Egg discrimination along a gradient of natural variation in eggshell coloration

Accurate recognition of salient cues is critical for adaptive responses, but the underlying sensory and cognitive processes are often poorly understood. For example, hosts of avian brood parasites have long been assumed to reject foreign eggs from their nests based on the total degree of dissimilarity in colour to their own eggs, regardless of the foreign eggs' colours. We tested hosts' responses to gradients of natural (blue-green to brown) and artificial (green to purple) egg colours, and demonstrate that hosts base rejection decisions on both the direction and degree of colour dissimilarity along the natural, but not artificial, gradient of egg colours. Hosts rejected brown eggs and accepted blue-green eggs along the natural egg colour gradient, irrespective of the total perceived dissimilarity from their own egg's colour. By contrast, their responses did not vary along the artificial colour gradient. Our results demonstrate that egg recognition is specifically tuned to the natural gradient of avian eggshell colour and suggest a novel decision rule. These results highlight the importance of considering sensory reception and decision rules when studying perception, and illustrate that our understanding of recognition processes benefits from examining natural variation in phenotypes.

egg [sensu S7], and these nests remained active. Although we include both rejections of the model egg and rejection errors as 'rejections' in all analyses, the exclusion of these two cases produced nearly identical and statistically consistent results (therefore these reanalyses are not shown). Hosts were considered 'acceptors' when the foreign egg and all of their own eggs remained incubated until the end of this period. We did not include nest desertion (i.e., abandonment) as a response to experimental parasitism and removed both deserted and predated nests from all analyses [S8]; therefore, here we have used the general term 'rejection' to refer to host responses where an egg disappeared from a nest after experimental introduction. Recent experimental research has shown that desertion is not a response to parasitism in this and other European populations of the blackbird [S3,S8-S10], and only a single robin pair abandoned its nest during this study; nonetheless, our rationale is the same [S9], these mid-sized hosts are able to grasp these models to remove them [see Video S1 from, S11].

(b) Experimental egg models
To assure rejection responses were possible, we used artificial plaster eggs similar to those used in previous experiments in both populations [S3,S4,S8,S12,S13]. The size of the eggs (mean ± SD: 22.5± 0.36 x 16.8 ± 0.29 mm, N = 82) used for blackbirds matched those of cuckoo Cuculus canorus eggs found in common redstart nests Phoenicurus phoenicurus (mean ± SD: 22.2 ± 1.0 x 16.8 ± 0.6 mm, N = 33) [data from, S14], and the size of the eggs used in robin nests (mean ± SD: 22.7 ± 0.83 x 17.4 ± 0.58 mm, N = 52) approximated those of brown-headed cowbirds (mean ± SD: 21.1 ± 1.1 x 16.47 ± 0.7 mm, N = 113) [data from, S15]. Importantly, these same egg models were successfully used in previous egg-rejection studies in both species and populations [S3,S4,S8,S12,S13], which ensures that rejection responses were possible and that responses were not constrained by the dimensions, material, or mass [S11,S16]. Similarly, it was important that the experimental eggs used on both species were similarly immaculate and similarly coloured to aid interpretation and comparability of our findings.
We originally formulated the paint mixtures to approximate avian perceived eggshell colours based on freshly abandoned natural blackbird eggs found in 2013 as well as the full range of natural avian eggshell colours [S17], and we also created an additional mixture that generated colours along an gradient of variation that was orthogonal to the natural egg colour range within the avian colour space (figure 2). These abandoned eggs were not used as an estimate of host eggshell colour; they were only used to formulate paint mixtures. To create these mixtures we used combinations of Koh-i-Noor Hardtmuth A.s. (České Budějovice, Czech Republic) high-quality acrylic paints: brown light (0640), khaki (0530), permanent green (0520), red light (0300), turquoise (0460), and ultramarine (0410). Then prior to the 2014 field season, each foreign egg model was hand-painted with a unique paint mixture evenly across the entire egg surface such that its colour would have a unique position along either axis within the avian tetrahedral colour space (details below).
To determine how closely the freshly painted foreign eggs matched the natural eggshell colours or the orthogonal gradient, after the foreign eggs dried we measured each using a reflectance spectrometer and plotted its coordinates (details below) within the blackbird's tetrahedral colour space [S18,S19]. We then visually assessed if each egg corresponded to one of the continuous gradients of colour variation. If it did not, the egg was considered unsatisfactory and we repainted it until it did correspond with one of the two colour gradients. The exact coordinates for each foreign egg used in our experiment were statistically controlled for as a covariate in every analysis.

