Aggressive mimicry in a coral reef fish: The prey's view

Abstract Since all forms of mimicry are based on perceptual deception, the sensory ecology of the intended receiver is of paramount importance to test the necessary precondition for mimicry to occur, that is, model‐mimic misidentification, and to gain insight in the origin and evolutionary trajectory of the signals. Here we test the potential for aggressive mimicry by a group of coral reef fishes, the color polymorphic Hypoplectrus hamlets, from the point of view of their most common prey, small epibenthic gobies and mysid shrimp. We build visual models based on the visual pigments and spatial resolution of the prey, the underwater light spectrum and color reflectances of putative models and their hamlet mimics. Our results are consistent with one mimic‐model relationship between the butter hamlet H. unicolor and its model the butterflyfish Chaetodon capistratus but do not support a second proposed mimic‐model pair between the black hamlet H. nigricans and the dusky damselfish Stegastes adustus. We discuss our results in the context of color morphs divergence in the Hypoplectrus species radiation and suggest that aggressive mimicry in H. unicolor might have originated in the context of protective (Batesian) mimicry by the hamlet from its fish predators rather than aggressive mimicry driven by its prey.

Indeed, in a recent genome-wide analysis, hamlet species only consistently differed from each other at genomic regions that contained loci implicated in the production or perception of color pattern (Hench et al., 2019). Various authors have suggested that the hamlets' exceptional color diversity might be the result of aggressive mimicry of a number of non-predator model species by different hamlet morphs (Domeier, 1994;Fischer, 1980;Holt et al., 2008;Puebla et al., 2018;Randall & Randall, 1960;Thresher, 1978;. Here, the mimic species takes the appearance of a non-predatory species in order to get close to a potential prey, small fish and epibenthic invertebrates, without eliciting an escape reaction.
For those hamlet morphs considered mimics, one or more candidate models have been proposed, typically co-occurring herbivore, corallivore or spongivore fish species, harmless to hamlets' prey and exhibiting various degrees of resemblance, as judged by a human viewer, to the corresponding hamlet morph (Domeier, 1994;Fischer, 1980;Puebla et al., 2007;Randall & Randall, 1960;Thresher, 1978). However, the plausibility of aggressive mimicry in hamlets rests only on these apparent color pattern similarities. A notable exception is the work of Puebla and coworkers on a butter hamlet H. unicolor population in Panama (Puebla et al., 2007(Puebla et al., , 2018. The authors showed that the proportion of butter hamlet strikes toward their prey was significantly higher when associating with their putative model, the four-eye butterflyfish Chaetodon capistratus, than when striking alone, suggesting a possible fitness advantage consistent with aggressive mimicry in the butter hamlet. Despite frequent reference to aggressive mimicry as an evolutionary engine of hamlet diversification (Domeier, 1994;Fischer, 1980;Puebla et al., 2007;Thresher, 1978), we still lack a basic understanding of hamlet preys' visual abilities and their potential for effective discrimination of predatory hamlet color morphs from harmless (putative) models. Here we consider three widely distributed hamlet species, the putative mimics butter hamlet (H. unicolor) and black hamlet (H. nigricans), and the non-mimic barred hamlet (H. puella). We examine the visual system of two of their most common prey, namely an epibenthic coral reef fish and an open-water mysid shrimp, both in terms of color vision and visual acuity. Using spectral reflectance measurements of equivalent patches on each hamlet morph and their putative models and modeling of preys' visual sensitivity and acuity, we gain insight into the potential for deception of each mimic hamlet morph through the eyes of their prey.

| Study site and species
Field work was conducted in the Bocas del Toro Archipelago, Panama, on the same reef complex (Punta Caracol;GPS 9°21'38.449'' N,82°16'40.803'' W), where the association between H. unicolor hamlets and the butterflyfish C. capistratus had been previously observed by Puebla et al. (2007). Fish were collected while SCUBA diving by hook-and-line or with hand nets at depths of between 3−8 m and then kept briefly in 80 cm × 80 cm × 50 cm outdoor aquaria with running seawater, before data collection.
We considered a non-mimic hamlet, the barred H. puella, and two model-mimic putative pairs: (i) the butter hamlet (H. unicolor) and its model, the four-eye butterflyfish (Chaetodon capistratus); (ii) the black hamlet (H. nigricans) and its model the dusky damselfish (Stegastes adustus). In addition, we collected the two most common hamlet prey encountered in hamlet stomach contents, in the Bocas del Toro populations (Puebla et al., 2007), the masked goby (Coryphopterus personatus) and a mysid shrimp (Mysidium columbiae). C. personatus is a microbenthic goby occurring in large schools hovering above coral heads and feeding on plankton (Böhlke & Robins, 1962).

| Underwater spectral irradiances
We characterized the underwater photic environment on the Punta Caracol shallow coral reefs (Bocas del Toro, Panama) where the hamlet morphs, their models and their prey were collected by measuring spectral irradiances just under the surface and at 2.5 m, 5.0 m and 7.5 m depth above hamlet territories, from downwelling, upwelling and sidewelling underwater light (detailed methods in Appendix 1).

