curr-biol_si

Supplemental Experimental Procedures

Materials and Methods

Study Sites, Species and Measurements

We conducted field investigations at three sites on the main island (Grande Terre) of New Caledonia during three breeding seasons (September-January) from 2011 to 2014: Parc provincial des Grandes Fougères (main study site) and near surroundings (21°37’39.44” S, 165°45’41.75” E), approx. 40 km west (21°35’58.89” S, 165°23’55.61” E) of the main study site, and approx. 130 km northwest (20°41’45.55” S, 164°59’38.41” E) of the main study site.

The fan-tailed gerygone Gerygone flavolateralis flavolateralis is a passerine bird of the family Acanthizidae and an endemic subspecies to New Caledonia. The shining bronze-cuckoo Chalcites lucidus layardi is a brood parasitic cuckoo of the family Cuculidae, and also an endemic subspecies to New Caledonia. Both are abundant and widespread throughout Grande Terre year-round, and the gerygone is exclusively parasitised by the bronze-cuckoo [S1].

To measure reflectance, we captured 32 gerygone chicks from 18 broods (dark: N = 5; bright: N = 11; polymorphic: N = 2), out of which 22 were of the bright morph and 10 were of the dark morph. We also captured 3 shining bronze-cuckoo chicks to measure reflectance, which all were of the bright morph. We measured reflectance spectra of light from 300 nm to 700 nm wavelengths from their skin (Figure S1a) using spectrophotometers (USB-2000 and Jaz-EL-200, Ocean Optics, Dunedin, Florida, USA) with light irradiated by a deuterium-tungsten-halogen light source (DT-MINI-2-GS, Ocean Optics, Dunedin, Florida, USA). Before measurements, we calibrated the spectrometer with a diffuse reflectance standard (WS-1, Ocean Optics, Dunedin, Florida, USA). Measurements were carried out in a film-changing bag (E-7041, Etsumi, Tokyo, Japan) to block ambient light. while holding chicks by hand, we placed the probe vertically above their skin, keeping an approximately 2-mm distance ensured by insulating tape winded around the probe. To avoid injuring gerygone chicks, we conducted measurements when they were at least 3 days old, while cuckoo chicks were measured on the day of hatching before host parents ejected them. We measured reflectance spectra of bare skin on the back of each chick twice (except for 4 chicks that we could only measure once). This usually took only few minutes, thereby avoiding potential negative effects on chicks. From the 35 chicks, we obtained 66 reflectance spectra in total (dark: n = 18; bright: n = 42; cuckoo: n = 6).

Because host parents were likely to eject cuckoo chicks, we artificially incubated 2 cuckoo eggs to measure reflectance spectra of hatchlings (Mini Advance Incubator, Brinsea, Wiscombe, North Somerset, UK). We conducted measurement for one cuckoo chick that hatched naturally in the host nest before being ejected by the host. All artificially hatched cuckoo chicks were reintroduced in the nearest active nest on the day of hatching in the case that the original nest was depredated. We placed an artificial cuckoo egg in the nest at least 24 h before we replaced it with a cuckoo chick.

Skin Colour Polymorphism in Chicks

There was neither a sign of colour polymorphism in adults nor a sign of assortative mating in relation to the chick skin colour polymorphism in the gerygone since there were no detectable differences in adult songs and plumages between parents of dark and bright chicks (authors’ unpublished data), which are known as indices of prezygotic isolation in birds [S2, S3]. Both dark and bright gerygone chicks were found sympatric in all study sites.

The skin colour polymorphism of host chicks was most remarkable just after hatching, and weakened with chick age (authors’ unpublished data). It became almost indistinguishable in chicks of ca. 13-15 days of age. We occasionally measured reflectance from chicks older than 5 days (2 bright and 3 dark chicks in 3 nests), but not from chicks 10 days or older. The polymorphism was not related to deformation of pigmentation such as albinism [9], since no bright chick had red irises or a pinkish bill, or fibromelanosis [S4].

We have no evidence for sympatric polymorphism in the bronze-cuckoo but photo evidence of a dark morph (Figure 1C) was published 35 years ago [S5] and taken in Parc provincial de la Rivière Bleue, approx. 100 km southeast of the main study site. Chick colour polymorphism is known in the shining-bronze cuckoo, though in different subspecies, and respective cuckoo morphs mimic chicks of respective hosts in different colours [7, 9, S6].

