Symmetric Responses to Diet by Plumage Carotenoids in Violet-Sensitive Piciform–Coraciiform Birds

Abstract

Biological studies on symmetry can be expanded to consider red (longer wavelengths) and blue (shorter wavelengths) shifts as antisymmetries (opposite-pattern symmetries), which may arise from similar underlying causes (invariant process symmetries). In this context, classic shift asymmetries of redder plumage in response to higher dietary carotenoids appear conceptually incomplete, as potential blue-shifted counterparts were not considered. A latent symmetric response is highlighted by recent evidence showing that the maximum absorbance bands of various colorful plumage pigments are red-shifted in birds with ultraviolet-sensitive (UVS) color vision but blue-shifted in those with violet-sensitive (VS) color vision. Blue-shifted responses to increased dietary carotenoid contents may also be underestimated, as relevant studies have focused on species-rich but uniformly UVS Passerida passerines. This study explored the relationship between pattern–process symmetries and diets of VS Piciformes–Coraciiformes by gauging the responses of their plumage reflectance to a modified diet index (Diet_c), where the overall rank carotenoid contents of food items were weight-averaged by three levels of importance in a species’ diet. In the case of both sexes, the main long-wavelength reflectance band for the three carotenoid-based pigment classes defined the same graded series of blue shifts in response to higher Diet_c. Yellow showed a strong absolute (negative slope) blue shift, orange showed a weaker absolute blue shift, and red exhibited only a blue shift (flat, non-significant slope) relative to absolute red shifts (positive slope). The secondary shorter-wavelength reflectance band was also unresponsive to Diet_c in the VS Piciformes–Coraciiformes (relative blue shift) compared with earlier evidence for it decreasing (absolute red shift) at higher Diet_c in UVS species. Results for the intervening minimum reflectance (maximum absorbance) band were intermediate between those for the other reflectance bands. No pigment class monopolized lower or higher Diet_c, but red was less variable overall. Phylogenetic independence, sexually similar responses, and specimen preservation reinforced characterizations. A review of avian perceptual studies suggested that VS models discriminate yellows and oranges extremely well, consistent with the importance of the corresponding carotenoids as Diet_c indicators. Both UVS and VS species appear to produce putatively more costly and possibly beneficial carotenoid metabolites and/or concentrations in response to higher Diet_c, supporting underlying invariant processes in relation to carotenoid limitations and honest signaling despite opposite plumage shifts and their different chemical bases. In symmetry parlance, pigment classes (red) or wavebands (short) that lack responses to Diet_c suggest broken pattern and process symmetry. The biology of VS Piciformes–Coraciiformes may favor such exceptions owing to selection for visual resemblance and tuning specializations, although universal constraints on physical and chemical properties of (particularly red) carotenoids may favor certain functional tendencies. Thus, symmetry principles organize carotenoid diversity into a simplified and predictive framework linked to color vision.

1. Introduction

Organic symmetry implies a wide range of evolutionary phenomena, including patterns of phylogenetic relationships [1,2], progressive change [3,4], co-adaptation of form and function [5], developmental canalization [6], esthetic preferences [7,8], and missing phenomena for apparent asymmetries [9,10]. Despite this rich potential, most evolutionary applications of symmetry consider only structural morphology in terms of body shapes, i.e., bilateral (vertebrates), radial (anthozoans), pentameral (echinoderms), or other geometric forms (Figure 1A,B). However, symmetry concepts can be abstracted into various contexts. Thus, symmetry can also be applied to the physical geometry of any form that can be divided into a scheme of similar pieces. In this case, symmetry is still demonstrated if the form retains its overall shape despite transformations that move around the individual pieces. The specific symmetry then depends on piecemeal organization and transformation, which can include one (reflection, rotation, scaling, or translation) or more (glide reflection) operations [11,12]. For example, in simple line or reflection symmetries, features retain their inter-relationships when flipped across a dividing line or axis (Figure 1C). This more formal type of symmetry can be further expanded to include operations that reverse the form or function, referred to as antisymmetry (Figure 1D–F). Such considerations reveal that symmetry concepts can be applied to any situation wherein the underlying phenomena are preserved, despite arbitrary quantitative transformations. For this reason, symmetry has been generalized to mean invariance under any transformation, which can apply just as well to a process as to a pattern [13]. Moreover, disruptions to these relationships can be viewed as broken symmetries of the corresponding cases [10]. Therefore, generalized symmetry concepts appear fundamental to the study of ecology and evolution, as they provide simplified and predictive frameworks that can help distinguish general phenomena amidst the diversity of nature.

In this regard, an expanded conception of symmetries may be an underappreciated aspect of the exceptional diversity in organismal colorations and their physical bases (wavelengths). In addition to more typical color symmetries associated with body form, color antisymmetries incorporate the reversal of wavelengths by which long (“red”) ones are interchanged with short (“blue”) ones [14]. These reversals are dichromatic if only two colors or wavelengths are involved, or polychromatic if many are involved, as in a gradient (Figure 1E,F). It is therefore noteworthy that animals that manipulate carotenoid pigments as plumage colorants appear to favor visible red shifts in response to an increased uptake of carotenoids in their diet, which is the ultimate source of these epidermal biochromes in virtually all animals [15]. Thus, numerous asymmetric red shifts (to longer wavelengths), but no comparable blue shifts (to shorter wavelengths), have been documented within and among individuals or species that ingest greater quantities of these human-perceived yellow, orange, and red pigments in their diets [16,17,18,19,20,21,22,23]. Although perceptions of light are subjective, red shifts have an objective physical basis because of the association between perceived carotenoid yellowness and redness with distinct absorbance and reflectance properties [24,25,26]. These dietary red shifts also transcend pigmentation details—being expressed by a yellower (shorter wavelength) pigment class at lower to a redder (longer wavelength) pigment class at higher dietary carotenoid levels [16,21]—by a single pigment class (e.g., concentrations of yellow, orange, or red) across dietary carotenoid levels [16,17,20,27,28,29], through various mechanisms influencing feather characteristics, such as thickness, nanostructures, and pigment × protein interactions alone or in combination [20,21,22,30,31], and by patches or plumages [20,21]. Thus, plumage red shifts appear to be general physical phenomena not associated with any particular divergence level, chemistry, or anatomy, suggesting their pertinence to general patterns and processes. These shifts are of fundamental biological importance, as animals appear to have exploited connections between ecology and red shifts to provide visual information regarding the underlying qualities that affect individual survival and reproduction related to foraging, health, and fitness costs and benefits of carotenoid use [18,32,33,34,35]. Despite intensive studies, current asymmetries in carotenoid-based plumage expression require further exploration to determine if they are part of even broader symmetries.

A latent capacity for carotenoid-related blue shifts as opposed to red shifts and insights into how they may arise are suggested by subtle differences in plumage carotenoids between birds with ultraviolet-sensitive (UVS) or violet-sensitive (VS) tetrachromatic color vision systems [36,37]. Many diurnal birds with either of these main color vision systems develop various yellow-, orange-, and red-carotenoid-based plumages. However, a relation between plumage and visual pigment characteristics is suggested by an alignment between the maximal absorption wavebands of plumage carotenoids and those of the V and S single-cones distinguishing the color vision systems (350–500 nm) in the four-cone array (λ of maximum sensitivity ranked V_Violet < S_Short < M_Medium < L_Long). This connection appears to be borne out by evidence that the average spectral location of plumage carotenoid absorption maxima (i.e., of reflectance minima, λR_min) occurs at longer wavelengths for UVS Passeriformes [21,38] and Trogoniformes [26] compared with VS Piciformes and Coraciiformes [26]. Notably, the average spectral locations of λR_min are extremely similar between carotenoids in VS Piciformes–Coraciiformes and colorful plumage porphyrins unique to VS non-passerines (Galliformes, Musophagiformes, and Charadriiformes) [39]. Thus, λR_min values for colored plumage pigments appear relatively “red-shifted” (to longer wavelengths) for UVS and relatively “blue-shifted” (to shorter wavelengths) for VS. The quantitative alignments of the λR_min of plumage carotenoids and porphyrins with diagnostic V and S single-cone maximum sensitivity values in each color vision system suggest that concerted UVS-red versus VS-blue shifts in λR_min have some relationship with the key differences between visual systems [26,38,39]. These various shifts and alignments could relate to signaling as λR_min integrates many informational pigment properties, including their chemistry, optical density, and dietary or metabolic origin. The possible salience of wavelength-based shifts described for λR_min seems less intuitive than that of those described for reflectance maxima. Nevertheless, pigments create color via selective wavelength subtraction (absorption) from the white light spectrum [24]. Hence, absorption and reflection are complementary phenomena in pigment-based color mechanisms.

Considering these patterns, sampling bias could explain the apparent asymmetry in shift patterns if the red-biased UVS system is the only one considered. This explanation is plausible, as relevant studies have focused mainly on the extraordinarily diverse Passerida passerine clade [25,40,41], whose members appear exclusively UVS [42,43,44]. To broaden the exploration of wavelength-based shifts in carotenoid-based plumage evolution, this study analyzes carotenoid-based plumage shift patterns in relation to dietary carotenoid composition in VS Piciformes–Coraciiformes with the physical blue shift in average λR_min described above. This species-rich assemblage, which includes woodpeckers, barbets, toucans, and bee-eaters, provides several advantages for examining plumage-shift dynamics. First, many members of the VS Piciformes–Coraciiformes orders have developed spectacular carotenoid-based plumages comparable to or rivaling those of many UVS groups [45,46,47,48]. Second, the VS piciform–coraciiform group is minimally paraphyletic in that only a single derived, depauperate, and carotenoid-lacking lineage (Momotidae) has evolved the UVS characteristic within this radiation [37,49,50], providing a practical way to define the study system [26]. Third, the VS Piciformes–Coraciiformes have undergone dramatic diversification in their diets, covering the gamut of carotenoid contents in avian foods [51,52,53,54,55]. Finally, a large body of evidence from wild [56,57] and captive [58,59,60,61] VS Piciformes–Coraciiformes strongly suggests that their carotenoid-based plumages are highly sensitive to dietary changes. Therefore, morphological, historical, ecological, and physiological factors appear to favor a response of carotenoid-based plumages to diet among VS Piciformes–Coraciiformes.

I evaluated carotenoid-based plumage responses to diet by VS Piciformes–Coraciiformes by analyzing carotenoid pigment classes and their key spectral features in the visible range of diurnal birds. These attributes were treated as standardized physical measures of fundamental traits potentially related to shift patterns that could be compared across taxa and used to diagnose physical and chemical processes that underlie plumage information content. Subjective visual models are not applied because of the paucity of realistic parameter values and categorical color spaces assigned for Piciformes–Coraciiformes [62]. Relevant to the physical approach of evaluating dietary responses in relation to color vision, contour plumage carotenoids of UVS birds actually respond to higher dietary carotenoids with three forms of red shift. More intuitively, the characteristic main reflectance band shifts to longer wavelengths as dietary carotenoid amounts increase [16,17,20,28,63,64]. Less intuitively, the prominence of a characteristic secondary reflectance band at shorter wavelengths diminishes greatly as dietary carotenoid amounts increase [20,21,22], reinforcing the parallel long-wavelength bias of the main reflectance band [22]. Both of these responses are related to λR_min, which marks the boundary between the main (at its short-wavelength end) and secondary (at its long-wavelength end) reflectance bands. Consequently, λR_min can also be red-shifted at relatively high dietary carotenoid levels [21]. Thus, wavelength-based reflectance enables shift patterns (wavelength compositions as longer = “redder” or shorter = “bluer”) and processes (chemistry, cost, and benefits) for these spectral components to be compared objectively on the same scale across studies, physical components, and color vision systems. Therefore, the aims of this study are twofold: (1) to assess shift pattern symmetries in functional responses to dietary carotenoid contents across pigment classes and spectral features as related to the color vision system; (2) to explore internal evidence that shift process symmetries in carotenoid limitations, honest signaling, and other factors may underlie these patterns. The results support the importance of the symmetry principles in plumage carotenoids, similar to other photonic systems.

2. Materials and Methods

2.1. Data Collection

Plumage Carotenoids. Analyses were limited to piciform and coraciiform taxa with known (VS) color visual systems at the species to family level [26], and plumage patches colored predominantly by carotenoid pigments (e.g., no carotenoid–melanin mixes), as determined by their visual appearance and electronic spectra [21,26,38,46,47,65,66]. A gonadal definition of sex implied by specimen label data was applied in accordance with best ornithology practices. The species and adult specimens analyzed by sex in this study are listed in Table S1. All VS specimens were used in previous studies [26], except that another female Northern Flicker (Colaptes auratus; Picidae) was added for the red cockade. Chemically based (as opposed to physically based) [67,68] carotenoid pigmentation encompassed colors that humans perceive from yellow to orange to red (Figure 2), although objective groupings corresponding to these perceived categories are evident from the electronic spectra [26]. Additional sampling criteria applied to the specimens, patches, and spectra have been described previously [26].

Spectral Features. Raw plumage reflectance data generated during an earlier study on plumage maximum absorbance (λR_min) in VS Piciformes–Coraciiformes [26] were further analyzed. The nanometer range analyzed here encompasses the lower (320 nm) and upper (700 nm) general physical limits for avian VS wavelength sensitivities based on V (sensitivity to shortest wavelengths) and L (sensitivity to longest wavelengths) single-cone responses [36] and ocular medium transmission [69]. In addition, alignments of the four avian single-cone (V, S, M, and L) maximum sensitivity values with physical features of these spectra provided insights into shift patterns and processes for each avian color vision system [26].

Principal shift patterns in plumage carotenoid spectra were embodied by both their main and secondary reflectance bands (Figure 3), of which only the former band occurred entirely above the normal lower limit of the human visible range (>400 nm). However, all carotenoid pigments act as optical cutoff filters that strongly absorb light only below a certain wavelength range [26]. As such and by convention [22,25], the spectral location of the main reflectance band was identified with that of the cutoff feature, a rapid transition from the highest (R_max) to the lowest (R_min) reflectance at longer and intermediate wavelengths, respectively, summarized as the wavelength of half-maximal reflectance using Equation (1) as follows:

λR₅₀ = λ[(R_max + R_min)/2],

(1)

where the average of the maximum (R_max) and minimum (R_min) reflectance (Figure 3) provides the reflectance value from which to obtain the spectral location of the cutoff feature [21,22,70].

