Turning induced plasticity into refined adaptations during range expansion

Robustness against environmental fluctuations within an adaptive state should preclude exploration of new adaptive states when the environment changes. Here, we study transitions between adaptive associations of feather structure and carotenoid uptake to understand how robustness and evolvability can be reconciled. We show that feather modifications induced by unfamiliar carotenoids during a range expansion are repeatedly converted into precise coadaptations of feather development and carotenoid accommodation as populations persist in a region. We find that this conversion is underlain by a uniform and coordinated increase in the sensitivity of feather development to local carotenoid uptake, indicative of cooption and modification of the homeostatic mechanism that buffers feather growth in the evolution of new adaptations. Stress-buffering mechanisms are well placed to alternate between robustness and evolvability and we suggest that this is particularly evident in adaptations that require close integration between widely fluctuating external inputs and intricate internal structures. Phenotypic robustness to environmental variation is seemingly at odds with evolvability. Here, the authors analyze carotenoid use and accommodation in feather development across a recent avian range expansion and show that cooption of a stress-buffering mechanism can reconcile robustness and evolvability.

T here is an evolutionary tension between the preservation of functioning phenotypes and the exploration of alternative phenotypic states [1][2][3] . Cooption of stress-buffering mechanisms that maintain each adaptive state 4-6 is thought to bridge sequential adaptive states [7][8][9][10][11][12] . However, it is difficult to infer the historical role of stress-buffering mechanisms from comparisons of contemporary adaptations alone, because homeostatic systems necessarily suppress variation that interferes with current functioning and new adaptations subsume preceding adaptations in evolution 13 . Thus, extant adaptations are not each other's evolutionary stages, even in related species, and the debate on whether transitions between adaptations are more concordant with functionally relevant (i.e., adaptive) or stress-induced (i.e., nonadaptive) contemporary variation is often inconclusive [14][15][16][17][18][19] . A more inferential approach is to study transitions between adaptations as a process. This requires an empirical system where it is possible to observe both the developmental effects of an environmental factor that has varied during the evolution of the lineage and changes in its developmental effects over time. Here, we show that an ongoing range expansion of a passerine bird satisfies these criteria by enabling direct observation of sequential historical changes in how growing feathers accommodate the diverse carotenoids that color them.
Many bird species color their feathers with carotenoids acquired from the diet. Carotenoid metabolic networks are wellcharacterized for many bird species, allowing classification of feather carotenoids into dietary carotenoids (those obtained directly from the diet and deposited into feathers unchanged) and metabolized carotenoids (those biochemically converted by birds prior to deposition in feathers) 20 . Further, some metabolized carotenoids are interchangeably derived from several dietary carotenoids (e.g., Supplementary Fig. 1)-a phenomenon known as metabolic degeneracy 21 . The more degenerate a metabolized carotenoid compound is, the more reliably it will be produced across a range of environments by conversion of variable dietary carotenoids. Metabolized carotenoids, especially the degenerate compounds, are thus more reliably present across environments and have likely had a longer time to coevolve with and integrate into other organismal systems than dietary carotenoids or their nondegenerate metabolized derivatives 22,23 .
The incorporation of carotenoids into the barbs of growing feathers commonly causes feather structural modifications that range from transient malformations to intricate co-evolutionary adjustments [24][25][26] . A particularly striking modification is the effect of carotenoid uptake on an iconic feature of feathers-interlocking barbules ( Supplementary Fig. 2)-which are responsible for a variety of functions, from water repellency and insulation to flight. For nearly a century, it has been known that the uptake of carotenoids into barbs often interferes with barbule development (hereafter "feather differentiation"; Fig. 1a, c), underpinning a textbook explanation for why feathers that are structurally specialized, such as flight and down feathers, are buffered against significant carotenoid uptake and are rarely colorful 27 . Yet, the relationship between feather differentiation and carotenoid input is highly variable: in some species, carotenoid-bearing feathers develop barbules that subsequently break off to enhance ornament display, in others, feathers develop deformed or partial barbules, while yet in others, feathers completely lack barbules from the onset of development, which decreases diffuse scattering and amplifies color intensity 25,26,28 . The extent to which phenotypic associations such as these are stages of an evolutionary process has not been studied. Thus, it is not known whether the feather modifications resulting from uptake of external carotenoids are adaptations to maximize coloration (Fig. 2b), transient malformations that require subsequent evolution of greater buffering of feather growth (Fig. 2c), or evidence of evolved plasticity, where local carotenoids directly induce feather growth modification 29,30 (Fig. 2d).