Avian visual model

Birds are thought to have two distinct pathways to perceive a colour, i.e., chromatic (hue) and achromatic (luminance, or perceived lightness) [S7-S9]. We estimated both chromatic [S7] and achromatic [S9] discrimination thresholds of the chick skin colours, respectively, based on the Vorobyev-Osorio model [S7, S9]. Birds of the genus Gerygone have VS (violet-sensitive) vision [S10]. However, because data of the visual performance of the study species were not available, we applied hitherto available single-cone sensitivity of a VS-type bird, the wedge-tailed shearwater Puffinus pacificus [S11], the double-cone sensitivity of the blue tit Cyanistes caeruleus [S12], and the single-cone abundance in the posterior dorsal area of retina of the satin bowerbird Ptilonorhynchus violaceus [S13], all phylogenetically closest to the gerygone among species with available information.

We first calculated photon capture Q_i with sensitivity of respective photoreceptors C_i (λ) and measured reflectance spectra R (λ) according to the following equation:

.

We then calculated the colour discrimination threshold, i.e., just noticeable difference (jnd), between a given pair of colours. Jnds were obtained from the following equations:

Figure S2. a) Expected brood-type frequency at Hardy-Weinberg equilibrium in relation to recessive allele frequency, with a constant brood size C within population, according to the model described in the supplementary text. y and z represent the frequencies of parental genotypes in population, heterozygotes and recessive homozygotes, respectively. Red lines indicate the frequencies of polymorphic broods (b_p), and the blue line that of monomorphic broods (b_m) among the potential mating combinations (note that b_p = potential – b_m). b) Simulated expected frequencies by the model in relation to recessive allele frequency. Line colours denote each brood type. Horizontal lines indicate the observed frequencies of phenotype, assuming the dark morph as dominant (solid) and as recessive (dashed); observed frequencies of brood types (red): polymorphic (solid), dark monomorphic (dotted), and bright monomorphic broods (dashed). c-f Positions of the observed frequencies (indicated by red arrows and percentile values) of respective categories among the distributions of simulated expected frequencies, assuming the dark morph as dominant (shaded bars) and as recessive (open bars): phenotype (c), dark monomorphic (d), bright monomorphic (e), and polymorphic broods (f). Percentile values are underlined for dominant. Vertical lines indicate the mean of simulated frequencies when assuming the dark-morph as dominant (dashed) and as recessive (solid). Bin widths of all histograms were optimised by setting the breaks argument as “Scott” for the hist function default in R [S18].

(S1b)

for luminance [S7], where ∆f denotes the log ratio of photon captures of the focal pair of measured colours by a given type of photoreceptors:

,

and ω denotes the relative abundance of each single-cone type in the posterior dorsal area of the retina, with incorporating the Weber fraction of 0.05, the conventionally adopted error rate (i.e., noise-to-signal ratio) in the Weber-Fechner law [S7]. Since fan-tailed gerygones build domed nests in which the inside is dimly lit, we considered fluctuation of the number of photons captured by cone cells (i.e., shot noise) as a relatively great quantal flux of 10³ [S14]. We did not consider colour constancy because the ambient light condition should be very similar for all chick types.

Statistics

We first calculated jnds between all possible combinations of measured colours for both hue and luminance respectively based on equations S1a and S1b [S5, S7]. Next, we converted these jnds into respective distance matrices, from which we calculated tridimensional coordinates through a principal coordinate analysis (PCoA, or multi-dimensional scaling, MDS) [S15, S16].Each principal coordinate consists of a set of data, each of which corresponds to each photospectral measurement, and thus the total number of replicates analysed was n = 66. Each coordinate value indicates the relative position of each datum among the whole dataset, i.e., distance from the centroid, on each coordinate axis in its unit (jnd in this case) (see Figure S1d). Unlike jnd (i.e., psychophysical distance), all coordinate values are geometrically independent of each other, and thus the dataset is compatible with linear models [S15, S16]. Eigenvalues were used to assess the accuracy of primary eigenvectors (i.e., first principal coordinates). The rationale underlying this procedure is illustrated in [S15] and [S16].

We analysed the first principal coordinates for hue and luminance with linear mixed models (LMMs), in which brood ID and nestling ID nested within brood were assigned as random effects to avoid pseudoreplication [S15]. We assigned dummy variables [S16, S17] to each chick type, i.e., dark chick, bright chick and cuckoo chick, and set bright chick as the intercept in the LMMs. Representative values for respective chick types were calculated as the absolute value of the difference of partial coefficient from the intercept, i.e., |cuckoo chick – bright chick| and |dark chick – bright chick|. These values represent the perceivable difference of respective chick types from bright chick on average, and thus can be interpreted as chromatic (hue) or achromatic (luminance) discriminability [S15, S16]. We assumed jnd > 3 as discriminable by convention [S9]. Goodness of fit was tested by the likelihood ratio (χ²) test.