Two related shorter-wavelength spectral features typical of carotenoids were also assessed to test the predictions for short wavelengths and consider the consistency of shift patterns across the avian VS-visible spectrum. The wavelength of R_min (λR_min) was the nadir of the strongest relevant absorption band and a characteristic feature of all carotenoids. The values of λR_min were located well below (usually between 400 and 500 nm) the longer-wavelength values for λR₅₀ (Figure 3) and, therefore, embodied distinct shorter-wavelength features. In addition, the secondary reflectance band located at even shorter wavelengths rose below λR_min and then tapered off at the limits of avian visual perception, well into the ultraviolet (≤400 nm) wavelengths (Figure 3). To quantify this feature while controlling for the levels of overall reflectance, the relative amount of short-wavelength reflectance was estimated using Equation (2) as follows [21,70]:

R_contrast = [(R_λRmin–700) − (R_320–λRmin)]/(R_320–700).

(2)

Based on this equation, R_contrast increased with a greater proportion of longer wavelengths and decreased with a greater proportion of shorter wavelengths (Figure 3).

Pigment Classes. The reflectance and (inverse) absorbance data were used to classify plumage patches into chemical classes based on diagnostic absorption features [26,39]. Typical yellow carotenoids exhibit a narrow cluster of absorption bands at relatively short wavelengths (Figure 3A,B), whereas typical red carotenoids exhibit a single broad absorption band at relatively long wavelengths (Figure 3E,F). These properties of yellow and red carotenoids depend on the extent of electronic conjugation, a system of resonating double bonds, in their hydrocarbon backbones. The classification of patches into those with predominantly yellow or red pigments (“pigment classes”), therefore, has objective validity at both the physical (spectral form) and chemical (molecular form) levels even if human color names are applied.

The same holds for relatively rare, visibly “orange” (described as such in the literature) plumages, which exhibited characteristics between those of yellow and red plumages (Figure 3C,D). The shortest λR₅₀ obtained for these orange plumages was approximately 530 nm (males: 530.675 nm; females: 531.2 nm), and the longest λR₅₀ did not exceed 555 nm (males: 552.895 nm; females: 540.245 nm). Moreover, these ranges were contiguous but non-overlapping at their short ends with the longest yellows, and widely separated at their long ends from the shortest reds (males: 575.517 nm; females: 568.745 nm). Orange pigmentation may arise from concentrated yellow, a mixture of yellow and red, or inherently orange carotenoids [71,72,73]. Taken together, these considerations support orange as an intermediate third category, indicating that it is closer to yellow than to red, but that its physical and chemical composition may combine aspects of the other two pigment class categories. Therefore, an orange pigment class was distinguished for shift pattern analysis.

Dietary Carotenoid Contents. Dietary carotenoid content for all species included in this study was estimated from publicly available data. The online version of the Birds of the World database was used to inventory diets [53,54,74]. Using the same source for each species aids in standardizing diet contents by limiting variation in how diets are reported and described. Dietary carotenoid content was calculated in several steps based on the considerations described earlier [75]. First, each item was placed into one of 32 ranked content categories based on carotenoid concentrations from lowest (1) to highest (32), which differed by several orders of magnitude in mg/kg (Table 1 in [75]; Table S2). Additional items consumed by Piciformes–Coraciiformes but not enumerated earlier [75] (bold items in Table S2) were added to the appropriate content category based on concentration values provided in the literature (Table S2). Each item was then assigned to one among the predominant (1°), secondary (2°), or tertiary (3°) importance categories of the diet based on adjectives (rarely percentages) used to describe how often the item was consumed by a species (Table 3 in [75]). Finally, the dietary carotenoid content index (hereafter Diet_c) was calculated as a weighted average of the average ranked carotenoid contents of dietary items in each importance category, a modification avoiding bias caused by the number of items reported in each category, using Equation (3) as follows:

Diet_c = [3(1°_{AveRankContent}) + 2(2°_{AveRankContent}) + 1(3°_{AveRankContent})]/(Sum of Weights).

(3)

In this equation, the terms include the average rank carotenoid contents (AveRankContent) of items within each importance category (importance ordered 1° > 2° > 3°) weighted based on the importance category (3 × 1°, 2 × 2°, and 1 × 3°; 0 = item not consumed). The calculated Sum of Weights for diets with all three importance categories was six, which was reduced for diets with fewer importance categories (e.g., five for 1° and 2°, four for 1° and 3°, and three for 1° only). A rank/importance approach provided a robust continuous scale from carotenoid-poor (generally more animal-based) to carotenoid-rich (generally more plant-based) diets (Table S2), lending itself to the quantitative evaluation of wavelength-based shift patterns in relation to diets. Only adult diets were analyzed because of the consistent bias towards more animal foods in nestling diets and the unavailability of plumage measurements for nestlings. Sex differences in diet were not distinguished because of the lack of available information.

2.2. Statistical Treatments

Data Treatments. All measured patches were contour feathers, with one exception (i.e., flight feathers of Colaptes auratus); therefore, feather type was not distinguished. Each plumage data point used in the analysis was the average of (2–4) replicate scans per patch × number of patches × carotenoid pigment class × sex of each species [26]. The final dataset included information on a maximum of 54 species, although the females of a few species lacked plumage carotenoids. However, the sample sizes analyzed for each sex were greater than the number of species because patches that differed in the predominant pigment class were averaged separately, producing up to three data points × sex for the species in question. As the data used to determine Diet_c did not distinguish between male and female food preferences, only the plumage spectral features could be estimated separately for each sex within a species. However, the exact combination of species and plumages also differed for each sex (see Figures S1 and S2), providing additional independence in their estimated responses to Diet_c. These considerations are implicit in the following analyses.

Multiple Regression Models. Multiple regressions exploring functional responses of the three spectral features (λR₅₀, R_contrast, and λR_min) were constructed to include two dummy variables to encode the three pigment classes, and the continuous covariate Diet_c (Table 1). The variable Year (specimen collection year) was also included to control for possible post-mortem changes that often occur in carotenoid-based coloration [21,76,77]. Exploratory models indicated that multiplicative terms (Year × Year, Year × Diet_c, and Diet_c × Diet_c) and their interactions made small and non-significant contributions. Therefore, only full models that included all main effect terms and their interactions (see Table 1) were systematically explored.

Table 1. Definitions of independent variables used in multiple regression analyses.

	Interpretation of Independent Variables
Model Independent Variables a	Description	Property
Year b	Specimen collection year	Continuous
YO c,d	DummyYellowOrange	Categorical
YR c,d	DummyYellowRed	Categorical
Dietc d,e	Dietc (ReferenceCategory)	Continuous
YYearOYear f	YellowYear × OrangeYear	Interaction
YYearRYear	YellowYear × RedYear	Interaction
YDietcODietc f	YellowDietc × OrangeDietc	Interaction
YDietcRDietc	YellowDietc × RedDietc	Interaction

^a Specimen collection year averaged for more than one specimen × sex × species. ^b Model: dependent variables used are λR₅₀, R_contrast, and λR_min (spectral features; see Section 2). ^c Pigment class categories: Y = Yellow, O = Orange, and R = Red. The leading term is the Reference Category for the pigment classes, Yellow (Y) in this case. ^d If Yellow is the Reference Category, then dummy variables used for the Reference Category (0, 0), dummy variables used for Yellow versus Orange (0, 1), and dummy variables used for Red versus Yellow (1, 0) jointly encode the three pigment classes. ^e The regression coefficient for Diet_c is the functional response by Reference Category pigment class to Dietc. ^f Interaction (×) tests the differences in functional responses to Year or Diet_c based on Reference (Y) compared with that in the other pigment class category in that interaction term.

Table 1. Definitions of independent variables used in multiple regression analyses.

	Interpretation of Independent Variables
Model Independent Variables a	Description	Property
Year b	Specimen collection year	Continuous
YO c,d	DummyYellowOrange	Categorical
YR c,d	DummyYellowRed	Categorical
Dietc d,e	Dietc (ReferenceCategory)	Continuous
YYearOYear f	YellowYear × OrangeYear	Interaction
YYearRYear	YellowYear × RedYear	Interaction
YDietcODietc f	YellowDietc × OrangeDietc	Interaction
YDietcRDietc	YellowDietc × RedDietc	Interaction

^a Specimen collection year averaged for more than one specimen × sex × species. ^b Model: dependent variables used are λR₅₀, R_contrast, and λR_min (spectral features; see Section 2). ^c Pigment class categories: Y = Yellow, O = Orange, and R = Red. The leading term is the Reference Category for the pigment classes, Yellow (Y) in this case. ^d If Yellow is the Reference Category, then dummy variables used for the Reference Category (0, 0), dummy variables used for Yellow versus Orange (0, 1), and dummy variables used for Red versus Yellow (1, 0) jointly encode the three pigment classes. ^e The regression coefficient for Diet_c is the functional response by Reference Category pigment class to Dietc. ^f Interaction (×) tests the differences in functional responses to Year or Diet_c based on Reference (Y) compared with that in the other pigment class category in that interaction term.

The functional response coefficient (slope B) of the dependent variable to Diet_c for each pigment class was estimated by decomposing the individual terms in the full model. Absent interaction terms, the Diet_c coefficient can be interpreted as the common slope across dummy variable categories [78]. However, Diet_c coefficients for each pigment class can be determined by including interaction terms based on the conditional interpretation of the coefficients for Diet_c and the interaction terms [79,80,81]. With the interaction terms (Table 1), the Diet_c coefficient and its significance pertain to the slope only for the pigment class designated as the Reference Category (the pigment class coded 0, 0 across both dummy variables). The Diet_c coefficients for the Non-Reference Categories (each of the other pigment classes) are then obtained by adding the coefficient for the Reference Category to that of the appropriate two-pigment interaction term in turn (“probing”). Designating Yellow as the (0, 0 dummy coded) Reference Category, for example, yields B_Yellow = B_Dietc, B_Orange = B_Dietc + B_{YellowDietcXOrangeDietc}, and B_Red = B_Dietc + B_{YellowDietcXRedDietc}. The magnitudes of the slope differences in the dependent variable response to Diet_c by pigment class were then determined in the usual way through the significance of the coefficients for the corresponding interaction terms.

Changing the Reference Category for pigment class allows the same information to be obtained for that class in a similar manner. Specification of the Reference Category does not otherwise affect the overall model fit for a given analytical method or coefficient estimates for the functional response of each pigment class to Diet_c. Accordingly, it is equally valid to use any pigment class as a Reference Category, with the qualification that a relatively small sample size will reduce the power to detect statistically significant interactions [82]. This consideration is applied here, particularly to orange as the Reference Category (N_male = 6, N_female = 10). However, coefficients calculated in this way are also heuristic for non-significant (p > 0.05) interactions [82].

Comparative Evolutionary Models. To explore the robustness of associations between carotenoid pigment class (yellow, orange, and red), plumage spectral features (λR₅₀, R_contrast, and λR_min), and dietary carotenoid content (Diet_c), a variety of comparative evolutionary regression models were implemented in the R software environment version 3.6.1 [83] using “ape” version 5.3 [84] and “nlme” version 3.1.141 [85] and linked packages. These models included one based on a conventional ordinary least squares (OLS) approach (equivalent to star phylogeny, which lacks historical constraints based on relatedness) and others based on phylogenetic generalized least squares (PGLS) regression, which incorporates explicit phylogenetic structure. The OLS approach does not consider non-independence among species owing to their shared history, whereas the PGLS approach does so by estimating the phylogenetic signal in the response variable, as expressed by any non-independence in the correlation structure among the regression residuals.

The phylogenetic trees used in the PGLS models (Figures S1 and S2) were based on those assembled for an earlier analysis of plumage carotenoid absorption patterns in the same piciform–coraciiform taxa [26], except that relationships among woodpeckers were updated [86] in Mesquite (version 3.04) [87]. The phylogeny was based on several sources and data types, including traditional taxonomy, and statistical models required the assignment of branch lengths to multiple pigment classes within a species’ sex. Accordingly, results for branch lengths assigned unit or ultrametric (arbitrarily ultrametric) values (Mesquite 3.02) [87] were explored. The consensus user tree containing all taxa was strictly dichotomous, except for two instances in which the occurrence of patches for all three pigment classes was modeled as a trichotomy for that species and sex. Male and female trees differed slightly because of some differences in carotenoid-based coloration between the sexes (Figures S1 and S2). Owing to tree variations, males and females were analyzed separately to assess sexual dimorphism in functional responses to Diet_c (see also Dietary Carotenoid Content).

The specific correlation structures for the PGLS models were based on Brownian motion under Ornstein–Uhlenbeck processes (OU, corMartins) or Grafen’s method (BM_Grafen, corGrafen). These models further aid in the interpretation of evolutionary process, although the values for the additional parameters are specific to each model. The constrained random walk model under an OU process includes α, which measures the strength of the evolutionary force that returns traits to the long-term mean μ. When α approaches 10, phylogenetic constraint is considered small and approximates the “white noise” of a star phylogeny, in which all taxa are equally related and evolve independently. By comparison, α’s that approach 0 are consistent with a Brownian process of phylogenetic constraint and the less parsimonious OU process can be rejected [88]. More objective support for either interpretation can be obtained by converting α to the phylogenetic half-life using Equation (4) as follows:

t_1/2 = (ln(2))/α,

(4)

which measures the time required for a niche-shifted species to evolve to its new optimum in comparison to the overall tree height (11 in all cases), such that relatively small values of t_1/2 imply weak constraints and vice versa. The modified Brownian motion model of Grafen estimates branch lengths through a different process, embodied by ρ [89]. A ρ < 1.0 indicates compression of internodes to the base of the tree, suggesting reduced phylogenetic signal and an approach to a star-type phylogeny. Conversely, a larger ρ indicates a more structured phylogeny in which internodes are more spaced out from the root of the tree to its tips. I explored three values for ρ, including (BM_GrafenF) ρ = 1.0 (the unit or ultrametric branch length starter trees), ρ = 0.5 (modest compression of internodes), and (BM_GrafenE) ρ = estimated (empirically determined from the data). The implementation of all models assumed uniform evolutionary rates and a single trait optimum (OU), which were the default options. Alternatively, multiple-trait optima explored using Bayesian approaches require large sample sizes and the selection of appropriate priors a posteriori (dependent on this study).