Here, we test these scenarios using the recent colonization of western North America by house finches (Haemorhous mexicanus), which has produced replicated, hierarchical sequences of known-age populations across one of the widest ecological ranges of any extant bird species 31 (Fig. 3). From their native range in southwestern North America to their newly established range, house finches are exposed to diverse plant communities that provide widely distinct sources of carotenoid precurors 32 , use different subsets of a carotenoid-producing metabolic network, and show an array of feather modifications in response to carotenoids 22,33 . These modifications, illustrated in Fig. 1, vary from a near complete loss of barbules in ancestral and older populations to full barbule development in new populations, with a variety of intermediate stages.
Here we examine whether this diversity represents evolutionary stages by tracing historical changes in developmental responses of feathers to the uptake of 19  First, we test whether historical changes in the association between presence of feather barbules and carotenoid uptake are concordant with those predicted by evolution for greater display of carotenoid-based ornamentation, evolution of buffering mechanisms that decouple feather differentiation and carotenoid uptake, or mechanical interference, where plasticity of feather growth accommodates local carotenoids without long-term evolutionary consequences (Fig. 2). Because the mechanisms underlying these hypotheses depend on the familiarity of an evolving lineage with carotenoids, and because degenerate carotenoids have greater predictability and integration with organismal processes that dietary compounds, these hypotheses make opposite predictions for the effects of degenerate vs. dietary carotenoids in the transitions between feather-carotenoid associations ( Fig. 2b-d). To test these hypotheses, we investigated the historical changes in both the carotenoid concentration that induces feather structure response and the shape of the response across populations (Supplementary Fig. 3).
Second, we capitalize on within-individual differences in the timing of molt of different ornamental areas (Fig. 4) to establish whether variation in feather differentiation is triggered locally by each feather's own carotenoid uptake, or reflects an organismwide response where carotenoid accumulation in earlier molting feathers influences the development of later growing feathers (i.e., anticipatory response). We then examine historical changes across populations in the coordination of feather responses across ornaments and discuss potential regulatory mechanisms behind the three main hypotheses (Fig. 4).
Across an array of diverse carotenoids, and thus a diversity of starting points, we uncover a remarkably uniform historical increase in the sensitivity of developing feathers to carotenoid uptake as populations persist in their environments. Within each population, the sensitivity of the developing feather to carotenoid uptake primarily depends on carotenoid metabolism (dietary, metabolized, and degenerate) and on a population's familiarity with a particular suite of local carotenoids. These findings suggest that the coevolution of feather differentiation and pigment deposition coopts a b c d e f g h Fig. 1 Feather differentiation responses to carotenoid uptake in house finches. a, b the full response-complete lack of barbule differentiation, c, d no response-complete differentiation, e the partial response-partial differentiation with either few differentiated barbs or parts of individual barbs differentiated (6× panel, arrow), f an example of mismatch of anticipatory response in feather differentiation-i.e., lack of differentiation in the absence of carotenoid uptake, g typically, in fully-differentiated feathers, only the rami of barbs contain carotenoids, but h unusually thick barbules occasionally trap carotenoids (arrow). Only crown feathers are shown to facilitate comparison. general mechanisms that buffer feather growth, where the initial disruption of feather differentiation by unfamiliar compounds is transformed into increasingly robust and diverse states of feathercarotenoid associations across populations (scenario of Fig. 2b, Supplementary Fig. 3c, d). Further, these results establish that the loss of barbules in carotenoid-bearing feathers are adaptations and explain the diverse associations between feather structure and carotenoid uptake across the ecological range of this species (Fig. 1). More generally, modification of the mechanisms that maintain robustness of each adaptive state facilitates transitions between subsequent adaptive states, illustrating an empirical reconciliation of robustness and evolvability.