| Fish body reflectance
A number of equivalent areas on the fish body showing clear differences in coloration between two or more species were identified and used to build a set of 7 "homologous" landmarks, shared by all hamlets and their putative models. Reflectance measurements were taken from these landmarks across species, with a 200 µm UV/vis bifurcated fiber optic cable connected to an Ocean Optics USB2000 spectrometer and an Ocean Optics PX-2 pulsed xenon light source.
Individuals were placed over a damp cloth and their skin maintained wet, following the guidelines of Marshall (2000). Reflectance records, obtained keeping both ends of the bifurcated fiber at approximately 45 degrees above the color patches, were calibrated against a Spectralon (Labsphere, North Sutton, NH) white standard.

| Masked goby
We characterized the spectral sensitivity of the masked goby visual pigments by microspectrophotometry, as in Loew (1994) (detailed in Appendix 1). Lens transmission was measured directing light from the pulsed xenon light source through the lens mounted on a pinhole into a UV/vis fiber optic cable connected to the Ocean Optics USB2000 spectrometer. Lens transmission was expressed in terms of the 50% cutoff wavelength (T 50 ) calculated from transmission spectra normalized to their maximum transmission between 300-700 nm.

| Mysid shrimp
Opossum shrimp (Crustacea: Mysida) have superposition eyes (Hallberg, 1977). Visual sensitivity has been studied in depth in the genus Mysis, with evidence for a single visual pigment, with peak of spectral absorbance (λ max ) positioned in the waveband 520-525 nm in marine populations (Audzijonyte et al., 2012;Jokela-Määttä et al., 2005). In the absence of available data on visual sensitivities in Mysidium, we chose a value of 520 nm, consistent with values in the related Mysis. Vorobyev and Osorio's (1998) color discrimination model was used to derive chromatic distances between corresponding color patches in hamlets, their models and natural backgrounds as perceived by a masked goby and by a mysid shrimp (visual modeling detailed in Appendix 1). The model assumes that the limits to color discrimination are set by noise arising at the photoreceptor level and color distances are expressed in multiples of the theoretical detection threshold, the just noticeable difference (JND). We tested whether perceptual distances in color (dS) and luminance (dL) of corresponding patches on hamlets and their putative models were statistically different with a PERMANOVA approach, using color and luminance distances in just noticeable difference units (JNDs), with the adonis function in the R package vegan (Oksanen et al., 2007). Prior to this, we tested the assumption of homogeneity of multivariate dispersions for each patch across species using a multivariate extension of Levene's test for homogeneity, with the "betadisper" function in vegan, followed by Tukey's HSD test to inspect differences between the multivariate dispersions (Anderson, 2006;Seber, 1984). The distance-based PERMANOVA analysis was used to generate a pseudo-F statistics from the ratio of among/within distances between groups, and to obtain a null distribution by randomizing distances between observations (Anderson, 2005). We used 999 permutations to test for significant deviation from the null distribution and used the R 2 as an estimate of effect size. Post hoc tests were performed with the pairwiseAdonis function (Martinez Arbizu, 2019), returning adjusted p-values on the pairwise comparisons.

| Color and luminance discrimination
We then assessed whether the effect size of the above differences between model and mimic was sufficiently large for the visual system of the receiver (i.e., the prey: masked goby, mysid shrimp) to perceive them, using a bootstrap procedure (Maia & White, 2018) as implemented in pavo. For each bootstrap run, Maia and White (2018) approach samples points (patches) from each group (species) of the same size of the original group and with replacement and then estimates the distance in color space, based on noise-corrected quantum catches, between the geometric means of the bootstrap resample.
Bootstrapping allows to generate a distribution of these means and a confidence interval to be calculated. Confidence intervals above the perceptual threshold are considered likely discriminable by the viewer. All analyses were run separately using the mysid shrimp and the masked goby visual systems, the latter under both a dichromatic and a trichromatic scenario.

| A prey's view of natural scenes
We wished to gain insight into the spatial information available to masked gobies and mysid shrimp, when attempting the discrimination of a hamlet from its model in a natural scene. We applied the method of Caves and Johnsen (2018), implemented in the R package AcuityView (R Development Core Team, 2016) which uses a Fourier transform approach to convert an image from spatial into frequency domain, then multiply it pixel by pixel by a modulation transfer function (MTF). This method uses Snyder's (1977) MTF, which is a function of the minimum resolvable angle of the viewer. The result is an image that is devoid of all the frequencies above a threshold corresponding to the viewer's acuity. After inverse Fourier transform to spatial domain, the image retains the level of detail that lies above the contrast threshold dictated by the viewer's acuity and therefore provides us with insight into the information content available to the prey viewing a scene including a predator, the hamlet, or a harmless "passer-by," the model species (image collection and processing detailed in Appendix 1).
Underwater observations of feeding hamlets in Bocas del Toro populations (pers. obs., 2015-2017) showed that they can rush from a distance of more than 4ft toward a dense cloud of mysids or masked gobies, stopping for about 1-2 s at a distance of less than 50 cm (i.e., about five body lengths) away from the prey, for precision aiming at a single individual. They then strike horizontally when preying on mysids and from above at about 45° when striking at masked gobies.
Given this pattern of predatory behavior, we considered that a mysid or a masked goby would have a reasonable chance of evading a predatory strike if it recognized an approaching predator and initiated escape at a distance over three hamlet body lengths away, that is, about 25 cm distance. We used these two values, 50 cm and 25 cm as the relevant viewing distances d, in the image analysis. The angle α subtending the scene is then α = 2arctg(actual width/2d).