Statistics for Model Selection. The main advantage of evaluating a suite of process models is that it allows interpretations of functional relationships based on best-fit criteria. Corresponding multiple regressions across evolutionary models were ranked by ln maximum likelihood support (more positive) estimated in ape for each model. The significance of differences in support was assessed using likelihood-ratio tests (LRTs) not available for the related Akaike information criterion. However, a caveat to the LRT approach is that simulation studies [88] suggest that these tests may incorrectly favor OU over BM models because of the formal properties of the data and the violation of LRT assumptions (which are based on an unbounded χ² distribution with one degree of freedom) by the bounded parameter values of OU models, particularly with small sample sizes (<200, as here). Mistakes in model selection and subsequent interpretations based on fit alone can be further avoided by considering the values of the parameters estimated for the PGLS models (see above) [88]. Additional support was assessed by adjusted R² calculated from R²_lik generated in the R package “rr2” version 1.0.2 [90,91,92].

Sex was characterized separately using identical methods. Analyses focused on functional responses (slopes) of spectral features to the covariate Diet_c and on probing related interactions of Diet_c with pigment class, which are unaffected by the choice of the y-intercept (x = 0, no mean centering or other transforms) [93]. The regression coefficients were unstandardized effect sizes (B) comparable across structurally parallel models for variables in the same original units. Multicollinearities assessed by the variance inflation factor estimated with the R package “car” version 3.0.13 [94] for continuous control (Year) or covariate (Diet_c) predictors were within acceptable (<3) limits, and inconsequential for dummy-variable interactions with continuous predictors [82,95]. The degrees of freedom were not adjusted for the two (yellow, orange, and red) trichotomies in the tree, which slightly increased Type I errors [96]. However, the nearly identical results for OLS and PGLS indicate that this modification has little impact on the results or conclusions. Two-tailed tests are mainly reported throughout, but these can be readily converted (P/2) to one-tailed tests for directional predictions in relation to an expected red or blue shift (e.g., effects of Diet_c) based on prior results (see Section 1) [26]. No adjustments were made for multiple comparisons [97]. Additional data processing and statistics were implemented in SAS (version 9.4) [98], Microsoft^® Excel for Mac version 16.16.27, or Social Science Statistics http://www.socscistatistics.com/ (accessed on 9 October 2023) [99].

3. Results

3.1. Dynamic Responses to Diet_c

The characteristics of the raw data suggested a phenotype space best described as covariant in that all three pigment class categories overlapped broadly across the span of Diet_c values (Figure 4, Figure 5 and Figure 6). This formal structure contrasts strongly with a more collinear one in which, for example, yellow pigments are expressed at lower Diet_c and red pigments are expressed at higher Diet_c [16,21]. However, a small gap among species with intermediate Diet_c suggests that specializations for dietary taxa with these contents are underrepresented or underestimated (Figure 4, Figure 5 and Figure 6). Although the possible unevenness of Diet_c is of biological interest, regression imposes no assumptions on the distribution (e.g., normal or continuous) of independent variables. Instead, the raw data suggested analyses using relatively simple multiple regressions that treat pigment class as a categorical variable and Diet_c as a covariate. The control variable Year (Table 1) is included in these models but is not discussed further because of inconsistent and mostly weak effects.

Wavelength of Half-Maximal Reflectance (λR₅₀). Results for λR₅₀ were similar for both sexes (Table 2, Table 3 and Table 4, and Figure 4). Values for R²_adjusted were notably high (~0.9) for all models, suggesting that the suite of terms provided an excellent fit to the data that was robust to the starter tree branch length specification (Table 2). However, LRT assessed OLS, OU, and BM_GrafenE models as significantly and equally superior to those that place greater emphasis on Brownian motion (BM_GraftenF, ρ = 1.0, 0.5) phylogenetic structuring. Specifically, the three best-supported models provided mutually reinforcing evidence for little or no phylogenetic constraint on λR₅₀ evolution. OLS models do this implicitly because of their lack of an implied phylogenetic correlation structure (equivalent to star phylogeny). The OU models do this explicitly through the relatively large values of α (~10) and small values of t_1/2 (<<<1) relative to tree height (11). The BM_GrafenE is as explicit through its tiny estimated ρ (<<< 0.5), which suggests approximation to a star phylogeny. By comparison, fixing ρ at 1.0 or 0.5 to emphasize phylogenetic structure resulted in the inferior BM_GraftenF models. Considering the evidence of equal support among the OLS, OU, and BM_GraftenE models for both sexes, the OU model was used to enumerate the full multiple regression (Table 3) and parallel the results for the other dependent variables. However, the OLS results for λR₅₀ were virtually identical to those obtained under OU and BM_GrafenE (Table 2).

For all “favored” (OLS, OU, and BM_GrafenE) models, each Reference Category supported a graded series of blue shifts by λR₅₀ in response to higher Diet_c, in the order yellow > orange > red among pigment classes for both sexes (Table 3 and Table 4, and Figure 4). Under explicit multiple regressions with each pigment class used in turn as Reference Category (ultrametric OU model shown for consistency, Table 3; other favored models similar), the slope for yellow was the most significant and strongly negative (males: B~−1.95; females: B~−2.15), that for orange was of intermediate significance and less negative (males: B~−0.9; females: B~−0.35), and that for red not nearly significant and almost zero (males: B~0.02) or slightly positive (females” B~0.15). Thus, at a higher Diet_c, yellow and orange are blue-shifted, whereas red is blue-shifted only compared to a red shift. Probing the additive properties of Bs across all favored models and Reference Categories revealed similar patterns (Table 4). Consistent with these results, enumerated interaction terms supported larger and more significant slope differences between yellow and red than for either compared to orange (Table 3 and Table 4). For pigment classes with small sample (orange) or effect (red) sizes, shift patterns were consistently negative (orange) or slightly positive (red) across all favored models and both sexes (12 of 12 in the binomial one-tailed test: p < 0.001, for a 0.5 probability of obtaining the same slope sign for each trial). Despite significant interactions with Diet_c, the λR₅₀ response lines for each pigment class did not cross over the range of observed Diet_c values, with yellow at shortest and red at longest wavelengths (Figure 4). Thus, the functional responses by pigment class to Diet_c are unambiguous for λR₅₀ (Table 3 and Table 4, and Figure 4), as statistical analyses and general trends for λR₅₀ support the same conclusions.

Table 2. Full model (Table 1) selection table for wavelength of half-maximal reflectance (λR₅₀). Note greater support for models with no (OLS) or weak (OU, BM_GrafenE) compared to stronger (other BM models) phylogenetic constraints.

	Model Results
	Fit				Parameters
Model a	R2adjusted b	MLK c	LRT d	RANK d	PARM e	t1/2 f
Males
Unit
OLS	0.91664534	−330.5871	*	1
OU	0.91664534	−330.5871	*	1	8.727854	0.07941782
BMGrafenE	0.91667659	−330.5715	*	1	0.00869885
BMGrafenF	0.88390606	−344.3358		2	0.5
BMGrafenF	0.87547702	−347.2446		3	1.0
Ultrametric
OLS	0.91664534	−330.5871	*	1
OU	0.91664534	−330.5871	*	1	8.755829	0.07916408
BMGrafenE	0.91667659	−330.5715	*	1	0.00869885
BMGrafenF	0.88390606	−344.3358		2	0.5
BMGrafenF	0.86844175	−349.5254		3	1.0
Females
Unit
OLS	0.919511529	−301.6970	*	1
OU	0.919511529	−301.6970	*	1	9.117833	0.07602104
BMGrafenE	0.919511529	−301.6970	*	1	9.12 × 10−9
BMGrafenF	0.882718141	−316.1910		2	0.5
BMGrafenF	0.875707588	−318.4262		3	1.0
Ultrametric
OLS	0.919511529	−301.6970	*	1
OU	0.919511529	−301.6970	*	1	9.044239	0.07663964
BMGrafenE	0.919511529	−301.6970	*	1	9.12 × 10−9
BMGrafenF	0.882718141	−316.1910		2	0.5
BMGrafenF	0.8639429	−321.908		3	1.0

^a Evolutionary process models (models) include non-phylogenetic ordinary least squares (OLS) and phylogenetic generalized least squares (PGLS) under an Ornstein–Uhlenbeck (OU) or Brownian motion (BM) process. BM models were further subdivided by parameterization with Grafen’s ρ (BM_Grafen), with ρ estimated by the model (BM_GrafenE) or pre-set to 0.5 or starter tree 1.0 (BM_GrafenF). All PGLS models were tested two ways, using trees assigned unit (set to 1) or ultrametric (arbitrary ultrametrization) branch lengths in Mesquite v 3.03 [87]. ^b All parameter values were unchanged by the Reference Category designation. R²_adjusted is based on 1 − {[(1 − R²) (N − 1)]/(N-p-1)}, where R² = sample R², p = number of predictors, and N = total sample size. ^c ln restricted maximum likelihood (MLK). A more positive value indicated an improved model fit. ^d The likelihood ratio test (LRT) for significant differences in model fit. Significance was based on the assumption that twice the difference in the paired ln ML values followed a χ² distribution with 1 df, for which the critical value was 3.841 at p < 0.05. The best model(s) are indicated by * and RANK (rank support). ^e The values of key model parameters (PARM). OU α = evolutionary force strength returning trait to long-term optimum; GrafenE = Grafen’s ρ estimated; and GrafenF = Grafen’s ρ pre-set to 0.5 or 1.0. ^f Phylogenetic half-life (t_1/2 = (ln(2))/α). All model values of t_1/2 were small relative to tree height (11 for both sexes), supporting a rapid return to the trait optimum in both sexes.

Table 2. Full model (Table 1) selection table for wavelength of half-maximal reflectance (λR₅₀). Note greater support for models with no (OLS) or weak (OU, BM_GrafenE) compared to stronger (other BM models) phylogenetic constraints.

	Model Results
	Fit				Parameters
Model a	R2adjusted b	MLK c	LRT d	RANK d	PARM e	t1/2 f
Males
Unit
OLS	0.91664534	−330.5871	*	1
OU	0.91664534	−330.5871	*	1	8.727854	0.07941782
BMGrafenE	0.91667659	−330.5715	*	1	0.00869885
BMGrafenF	0.88390606	−344.3358		2	0.5
BMGrafenF	0.87547702	−347.2446		3	1.0
Ultrametric
OLS	0.91664534	−330.5871	*	1
OU	0.91664534	−330.5871	*	1	8.755829	0.07916408
BMGrafenE	0.91667659	−330.5715	*	1	0.00869885
BMGrafenF	0.88390606	−344.3358		2	0.5
BMGrafenF	0.86844175	−349.5254		3	1.0
Females
Unit
OLS	0.919511529	−301.6970	*	1
OU	0.919511529	−301.6970	*	1	9.117833	0.07602104
BMGrafenE	0.919511529	−301.6970	*	1	9.12 × 10−9
BMGrafenF	0.882718141	−316.1910		2	0.5
BMGrafenF	0.875707588	−318.4262		3	1.0
Ultrametric
OLS	0.919511529	−301.6970	*	1
OU	0.919511529	−301.6970	*	1	9.044239	0.07663964
BMGrafenE	0.919511529	−301.6970	*	1	9.12 × 10−9
BMGrafenF	0.882718141	−316.1910		2	0.5
BMGrafenF	0.8639429	−321.908		3	1.0

^a Evolutionary process models (models) include non-phylogenetic ordinary least squares (OLS) and phylogenetic generalized least squares (PGLS) under an Ornstein–Uhlenbeck (OU) or Brownian motion (BM) process. BM models were further subdivided by parameterization with Grafen’s ρ (BM_Grafen), with ρ estimated by the model (BM_GrafenE) or pre-set to 0.5 or starter tree 1.0 (BM_GrafenF). All PGLS models were tested two ways, using trees assigned unit (set to 1) or ultrametric (arbitrary ultrametrization) branch lengths in Mesquite v 3.03 [87]. ^b All parameter values were unchanged by the Reference Category designation. R²_adjusted is based on 1 − {[(1 − R²) (N − 1)]/(N-p-1)}, where R² = sample R², p = number of predictors, and N = total sample size. ^c ln restricted maximum likelihood (MLK). A more positive value indicated an improved model fit. ^d The likelihood ratio test (LRT) for significant differences in model fit. Significance was based on the assumption that twice the difference in the paired ln ML values followed a χ² distribution with 1 df, for which the critical value was 3.841 at p < 0.05. The best model(s) are indicated by * and RANK (rank support). ^e The values of key model parameters (PARM). OU α = evolutionary force strength returning trait to long-term optimum; GrafenE = Grafen’s ρ estimated; and GrafenF = Grafen’s ρ pre-set to 0.5 or 1.0. ^f Phylogenetic half-life (t_1/2 = (ln(2))/α). All model values of t_1/2 were small relative to tree height (11 for both sexes), supporting a rapid return to the trait optimum in both sexes.

Table 3. Full model multiple regressions based on an OU process model and ultrametric tree for the wavelength of half-maximal reflectance (λR₅₀) as a dependent variable. The eight predictor variables differ only in which of the three pigment classes is designated as the Reference Category (0, 0) for these dummy variables.