Results
Carotenoids differ in variability and predictability. We measured structural differentiation in response to the accumulation of 19 carotenoids ( Supplementary Fig. 1 Familiar carotenoids exert stronger feather responses. In the ancestral population, only 4% of birds showed full differentiation of barbules (Fig. 3a). However, within a few generations of  Fig. 2 Proposed pathways for feather differentiation and carotenoid uptake coevolution. a Stage 1 (default state of fully-differentiated barbules) and Stage 2 (induction of barbule non-differentiation by novel carotenoid uptake) are well-documented. Subsequent Stage 3 depends on the mechanisms underlying the feather-carotenoid association. We test three alternative scenarios (predicted responses shown in red). b H1: selection for enhancing carotenoid expression strengthens the link between feather non-differentiation and carotenoid uptake, predicting a lower threshold (higher sensitivity) of response (shown as a bracket) to carotenoid concentration (gray area under concentration curve), especially for degenerate carotenoids and in older populations. c H2: selection for restoring feather differentiation and buffering it from disruption by novel carotenoid uptake, predicts a higher threshold of response (lower sensitivity) to carotenoid concentration, especially for degenerate carotenoids and in older populations. d H3: no evolutionary change-i.e., continuation of Stage 2 where feather plasticity allows feather differentiation in proportion to local concentration of carotenoids (shifting concentration curves and proportional feather response). No difference in response to degenerate and dietary carotenoid accumulation is predicted. Supplementary Fig. 3 outlines tests of these hypotheses.
colonizing new environments and accumulating different combinations of carotenoids (Supplementary Data 1, 2), finches showed full or partial feather differentiation (Fig. 3). Feathers that did not develop barbules had wider barb diameters than differentiated feathers, which was associated with greater accumulation of carotenoids (Fig. 5).
For each carotenoid compound in each population, we estimated the relative concentration needed to produce feathers without barbules in 50% of individuals (L50), and also established whether the response curve was linear or threshold-like (Methods, Supplementary Fig. 3, Supplementary Data 4). We found that, in all populations, degenerate carotenoids caused   (Fig. 6c).
Feather responses differ mostly in sensitivity. We then asked whether the observed historical changes in thresholds of carotenoid concentration that causes feather responses (Fig. 6a) were specific to carotenoid type or resulted from changes in sensitivity of response (i.e., scaling of response curve, Supplementary Fig. 3c). We fitted an accelerated failure time (AFT) regression to all feather responses within ornamental areas (populations combined, see Methods) to remove the effect of scaling, such that population-or carotenoidspecific responses that only differed in sensitivity to a given concentration ( Supplementary Fig. 3c), would have an identical distribution of residuals from this regression. We found that, with the exception of adonixanthin (which had linearly-proportional effects on feather response in four populations, Supplementary Data 4, Supplementary Fig. 3d), the responses to metabolicallyderived carotenoids across all populations and ornaments differed only in sensitivity (i.e., a decrease or increase in population response in relation to a given carotenoid concentration, Supplementary  Fig. 3c). Thus, across most metabolized carotenoids, the observed decrease in response threshold with population age (Fig. 6a, b, d) was caused by increased sensitivity (Fig. 7a, Data 4), where the sensitivity of response progressively increased with populations age (Fig. 7a, c; Supplementary Fig. 3d).   Fig. 4 Evolution of regulation of feather differentiation. a The tip is the oldest part of a feather and a presumed time of developmental decision (t n ) that determines whether barbules separate from barbs, ultimately producing either a non-differentiated (2) or differentiated (0) feather in response to carotenoid uptake ( Supplementary Fig. 2). Partial differentiation (1) can be produced by shifting the decision point to later developing, more basal, parts of the ornamental feather (t n ′). Within-individual heterochrony of the molt of ornamental areas (rump: Part 1, breast: Part 2, and crown: Part 3 are shown as examples) allows assessment of organismal coordination of feather differentiation decisions. b H1 and H2 (Fig. 2) predict a greater anticipatory response of feather differentiation to carotenoids, affecting differentiation of earlier molting parts (e.g., angled arrow c 1 → t 2 , between carotenoid concentration at the time of the differentiation decision of Part 1 feathers and that of Part 2 feathers), especially for degenerate carotenoids and in older populations. H3 predicts no such anticipatory response, but consistent induction of feather differentiation by carotenoids available at the time of feather growth (e.g., vertical arrow c 2 → t 2 ). c Greater organismal integration of feather differentiation decisions and a lower threshold response (Fig. 2b) should lead to greater precision (lesser variation) in response of feather differentiation to carotenoid uptake, especially in degenerate carotenoids ( Supplementary Figs. 1b and 3).