| Masked goby acuity
We assessed the acuity of the masked goby C. personatus in terms of its optical anatomy, based on ganglion cell densities (Coimbra et al., 2012;Collin & Pettigrew, 1988a, 1988b. Therefore, we consider these estimates as representing an upper limit to the masked goby acuity. To do this, we analyzed the population of ganglion cell layer (GCL) cells and estimated the upper limits of spatial resolving power from two retinas from two C. personatus individuals. (see Appendix 1 for protocol).

| Mysidium shrimp acuity
Behavioral estimates of visual acuity are available for the mysid shrimp Mysidium columbiae, based on optomotor response experiments (Buskey, 2000). Under conditions of optimal illumination, individuals placed in an optokinetic drum, followed vertical black and white stripes of varying width consistently resolving differences down to 6 mm from a minimum distance of 15 mm. Given the known relationship between subtended angle α, reactive distance d and stripe width w: α = 2arctg(0.5w/d), this corresponds to a subtending arc of 7.66 degrees, the value of behavioral acuity we used in the spatial patterns analyses.

| Underwater spectral irradiances
Downwelling spectral irradiance over our study site had typical characteristics of tropical reef waters ( Figure 1) with similar λP 50 (the wavelength that halves the total number of photons, Munz & McFarland, 1973), across depths (under the surface: 516 nm; 2.5 m: 516 nm; 5.0 m: 512 nm; 7.5 m: 520 nm) and values very close to those measured by McFarland and Munz (1975)  Upwelling irradiance at maximum depth, closer to the bottom of this shallow reef system, was shifted to longer wavelength ( Figure 1) as a result of the mixed composition of the bottom, consisting of coral outcrops interspersed with yellow sand patches. As the distance from the bottom increased, the upwelling spectrum shifts to shorter wavelengths and to a spectral profile similar to the downwelling and sidewelling spectra (see also Appendix 1).

| Fish body reflectances
Spectral reflectance measurements were collected from 7 homol-

| Masked goby visual sensitivity
We collected spectral sensitivity of both rods and cones from the retinas of n = 4 C. personatus individuals. The retina of masked gobies appeared rod-dominated (rods mean and SD: λ max = 500.2 ± 1.48 nm, range 497 ÷ 503, n = 17). Double cones showed either the same visual pigment at 539 nm (λ max = 538.8 ± 1.28; range 537 ÷ 541; n = 13) or one member with λ max = 539 nm and the other with λ max = 531 nm (λ max = 530.9 ± 1.51; range 527 ÷ 533; n = 21). We did not find any evidence for short-wavelength cones. The very small distance between the two green-sensitive cone λ max (531 nm, 539 nm) is unlikely to provide the masked goby with true color vision (see also the results of the visual models with dichromatic and trichromatic vision, Figure 4 and Figure A2) but might confer the fish broader sensitivity in that particular region of the light spectrum. Overall, these results are in line with previously reported spectral sensitivities from other tropical gobies (Table A1). In particular, the absence of a short-wavelength cone in C. personatus is a condition shared with the only other coral reef goby for which MSP data are available. However, we cannot exclude that small blue or violet cones might be present in very low frequencies in the masked goby retina, given the sampling design typical of microspectrophotometry. For this reason (see below), we considered both a visual model that includes the cone repertoire found by our MSP study and an additional one that incorporates a third short-wavelength cone, positioned in the region of sensitivity characteristic of other gobies (λ max ≈ 455 nm), that would potentially confer trichromatic color vision to the goby (Figure 3 top, main text; Table A1, Appendix 1).

| Masked goby lens transmittance
We examined the eye lenses of n = 3 individuals. The wavelength at which 50% of the maximal transmittance was reached F I G U R E 1 Downwelling (top), upwelling (center), and average sidewelling (bottom) irradiances, measured at Punta Caracol, Bocas Del Toro, Panama, on a vertical depth profile, just under the surface (-), 2.5 m (-), 5.0 m (---) and 7.5 m (⋯) (T 50 = 410÷411 nm) and the shape of the transmittance curve suggest that there is little scope for UV signals reception in this goby species (Figure 3, bottom).