Pigment Class Reference Category a
Yellow			Orange			Red
Model b,c	B	P	Model	B	P	Model	B	P
Males
Year	−0.2357	0.0103	Year	−0.5789	0.6246	Year	0.0905	0.3644
YO	683.5101	0.7689	OY	−683.5101	0.7689	RY	583.5387	0.0291
YR	−583.5387	0.0291	OR	−1267.0487	0.5864	RO	1267.0487	0.5864
Dietc d	−1.959	0.0000	Dietc e	−0.9167	0.3664	Dietc f	0.025	0.9579
YYearOYear	−0.3433	0.7722	OYearYYear	0.3433	0.7722	RYearYYear	−0.3262	0.017
YYearRYear	0.3262	0.017	OYearRYear	0.6695	0.573	RYearOYear	−0.6695	0.573
YDietcODietc	1.0423	0.3488	ODietcYDietc	−1.0423	0.3488	RDietcYDietc	−1.984	0.0033
YDietcRDietc	1.984	0.0033	ODietcRDietc	0.9417	0.4005	RDietcODietc	−0.9417	0.4005
Females
Year	0.0737	0.5357	Year	0.0216	0.8866	Year	−0.0265	0.7661
YO	95.8273	0.8008	OY	−95.8273	0.8008	RY	−239.9381	0.41
YR	239.9381	0.41	OR	144.1109	0.6788	RO	−144.1109	0.6788
Dietc d	−2.1535	0.0000	Dietc e	−0.348	0.6546	Dietc f	0.1463	0.7424
YYearOYear	−0.0522	0.7862	OYearYYear	0.0522	0.7862	RYearYYear	0.1003	0.5006
YYearRYear	−0.1003	0.5006	OYearRYear	−0.0481	0.7842	RYearOYear	0.0481	0.7842
YDietcODietc	1.8055	0.0495	ODietcYDietc	−1.8055	0.0495	RDietcYDietc	−2.2998	0.0006
YDietcRDietc	2.2998	0.0006	ODietcRDietc	0.4943	0.5814	RDietcODietc	−0.4943	0.5814

^a Pigment classes: Y = yellow, O = orange, and R = red. ^b N_male = 83, N_female = 77. Likelihood ratio tests revealed no significant differences between the best-fit models (OLS, OU, and BM_GrafenE in the case of both sexes). Near-identical results for OLS and PGLS suggest that the df corrections for (two) tree polytomies were inconsequential. All the model term probabilities were two-tailed. ^c The interaction terms by pigment class (Y, O, and R). The intercept terms included in the models are not shown. Higher-order and multiplicative terms were excluded (non-significant). ^d Slope determination based on the additive properties of Bs. Yellow λR₅₀ on Diet_c = Diet_c; Orange λR₅₀ on Diet_c = Diet_c + Y_DietcO_Dietc; and Red λR₅₀ on Diet_c = Diet_c + Y_DietcR_Dietc. ^e Slope determination using the additive properties of Bs. Orange λR₅₀ on Diet_c = Diet_c; Yellow λR₅₀ on Diet_c = Diet_c + O_DietcY_Dietc; and Red λR₅₀ on Diet_c = Diet_c + O_DietcR_Dietc. ^f Slope determination using the additive properties of Bs. Red λR₅₀ on Diet_c = Diet_c; Yellow λR₅₀ on Diet_c = Diet_c + R_DietcY_Dietc; and Orange λR₅₀ on Diet_c = Diet_c + R_DietcO_Dietc.

Table 3. Full model multiple regressions based on an OU process model and ultrametric tree for the wavelength of half-maximal reflectance (λR₅₀) as a dependent variable. The eight predictor variables differ only in which of the three pigment classes is designated as the Reference Category (0, 0) for these dummy variables.

Pigment Class Reference Category a
Yellow			Orange			Red
Model b,c	B	P	Model	B	P	Model	B	P
Males
Year	−0.2357	0.0103	Year	−0.5789	0.6246	Year	0.0905	0.3644
YO	683.5101	0.7689	OY	−683.5101	0.7689	RY	583.5387	0.0291
YR	−583.5387	0.0291	OR	−1267.0487	0.5864	RO	1267.0487	0.5864
Dietc d	−1.959	0.0000	Dietc e	−0.9167	0.3664	Dietc f	0.025	0.9579
YYearOYear	−0.3433	0.7722	OYearYYear	0.3433	0.7722	RYearYYear	−0.3262	0.017
YYearRYear	0.3262	0.017	OYearRYear	0.6695	0.573	RYearOYear	−0.6695	0.573
YDietcODietc	1.0423	0.3488	ODietcYDietc	−1.0423	0.3488	RDietcYDietc	−1.984	0.0033
YDietcRDietc	1.984	0.0033	ODietcRDietc	0.9417	0.4005	RDietcODietc	−0.9417	0.4005
Females
Year	0.0737	0.5357	Year	0.0216	0.8866	Year	−0.0265	0.7661
YO	95.8273	0.8008	OY	−95.8273	0.8008	RY	−239.9381	0.41
YR	239.9381	0.41	OR	144.1109	0.6788	RO	−144.1109	0.6788
Dietc d	−2.1535	0.0000	Dietc e	−0.348	0.6546	Dietc f	0.1463	0.7424
YYearOYear	−0.0522	0.7862	OYearYYear	0.0522	0.7862	RYearYYear	0.1003	0.5006
YYearRYear	−0.1003	0.5006	OYearRYear	−0.0481	0.7842	RYearOYear	0.0481	0.7842
YDietcODietc	1.8055	0.0495	ODietcYDietc	−1.8055	0.0495	RDietcYDietc	−2.2998	0.0006
YDietcRDietc	2.2998	0.0006	ODietcRDietc	0.4943	0.5814	RDietcODietc	−0.4943	0.5814

^a Pigment classes: Y = yellow, O = orange, and R = red. ^b N_male = 83, N_female = 77. Likelihood ratio tests revealed no significant differences between the best-fit models (OLS, OU, and BM_GrafenE in the case of both sexes). Near-identical results for OLS and PGLS suggest that the df corrections for (two) tree polytomies were inconsequential. All the model term probabilities were two-tailed. ^c The interaction terms by pigment class (Y, O, and R). The intercept terms included in the models are not shown. Higher-order and multiplicative terms were excluded (non-significant). ^d Slope determination based on the additive properties of Bs. Yellow λR₅₀ on Diet_c = Diet_c; Orange λR₅₀ on Diet_c = Diet_c + Y_DietcO_Dietc; and Red λR₅₀ on Diet_c = Diet_c + Y_DietcR_Dietc. ^e Slope determination using the additive properties of Bs. Orange λR₅₀ on Diet_c = Diet_c; Yellow λR₅₀ on Diet_c = Diet_c + O_DietcY_Dietc; and Red λR₅₀ on Diet_c = Diet_c + O_DietcR_Dietc. ^f Slope determination using the additive properties of Bs. Red λR₅₀ on Diet_c = Diet_c; Yellow λR₅₀ on Diet_c = Diet_c + R_DietcY_Dietc; and Orange λR₅₀ on Diet_c = Diet_c + R_DietcO_Dietc.

Table 4. Best-fit full model pigment class functional responses of the wavelength of half-maximal reflectance (λR₅₀) to Diet_c determined from the additive properties of the functional responses of the Reference Category (yellow) with interactions of the reference with the other two (orange and red) pigment classes.

	Reference Category		Interaction b				Pigment Class B λR50 on Dietc
	YDietc		YDietcODietc		YDietcRDietc		Yellow	Orange	Red
Model a	B	P	B	P	B	P	YDietc	YDietc + YDietcODietc	YDietc + YDietcRDietc
Males
Unit
OLS	−1.9590	0.0000	1.0423	0.3488	1.9840	0.0033	−1.9590	−0.9167	0.0250
OU	−1.9590	0.0000	1.0423	0.3488	1.9840	0.0033	−1.9590	−0.9167	0.0250
BMGrafenE	−1.9295	0.0001	1.1169	0.3145	2.0002	0.0029	−1.9295	−0.8126	0.0707
Ultrametric
OLS	−1.9590	0.0000	1.0423	0.3488	1.9840	0.0033	−1.9590	−0.9167	0.0250
OU	−1.9590	0.0000	1.0423	0.3488	1.9840	0.0033	−1.9590	−0.9167	0.0250
BMGrafenE	−1.9295	0.0001	1.1169	0.3145	2.0002	0.0029	−1.9295	−0.8126	0.0707
Females
Unit
OLS	−2.1535	0.0000	1.8055	0.0495	2.2998	0.0006	−2.1535	−0.348	0.1463
OU	−2.1535	0.0000	1.8055	0.0495	2.2998	0.0006	−2.1535	−0.348	0.1463
BMGrafenE	−2.1535	0.0000	1.8055	0.0495	2.2998	0.0006	−2.1535	−0.348	0.1463
Ultrametric
OLS	−2.1535	0.0000	1.8055	0.0495	2.2998	0.0006	−2.1535	−0.348	0.1463
OU	−2.1535	0.0000	1.8055	0.0495	2.2998	0.0006	−2.1535	−0.348	0.1463
BMGrafenE	−2.1535	0.0000	1.8055	0.0495	2.2998	0.0006	−2.1535	−0.348	0.1463

^a For a full list of models, see Table 2. ^b For a full list of independent variables, see Table 3.

Table 4. Best-fit full model pigment class functional responses of the wavelength of half-maximal reflectance (λR₅₀) to Diet_c determined from the additive properties of the functional responses of the Reference Category (yellow) with interactions of the reference with the other two (orange and red) pigment classes.

	Reference Category		Interaction b				Pigment Class B λR50 on Dietc
	YDietc		YDietcODietc		YDietcRDietc		Yellow	Orange	Red
Model a	B	P	B	P	B	P	YDietc	YDietc + YDietcODietc	YDietc + YDietcRDietc
Males
Unit
OLS	−1.9590	0.0000	1.0423	0.3488	1.9840	0.0033	−1.9590	−0.9167	0.0250
OU	−1.9590	0.0000	1.0423	0.3488	1.9840	0.0033	−1.9590	−0.9167	0.0250
BMGrafenE	−1.9295	0.0001	1.1169	0.3145	2.0002	0.0029	−1.9295	−0.8126	0.0707
Ultrametric
OLS	−1.9590	0.0000	1.0423	0.3488	1.9840	0.0033	−1.9590	−0.9167	0.0250
OU	−1.9590	0.0000	1.0423	0.3488	1.9840	0.0033	−1.9590	−0.9167	0.0250
BMGrafenE	−1.9295	0.0001	1.1169	0.3145	2.0002	0.0029	−1.9295	−0.8126	0.0707
Females
Unit
OLS	−2.1535	0.0000	1.8055	0.0495	2.2998	0.0006	−2.1535	−0.348	0.1463
OU	−2.1535	0.0000	1.8055	0.0495	2.2998	0.0006	−2.1535	−0.348	0.1463
BMGrafenE	−2.1535	0.0000	1.8055	0.0495	2.2998	0.0006	−2.1535	−0.348	0.1463
Ultrametric
OLS	−2.1535	0.0000	1.8055	0.0495	2.2998	0.0006	−2.1535	−0.348	0.1463
OU	−2.1535	0.0000	1.8055	0.0495	2.2998	0.0006	−2.1535	−0.348	0.1463
BMGrafenE	−2.1535	0.0000	1.8055	0.0495	2.2998	0.0006	−2.1535	−0.348	0.1463

^a For a full list of models, see Table 2. ^b For a full list of independent variables, see Table 3.

Relative Short-Wavelength Reflectance (R_contrast). As with λR₅₀, responses by R_contrast to higher Diet_c were similar for both sexes (

Table 5. A full model (Table 1) selection table for relative short-wavelength reflectance (R_contrast). Note the greater support observed for models with no (OLS) or weak (OU, BM_GrafenE) compared with that for models with stronger (other BM models) phylogenetic constraints.

	Model Results
	Fit				Parameters
Model a	R2adjusted b	MLK c	LRT d	RANK d	PARM e	t1/2 f
Males
Unit
OLS	−0.9111781	51.58054	*	1
OU	−0.894191911	51.95103	*	1	0.6211237	1.11595674
BMGrafenE	−0.848978773	52.95362	*	1	0.06682804
BMGrafenF	−1.257530919	44.66864		2	0.5
BMGrafenF	−1.395227757	42.21156		3	1.0
Ultrametric
OLS	−0.9111781	51.58054	*	1
OU	−0.9111781	51.58054	*	1	10.64936	0.065088154
BMGrafenE	−0.848978773	52.95362	*	1	0.06682804
BMGrafenF	−1.257530919	44.66864		2	0.5
BMGrafenF	−1.465181514	41.0169		3	1.0
Females
Unit
OLS	−1.064488253	47.82255		2
OU	−0.937947582	50.25778	*	1	0.4758947	1.456513764
BMGrafenE	−0.975733441	49.51434	*	1	0.1161438
BMGrafenF	−1.225509788	44.93106		3	0.5
BMGrafenF	−1.327273118	43.20967		4	1.0
Ultrametric
OLS	−1.064488253	47.82255		2
OU	−0.927931229	50.45729	*	1	0.4245463	1.632677474
BMGrafenE	−0.975733441	49.51434	*	1	0.1161438
BMGrafenF	−1.225509788	44.93106		3	0.5
BMGrafenF	−1.363365294	42.61718		4	1.0

^a Evolutionary process models (models) include non-phylogenetic ordinary least squares (OLS) and phylogenetic generalized least squares (PGLS) under an Ornstein–Uhlenbeck (OU) or Brownian motion (BM) process. BM models were further subdivided by parameterization with Grafen’s ρ (BM_Grafen), with ρ estimated by the model (BM_GrafenE) or pre-set to 0.5 or starter tree 1.0 (BM_GrafenF). All PGLS models were tested in two ways, using trees assigned unit (set to 1) or ultrametric (arbitrary ultrametrization) branch lengths in Mesquite v 3.03 [87]. ^b All parameter values were unchanged by the Reference Category designation. R²_adjusted is based on 1 − {[(1 − R²) (N − 1)]/(N-p-1)}, where R² = sample R², p = number of predictors, and N = total sample size. ^c ln restricted maximum likelihood (MLK). A relatively more positive value indicates an improved model fit. ^d The likelihood ratio test (LRT) was applied for testing significant differences in model fit. Significance was based on the assumption that twice the difference in the paired ln ML values followed a χ² distribution with 1 df, for which the critical value was 3.841 at p < 0.05. The best model(s) are indicated by * and RANK (rank support). ^e The values of key model parameters (PARM). OU α = evolutionary force strength returning the trait to long-term optimum; GrafenE = Grafen’s ρ estimated; GrafenF = Grafen’s ρ pre-set to 0.5 or 1.0. ^f Phylogenetic half-life (t_1/2 = (ln(2))/α). The model values of t_1/2 relative to tree height (11 for both sexes) supported a more rapid return to trait optimum in males (smaller) than in females (larger).

,

Table 6. Full model multiple regressions based on an OU process model and ultrametric tree for relative short-wavelength reflectance (R_contrast) as dependent variable. The eight predictor variables differ only in which of the three pigment classes is designated as the Reference Category (0, 0) for these dummy variables.