Organismal coordination of feather responses to carotenoids.
Having established that the feather response to carotenoid input is determined by consistent increase in sensitivity of feather development to local carotenoid uptake (Fig. 7), we investigated the regulation of this precision. We capitalized on the temporal ordering of developmental events within a feather (Supplementary Fig. 2), and the different timing of feather growth across ornamental patches within an individual (Fig. 4), to determine whether feather responses were anticipatory (a coordinated uniform response across feathers despite differences in local carotenoid uptake) or locally induced (each ornaments' feathers are independently modified by local uptake of the carotenoids circulating at the time of its' development). We adapted a statistical technique that allowed us to directly compare feather responses from linear, accelerating, and threshold distributions (Methods). We found that young populations showed greater coordination of barbule loss across ornaments in response to dietary carotenoids (Fig. 8), especially those most frequently found in feathers (e.g., zeaxanthin, lutein, β-carotene, Supplementary Data 4). These anticipatory responses might have enabled birds in these populations to accumulate greater amounts of dietary carotenoids (Fig. 3a). As populations persisted in their environment, anticipatory responses to dietary carotenoids notably diminished, and were replaced with anticipatory responses to derived carotenoids (Fig. 8, Supplementary Data 2). Interestingly, these anticipatory responses occasionally resulted in mismatches between feather differentiation and actual carotenoid uptake. For example, even when they did not receive pigment themselves, some later molting feathers did not develop barbules when earlier molting ornamental feathers accumulated carotenoids (Fig. 1f).

Discussion
We traced historical trajectories of organismal accommodation of novel external inputs, from induction and proliferation of stress-like effects in young populations, to progressive buffering and fine-tuning of local responses as inputs become familiar in older populations. We observed that, following introduction into a novel environment, house finches express full structural differentiation in ornamental feathers (a response which had been largely lost in older populations), and then gradually lose it again, but in response to different combinations of carotenoids. This sequence is congruent with the scenario outlined in Fig. 2b, establishing a lack of barbule development in carotenoid-bearing feathers as an adaptation, which evolved by strengthening the link between barbule loss and carotenoid uptake. We further document a remarkably uniform increase in feather response sensitivity across an array of biochemically distinct carotenoids (Fig. 7a), and show that this increase is underlain by familiarity with a carotenoid-reflected by both its prevalence within population and its metabolic degeneracy, which corresponds to a longer coevolution time (Figs. 6, 7). Lastly, both induced responses in new populations and the maintenance of specific responses in old populations were accomplished through organism-wide coordination of responses (Fig. 8a).
Taken together, these findings suggest that the association between feather differentiation and carotenoid accumulation evolved though cooption and modification of the mechanisms that normally shield feather growth from incorporation of unwanted components from plasma or regular pigment uptake. Two aspects of these mechanisms are particularly relevant to our results-the link between total concentration of accumulated carotenoids and feather growth differentiation 34 and evolving selectivity of feather follicular membrane for chaperoning carotenoids into developing feather [35][36][37][38] .