| Masked goby
The PERMANOVAs of differences in dS and dL between corresponding patches across species, calculated at different depths, and with either two (531 nm, 539 nm) or three (455 nm, 531 nm, 539 nm) cone classes, were all significant (p < .001; Table S1-Dryad Archive).
Post hoc tests on chromatic distances dS showed that for almost all species pair contrasts, at least three or more patches on the body were significantly different between species. The exceptions were the two putative model-mimic pairs: the butter hamlet H. unicolor and its model, the butterflyfish C. capistratus, were not significantly distinguishable in color at any of the measured patches, when the viewer had the 531/539 nm cone set and distinguishable by one patch (#1) only, when the viewer was provided with a 455/531/539 nm cone set, and this irrespective of depth. In the black hamlet H. nigricans and its putative model, the damselfish S. adustus, two patches (#3, #7) were significantly different in color between species when seen by a 531/539 nm viewer and three patches (#1, #3, #7) when seen by a 455/531/539 nm viewer, although not at all three depths (Table S1-Dryad Archive). Post hoc tests on achromatic distances dL reveal that at least four and up to all seven patches were significantly different (p < .05) across species at any depth, with the only exception of the model-mimic pair butter hamlet H. unicolor and butterflyfish C. capistratus for which all seven patches were indistinguishable (p > .21) between species, irrespective of depth and cone set of the goby.
Whether the significant differences in color and luminance found between species are of a magnitude detectable by the viewer (perceptual effect size) was tested by calculating distances between the geometric means of each species and generating confidence intervals by bootstrapping (Maia & White, 2018). We found that the only patch that was significantly different in the PERMANOVA analysis between the H. unicolor-C. capistratus mimic-model pair, when the goby was provided with three visual pigments 455/531/539, is effectively in-  (Table S2-Dryad Archive), in line with a model-mimic hypothesis. All other species pair contrasts were above threshold when modeled with a 455/531/539 cone set, while chromatic contrasts between the pair S. adustus-C. capistratus were below threshold when modeled with a 531/539 goby visual system (Table S2-Dryad Archive).
The bootstrap analysis of achromatic contrasts revealed that for one species pair only, the putative mimic-model pair H. unicolor-C. F I G U R E 2 Mean spectral reflectance and standard deviation of body patch #5 (center of left pelvic fin, indicated here as a red spot on the images) across species. Top: from top, four-eye butterflyfish C. capistratus (putative model 1), butter hamlet H. unicolor (putative mimic 1) and the non-mimic barred hamlet H. puella. Bottom: from top, the non-mimic barred hamlet H. puella and the black hamlet H. nigricans (putative mimic 2), and bottom, the dusky damselfish S. adustus (putative model 2) capistratus, luminance distances were always below threshold (mean dL < 1 for all patches, trichromatic goby: Figures 4 and 5), consistent with a model-mimic scenario. All other species contrasts contain more than one patch that can be discriminated between species by the goby based on achromatic distances, including the second putative pair, H. nigricans-S. adustus ( Figure 4 and Figure A2, Table S3-Dryad Archive).

| mysid shrimp
The PERMANOVAs of differences in dL between corresponding patches across species, modeled with a single visual pigment and calculated at different depths were all significant (p < .004). Post hoc tests showed that at least four and up to all seven patches were significantly different (p < .05) across species at any depth, with the single exception of the model-mimic pair butter hamlet H. unicolor and butterflyfish C. capistratus for which all seven patches were indistinguishable (p > .23) between species, irrespective of depth (Table S3-Dryad Archive).
The bootstraps of species groups showed that at least five patches were above detection threshold (dL > 1) in any two species contrast ( Figure A3, Table S4-Dryad Archive). The notable exception is the pair H. unicolor-C. capistratus, for which all spots were below theoretical detection threshold (dL < 1), suggesting that putative mimic (H. unicolor) and model (C. capistratus) are unlikely to be discriminable by the mysid shrimp based on achromatic contrast between corresponding patches. The achromatic differences in the second putative pair, H. nigricans-S. adustus, are all above threshold.