Pigment Class Reference Category a
Yellow			Orange			Red
Model b,c	B	P	Model	B	P	Model	B	P
Males
Year	−0.001314	0.0123	Year	0.001884	0.7805	Year	−0.00074	0.1956
YO	−6.179388	0.6423	OY	6.179388	0.6423	RY	1.167104	0.4388
YR	−1.167104	0.4388	OR	5.012284	0.7064	RO	−5.012284	0.7064
Dietc d	0.000596	0.8183	Dietc e	−0.001581	0.7847	Dietc f	−0.00211	0.4368
YYearOYear	0.003198	0.6373	OYearYYear	−0.003198	0.6373	RYearYYear	−0.000574	0.455
YYearRYear	0.000574	0.455	OYearRYear	−0.002624	0.6989	RYearOYear	0.002624	0.6989
YDietcODietc	−0.002177	0.7315	ODietcYDietc	0.002177	0.7315	RDietcYDietc	0.002707	0.4714
YDietcRDietc	−0.002707	0.4714	ODietcRDietc	−0.00053	0.9339	RDietcODietc	0.00053	0.9339
Females
Year	−0.0008001	0.2244	Year	−0.002191	0.0121	Year	−0.000932	0.0842
YO	2.7609603	0.1808	OY	−2.76096	0.1808	RY	−0.171476	0.9075
YR	0.1714758	0.9075	OR	−2.589485	0.1321	RO	2.589484	0.1321
Dietc d	0.0004316	0.8847	Dietc e	−0.004634	0.2871	Dietc f	−0.001401	0.6168
YYearOYear	−0.0013905	0.1841	OYearYYear	0.00139	0.1841	RYearYYear	0.000132	0.8618
YYearRYear	−0.0001316	0.8618	OYearRYear	0.001259	0.1466	RYearOYear	−0.001259	0.1466
YDietcODietc	−0.005066	0.2826	ODietcYDietc	0.005066	0.2826	RDietcYDietc	0.001833	0.5667
YDietcRDietc	−0.0018326	0.5667	ODietcRDietc	0.003233	0.469	RDietcODietc	−0.003233	0.469

^a Pigment classes: Y = yellow, O = orange, and R = red. ^b N_male = 83, and N_female = 77. Likelihood ratio tests revealed no significant differences between the best-fit models (OLS, OU, and BM_GrafenE in males; OU and BM_GrafenE in females). The near-identical results obtained for OLS and PGLS suggest that the df corrections for (two) tree polytomies were inconsequential. All the model term probabilities were two-tailed. ^c The interaction terms by pigment class (Y, O, and R). The intercept terms included in the models are not shown. Higher-order and multiplicative terms were excluded (non-significant). ^d Slope determination based on the additive properties of Bs. Yellow R_contrast on Diet_c = Diet_c; Orange R_contrast on Diet_c = Diet_c + Y_DietcO_Dietc; and Red R_contrast on Diet_c = Diet_c + Y_DietcR_Dietc. ^e Slope determination using the additive properties of Bs. Orange R_contrast on Diet_c = Diet_c; Yellow R_contrast on Diet_c = Diet_c + O_DietcY_Dietc; and Red R_contrast on Diet_c = Diet_c + O_DietcR_Dietc. ^f Slope determination using the additive properties of Bs. Red R_contrast on Diet_c = Diet_c; Yellow R_contrast on Diet_c = Diet_c + R_DietcY_Dietc; and Orange R_contrast on Diet_c = Diet_c + R_DietcO_Dietc.

and

Table 7. Best-fit full model pigment class functional responses of relative short-wavelength reflectance (R_contrast) to Diet_c determined from the additive properties of the functional responses of the Reference Category (yellow) with interactions of the reference with the other two (orange and red) pigment classes.

	Reference Category		Interaction b				Pigment Class B Rcontrast on Dietc
	YDietc		YDietcODietc		YDietcRDietc		Yellow	Orange	Red
Model a	B	P	B	P	B	P	YDietc	YDietc + YDietcODietc	YDietc + YDietcRDietc
Males
Unit
OLS	0.0006	0.8183	−0.0022	0.7315	−0.0027	0.4714	0.0006	−0.0016	−0.0021
OU	0.0015	0.5984	−0.0034	0.5705	−0.0037	0.2756	0.0015	−0.0019	−0.0022
BMGrafenE	0.0010	0.7647	−0.0021	0.7291	−0.0030	0.3836	0.0010	−0.0011	−0.0020
Ultrametric
OLS	0.0006	0.8183	−0.0022	0.7315	−0.0027	0.4714	0.0006	−0.0016	−0.0021
OU	0.0006	0.8183	−0.0022	0.7315	−0.0027	0.4714	0.0006	−0.0016	−0.0021
BMGrafenE	0.0010	0.7647	−0.0021	0.7291	−0.0030	0.3836	0.0010	−0.0011	−0.0020
Females
Unit
OLS	−0.0001	0.9603	−0.0041	0.4449	−0.0001	0.9693	−0.0001	−0.0042	−0.0003
OU	0.0006	0.8431	−0.0050	0.302	−0.0013	0.6905	0.0006	−0.0043	−0.0007
BMGrafenE	0.0013	0.7335	−0.0041	0.4156	−0.0005	0.8937	0.0013	−0.0028	0.0008
Ultrametric
OLS	−0.0001	0.9603	−0.0041	0.4449	−0.0001	0.9693	−0.0001	−0.0042	−0.0003
OU	0.0004	0.8847	−0.0051	0.2826	−0.0018	0.5667	0.0004	−0.0046	−0.0001
BMGrafenE	0.0013	0.7335	−0.0041	0.4156	−0.0005	0.8937	0.0013	−0.0028	0.0008

^a For a full list of models, see Table 5. ^b For a full list of independent variables, see Table 6.

, and Figure 5). Relative support for the different models was also similar, except that the OLS models were slightly less favored in females (Table 5). Nevertheless, parameter estimates for the more consistently favored OU and BM_GrafenE models for R_contrast indicated only modest phylogenetic constraint on either sex (still relatively large α, small t_1/2, ρ), and no consistent sexual patterns among these parameter values (Table 5). However, the amounts of variation explained by models were no different than zero (all R²_adjusted were slightly negative, between −0.8 and −1.5).

Explicit multiple regressions were consistent with these results. Across all models, R_contrast lacked significance for any functional responses to a higher Diet_c for any pigment class used in turn as the Reference Category or for any enumerated interactions among pigment classes (ultrametric OU model shown in Table 6; other favored models similar). Moreover, the unstandardized effect sizes were near zero (Bs ± 0.00) and insignificant (even for a one-tailed test). Similar patterns were obtained by probing the additive properties of Bs of the Reference Category for the Diet_c term and its enumerated interactions among pigment classes with Diet_c (Table 7), indicating statistically uniform non-responses across pigment classes. Thus, the lack of R_contrast trends across Diet_c for all pigment classes (Figure 5) is a blue shift relative to the red shift implied by diminished short-wavelength reflectance at higher Diet_c [20,21,22].

Wavelength of Minimum Reflectance (λR_min). The model support patterns, including parameter estimates and sexual distinctions, were more similar between λR_min (

Table 8. The full model (Table 1) selection table for the wavelength of minimum reflectance (λR_min). Note greater support for models with no (OLS) or weak (OU, BM_GrafenE) compared to stronger (other BM models) phylogenetic constraints.

	Model Results
	Fit				Parameters
Model a	R2adjusted b	MLK c	LRT d	RANK d	PARM e	t1/2 f
Males
Unit
OLS	0.533508316	−349.8368	*	1
OU	0.533508316	−349.8368	*	1	8.830245	0.07849694
BMGrafenE	0.533508316	−349.8368	*	1	2.13 × 10−9
BMGrafenF	0.355745835	−363.2353		2	0.5
BMGrafenF	0.32127503	−365.3983		3	1.0
Ultrametric
OLS	0.533508316	−349.8368	*	1
OU	0.533508316	−349.8368	*	1	8.758807	0.079137168
BMGrafenE	0.533508316	−349.8368	*	1	2.13 × 10−9
BMGrafenF	0.355745835	−363.2353		2	0.5
BMGrafenF	0.278452746	−367.9374		3	1.0
Females
Unit
OLS	0.461572971	−323.9015		2
OU	0.493743324	−321.5296	*	1	0.461013	1.503530335
BMGrafenE	0.492237294	−321.644	*	1	0.1039528
BMGrafenF	0.414395635	−327.1352		3	0.5
BMGrafenF	0.391746741	−328.5962		4	1.0
Ultrametric
OLS	0.461572971	−323.9015		2
OU	0.496649094	−321.308	*	1	0.404894	1.711922579
BMGrafenE	0.492237294	−321.644	*	1	0.1039528
BMGrafenF	0.414395635	−327.1352		3	0.5
BMGrafenF	0.385947829	−328.9615		4	1.0

^a Evolutionary process models (models) include non-phylogenetic ordinary least squares (OLS) and phylogenetic generalized least squares (PGLS) under an Ornstein–Uhlenbeck (OU) or Brownian motion (BM) process. BM models were further subdivided by parameterization with Grafen’s ρ (BM_Grafen), with ρ estimated by the model (BM_GrafenE) or pre-set to 0.5 or starter tree 1.0 (BM_GrafenF). All PGLS models were tested in two ways, using trees assigned unit (set to 1) or ultrametric (arbitrary ultrametrization) branch lengths in Mesquite v 3.03 [87]. ^b All parameter values were unchanged by the Reference Category designation. R²_adjusted is based on 1 − {[(1 − R²) (N − 1)]/(N-p-1)}, where R² = sample R², p = number of predictors, and N = total sample size. ^c ln restricted maximum likelihood (MLK). A relatively more positive value indicates an improved model fit. ^d The likelihood ratio test (LRT) was used for testing significant differences in model fit. Significance was based on the assumption that twice the difference in the paired ln ML values followed a χ² distribution with 1 df, for which the critical value was 3.841 at p < 0.05. The best model(s) are indicated by * and RANK (rank support). ^e The values of key model parameters (PARM). OU α = evolutionary force strength returning the trait to long-term optimum; GrafenE = Grafen’s ρ estimated; GrafenF = Grafen’s ρ pre-set to 0.5 or 1.0. ^f The phylogenetic half-life (t_1/2 = (ln(2))/α). The model values of t_1/2 relative to tree height (11 for both sexes) supported a more rapid return to trait optimum in males (smaller) than in females (larger).

,

Table 9. Full model multiple regressions based on an OU process model and ultrametric tree for the wavelength of minimum reflectance (λR_min) as the dependent variable. The eight predictor variables differ only in which of the three pigment classes is designated as the Reference Category (0, 0) for these dummy variables.

Pigment Class Reference Category a
Yellow			Orange			Red
Model b,c	B	P	Model	B	P	Model	B	P
Males
Year	−0.167	0.1548	Year	−1.649	0.284	Year	0.054	0.6786
YO	2,916.7059	0.3351	OY	−2916.706	0.3351	RY	413.585	0.228
YR	−413.5854	0.228	OR	−3330.291	0.2718	RO	3330.291	0.2718
Dietc d	−0.4851	0.4112	Dietc e	−1.099	0.4038	Dietc f	0.461	0.4541
YYearOYear	−1.4825	0.3366	OYearYYear	1.483	0.3366	RYearYYear	−0.22	0.2073
YYearRYear	0.2205	0.2073	OYearRYear	1.703	0.2704	RYearOYear	−1.703	0.2704
YDietcODietc	−0.6135	0.67	ODietcYDietc	0.614	0.67	RDietcYDietc	−0.946	0.2684
YDietcRDietc	0.946	0.2684	ODietcRDietc	1.56	0.2838	RDietcODietc	−1.56	0.2838
Females
Year	−0.0586	0.7054	Year	0.2504	0.2169	Year	0.361	0.0057
YO	−620.4229	0.2019	OY	620.4229	0.2019	RY	806.9572	0.0228
YR	−806.9572	0.0228	OR	−186.5342	0.642	RO	186.5342	0.642
Dietc d	−1.0792	0.1331	Dietc e	0.4948	0.6306	Dietc f	−0.1925	0.774
YYearOYear	0.309	0.2104	OYearYYear	−0.309	0.2104	RYearYYear	−0.4196	0.0209
YYearRYear	0.4196	0.0209	OYearRYear	0.1106	0.5851	RYearOYear	−0.1106	0.5851
YDietcODietc	1.574	0.1576	ODietcYDietc	−1.574	0.1576	RDietcYDietc	−0.8866	0.2406
YDietcRDietc	0.8866	0.2406	ODietcRDietc	−0.6874	0.5127	RDietcODietc	0.6874	0.5127

^a Pigment classes: Y = yellow, O = orange, and R = red. ^b N_male = 83, and N_female = 77. Likelihood ratio tests revealed no significant differences between the best-fit models (OLS, OU, and BM_GrafenE in males; OU and BM_GrafenE in females). Near-identical results obtained for OLS and PGLS suggest that the df corrections for (two) tree polytomies were inconsequential. All the model term probabilities were two-tailed. ^c The interaction terms by pigment class (Y, O, and R). The intercept terms included in the models are not shown. Higher-order and multiplicative terms were excluded (non-significant). ^d Slope determination based on the additive properties of Bs. Yellow λR_min on Diet_c = Diet_c; Orange λR_min on Diet_c = Diet_c + Y_DietcO_Dietc; and Red λR_min on Diet_c = Diet_c + Y_DietcR_Dietc. ^e Slope determination using the additive properties of Bs. Orange λR_min on Diet_c = Diet_c; Yellow λR_min on Diet_c = Diet_c + O_DietcY_Dietc; and Red λR_min on Diet_c = Diet_c + O_DietcR_Dietc. ^f Slope determination using the additive properties of Bs. Red λR_min on Diet_c = Diet_c; Yellow λR_min on Diet_c = Diet_c + R_DietcY_Dietc; and Orange λR_min on Diet_c = Diet_c + R_DietcO_Dietc.

and

Table 10. Best-fit full model pigment class functional responses of the wavelength of minimum reflectance (λR_min) to Diet_c determined from the additive properties of the functional responses of the Reference Category (yellow) with interactions of the reference with the other two (orange and red) pigment classes.

