on flower color. These results open perspectives for future research in various directions.

Intraspecific trait variation (provided that it is heritable) is the cornerstones of evolution, and studies on the mechanistic underpinnings and consequences of such variation are paramount in understanding trait evolution (van der Kooi et al., 2021b). Generally, yellow colors are generated by carotenoids, white flowers by flavonols, and blue, purple, and red colors by anthocyanin pigments. Of these types of pigments, anthocyanins are most commonly associated with flower color polymorphisms (Sapir et al., 2021). Indeed, many species for which flower color variation was reported (Frey, 2004; Rakosy et al., 2012; Renoult et al., 2013; Sletvold et al., 2016; Dormont et al., 2019; Paine et al., 2019; Streinzer et al., 2019; Gómez et al., 2020; Whitney et al., 2020) have blue, pink or purple colors that are commonly due to anthocyanin pigments. It would be interesting to know, for these species, how standing variation in pigmentation relates to the flower’s conspicuousness to their pollinators.

The four cases considered here revealed (subtle) differences between types of pigment, as well as between bee and moth visual systems in how close the empirical amount of pigment is to the theoretical optimum and the variation around that optimum. Comparative studies covering species that are serviced by pollinators with different visual systems can elucidate the role of the amount of pigment in tuning flower color to pollinator vision. Something to consider is that the perceived flower color variation probably differs across pollinators. Whitney et al. (2020), for example, recently showed that for the same set of flowers, birds perceive more intraspecific variation than bees. It is known that different pollinators select for different flower colors (hues) owing to variation in spectral sensitivity and/or color preferences (Lunau et al., 2011; Shrestha et al., 2013; van der Kooi et al., 2019), but pollinators may also impose different selective pressures on the degree of variation around a certain hue. In other words, the degree of stabilizing selection on flower color probably varies with the type of pollinator, which would translate to different optima ranges in the amount of pigment.

To conclude, the amount of pigment is an important though often overlooked aspect of flower coloration. The amount of pigment shows a pattern of diminishing return and, corroborated by behavioral experiments with bees (Papiorek et al., 2013), I conclude that intermediate amounts often yield sufficient, if not maximal, visibility to pollinators. Future studies on how much floral pigment is needed to create conspicuous flowers will further our understanding on (the maintenance of) flower color variation and the costs of floral displays (Obeso, 2002; Roddy et al., 2020).