| A prey's view of natural scenes
Visual acuity in the masked goby was estimated from the total number of cells in the ganglion cell layer of two retinal wholemounts from different C. personatus individuals. An average cell population of 179,769 ± 12,914 was obtained (Table 1), with high densities observed in the retinal periphery and peak density located in the ventral region (89,400 cells/mm 2 ) while lowest densities were observed in the central retina (1,200 cells/mm 2 ). The upper limit of the spatial resolving power estimated from lens radius and the maximum density of GCL cells was 2.356 ± 0.14 cycles/deg, corresponding to a minimum resolvable angle (MRA) α = 0.425 ± 0.02 degrees ( Table 1). The number of sites counted for each retina, Scheaffer's coefficient of error (CE) and area of sampling fraction (asf) are described in Table 1. Shrinkage was below 5% and considered negligible (Coimbra et al., 2006). For the mysid shrimp, we used Buskey (2000)'s acuity estimate of α = 7.66 degrees (or 0.13 cycles/degree). F I G U R E 3 Top: Absorbance templates (from Govardovskii et al., 2000;Lipetz & Cronin, 1988), representing the rod (501 nm; in gray) and cone visual pigments (531 nm, 539 nm; in green) found in the retina of the goby Coryphopterus personatus; an additional blue cone pigment (455 nm; in blue) was added, in an alternative modeling scenario (see main text). Bottom: Lens transmission spectrum of the masked goby C. personatus. The T 50 is located at 410 ÷ 411 nm The underwater images taken at Punta Caracol and Punta Juan, in Bocas del Toro, Panama, were modified to account for the spatial resolution of C. personatus masked gobies and Mysidium shrimp.
After processing, they provide a first approximation of scenes including models or putative aggressive mimics, as perceived by the prey, masked goby or mysid shrimp, given their visual acuity. The Fourier analysis of natural scenes suggests that Mysidium columbiae shrimp are only able to discern, even at relatively small distances (25 cm) bright moving versus dark moving objects in their field of view. While temporal resolution was not considered in this study, overall the visual system of this mysid shrimp would be unable to distinguish, at the distances considered, a harmless moving target from a predator, F I G U R E 4 Color distances dS (on the left, in each box) and achromatic distances dL (on the right, in each box) and their 95% bootstrap confidence limits, for each species pair viewed by the prey, a masked goby visual system with 455 nm, 531 nm, 539 nm cone pigments, at a depth of 5 m. A continuous line, corresponding to dS (or dL) = 1, marks the perceptual threshold, below which a particular patch (#1-7, indicated in the fish silhouette on the left) is likely indistinguishable by the viewer. When distances dS, dL are larger than 5.5 units of JND, they are presented with an open dot at the top end of their respective box. Discriminable patches (either because dS or dL > 1, or both) are represented by gray-shaded boxes F I G U R E 5 Chromatic (dS) and achromatic distances (dL) and their 95% bootstrap confidence limits, for the mimicmodel pair H. unicolor and C. capistratus, at different depths (2.5 m, 5.0 m, 7.5 m), viewed by the prey, a masked goby with a trichromatic 455 nm, 531 nm, 539 nm visual system (red lines) or a dichromatic 531 nm, 539 nm visual system (black lines) TA B L E 1 Stereological assessment of the population of cells in the retinal GCL of Coryphopterus personatus and the anatomical parameters used to estimate the upper limit of spatial resolution