	Reference Category		Interaction b				Pigment Class B λRmin on Dietc
	YDietc		YDietcODietc		YDietcRDietc		Yellow	Orange	Red
Model a	B	P	B	P	B	P	YDietc	YDietc + YDietcODietc	YDietc + YDietcRDietc
Males
Unit
OLS	−0.4851	0.4112	−0.6135	0.67	0.946	0.2684	−0.4851	−1.0986	0.4609
OU	−0.4851	0.4112	−0.6135	0.67	0.946	0.2684	−0.4851	−1.0986	0.4609
BMGrafenE	−0.4851	0.4112	−0.6135	0.67	0.946	0.2684	−0.4851	−1.0986	0.4609
Ultrametric
OLS	−0.4851	0.4112	−0.6135	0.67	0.946	0.2684	−0.4851	−1.0986	0.4609
OU	−0.4851	0.4112	−0.6135	0.67	0.946	0.2684	−0.4851	−1.0986	0.4609
BMGrafenE	−0.4851	0.4112	−0.6135	0.67	0.946	0.2684	−0.4851	−1.0986	0.4609
Females
Unit
OLS	−1.1482	0.0786	1.6911	0.181	0.8012	0.3708	−1.1482	0.5429	−0.347
OU	−0.9522	0.2023	1.5613	0.17	0.827	0.2864	−0.9522	0.6091	−0.1252
BMGrafenE	−0.6121	0.4767	1.0839	0.3617	0.5609	0.4894	−0.6121	0.4718	−0.0512
Ultrametric
OLS	−1.1482	0.0786	1.6911	0.181	0.8012	0.3708	−1.1482	0.5429	−0.347
OU	−1.0792	0.1331	1.574	0.1576	0.8866	0.2406	−1.0792	0.4948	−0.1926
BMGrafenE	−0.6121	0.4767	1.0839	0.3617	0.5609	0.4894	−0.6121	0.4718	−0.0512

^a For a full list of models, see Table 8. ^b For a full list of independent variables, see Table 9.

, and Figure 6) and the other short-wavelength (R_contrast) spectral feature than between λR_min and the long-wavelength (λR₅₀) spectral feature. Similarly to R_contrast, OLS was less favored in females than in males (Table 8). Unlike for R_contrast, the additional parameters of the OU and BM_GrafenE models appeared to better describe λR_min evolution in males (much larger α, much smaller t_1/2 and ρ) than in females. However, the phylogenetic effects were modest, even for the latter sex. Otherwise, R²_adjusted values for λR_min were roughly midway (0.25–0.55) between those modeled for the other two spectral features, suggesting that the strength of functional response by λR_min to higher Diet_c was also intermediate by comparison (Table 8).

As with R_contrast, explicit multiple regressions for λR_min across all Reference Categories (ultrametric OU model shown, Table 9; other favored models similar) lacked any significant functional response to higher Diet_c, or significance to enumerated interactions between pigment classes with Diet_c (Table 9), implying similar non-responses across all three pigment classes. However, probing (Table 10) revealed that the yellow response by λR_min to higher Diet_c had consistently negative slopes (males: B~−0.5; females: B~−0.6 to −1.15) across all favored models and both sexes (12 of 12 in the binomial one-tailed test: p < 0.001, for a 0.5 probability of obtaining a negative slope for each trial). Moreover, these responses were occasionally marginally non-significant, particularly in females (Table 9). These consistent patterns suggest a parallel but weaker blue shift response to higher Diet_c by yellow plumage λR_min than that by λR₅₀ (Table 10). This blue shift tendency by λR_min carried over to orange plumage in males but not females and vice versa for red plumage, without ever approaching significance (Table 9). Thus, a few extremely minor and complex sexual differences also may exist in the response of yellow, orange, and red λR_min to higher Diet_c (Table 10).

3.2. Static Responses to Diet_c

Conventional OLS statistics can be considered more parsimonious than PGLS because both approaches yield virtually identical results, even though OLS is based on fewer assumptions and modeling parameters. Therefore, only conventional statistics were used to explore additional shift patterns related to the occupancy of reflectance × Diet_c phenotype space.

Pigment Class Biases. Models failed to support any obvious red shifts at higher Diet_c within the covariance structure of the VS piciform–coraciiform data. However, a red-biased pattern at higher Diet_c in the VS system could potentially be expressed if only species with red pigmentation occupied the “extensions” of phenotype space aligned with a higher Diet_c. This pattern resembles the aforementioned collinear one, with yellower plumages at lower and redder plumages at or extending to higher Diet_c as in some UVS passerines [16,21]. In the VS Piciformes–Coraciiformes, however, each pigment class spanned a similar range from the lowest to the highest Diet_c values within and between the sexes (

Table 11. Diet_c range and plumage phenotype space extensions by sex for three carotenoid pigment classes across species sampled.

	Carotenoid Class a
	Dietc Range b			Plumage Phenotype Space Extensions
Dietc c	Yellow	Orange	Red	Red–Yellow d	Red–Orange e	Orange–Yellow f
Males
High	26.83	26.25	26.83	0	0.58	−0.58
Low	9.5	9.5	9.5	0	0	0
Females
High	26.83	26.25	26.83	0	0.58	−0.58
Low	9.5	9.5	9.5	0	0	0

^a Yellow, orange, and red pigment classes (see Section 2). ^b The Diet_c as calculated by the methods described in the text and Table 1 (see Section 2). ^c The high and low values of Diet_c. ^d Plumage phenotype Red_High–Yellow_High: a positive number is a red extension and a negative number is a yellow extension. ^e Plumage phenotype Red_High–Orange_High: a positive number is a red extension and a negative number is an orange extension. ^f Plumage phenotype Orange_High–Yellow_High: a positive number is an orange extension and a negative number is a yellow extension.

, Figure 4, Figure 5 and Figure 6). Even species at the high end of Diet_c were equally likely to develop strongly blue-shifted yellows and oranges as they were to develop reds. Furthermore, both the yellow and red pigment classes extended to slightly higher Diet_c values than did the intermediate pigment class orange, even though the latter was physically much closer to yellow in λR₅₀ (Table 11, Figure 4, Figure 5 and Figure 6). Consistent with these patterns, OLS on mean differences for Diet_c between the pigment classes (Diet_c = YO + YR or OR) were also not significantly different in males (YO t = −1.051; OR t = 0.899; YR t = −0.290; all p > 0.296) or females (YO t = −0.754; OR t = 0.471; YR t = −0.426; all p > 0.453). Parallel OLS (λR₅₀ = year + YO + YR or OR) also demonstrated that blue shift strength in response to higher Diet_c (yellow > orange > red) was directly related to the blueness of the pigment class in males (YO t = 4.79; OR t = 8.012; YR t = 24.71; all p < 0.0001) and females (YO t = 5.65; OR t = 11.17; YR t = 24.84; all p < 0.0001).

Presence–Absence Expressions of Sexual Pigment Classes The sexes expressed similar qualitative (significant or non-significant) and quantitative (slope) functional responses to Diet_c for each of the three spectral features × pigment classes (Table 4, Table 7, and Table 10). Consistent with these sexually similar functional responses, presence–absence expressions for the three carotenoid pigment classes showed only minor sexual distinctions (

Table 12. Presence–absence expressions based on sex for the three carotenoid-based pigment classes across species sampled. Only 11 (20.37%) of 54 species were recorded as having these kinds of sexual expression differences.

	Pigment Classes a
	Singles			Combinations b
	Males c
	Y	O	R	Y + O	Y + R	O + R	Y + O + R	Missing
Females c
Y	12	0	0	0	1	0	0	0
O	1	1	0	0	0	0	0	0
R	0	0	8	0	1	1	0	0
Y + O	0	0	0	0	0	0	0	0
Y + R	0	0	0	0	19	0	0	0
O + R	0	0	1	0	2	1	0	0
Y + O + R	0	0	0	0	0	0	2	0
Missing d	2	0	2	0	0	0	0	NA d

^a Matrix values are sexual pigment expression (presence-absence) monomorphisms (bolded, on-diagonal entries) or dimorphisms (unbolded, off-diagonal entries). Three carotenoid-based pigment classes were distinguished, as described in Section 2. The data calculations are shown in Figures S1 and S2. Y = yellow, O = orange, and R = red. ^b A “+” indicates combinations among patches; different patches are averaged within but not between pigment classes. ^c Frequencies may differ for unmeasured subspecies owing to their different carotenoid-based pigmentations. ^d Missing = no yellow, orange, or red plumage patches; and NA = by definition, excluded from this study.

), supported by a conservative test for deviations from expectations of equal on (sexes similar, 43/27) and off (sexes dissimilar, 11/27) diagonal elements (χ² = 10.394, p < 0.002; 2 × 2 contingency table test). The few apparent sexual differences were because of the expression of carotenoid pigmentation in males, or the use of red in males versus yellow or orange in females. However, these differences were unexpectedly limited and contradicted by other patterns and pigments (Table 12). In summary, the sexes generally exhibited the same corresponding functional responses and pigmentations (Table 12), and their pigment differences (irrespective of patch location) were only infrequently expressed by their presence versus absence or by their carotenoid pigment class (Table 12). Thus, the sexually similar functional responses to Diet_c apparently transcend any sexually distinct pigmentations, such as reds.

Quantitative Variations. The sexual variability patterns within each of the three spectral features were similar (

Table 13. Levene’s tests of raw variational differences for spectral features between pigment classes within sex across species sampled.

Sex	Phenotypes		Test Statistic
Feature	Pigment Class (SD) a vs. Pigment Class (SD) a		F b	P c
Males d
lR50	Yellow (11.091)	Orange (3.603)	6.11649	0.0174
	Yellow (11.091)	Red (5.617)	36.46504	<0.0001
	Orange (3.603)	Red (5.617)	0.10253	0.7504
Rcontrast	Yellow (0.042)	Orange (0.023)	4.55636	0.0385
	Yellow (0.042)	Red (0.056)	1.08149	0.3017
	Orange (0.023)	Red (0.056)	1.19469	0.2806
lRmin	Yellow (10.605)	Orange (6.715)	0.92948	0.3404
	Yellow (10.605)	Red (12.692)	1.65064	0.2028
	Orange (6.715)	Red (12.692)	2.11074	0.1537
Females e
lR50	Yellow (10.583)	Orange (1.152)	16.01667	0.0003
	Yellow (10.583)	Red (7.372)	16.19436	0.0002
	Orange (1.152)	Red (7.372)	3.85122	0.0562
Rcontrast	Yellow (0.046)	Orange (0.075)	0.34963	0.5577
	Yellow (0.046)	Red (0.043)	0.89718	0.3470
	Orange (0.075)	Red (0.043)	1.4124	0.2412
lRmin	Yellow (10.291)	Orange (5.393)	3.12479	0.0847
	Yellow (10.291)	Red (12.710)	0.25805	0.6132
	Orange (5.393)	Red (12.710)	3.24521	0.0786

^a Pigment class (standard deviation, SD). Levene’s test of variance was used, but variation was summarized as SD to enable comparisons in the units of the original measures. ^b Levene’s test of variance homogeneity. ^c All probabilities are two-tailed. ^d Male sample size: N_yellow = 39, N_orange = 6, and N_red = 38. ^e Female sample size: N_yellow = 32, N_orange =10, and N_red = 35.

). However, variational characteristics based on pigment class differed greatly for λR₅₀ (four out of six comparisons were significant, with one nearly reaching significance) but not markedly for R_contrast or λR_min (one of twelve was marginally significant) spectral features (Table 13). Further consideration is limited to λR₅₀, without distinguishing sex. For raw λR₅₀ relative variability, yellow was consistently the most variable, orange was the least variable, and red was intermediate. Regarding statistically significant differences in variability, yellow and red differed the most, followed by yellow and orange, and orange and red—in that order (Table 13). In summary, for λR₅₀, the extremes in the functional response (yellow being the strongest and red the weakest) were consistent with the extremes in statistical variability (yellow being the most variable compared to red).

4. Discussion

The analysis of carotenoid-based reflectance in an ecological context among VS Piciformes–Coraciiformes is consistent with earlier evidence based on mean λR_min alone for changes towards bluer (shorter) or redder (longer) wavelengths depending on color vision system (see Section 1) [26,38,39], extending this distinction to dynamic responses at higher Diet_c. In the case of either sexual pattern in VS Piciformes–Coraciiformes, none of the three carotenoid-pigment classes were significantly red-shifted (i.e., no significant positive slopes) at higher Diet_c, red-extended (i.e., no collinear yellow to red pigmentation) at higher Diet_c, or red-dimorphic (i.e., no red-male expression bias), contrary to the red-shifted, largely UVS groups [16,20,21,41]. Instead, the VS piciform–coraciiform response to higher Diet_c revealed both absolute (i.e., significant negative slopes) and relative (i.e., non-significant zero slopes) blue compared with absolute red shifts at higher Diet_c, covariant (equal) expression of all pigment classes at higher Diet_c, and roughly equal sexual pigment class expression (Table 11 and Table 12, Figure 4, Figure 5 and Figure 6). Moreover, VS piciform–coraciiform tendencies were mutually reinforcing in that patterns at long (λR₅₀) wavelength were not contradicted by those at short (R_contrast non-shifts) or intermediate (λR_min blue shifts between those observed for λR₅₀ and R_contrast) wavelengths. These blue–red distinctions can be summarized as a series of physically objective opposite-pattern symmetries (Figure 7). In the case of yellow and orange pigment classes in VS Piciformes–Coraciiformes, absolute blue shifts and their negative slopes in response to higher Diet_c by λR_50, and to a lesser extent by λR_min, are antisymmetries when compared with absolute red shifts and their positive slopes (Figure 1D). The wavelength continuum within each shift pattern implied polychromatic symmetries between them, qualified by the fact that categorical perceptions could reduce these to dichromatic ones (Figure 1E,F). The flat responses by λR₅₀ in the case of the red pigment class, and R_contrast for all pigment classes, are relatively blue-shifted but not strictly opposite (Figure 7 bottom inset) to the positive slope (λR₅₀) or diminishing the short-wavelength reflectance (R_contrast) of their red-shifted counterparts at higher Diet_c. These responses can be considered broken symmetries [10] rather than antisymmetries (Figure 7). The nearly identical results of parallel OLS and favored PGLS models, and interpretation of their fitted parameter values (appropriate R²_adjusted; large α compared with small t_1/2 and ρ), provided strong statistical support for VS blue biases and symmetries, with little evidence for historical, sexual, or preservation (Year) contributions but strong evidence for process models that incorporated trait adaptation or ecophenotypy (Diet_c distribution, OU model support). Therefore, the next step in developing a symmetry framework is to determine whether the underlying processes are similar (invariance symmetry) for the antisymmetries but not for the broken symmetries (Figure 7). A certain level of process invariance is implied when concerted, antisymmetric shift responses to diet (higher Diet_c) are expressed between comparisons (e.g., color vision systems). However, no responses by VS Piciformes–Coraciiformes for other spectral features (e.g., R_contrast) or pigment classes (e.g., red) suggest altered processes. To further explore process symmetry and symmetry breaking, the well-studied red shifts of UVS Passerida passerines (UVS) best inform the VS piciform–coraciiform (VS) system.