The elements of feather growth most closely associated with carotenoid uptake are the barb addition rate and initial diameter of the carotenoid-bearing ramus of the barb ( Supplementary  Fig. 2). Both of these elements are determined prior to a feather's   34 , such that feather differentiation is predisposed to be affected by prior carotenoid presence in feather follicle and the mechanisms of feather differentiation can either capitalize on it or buffer against it. The lack of carotenoid specificity in feather differentiation, as well as the organism-wide coordination of feather responses found in this study, suggest shared regulation of carotenoid processing, delivery, feather growth and differentiation. A particularly likely candidate for this regulation is modification of the mechanisms that determine the structure of nonornamental feathers across the avian body. Barbule separation is routinely and reversibly truncated in many feather types in the absence of any pigment uptake 39,40 . Similar patterns of feather modification may be produced by biochemically distinct carotenoids if the mechanisms mediating carotenoid uptake can coopt the developmental processes that influence barbule development. Several lines of evidence support this hypothesis and point to integration of carotenoid deposition with general mechanisms of feather growth and differentiation. First, barbule separation is the earliest feather differentiation decision at the level of the barb 41,42 (Supplementary Fig. 2, Fig. 4), preceding the formation of the rami, where carotenoids are deposited ( Supplementary Fig. 2b). We found that barb diameters were wider on undifferentiated feathers (Figs. 1, 5), suggesting that accumulating barbule cells develop and fuse to the rami of the barb, rather than barbule development being truncated overall. Such early and irreversible non-differentiation can be triggered by either threshold-like effects of carotenoid accumulation in the focal follicle, or by anticipatory, organism-wide coordination based on carotenoids circulating in the plasma (Fig. 4b).
Second, the finding of partial differentiation of feathers in new populations (Fig. 1e)   underlining the hierarchical organization of feather development [42][43][44] . For example, carotenoids may truncate the development of barbules overall, or initiate keratinization of the barb prior to the differentiation of barbules. The length of a single-cellwide individual barbule depends on the height of the barb ridge ( Supplementary Fig. 2), which is determined by the rate of cell differentiation and growth in the ramogenic zone 42 . Intriguingly, production of growth-inducing Sonic Hedgehog (Shh) in the marginal plate ( Supplementary Fig. 2) occurs while Shh receptors are present only in the barbule, not the marginal plates 45 , indicating that the marginal plate may be the signaling center that regulates barbule cell proliferation and differentiation. If presence of carotenoids in feather follicles affect growth of the marginal plate cells 45 , as shown in some species 46,47 , then carotenoid uptake will directly influence barbule segregation. While experimental confirmation is needed, the common denominator of all these scenarios is that carotenoid uptake alters general, not pigment specific, mechanisms that normally maintain, and regulate feather growth.
Consumed and metabolized carotenoids differ in the rate and location of their absorption in the gut [48][49][50] , the type of plasma lipoproteins they are transported by 51,52 , and their ability to diffuse into a feather follicle [53][54][55] and bind to keratin of the feather matrix 56,57 . Given this diversity, what mechanisms could produce the observed organism-wide coordination of feather responses (Fig. 8)? And what accounts for the scaling of feather developmental responses to distinct carotenoids across historical contexts (Fig. 7)? Our findings suggest that the mechanisms that buffer growing feathers and maintain population robustness of carotenoid-feather associations may also channel transitions between them. A particularly good candidate that may link sensitivity to plasma circulating carotenoids with the developmental and evolutionary aspects of feather growth is the evolution of follicular membrane permeability. Carotenoids penetrate feather follicles attached to plasma lipoproteins and follicular membranes are thought to mediate the incorporation of carotenoids into developing barbs (Supplementary Fig. 2). Interestingly, uncommon carotenoids are known to overwhelm follicular membrane   buffering, resulting in failure of the membrane as a selective barrier and passive shunting of novel carotenoids into growing feathers, often with cascading effects on feather structure [35][36][37] .