For the analyses of the observed data, we conducted a contingency (χ²) test, a binomial test, and a generalised linear model (GLM) with a likelihood-ratio (χ²) test. All statistical procedures were conducted in R [S18]. PCoAs/MDSs were conducted with the cmdscale function, setting the dimensional parameter k as 3 because jnds existed in a tridimensional colour space. LMMs were conducted with the lmer function in the lme4 package [S19] and the GLM the glm.nb function in the MASS package [S20]. Likelihood ratio tests were conducted with the Anova function in the car package [S21]. Figure S1a was drawn with the aggplot function in the pavo package [S22].

Population Genetics Model

We assumed 1-locus-2-allele complete dominance as the inheritance mechanism, which was most probable in this case because the colour difference appeared to be discrete, as we have not observed hatchlings of an ambiguous type. The observed frequency of within-nest polymorphism might be biased or obscured in several ways: an inevitable bias caused by small brood sizes, i.e., no polymorphism in single-chick broods irrespective of parental genotypes; an observational bias, i.e., before we found a nest, polymorphism in there might have already vanished due to randomly caused partial brood mortality (including that caused by brood parasitism); and a small sample size. To deal with such bias and uncertainty, we simulated stochastic distributions for expected frequencies of phenotype, monomorphic brood of each morph, and polymorphic brood at Hardy-Weinberg equilibrium. These values represent the frequency of phenotype and respective brood-types, ideally obtainable in a limited number of observations and at a low average brood size of the population when the population is at the equilibrium. We assumed genetic monogamy of parents (i.e., chicks in a nest have the same genetic parents) and our observation to be random sampling for simplicity.

On allele frequencies at even intervals, offspring phenotypes were randomly sampled assuming a binomial distribution with coefficients for the emergence probabilities of respective brood types based on equations described below. parameter values were set at 33 for sample size assuming a Poisson distribution, and set for brood size ranging from 1.525 to 3.350 in integer assuming a uniform distribution (average 1.93), in reference to our observation (see Results). We iterated the sampling 500 times in R [S18].

We extracted a pair of simulated samples of phenotype frequency, each assuming the dark morph as either recessive or dominant, from samples in each iteration, among those which were nearest to the observed phenotype frequency of chicks. The brood-type frequencies and allele frequencies corresponding to the extracted phenotype frequencies were also extracted. We compared the position (i.e., percentile) of the observed frequencies of phenotype and respective brood-types within the corresponding simulated distributions of expected frequencies between recessive and dominant (see Figure S2). These simulated percentiles were resampled with the parametric bootstrapping method (iteration = 1000). The minimum requirement for Hardy-Weinberg equilibrium here is that all the observed frequencies are simultaneously contained within the corresponding simulated distributions respectively.

Equations for Population Genetics Model

When the genotype frequency in the parental generation is x for dominant homozygotes (AA), y for heterozygotes (Aa), and z for recessive homozygotes (aa), the expected genotype frequency in the offspring generation under Hardy-Weinberg equilibrium is

X =

, Y =

, and Z =

, where X denotes dominant homozygotes, Y heterozygotes, and Z recessive homozygotes; note that x + y + z = X + Y + Z = 1. The emergence of polymorphic broods is potentially limited in those from parents of the Aa-Aa pair (both heterozygotes; y²) and the Aa-aa pair (heterozygote and recessive homozygote; 2yz). However, the emergence of polymorphic broods is also limited in situations that brood size, C, is two or greater, and thus, the emergence probability of each brood type is:

b_D: x² + 2xy + 2xz (S2a)

b_p:

(S2b)

b_m:

(S2c)

b_R: z² (S2d)

where b_D denotes dominant monomorphic broods, b_p polymorphic broods, b_m monomorphic broods of either from the potential mating combinations, and b_R recessive monomorphic broods (Figure S2a). b_p and b_m are complementary to each other and thus sum up to y₂ + 2yz (“potential” in Figure S2a); when C is 1, b_p is always 0 and b_m is always y² + 2yz (Figure S2a).

Ethical Notes

We conducted fieldwork under permissions from Province Sud and Province Nord of New Caledonia. No chick died because of our treatments. The research protocol complies with the current laws in New Caledonia, and was approved by the ethical committee of life-sciences at Rikkyo University in Tokyo, Japan, and the First Warsaw Local Ethics Committee for Animal Experimentation in Warsaw, Poland.

Results

Colour Discriminability

We described the results for achromatic discriminability in the main text. The distribution of measured colours (in hue) overlaps in the tetrachromatic colour space of VS birds irrespective of chick types (Figure S1b, c). Eigenvalues of first principal coordinates were 3.00 (100% of variance explained) for luminance and 2.47 (82% of variance explained) for hue (Figure S1d, e), and thus they well represented the distribution of measured colours.