The extraordinary variation in color patterns between
Hypoplectrus hamlets has long been attributed to aggressive mimicry (Domeier, 1994;Fischer, 1980;Puebla et al., 2007;Randall & Randall, 1960;Thresher, 1978). However, apart from such comparisons frequently based on color flash-enriched photographs, no attempt has been made to examine the resemblance of hamlets to the proposed models from the meaningful perspective of the intended signal receiver under natural light conditions. In a case of aggressive mimicry such receiver is a hamlet prey. Here we exam-  In addition, the limited visual resolution of both preys suggests that, at biologically significant distances, differences in the fine patterns over a relatively homogeneous yellow coloration of butter hamlet and butterflyfish are likely to be imperceptible. The co-occurrence of model and mimic H. unicolor-C. capistratus in Figure 6, as seen by a masked goby, provides hints on how the deceit might be ob- to the human eye at close range and ideal illumination, but is much harder to detect in natural underwater illumination at any biologically meaningful distance. The anatomical acuity assays for both prey species and their representation in the Fourier image analysis suggest that at best only the black eyespot is discernible by either prey at the typical distances (25-50 cm) at which the species interact during a predation event, making color pattern analysis redundant for the purpose of this study focusing on these two pairs of models and mimics.
The non-mimic barred hamlet (H. puella) sports complex color patterns with high-contrast dark vertical bars and considerable differences in luminance and hue with both model species. A barred hamlet at close distance from its prey is likely to be easily identified by the typical highly contrasting dark vertical bars over a comparatively brighter yellowish body, even with the very limited acuity of a goby, as suggested by the Fourier transform analysis ( Figure 6). It is interesting to note that barred and more complex disruptive patterns are also typical of other sympatric basses and all invariably attack their prey almost horizontally while close to the substrate. On the contrary, butter hamlets are often seen attacking from about 45 degrees above F I G U R E 6 Monochromatic images of Hypoplectrus hamlets in a natural scene, at a depth of 5 m, on a coral reef in Bocas del Toro, Panama, as seen by the two main prey of hamlets, that is, the masked goby C. personatus and a M. columbiae shrimp, at the distances in which interactions between these species are known to occur. Acuity, expressed as minimum resolvable angle in degrees, is shown for each viewer masked gobies (pers. obs.). From this line of view the hamlet silhouette and color is remarkably similar to that of a four-eye butterflyfish, in particular the very conspicuous structural yellow pelvic fins ( Figure A4). Notably, while the color of pelvic fins in hamlets is highly variable between individuals within morphs, from colorless to bright yellow to highly saturated indigo or blue, this does not seem to be the case for butter hamlets, invariably sporting bright structural yellow on their pelvics with very similar hue to that of four-eye butterflyfish pelvics, as evidenced by the reflectance measurements and below threshold perceptual distances. Therefore, the observation that butter hamlets attack masked gobies from slightly above suggests they might be behaviorally optimizing the efficiency of their aggressive mimicry by presenting to the prey with best visual abilities, the masked goby, the closest model-resembling area of their body. We did not observe such top-down attack strategy by the butter hamlet when preying on mysids, possibly because of the mysid's limited visual system.
In conclusion, this set of results, together with previous behavioral work by Puebla et al. (2007) and Picq et al. (2019), lends support to the aggressive mimicry scenario for the butter hamlet and its model, the four-eye butterflyfish, at least in the Bocas del Toro population, where the "model following" behavior was observed and where this study was conducted. However, our results suggest that the main prey of butter hamlets, epibenthic masked gobies and mysid shrimp, might have not been the intended signal receiver driving the evolution of mimetic coloration, given that its main prey species are either completely devoid or possess very limited color vision. On the contrary, predators of hamlets, such as groupers and snappers, are generally at least fully dichromatic when not trichromatic, and represent more likely receivers of H. unicolor's mimic coloration than its own prey. This raises the possibility that the color patterns of the butter hamlet might not have evolved first for efficient aggressive mimicry by imitating appearance and behavior of a fish harmless to their prey but that other selective forces initially brought about the similar appearance which was later recruited for aggressive mimicry. Picq et al. (2019) found that the model-tracking aggressive mimicry behavior of butter hamlets represents in fact one of two alternative behavioral syndromes, associated with territoriality. Territory holders with defined permanent hide-outs only rarely engaged in aggressive mimicry, while roaming individuals, lacking a defined permanent hide-out and territory systematically took advantage of this behavioral strategy. The authors proposed that the aggressive mimic strategy might confer an advantage in terms of foraging opportunities, at the expense of higher exposure to predators and possibly fewer mating opportunities. In this context, before aggressive mimicry evolved, it would have been beneficial for exposed roaming individuals to mix with and mimic, in behavior and appearance, a coral reef fish species with simple color patterns and unpalatable for a wide number of small-to-medium sized hamlet predators. Adult butterflyfish in the Caribbean are not a common occurrence in stomach content records (Randall, 1967), a testament to their effective defenses, mainly high maneuverability, extremely deep bodies with long, robust spines, particularly in benthivore species, a challenge for their gape-limited predators (Hodge et al., 2018). In addition, C.
capistratus sports less complex color patterns than other Caribbean butterflyfish, a potentially easier starting point for the development of a hamlet mimic. The protection conferred to roaming hamlets by mimicking in behavior (Picq et al., 2019;Puebla et al., 2007) and appearance a less than desirable prey in the eyes of their potential predators, such as di-or trichromatic groupers and snappers with sharp acuity (Loew & Lythgoe, 1978;Losey et al., 2003;McComb et al., 2013), could have led to the butter hamlet mimic morph. On the contrary, the limited visual system of the most common hamlet prey, masked gobies and Mysidium shrimp, represent an unlikely source of selection for the origination (but not the maintenance) of the mimic butter hamlet. Although the close resemblance between butter hamlet and four-eye butterflyfish is unlikely to have evolved to deceive the visual system of the prey, and therefore not in the context of aggressive mimicry, the resemblance resulting from selection for protective mimicry did eventually start giving butter hamlets an advantage (Puebla et al., 2007) in accessing their prey. While not exerting direct selection on the butter hamlet's color patterns, aggressive mimicry is likely a significant contributor to the maintenance of this behavioral strategy.
Our study shows how the study of sensory systems not only broadens our understanding of animal communication and signaling but has the potential to generate new hypotheses on the origin and maintenance of mimicry and the evolutionary trajectory of species.