Evolving selectivity in membrane permeability may explain why historical familiarity with a particular carotenoid is associated with its precise deposition into feathers, and account for organismal coordination in follicular responses across ornaments. The evolutionary stability of an adaptation can be maintained by interconnectedness of its components or by homeostatic controls that maintain its functionality as a whole. Correspondingly, the transition between adaptations can involve either modifications of individual components or changes in the homeostatic controls that buffered a preceding adaptive state 58 . Here, we distinguished between these scenarios by directly studying the transition between adaptations. We show that variable feather structure induced by uptake of unfamiliar carotenoids during an avian range expansion was consistently converted into precise and stable coadaptations of feather development and carotenoid accommodation as populations persisted. We found that this conversion is underlain by a uniform increase in the sensitivity of feather development to local carotenoid uptake and organism-wide coordination of feather responses. Thus, the mechanism assuring functionality of each adaptive state also likely bridges the transition to new states.

Methods
Data collection and sample sizes. We collected 10-15 ornamental feathers (3-5 from each of the three ornamental areas-crown, breast, and rump, Fig. 1 in ref. 59 ) from 1196 free-living adult male house finches. To minimize temporal variation of feather wear and standardize sampling across long-term study populations, we only used feathers sampled during May-June from 2008 to 2018. Captures and sampling were conducted under US Federal Permit (23182) and annual permits for the states of Arizona and Montana. All animal procedures were approved by the University of Arizona Institutional Animal Care and Use Committee . To ensure sufficient sample sizes for some analyses, we combined populations that shared colonization age and routes (Fig. 3) to nine regions as shown in Supplementary  Table 1, which also lists the curated dataset used in all analyses.
Each collected feather was digitized with a modified Epson Perfection 1660 PhotoScanner (Long Beach, CA, USA) at 1000 dpi and also examined under a Nikon Eclipse Ti-E inverted light microscope (Nikon, Tokyo, Japan). Following assessment of feather microstructure, we extracted 19 carotenoid compounds from the pigmented parts of these feathers and obtained concentrations of these carotenoids by HPLC 23 (µg/g of pigmented feathers, Supplementary Data 1 and 2). Feathers within each ornamental area of each individual were combined for carotenoid extraction and analyses.
Carotenoid extraction and quantification. Feathers were trimmed, and the weighed pigmented portions were washed in hexane using Whatman GF/A glass filters and finely ground in 3 mL methanol for 10 min at 20 Hz using a Retsch MM301 mixer mill (Newtown, PA), equipped with ZrO grinding jars and balls. Carotenoids were extracted using a 0.2 µm filter (GHP Arcodisc 13 mm Minispike; Pall Life Sciences, East Hills, NY) and the filtrate was dried under vacuum at 40°C and reconstituted in 150 µL of HPLC mobile phase (methanol:acetonitrile 50:50, v/v).  Carotenoids were quantified by injecting 50 µL of pigment extract into an HPLC System (Shimadzu Corporation, Pleasanton, CA) fitted with an YMC Carotenoid 5.0 µm column (250 × 4.6 mm) and guard column (YMC America, Allentown, PA). Analytes were eluted at a constant flow rate of 1.1 mL/min using isocratic elution with 42:42:16 (v/v/v) methanol:acetonitrile:dichloromethane for the first 11 min, followed by linear gradient up to 42:23:35 (v/v/v) methanol: acetonitrile:dichloromethane through 21 min, isocratic elution at this condition until 30 min when it returned with step function to the initial isocratic condition at which it was held until 40 min. Carotenoids were detected using a Shimadzu SPD-M10AVP photodiode array detector, and data were collected from 200 to 800 nm. Peak areas were integrated at 450 or 470 nm depending on the absorbance maximum (λ max) for each compound.