(c) Colour measurements and perceptual models
For each species, we measured the reflectance of foreign and abandoned eggshells between 300-700 nm using an Ocean Optics USB 2000 spectrometer (Ocean Optics, Dunedin, Florida), a pulsed xenon light source (PX-2) for blackbirds and a Deuterium Tungsten lamp (DT-mini) for robins, and a white reflectance standard (WS-1). The blackbird and robin colour datasets (foreign egg models and natural eggs) were measured using two separate sets of equipment to assure the comparability of our colour data (i.e., host versus foreign egg colour). During the course of our fieldwork we collected freshly abandoned blackbird (N = 54) and robin (N = 18) eggs, from 24 and 10 clutches respectively. To avoid the potential confounds of annual eggshell colour differences [S20,S21], we only used these freshly abandoned eggs for estimates of perceivable differences in coloration. The mean host eggshell colour was established by first averaging the reflectance spectra of eggs within each abandoned clutch, and then taking the mean reflectance spectra of these clutches. All natural and foreign eggs were measured at three random locations over the entire egg surface or across the equatorial region, for blackbirds and robins respectively.
These raw reflectance spectra were analysed using the 'pavo' R package [S22]. All reflectance spectra were smoothed using a locally weighted polynomial with a 0.25 nm smoothing span, and averaged for each egg.
We modelled the relative sensitivities [S23-S25] of the blackbird's four photoreceptors with peak sensitivities at 373.0, 453.5, 504.3, and 557.2 nm [S26] and accounting for their oil droplet cut-offs at 330, 414, 515, and 570 nm respectively [S23]. We estimated achromatic quantum catch as the sum of the largest two cones. To quantify quantum catches for each photoreceptor [S27], we integrated the product of eggshell reflectance, blackbird spectral sensitivities, and standard daylight illumination scaled for bright viewing conditions (10,000) across the avian visual spectrum (i.e., 300-700nm). To generate avian tetrahedral colour spaces we used relative quantum catch estimates [S19,S27]. Then, for each species, we estimated the discriminability between the average host eggshell colour and the perceived colours of each foreign egg using a neural noise-limited visual model [S25,S28]. This model incorporated the quantum catches of each photoreceptor, while correcting for an experimentally derived signal-tonoise ratio such that the Weber fraction of the long-wave-sensitive cone was 0.1 [S29], and accounting for the abundance of cones and the principal member of the double cone [S23] of the blackbird. These calculations were performed for the four cone types and for the double cone estimates, and produced estimates for chromatic and achromatic contrast [S25,S30] between the average perceived colour of a host's egg and the foreign egg models in units of just noticeable difference (hereafter JND).

(d) Chromaticity diagrams
In addition, to the perceptual differences between host and foreign eggs (i.e., the multiple threshold decision rule) we were interested in the perceptual, directional differences within their colour space. That is, an infinite number of colours could differ from host egg colours by any particular JND value (e.g. 2 JNDs), but hosts may not respond to all of these different colours in the same way (i.e., the single threshold decision rule). Avian tetrahedral colour spaces [S19,S27] are not perceptually uniform, meaning the distance between two stimuli within the colour space does not directly translate into perceptual differences. Therefore, including the coordinates of foreign eggs within the avian colour space in our analyses would contain information on their directional differences, but the perceptual differences (e.g., Euclidean distances) between host eggs and these foreign eggs across the colour space would not be comparable.
To overcome this challenge and to account for the directionality of differences, we summarized perceivable variation in colour using perceptually uniform chromaticity diagrams [S31]. These chromaticity diagrams were calculated using the JND in colour between all experimental eggs and the mean colour for each species. These colour spaces were calculated such that, for each species, the species' average eggshell colour was set as the origin (i.e. zero on all three gradients). Within these chromaticity diagrams, the coordinates of each foreign egg represented the JND between that foreign egg and the mean host egg colour along each respective gradient. This approach allowed us to test the perceptual distances and their directionality, because along any gradient foreign eggs could have values greater (positive) or lower (negative) than the hosts' average eggs (e.g., an egg could differ by 1.9, 0.8, and −0.59 JND on the x, y, and z gradients respectively). When calculated in this way, the Euclidean distance between the origin and each point equalled that pair's JND in colour. We used the Cartesian coordinates from these chromaticity diagrams to examine both directional differences from the hosts' average eggshell colours and the perceptual differences of these comparisons.
The Cartesian coordinates from these perceptually uniform chromaticity diagrams spanned nonnoticeable and noticeable differences (i.e., −∞ ≤ JND ≤ ∞) along the two intentionally manipulated gradients (figure 2), but not the z gradient (ultraviolet variation) that was unintentionally manipulated by our treatment (figure S1). Importantly, all Cartesian coordinates were controlled for as covariates in our analyses, thus although ultraviolet variation did not span both negative and positive JNDs, we were able to control for the actual variation in each coordinate for the artificial eggs that were presented to each individual. In an absolute sense (i.e., the chromatic JND), 93% of the foreign eggs used on the blackbird and 100% those used on the robin were noticeably different (JND ≥ 1) from the hosts' average eggshell colours.