Relation to Color Vision. Several observations suggest that the blue shifts in VS Piciformes–Coraciiformes are linked indirectly or directly to color vision. First, blue shifts in VS Piciformes–Coraciiformes are particularly striking, considering the many dietary red shifts associated with the UVS system (see Section 1). This qualitative association is prima facie evidence that shifts and color vision patterns are conjoined. Second, VS Piciformes–Coraciiformes align the maximum sensitivity of their diagnostic V cone with the characteristic λR_min of their strongly blue-shifted yellow pigments, suggesting a mutual relationship [26]. Not only does alignment imply visual function, but λR_min embodies the chemical information content of any pigment [24] used as a signal. Third, the failure to detect any response by short-wavelength reflectance (R_contrast) to Diet_c for any carotenoid pigment class in VS (Table 5, Table 6 and Table 7) as compared with its strong response in UVS [20,21] is a pattern consistent with perceptual differences between the VS and UVS systems. Thus, the maximum sensitivities of the avian V and S cones mainly responsible for short-wavelength perception are 410 and 480 nm, respectively, in the VS system but 350 and 450 nm in the UVS system [36], whereas the secondary short-wavelength reflectance band of carotenoids (Figure 3) best covers the UVS sensitivity range [22]. Fourth, the S single-cone maximum sensitivity in the VS system subtends their most blue-shifted (470–490 nm) λR₅₀ values (Figure 4), whereas the maximum sensitivity of the S single-cone in the UVS system lies below these values [26]. Consequently, the VS tuning patterns provide multiple reasons that favor λR₅₀ over R_contrast for signaling in the observed order yellow over orange over red. Parallel evidence linking red shifts to the UVS cone characteristics complements these arguments [26,38]. In contrast, the red shifts known for VS groups (particularly in waders) arise from cosmetic coloration, which is strongly impacted by the environment [100,101,102].

Although most parameter values required to model the VS piciform–coraciiform system are lacking, the perceptual salience of blue-shift patterns is supported by experiments on VS visual behavior. The VS pigeon model (Columba livia) can discriminate wavelength differences between 2 and 10 nm for narrow-bandwidth visual stimuli (<10 nm) presented across a carotenoid-relevant spectral range of 450–625 nm [103]. Even relatively more realistic behavioral choice experiments with broad-band stimuli similar to those of carotenoids suggest that VS jungle fowl (Gallus gallus) are superior at discriminating wavelengths in the “yellow” and “orange” ranges, even when the physical differences are only a few nanometers and virtually indistinguishable to humans [104,105]. Remarkably, modeling studies of other pigeon data that account for subjective judgements indicate that maximal monochromatic discrimination also occurs in the physical yellow (500 nm) and orange (600 nm) ranges [106]. Thus, VS discrimination or categorical perception abilities of VS models encompass much of the variation and spectral range within and among carotenoid pigment classes in VS Piciformes–Coraciiformes and particularly fit the stronger yellow and orange shift responses to the Diet_c of the latter group. Conversely, the implication that red wavelengths are relatively less discriminated matches their weak response to Diet_c. This consistency supports the putative signal value of the VS piciform–coraciiform blue shifts (Figure 4). The opposite (absolute) or divergent (relative) signs of blue and red shifts between the color vision groups imply that these global patterns are even relatively more obvious for birds. Any dietary effects on oil droplet carotenoids [107,108,109] that filter light before it reaches the retinal cones presumably would amplify these discriminations across species. Therefore, even without an explicit VS piciform–coraciiform visual model, participation in carotenoid-based pigment classes and blue shifts in signaling and communication is likely.

Columbidae (pigeons and doves) are especially informative for VS Piciformes–Coraciiformes, considering their similar ecological habits and responsiveness to diet by plumage carotenoids (extent in fruit doves) [110]. The strong association of λR₅₀ with generic colorimetric perceptions such as hue and saturation in vertebrate visual systems [35] is also useful for inferring avian from human perceptions of shift patterns. Thus, the ability of humans to distinguish blue-shift patterns based on generic color parameters (Figure 2) implies salience to birds, given the latter’s ability to discriminate among yellows and oranges that are difficult for humans to distinguish [104,105]. For us, the physical blue shift in λR₅₀ (Figure 3 and Figure 4) by yellow plumage (pigment class) among species with higher Diet_c because of more plant-based diets (Figure 2A,C,E) translates to a consistently less saturated (broader reflectance plateau), lemon-yellow (shorter λR₅₀) compared to a golden-yellow in species with more animal-based diets (Figure 2B). Compatible with its overall insignificant response to Diet_c, the red pigment class appears to lack any human-visual tendencies among species with more plant- (Figure 2A,C,E) or animal-based (Figure 2D,F) diets. Though slightly ambiguous, the intermediate response by orange λR₅₀ to Diet_c seems visually intermediate to humans in relation to these dietary distinctions between more plant- (Figure 2C) versus more animal- (Figure 2D) based diets. Moreover, the lack of any UV-based (<400 nm) trends (incorporated into R_contrast) that would be invisible to humans implies that our perceptions of plumage differences (compare Figure 2 and Figure 3) provide a conservative assessment of what avian systems can distinguish [111]. Thus, quantitative and qualitative variations (perceivable to humans) are mutually consistent. Therefore, human-visible λR₅₀ variations should provide useful biomarkers of Diet_c for VS such that trophic habits can (yellow and orange) or cannot (red) be appreciated from plumage appearance, even to us.

General sexual similarities in color vision [36,37,42,112] are also consistent with the observed sexual similarities in carotenoid-based shift (Figure 4, Figure 5 and Figure 6) and expression (Table 12) patterns, or at least allow for them indirectly, including by genetic correlations between the sexes. Compatible with this interpretation, a few typical UVS Passerida passerines (Parulidae) exhibit sexual differences in their visual opsin sensitivities that correlate with plumage sexual dimorphisms [43]. However, other considerations suggest that the inter-relationships between sexual distinctions in vision and plumage are more complicated. In particular, the primary diet data did not distinguish between the sexes or account for any diet-related sexual perceptions related to oil-droplet carotenoids [107,108,109] or the foraging environment, which could have altered the interpretation of resemblance. The sexes of the UVS Passerida passerines and VS Piciformes-Coraciiformes may also differ in their visual environments. For example, most Passerida passerines build arboreal open-cup nests that expose the sexes to visual detection by predators, which can select for plumage divergence based on male versus female reproductive roles [113]. In comparison, VS Piciformes–Coraciiformes are cavity nesters [74], a habit that may better conceal both sexes from visually hunting predators, thereby reducing that source of divergent selection on plumage [114]. Moreover, nest cavities are usually limited resources that lead to strong competition among pairs, which may select for mutual resemblance through social selection [115,116]. These general habits of VS Piciformes–Coraciiformes could, therefore, explain why their sexual carotenoid-based shifts and expression patterns are similar, even across a wide range of Diet_c values from associated foraging preferences. How these and other factors interact to produce the observed patterns requires further study.

Yellow and Orange Responses. Physically different plumage responses to diet by birds with different color vision systems could result from different adaptive processes. However, the VS absolute blue-shifted (yellow and orange pigment classes) and UVS absolute red-shifted responses to Diet_c share many attributes suggestive of process symmetries. The most descriptive of these is that in both systems, some plumage spectral features within one or more carotenoid-based pigment classes are reliable markers of diet. A relatively more mechanistic shared process is suggested by evidence for a shared role of limitations in dietary carotenoid content (Diet_c) on λR₅₀ and (less) λR_min plumage expression. This sensitivity has been supported in VS Piciformes–Coraciiformes by their captive counterparts [58,59,60]. However, general fading of all carotenoid-based plumages for individuals on captive diets [58] suggests that evolutionary in addition to ecophenotypic factors are responsible for the different sensitivities (yellow > orange > red) of pigment classes to Diet_c among wild taxa. Qualitatively, both color vision systems appear to lack any obvious bias in using carotenoids when they are scarce or abundant [16,32,41,115,117]. In the VS system for example, carotenoid pigments were expressed in species over a wide span of trophic habits (Table 11), whose Diet_c values range from 9.5 (emphasizing low-content arthropods) to 26.83 (emphasizing high-content fruits). Furthermore, the response by especially VS yellow λR₅₀ remained linear over the same Diet_c range (Table 2, Table 3 and Table 4, and Figure 4) whereas non-linear (saturation) effects occur in certain UVS birds [21,22]. Notably, many VS piciform–coraciiform frugivores favor so-called “superfruits” [74], whose high nutritional along with carotenoid content could maintain informativeness regarding dietary limitations even at the highest Diet_c levels. In this regard, assessing dietary carotenoid content as the richness of food items (Figure 4, Figure 5 and Figure 6, and Table S2) rather than the amount of food consumed simply emphasizes signal design through dietary specialization rather than through food-gathering abilities per se. Conversely, the specific taxonomies for the carotenoid content of dietary items used to estimate Diet_c (see Table S2) qualify other effects on bioavailability, including indirect climate–humidity [34] or internal physiological [118] regulations.

Whether the similar responsiveness of VS and UVS to dietary limitations reflects deeper shared processes depends on whether similar active mechanisms of carotenoid handling produce similar color vision-appropriate shift patterns. Further understanding can be gained by examining the underlying chemistries. In these terms, UVS that eat carotenoid-poor foods (typically grains or arthropods) often deposit dietary “native” yellow carotenoids (typically the xanthophylls lutein, zeaxanthin, β-cryptoxanthin, or rarely the carotene β-carotene) directly to produce yellow to orange plumage [19,25]. However, endogenous processes acting on higher levels of dietary natives in UVS produce mainly red shifts in individuals and species with higher Diet_c [16,20,21], either by depositing carotenoids at higher concentration or greater thickness to increase optical density [16,17,20,21], by enhancing carotenoid X protein interactions [30], or by converting yellower carotenoids to intrinsically more orange to red xanthophylls [16,17,19,25,72,119]. Many UVS also convert dietary natives to yellow metabolites, providing another way to encode Diet_c. However, these UVS yellow carotenoids (canary xanthophylls, 3′-dehydrolutein, 2′,3′-anhydrolutein) are not strongly blue-shifted (λR_min usually ≤ 3 nm, up to 9 nm shorter) compared with dietary natives [17,63,120,121], which they closely resemble. Birds may still be able to distinguish small blue shifts to a certain extent [104]. However, the greatly restricted physical magnitude of these blue shifts leaves little room for encoding ecological radiation in Diet_c this way, thereby reinforcing a red bias in terms of interspecific wavelength-based shifts. Considering the basic yellow-to-orange carotenoid chemistry in UVS, the universal physical properties of carotenoids [20,21,122] pertaining to increased optical density (by concentration, thickness, and carotenoid type) are more likely to produce a red shift in response to a higher Diet_c.

In contrast to UVS, however, many VS Piciformes-Coraciiformes can convert dietary native yellow to metabolized yellow “picofulvin” (dihydro- or tetrahydro- derivatives of dietary natives) [25,123,124] carotenoids characterized by strong blue shifts of up to approximately 70 nm compared with dietary natives. At least five empirical observations support the hypothesis that picofulvins cause absolute blue shifts in yellow carotenoids at high Diet_c in VS Piciformes–Coraciiformes. First, picofulvins are common in this group (various woodpeckers) [123]. Second, λR_min of picofulvins in vitro [123,124] match those observed for the most blue-shifted yellow plumages (Figure 3A and Figure 6) [26]. Third, the maximum blue shifts of λR₅₀ (Figure 4) and λR_min (Figure 6) are similar. Fourth, the distinctive undulating series of R_mins across the overall low reflectance at short visible (400–500 nm) wavelengths in spectra from species with the highest Diet_c (Figure 3A) resemble those obtained from yellow plumages known to be picofulvin-rich [26,119,124]. Fifth, endogenous metabolite use is consistent with evolutionary influences. Conversely, picofulvins are rare or absent in UVS [25], whereas native-like yellow carotenoid metabolites produced by UVS are rare (small amounts in the red plumage of one toucan) [46] or absent [72,119,123] in VS Piciformes–Coraciiformes. These patterns also imply that more red-shifted (λR₅₀ = 510–530 nm) yellows produced by many VS Piciformes-Coraciiformes (Figure 3B and Figure 4) at low Diet_c are dietary natives, consistent with chemical analyses of a few woodpeckers (Colaptes, Picoides) [123]. Therefore, for VS Piciformes–Coraciiformes, absolute or relative amounts of picofulvins in reciprocal combination with their relatively red-shifted (Figure 3A,B) dietary native precursors provide a consistent basis for the variation in blue shifts with Diet_c. Intermediate blue shifts (Figure 4) by oranges most parsimoniously arise from mixes of yellow picofulvins with orange or red xanthophylls, as suggested by orange’s intermediate spectra (Figure 3C,D) and occasional formation within yellow patches in species that also produce red (Ramphastos dicolorus; Figure 2C). Mixes containing metabolized picofulvins also seem to be the only way to achieve a blue shift with a higher Diet_c, as greater amounts of dietary or metabolized orange or red xanthophylls would create a red shift. Therefore, species in both color vision systems appear to use native yellows at lower Diet_c but diverge in the carotenoid metabolites they produce at higher Diet_c.