Carotenoid identification. Fifteen μg/mL stock solutions of pure powdered carotenoid compound dissolved in a mobile phase of 50:50 methanol:acetonitrile were made for 3′-hydroxy-echinenone, 3′-dehydrolutein, α-carotene, adonixanthin, adonirubin, astaxanthin, β-carotene, β-cryptoxanthin, canthaxanthin, echinenone, lutein, retinol, rubixanthin, tocopherols, vitamin D, and zeaxanthin. Five serial dilutions of each carotenoid standard (15, 7.5, 3.75, 1.875, and 0.9375 μg/mL) were run individually through the same HPLC protocol as used for the feather samples above. The serial dilutions enabled us to identify the unique shape of a standard's peak and determine whether the retention time of a standard shifts in different concentrations. Following the identification of the standard peaks, over 20 unique mixtures of 4-5 known standards of known concentrations were run through the same HPLC protocol as the feather samples to assess how the peaks of different compounds separate when mixed with other compounds, since this is how they are analyzed in the feather samples. As a result of these trials, peaks in feather samples were assigned to compounds based on three key, repeatable features: retention time in the chromatogram, relative retention time to other peaks in the sample, and the shape of the peak.
For fourteen carotenoid compounds, the concentrations of compounds (µg/g) were calculated using calibration curves of these standards (Sigma-Aldrich, St. Louis, MO; Indofine Chemical, Hillsborough, NJ; CaroteNature, Ostermundigen, Switzerland; Santa Cruz Biotechnology, Dallas, TX). For five compounds without available standards, concentrations were derived based on biochemical structural similarity to known standards as follows: the peaks of canary xanthophyll A and canary xanthophyll B were identified based on their proximity to the known peak of 3′-dehydrolutein, 4-oxo-rubixanthin was the peak that appears in the rubixanthin standards when they are exposed to oxygen, the peak for gaziaxanthin was identified based on its proximity to the known peaks of rubixanthin and 4-oxorubixanthin, the peak for β-isocryptoxanthin-based on its proximity to the known peak for β-carotene, and the peak for α-doradexanthin-based on its structural similarity to canthaxanthin. We used the serial dilutions to calculate the concentration equation for each standard. The equation was derived from a linear regression of the area of the peaks at the five known concentrations (15, 7.5, 3.75, 1.875, and 0.9375 μg/mL). The concentration of a compound in a feather sample was determined by entering the area of its peak into the equation for its corresponding standard. Supplementary Data 1 and 2 list prevalence of identified carotenoids in feathers (% of individuals), mean and range of their concentration, proportion of the total amount of carotenoids in pigmented feather, and coefficient of variation of that proportion.
Feather differentiation. Differentiation of collected feathers was assessed in two ways. First, using high resolution scans of all feathers, we examined the microstructure of four feathers from each ornament to derive a mean score of barbule loss within each ornamental area of each bird (Supplementary Data 3, see below). Second, we examined one feather from each ornament of n = 217 males under a light microscope at ×4, ×6, and ×10 magnifications. For n = 651 feather samples in this subset, we assigned a barbule loss score to confirm reliability of the first method, and also measured the proportion of the barb that did not develop barbules relative to total barb length to derive percentage of barbule loss. We then measured barb width at the base, middle and distal tip of barb (Supplementary Data 3). All measures of differentiation were performed on the two most distal, innermost barbs. We assigned a measure of differentiation as follows: 0-no response: full structure, barbules from base to tip (Fig. 1c, d), including feathers with full structures, but partially broken barbules, 1-partial response: partial structure, some barbules developed while others did not separate from barb (Fig. 1e), 2-full response: no barbules present (Fig. 1a, b). All measures of barbule loss were performed by a single observer. The measurement error, assessed in repeated measures of a subsample of 40 crown feathers using one-way ANOVA was less than <5% of the individual identity effect (mean squares 0.06 vs. 1.24).
Assessment of distribution shape and 50% response threshold. To derive response curve and response threshold values, we needed a technique that would accommodate continuity in response assessments (values 0-2), but also discreteness of these categories. Further, the method needed to accommodate differences in the response distribution-e.g., threshold vs. linear, symmetric around zero vs. accelerating. Thus, we used PROC PROBIT in SAS 9.4, which satisfies these requirements, to calculate the threshold response (our L50 parameter is LD50 probability value in PROC PROBIT), parameter estimates, and the response distribution patterns. The procedure obtains and compares maximum likelihood estimates from linear, probit, logit, ordinal logistic, and accelerating value regression models. Supplementary Data 4 lists calculated threshold response (L50) for the best fit models. Supplementary Fig. 3 outlines the sequence of tests for comprehensive assessment of response threshold and shape.