ACK N OWLED G EM ENTS
We

CO N FLI C T S O F I NTE R E S T
None declared. Additional methods and results

U N D ERWATER I R R A D I A N CE S
We used an Ocean Optics USB2000 spectrometer connected to an Ocean Optics ZPK600 UV/VIS optical fiber and fitted at one end with a CC-3-UV cosine corrector. The probe was secured at the tip of the longer arm of a white 1 m long L-shaped pole and directed by a scuba diver vertically upwards and downwards, and horizontally perpendicularly to the shoreline, toward and away from shore, and the two directions parallel to the shoreline. This was repeated at different depths (just below surface, 2.5 m, 5.0 m, 7.5 m) just above hamlet territories. All measurements were taken between 11.00 and 13.00 on a sunny clear day.
The spectral distribution of irradiance was characterized by calculating λP 50 , the wavelength that halves the total number of photons (Munz & McFarland, 1973), and the breadth of the light spectrum by calculating the difference Δλ between λP 25 and λP 75 cumulative photon frequency, in the range 350-650 nm, most relevant for visual functions. The depth and wavelength dependence of the downwelling irradiance can be expressed in terms of the diffuse attenuation coefficient, K d (λ) (Mobley, 1994): where E d (z, ) is the downwelling irradiance at depth z and E d (0, ) is the downwelling irradiance just below the water surface. If we consider the average K d (z, ) over the depth interval from below the surface to the maximum depth recorded, this is We calculated the average diffuse attenuation coefficient using the below surface and 7.5 m depth downwelling spectral irradiance measurements.
The downwelling irradiance had, in general, similar characteristics to those measured in other tropical reefs (McFarland & Munz, 1975)  We used a single-beam, computer-controlled MSP, with a 100 W quartz iodine lamp that allowed for accurate absorption measurements down to 340 nm (Loew, 1982;Losey et al., 2003). The peak of maximum absorption (λ max ) of photoreceptors was obtained by fitting A1 or A2 templates to the smoothed, normalized absorbance spectra (Govardovskii et al., 2000;Lipetz & Cronin, 1988).
We used the criteria for data inclusion into the analysis of λmax described in Loew (1994) and Losey et al. (2003).

V I S UA L M O D ELI N G
Photoreceptor quantum catch Q i for a receptor of class i was calculated as: where R i ( ) is the absolute spectral sensitivity for receptor class i, S a (λ) is the reflectance spectrum of a color patch a, I(λ) is the irradiance spectrum, and integration is over the range λ = 350÷650 nm. Given the small distances (d = 25-50 cm) over which models and mimics interact with the receiver (i.e., the prey: masked goby or mysid shrimp) in clear coral reef waters, we considered light attenuation effects negligible.
If we take the signal f i of each receptor of class i as proportional to the natural logarithm of the receptor quantum catch q i , according to Weber-Fechner's law, the contrast between two homologous patches, for example, on the model versus on its mimic, will be: The Vorobyev-Osorio model assumes that discrimination thresholds are limited by photoreceptor noise. Color contrasts ΔS between corresponding patches on model and mimic viewed by the goby were calculated as: for a dichromatic species with short-wavelength (1) and long-wavelength (2) sensitive photoreceptors, with e 1 , e 2 , representing the photoreceptor noise associated with each class. For a trichromatic species with short-(1), medium-(2) and long-wavelength (3) sensitive photoreceptors, the expression becomes: In relatively bright light conditions, as in the case of shallow waters in well-illuminated coral reefs, the photon shot component of noise is negligible and neural noise will be largely accounting for the photoreceptor noise e i . Neural noise is inversely proportional to the relative frequency of the receptor types as given by the following equation: where ω is the Weber fraction and η i the relative density of photoreceptors of type i. For the masked goby, we set a Weber fraction ω = 0.05 for the long wavelength sensitive cone, a conservative estimate for fishes (Champ et al., 2016;Cheney & Marshall, 2009). During preliminary MSP work, we did not find any evidence of short-wavelength sensitive cones in this species. Taking a conservative approach, we decided to consider both a dichromat scenario with the MSP values obtained in this study as well as a hypothetical trichromat condition, adding a blue-sensitive cone located in a region of spectrum typical of other gobies (Table A1). For the dichromat, we set the relative proportions of the different cone types as 1:1 and at 1:4:4 for the trichromat scenario, to account for the apparent rarity (if present) of the putative short-wavelength sensitive cone class in this species. The Weber fraction for the mysid was set at 0.05.
Masked gobies and mysids might be able to discriminate mimic hamlets from models based on differences in luminance. Based on studies of other fish and terrestrial animals (Kelber et al., 2003;Neumeyer et al., 1991), we assumed that the longwave sensitive photoreceptor in the masked goby and mysid shrimp is responsible for the achromatic perception of luminance. Thus, we computed the luminance contrast ΔL between patches on model and mimic as: where ω = 0.05, a value close to that observed in other teleosts (Olsson et al., 2017). Color and luminance distances were calculated separately at three different depths, using horizontal irradiance (averaged over the 4 cardinal directions), measured at 2.5 m, 5.0 m and 7.5 m of depth, spanning the range of hamlet territories on the studied reef.