Although these chemical hypotheses require confirmation, they are consistent with the active control of plumage carotenoids, as suggested by the greater specificity of responses among species compared to those by individuals in feeding trials (see above). Consequently, the yellow carotenoids available to VS Piciformes–Coraciiformes can produce dramatic (λR₅₀) or modest (λR_min) absolute blue shifts at higher Diet_c through the increased deposition of their metabolized picofulvins over dietary natives, whereas comparable shifts are constrained for the combinations of metabolized and dietary yellows available to UVS (see above). In turn, these properties represent divergent processes between VS and UVS yellows, but convergent ones between VS yellows and UVS reds. In the convergent cases, a metabolized carotenoid that is strongly λR₅₀-shifted compared to dietary native carotenoids strengthens the shift response to higher Diet_c [19]; however, this produces absolute blue shifts in VS and absolute red shifts in UVS. Higher concentrations of yellows at higher Diet_c apparently also contribute to corresponding shifts, but the VS blue shift may require metabolized picofulvins to avoid the red shift created by higher concentrations of dietary native [17] or UVS-type metabolized [30] yellows. The production and deposition of more or metabolized pigmentation at higher Diet_c in both VS (blue) and UVS (red) shift systems suggests invariant processes consistent with several models of honest signaling based on costs and benefits [16,17,34,64]. This mutually reinforcing evidence for shared honesty could extend to more detailed invariances related to diet, including ecological signaling [20,21,22], imposition of signal costs (higher concentrations and metabolites) when carotenoids are abundant (higher Diet_c) to avoid cheating [34], possible costs or benefits of native or metabolite carotenoids in (different) physiological processes [19,34,125], trade-offs between these or other influences [118], or some combinations thereof. Notably, λR_min values typical of picofulvins also occur at low Diet_c (Figure 6). In the one species (Pileated Woodpecker, Dryocopus pileatus; Picidae) analyzed both ecologically (Diet_c = 12.543, λR₅₀ = 474.155 nm) and chemically [123], the blue shift is associated with mostly picofulvins but at very low concentrations, consistent with a lower cost. Accordingly, using picofulvins alone at various concentrations may augment the changing ratios of picofulvins and dietary natives (see above) to produce an honest-signaling system that achieves even greater flexibility across Diet_c. The spread-out distribution of picofulvins may also explain why λR_min has an intermediate association with Diet_c, even though this feature should correlate strongly with λR₅₀ [21,22]. With regard to λR₅₀, however, a strong functional blue shift by yellow and orange in VS Piciformes–Coraciiformes up to nearly the maximal possible terrestrial Diet_c (30 for a pure fruit diet; see Table S2) suggests little limitation on their signal informativeness, which is consistent with predictions that honest signals must span the range of costs and benefits to be fully reliable [7]. Nevertheless, ambiguities for orange through its physical proximity to yellow and possible mixed signal content (informative yellow + uninformative red), combined with avoidance of common dietary orange carotenes as pure plumage colorants [25], may help explain the surprising scarcity of orange plumages in honesty systems, both in VS (herein) and UVS (“orange gap” in UVS Thraupidae) [22] birds.

Red Response. Considering that red plumage in VS Piciformes–Coraciiformes responds to individual diets in captivity [58], the absence of a response by any of the measured spectral features for red pigments to Diet_c across wild VS piciform–coraciiform taxa suggests a certain evolutionary control in the latter context. This inference is consistent with the evidence that most terrestrial birds produce red plumage by metabolizing red keto-carotenoids from yellow dietary precursors [25,123] rather than by ingesting red pigments [41]. However, a countergradient selection-type mechanism [126] appears unlikely because red plumage in VS Piciformes–Coraciiformes otherwise contains little, if any, of the diet-dependent yellow natives or their picofulvin derivatives (woodpeckers) [123], whose relative blue shifts could otherwise cancel a genetic red shift expressed in birds with a higher Diet_c. The reduced response of red to Diet_c is consistent with claims for the same pattern (in plumage coverage) in UVS [41], but the complete absence of a shift response in VS Piciformes–Coraciiformes challenges expectations for carotenoids, considering the past emphasis on metabolized red carotenoids as central to honest plumage colors in UVS [16,32]. Instead, different (yellow and orange versus red within VS) or the same (red between VS and UVS) carotenoid pigment classes may evolve under different constraints or functional specializations. As with yellow and orange, the different physical mechanisms for producing red [66] presumably vary in costs and benefits, which could undermine honesty if their deployment strategy varies with respect to Diet_c across species. However, both the chemical data [123] and the distinctness of VS piciform–coraciiform pigment class spectra (Figure 3) in λR₅₀ phenotype space (Figure 4) suggest that reds here are distinctive keto-carotenoid metabolites, inconsistent with the main alternative route to increasing carotenoid-based redness through greater optical densities of yellow to orange pigments [17,20,31]. Any inherent limitations on red-pigment variation (e.g., saturation) also seem unrelated to the non-response of red carotenoids to Diet_c in VS Piciformes–Coraciiformes, in that the same red keto-carotenoids [123] participate in plumage red shifts in UVS [16]. Therefore, how much the different functional response by reds in VS and UVS systems indicate divergent processes depends on whether mechanisms differ only in degree (remain honesty-enforcing) or also in kind (related to dishonesty, or to communication outside the honesty rubric).

In principle, chemical constraints on red plumage could also prevent its use as an accurate indicator of dietary carotenoid content. Thus, if red was too cheap (cheatable) to be honest, then we would expect Diet_c values for red to move lower relative to yellow. Conversely, if red was ineffective because it was too expensive (limiting) to be universally honest, then we would expect Diet_c values for red to move higher relative to yellow. Instead, the extensive overlap among pigment classes across Diet_c (Table 11, Figure 4, Figure 5 and Figure 6) suggests that red is not different from other carotenoids in terms of more traditional honesty potential in relation to Diet_c. With respect to alternative honesty-enforcing processes, the shared pathway hypothesis [18,19,33,125] suggests that carotenoids are more sensitive to the internal (cellular) environment than to the external (dietary) environment because of links between carotenoid metabolism and vital cellular processes. Accordingly, carotenoid-based signal honesty may still vary, but its expression may arise from the disruption of these internal cellular processes rather than from a response to external factors, such as Diet_c. This mechanism is, therefore, consistent with the metabolic origin [123] and dietary independence (herein) demonstrated by red carotenoids in VS Piciformes–Coraciiformes. Moreover, vital effects favoring plumage redness have been linked specifically to physiology, which may depend on many traits not examined here [125]. However, in light of traditional links between diet, carotenoids, and liver function, for example [127], variation in reds that is strongly independent of Diet_c (Table 13, Figure 4, Figure 5 and Figure 6) implies additional or other complex processes. Additionally, the blue shift of red pigments in VS relative to their red shifts in UVS suggests an active mechanism against greater redness with a higher Diet_c among VS Piciformes–Coraciiformes. Notably, studies on a few woodpeckers suggest that their red plumage functions differently based on species-specific morphological or ecological contexts [128,129]. Any widespread selection influenced by this plasticity could eliminate or obscure dietary trends in red plumages with Diet_c. Therefore, other natural history features of red plumage in VS Piciformes–Coraciiformes may also incorporate additional or alternative signal properties and functions that account for the unresponsiveness of red pigment reflectance to Diet_c.

Based on these considerations, variation by red in all three spectral features at each level of Diet_c (Table 13, Figure 4, Figure 5 and Figure 6) suggests that the red pigment class has some potential to respond to Diet_c but that selection operates differently. Adaptive explanations based on processes actively favoring resemblance among reds plausibly explain no significant functional response to Diet_c. An intrinsic sensory preference [126,130,131,132,133] shared among the VS Piciformes–Coraciiformes would potentially be strong enough to override any response to Diet_c. In this regard, a striking feature of VS Piciformes–Coraciiformes is that red carotenoids are surprisingly ubiquitous among the plumages of both sexes (Table 11 and Table 12, Figure 4, Figure 5 and Figure 6), compared with the general avian patterns for yellow plumage carotenoids to predominate [116] and for a red bias in males [32]. Moreover, many of these red plumage patches occur around the head, face, and rump and are most likely to be important in visual communication. These patterns suggest a deep-seated preference for red pigmentation by various means. For example, if the red carotenoid content of neither plumage nor the oil droplets of longer wavelength-sensitive M and L cones respond to Diet_c, then a bias for certain reds may emerge or be reinforced. Sensory preference also could compromise honest Diet_c signaling through related foraging biases that allow “expensive” red pigments to be obtained more cheaply as a component of sought-after foods [134]. Thus, certain Colaptes woodpeckers appear to obtain their red pigments through narrow myrmecophilous diets [56], which otherwise have a very low overall carotenoid content (Table S2). Foraging specializations associated with terrestrial habits in Colaptes [55] could further reduce the cost of seeking these red pigment sources, thereby circumventing the usual intrinsic physiological costs and benefits relating red pigmentation to Diet_c and honesty. However, broad variation in reds at each level of Diet_c challenges sensory preference explanations whereas the relative constancy of variation in reds across Diet_c values supports them (see Figures). Other sensory factors such as habitat, light environment, and biotic interactions may contribute to these complexities.

Resemblances driven by social mimicries directed towards competitors or aposematic mimicries directed towards predators are also particularly relevant for VS Piciformes–Coraciiformes [45,135,136,137]. Typical VS piciform–coraciiform traits favoring such resemblances include bold markings, large size, physical prowess, sexual resemblance, intense competition (e.g., for nest cavities), and interspecific communication [137,138,139,140,141]. Moreover, the strong OLS and OU model support for the non-response of red to Diet_c is consistent with evolutionary convergence and not relatedness as the cause of resemblance. Evolved resemblance does not need to be independent of any tendency for red to saturate (physically similar) or create sensory biases (perceptually similar), as both phenomena enhance functional resemblance. Furthermore, the many physical mechanisms by which a red appearance can be achieved with carotenoids [17,22] and other pigments [66] could produce corresponding variations in production costs and benefits that would further undermine honest signaling, potentially favoring numerous social and aposematic mechanisms based on deception/dishonesty. Reduced variation of red compared with yellow λR₅₀ (Table 13), the large gap between yellow + orange versus red λR₅₀ values (Figure 4), and overall strong support for OU models of λR₅₀ covariation (Table 2, Table 3 and Table 4) suggest a favored zone of long-wavelength (red) plumage phenotypes consistent with resemblance hypotheses. Conversely, the scatter of λR₅₀ at a given Diet_c is not disqualifying in that resemblance need not be exact to be effective, as different species may be perceived as members of the same category, be at different stages of perfecting resemblance, or belong to different resemblance rings [137]. The only requirement in the present case is that the importance of resemblance overrides the response to carotenoid limitation, resulting in no functional response to Diet_c (cf. yellow and orange). The slight and non-significant but more positive functional response to higher Diet_c by red λR₅₀ in females (B~0.15) than in males (B~0.02) may, therefore, indicate marginally stronger selection for honesty over resemblance in females, consistent with sexual differences in certain behaviors (see above references). Physical and perceived similarities could favor red over yellow and orange under any resemblance scenario for the red response, although all pigments, particularly their Diet_c-independent wavebands, could participate. Thus, if VS incorporates yellow and orange as diet-limited to honesty-based signals, then the different characteristics of reds may lead to alternative functions, including ones related to dishonesty.

5. Conclusions

The results obtained in this study highlight the absence of a universal response of plumage carotenoids to diet within and among selected categories (pigment class, clade, and color vision system). However, a simplified symmetry framework for this variation (wavelength shifts at higher Diet_c) appears to illustrate a few universal principles for natural carotenoid diversity and physical systems in general [10,13]. In the symmetric vernacular, blue (VS) versus red (UVS) shifts are overlain by both invariant (e.g., color vision, dietary limitations, metabolites, honest signaling, pigment class effects, and dietary biomarkers, all for yellow and orange) processes under antisymmetries, but also different (e.g., for VS Piciformes–Coraciiformes, de-emphasis of certain wavebands, emphasis on resemblance, and deceptive signaling for red) processes under broken symmetries. If orange combines yellow and red, then a gradient between symmetries and broken symmetries may parallel the gradient from yellow to red in functional responses to Diet_c. These regularities may be underestimated if provisional evidence holds that the strength of the shift at higher Diet_c by pigment class is usually in the order yellow > orange > red, regardless of the blue (herein) or red [41] shift. Notably, the shifts by the in vivo ocular sensitivities of the V and S cones of the two diurnal color vision systems acquire a new interpretation as underlying antisymmetries themselves. In this regard, the apparent linkage between color vision system and shift form in response to Diet_c modifies the common dictum that birds are “what they eat” to include “what they see.” This elaboration recognizes the possibility that intrinsic factors, such as different color vision and metabolism, may lead to divergent functional responses, even though extrinsic dietary inputs are the ultimate sources of plumage carotenoids. Thus, symmetry principles appear to organize carotenoid diversity into a simplified predictive framework linked to color vision.

Ascertaining more specific ecological similarities or differences within a symmetry framework is beyond the scope of this study. However, the aforementioned symmetries are ultimately integrated specializations in color vision, pigmentation, and ecology that require careful consideration of evolutionary phenomena. Thus, divergent plumage shift patterns may arise from the convergent processes of honest signaling. Conversely, convergent pigmentation may have divergent functions (honest versus dishonest). Importantly, this additional complexity enables functional divergence between different carotenoid-based plumage patches within and between individuals, sexes, species, and color vision systems, thereby augmenting their signal diversity, adaptive potential, and homoplasies [21]. Within VS Piciformes–Coraciiformes, for example (Table 12), yellows and oranges may permute diet-limitation, honesty, and mimicry (toucan) [45], and reds may emphasize sensory bias and mimicry (woodpecker examples) [136]; however, all three pigment classes may be good indicators of condition (e.g., in captive or wild birds; personal observations) [58]. Between color vision systems, blue-shifted metabolites may be more integral to VS, and vice versa for UVS. Consequently, ignoring covariance by lumping pigment classes or color vision systems may obscure more structured dynamics within (VS) or between (VS and UVS) these systems. In this regard, comparisons among other VS birds should determine whether broken responses to Diet_c in VS Piciformes–Coraciiformes are typical of this visual system or an idiosyncrasy of certain members. Conversely, the differences and similarities between VS Piciformes–Coraciiformes and their UVS relatives (Trogoniformes) provide critical tests for the association between opposite shift patterns and color vision. Such symmetries and their underlying causes are general enough to be expected for many pigments and organisms.