(e) Additional statistical details
Whole model significance was assessed by comparing a parameterized model with a null model including only an intercept using a test assuming asymptotic chi-squared distribution [S32]; while, for model coefficients we assessed significance using likelihood ratio tests [S32-S35]. To illustrate model fit we present Nagelkerke's R 2 and the small sample size corrected Akaike's Information Criterion (AIC c ) [S36,S37]. We examined potential interactions between chromatic JNDs and the x, y, and z Cartesian coordinates. These were non-significant and therefore not included in the global model; however, the significances, relative importance, and direction of parameter effects were the same. Similarly, we considered the possibility that laying date had a quadratic relationship with host response, but this did not influence our final models. Laying date controlled for the possibility that as the season progresses hosts become more experienced with parasitic eggs of if older experienced birds initiated nests earlier [S38]. Statistical parameters were chosen because each has the potential to impact our study species' response [S8,S11,S13,S39,S40].
We established a candidate set based on the relative likelihood of potential models.
Specifically, models with evidence ratios greater than 1/8 were considered reasonable and we included these models in the candidate set [S41,S42]. Although other methods are available for establishing a candidate set, this method is recommended [S41,S42] and produced very similar results to alternative approaches (e.g., based on delta AIC c and cut-offs and the 95% candidate set). We averaged models in this candidate set using the 'MuMIn' package version 1.13.4 [S43].
The relative importance of each predictor of host response was calculated as the sum of AIC c weights over all the models in the candidate set where that predictor occurs, setting the effect of a parameter at zero if it was not included in a particular model within the candidate set, to avoid biasing our model averaged estimates away from zero [S41].

(f) Host discrimination ability
To examine if blackbirds and robins expressed different discrimination abilities to experimental parasitism we compared the regression coefficients (i.e., slopes) of their predicted response curves, with respect to the blue-green to brown colour variation. To compare these parameters, we employed a non-replacement subsampling approach [S44-S46]. Specifically, we randomly selected 90% of the blackbird and robin data respectively and reran the GLM testing the single threshold decision rule, recording the regression coefficient (i.e., slope) for blue-green to brown variation repeatedly (10,000 times). This approach can consistently estimate statistic distributions under conditions where the bootstrap estimation would fail [S44]. The selection of subset size can be important for this approach [S47,S48], and we chose 90% because the subsampled distributions of blue-green to brown variation parameter estimates were stable for this value and approximated that of the entire (100%) dataset. We assessed normality using the 'ks.boot' function in the 'Matching' package version 4.8-3.4. These findings were corroborated using bootstrap estimates [S46,S49].
Due to the computational challenges of examining these subsampled and bootstrapped estimates (n =100,000,000), we conducted these nonparametric tests using the high performance cluster provided by MetaCentrum/CERIT-SC. This is a network of computers that have been made available by the Czech Education and Scientific Network and numerous participating universities within the Czech Republic.   Table S1. The approach employed by many studies makes assessing whether hosts base rejection decisions on either absolute perceived differences (e.g., multiple thresholds) or directional differences (e.g., single threshold) impossible. Studies often employ one of two common approaches: they examine directionless metrics of phenotype dissimilarity (e.g. just noticeable differences, JNDs), or they assess phenotypic variation on only one side of a host's phenotypic range. Here we provide a non-comprehensive account of how host responses have been investigated. These works are not limited to colour-based host responses because these cognitive mechanisms also apply to other traits. We indicate study focus (empirical: the focal host(s); theoretical: mathematical modelling), the phenotypic range considered (directionless: directionless metrics like JNDs or the statistical null hypothesis that disparate egg features elicit similar responses; unidirectional: one side of the hosts' phenotypic range was considered; bidirectional: both sides of the hosts' phenotypic range were considered), the phenotypic parameter used in the study (e.g., size, pigmentation, or mimicrywe distinguish theoretical estimates of mimicry from empirical estimates based on JNDs), whether this approach has the ability to detect responses based on either multiple or single thresholds, the basis for assumptions made (quote or equations, if any), and the reference. Few studies, including many of our own, were designed such that detecting directional differences was possible. For further information please see the main text. The cases are listed in chronological order. [S16] a This study also manipulated or examined other aspects of eggshell appearance. b The notation |mp−mH| denotes absolute value. This assumption (or similar assumptions) apply to even the most recent mathematical models considering host-brood parasite coevolution [S81]. Table S2. Generalized linear models predicting the rejection probability of foreign eggs by blackbirds and robins. Here the data were fit to a signal detection theory model based on the Gaussian cumulative distribution by specifying a probit link function [S82]. Parameter estimates and model specification is otherwise identical to table 2 (main text). We present statistical tests associated with the multiple threshold and single threshold decision rule scenario, including Nagelkerke's R 2 , AICc, and AICc weight (w i ) as whole model statistics. For each parameter we show the estimate, its standard errors (SE), 95% lower and upper confidence limits (LCL and UCL), z-score, and variance inflation factor (VIF). Significant models and effects are bolded.