Assessment of scaling and deviation from scaling. A change in the shape of feather response in relation to carotenoid concentration can be due to changes in the threshold of concentration that causes a 50% response in a population or changes in the shape of this response ( Supplementary Fig. 3). A change in shape can be caused either by a scaling of response-e.g., stretching or compression of the x-axis (carotenoid concentration) associated with L50 value (Supplementary Fig. 3c) or a different pattern of response-such as linear or sigmoid ( Supplementary Fig. 3d). To identify changes in the response curve that were produced by simple rescaling of population-and ornament-specific responses to carotenoid uptake (e.g., when twice higher concentration is associated with the same percentage of response in one population vs. another), we applied Kolmogorov-Smirnov (K-S) tests to residuals from an AFT regression model, as implemented in PROC PHREG of SAS 9.42. We fitted the regression model to each ornamental area separately, with all study populations combined, but kept identity of populations for regression grouping ( Supplementary Fig. 4). The AFT model is particularly appropriate for our analyses because it assumes a parametric form for both the feather response and carotenoid uptake. We then used the K-S test to assess the probability that K-S maximum distance (Supplementary Data 4, double-headed arrow on Fig. 7 inset) between estimated distribution function (EDF) and observed scaling function are obtained by chance. We derived EDFs of feather responses separately for residuals of each population, relative concentration of each carotenoid, and ornament area and then compared these EDFs with observed scaling functions with the K-S framework implemented in PROC NPAR1WAY of SAS 9.42 for two class comparisons. The procedure computes the maximum deviation of the EDFs and outputs values where the maximum deviation occurs, the two-sample K-S statistic D and associated probability that D is greater than the observed value under the null hypothesis of no difference between the two distributions. Across all ornamental areas, |K-S max distances| ≥ 1.49 were different from 0 under P < 0.05 ( Supplementary Fig. 4), such that responses with |K-S| < 1.49 come from the same underlying distribution and differ only by rescaling the concentration of carotenoids needed for response, whereas residuals above dashed line in Fig. 7 correspond to responses that differ more than just in sensitivity of response to concentration ( Supplementary Fig. 3, all data and tests in Supplementary Data 4).
Assessment of anticipatory and induced response. To measure organism-wide coordination of feather response, i.e., the indirect effects of carotenoids accumulated in other feathers on feather response in a focal area (e.g., paths c1 → t2, c2 → t3 in Fig. 4), we needed a technique that would allow us to directly compare responses even though they might come from different distributions (e.g., linear vs. threshold; Supplementary Data 4). This ruled out commonly used multiple leastsquare regression models or structural equation models (e.g., path analysis). We instead used a new procedure for indirect response comparison implemented in logistic regression models of SAS 9.4.
The plots of (1-specificity) by sensitivity form the receiver operating characteristic (ROC) curves (Fig. 8 inset). Diagonals of these plots correspond to an area under the curve (AUC) of 0.5 and represents the area where the fraction of true positives and false negatives are equal and hence the effect is not different from random. The new ROCCONSTRAST procedure in PROC LOGISTICS of SAS 9.42, uses a nonparametric test to compare AUC and associated probabilities, allowing direct comparisons of AUC that come from different distributions (e.g., Supplementary Fig. 5). For each carotenoid compound, we used a focal feather response as a reference point, and compared indirect effects of carotenoids influencing response of feathers in a focal ornament (e.g., c1 → t1, Fig. 4) to the feather response in other ornaments. Values significantly different from 0.5 (and thus nonrandom) are reported in Supplementary Data 4. Figure 8 plots absolute amounts by which these significant values exceed 0.5.
Reporting summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.