M A S K E D G O BY ACU IT Y
Optical properties of the eye and spacing of photoreceptors and retinal ganglion cells are considered the main anatomical factors limiting acuity, with the former generally playing a minor role in affecting visual resolution in fishes. While photoreceptor densities are intuitively expected to influence the minimum resolvable angle (Northmore & Dvorak, 1979), visual processing by neural cells in the retina and, in particular, visual summation by ganglion cells, can significantly reduce resolution (in favor of increased sensitivity).
Higher-level processing might, in certain cases, lead to further loss of spatial information (Warrant, 1999). This is consistent with the frequent observation of higher anatomical than behavioral acuity values in fishes.
The eyes of masked gobies were enucleated and fixed in para- and flattened onto a gelatinized glass slides with the ganglion cell layer facing up. The slides were exposed to 4% PFA vapors overnight, at room temperature, in order to increase the adhesion of the retina to the slide and for differentiation of the stained neurons (Coimbra et al., 2006;Stone, 1981 To estimate the total population of GCL cells, we applied the optical fractionator method (West et al., 1991) with modifications for retinal wholemounts (Coimbra et al., 2009(Coimbra et al., , 2012. The retina was F I G U R E A 2 Color distances dS (on the left, in each box) and achromatic distances dL (on the right, in each box) and their bootstrap confidence limits, for each species pair viewed by the prey, a masked goby with a 531/539 nm set of cone pigments, at a depth of 5 m. A value of dS (or dL) = 1 marks the theoretical perceptual threshold for each patch (#1-7). Figure conventions as in Figure 4, main text considered a single section, and so the section sampling fraction was equal to one. The total population of cells N tot was estimated based on the total number of counted cells ΣQ and the area of the sampling fraction asf, which corresponds to the ratio between the counting frame and the sampling grid (Coimbra et al., 2009): The cells were counted using a Leica DM5500B trinocular microscope with a motorized stage, connected to a computer running the Stereo Investigator software (MicroBrightField, Colchester, VT). The edges of the retina and the optic nerve were delineated using a 5×/NA 0.15 objective. Counts were made using ×100/NA 1.4-0.7 oil immersion objective, at regular intervals defined by a sampling grid at 150 × 150 μm placed in a random, uniform and systematic fashion, covering the entire retinal area. An unbiased counting frame at 50 × 50 μm was imposed at each sampling frame and cells were counted if they lay entirely within the counting frame or if they touched the acceptance lines without touching the rejection lines (Gundersen, 1977). The coefficient of error was calculated using the method of Scheaffer et al. (1996). All cellular elements located within the GCL were counted, independent of size (Collin, 1989;Collin & Partridge, 1996;Collin & Pettigrew, 1988a, 1988b.
N tot = ΣQ 1 asf F I G U R E A 3 Achromatic contrasts dL across species, viewed by a Mysidium columbiae shrimp visual system with a single pigment of λ max = 520, at a depth of 5 m. Conventions as in Figure 4, main text The theoretical spatial resolving power of each eye was estimated based on the maximum density of presumed retinal ganglion cells D and the focal length of the eye f, obtained from a Matthiessen's ratio of 2.34, appropriate for gobies (Hansen, 1988;Matthiessen, 1880;Ota et al., 1999;Wanzenbock et al., 1996). Considering a square array of retinal ganglion cells, the mean cell-to-cell spacing S is related to the maximum density D of ganglion cells per mm 2 through the expression S 2 = 1/D. The maximum spatial (Nyquist) frequency (ν) of a sinusoidal grating resolvable by a square arrangement is ν = 1/(2ΔΦ), where ΔΦ is the inter-receptor angle ΔΦ = S/f (Snyder & Miller, 1977). Substituting, we obtain: or its inverse, the smallest resolvable angle α, in degrees.

I M AG E CO LLEC TI O N A N D PRO CE SS I N G
Underwater scenes were captured with either a Canon 5D Mark III camera with a 24-70 mm f2.8 lens set on 50 mm or with a Canon G7X, under natural illumination. Two sets of high-resolution photographs were taken. First, hamlets and their models were photographed underwater at a depth of about 5 m, from an approximately horizontal line of view, against different natural backgrounds. In addition, during preliminary observations, we noted that the ventral silhouette of the butter hamlet H. unicolor closely resembles in shape and colors that of its putative model, the butterflyfish C. capistratus, despite having very different lateral profiles. In order to compare the appearance of the butter hamlet and its model (and, for comparison, the black hamlet H. nigricans and the barred hamlet H. puella), as seen from below at a 45° angle, as a masked goby hovering above a coral is likely to do, we collected one individual for each hamlet morph and a four-eye butterflyfish. Fish were euthanized with an overdose of MS-222 in an aerated aquarium then moved for few minutes at −20°C. A hole was then drilled on the dorsal area of each fish allowing a thin metal bar to be passed through the body so that the butter, black, and barred hamlets and the four-eye butterflyfish could be placed side by side on a common base and brought underwater.
A series of photographs were taken at a depth of 5 m in proximity to hamlets territories, at about 45° and 40 cm from the metal rod placed against different natural backgrounds. We did not note appreciable differences in color patterns between live non-stressed individuals as observed in the wild and the sacrificed individuals as treated in our protocol, but their eyes did take a cloudy appearance and the tips of their fins showed some minor damage. However, it is = 1∕ (2ΔΦ) = f∕ (2S) cycles∕radian or = f∕ (2S) 2 ∕360 cycles∕degree,

F I G U R E A 4
From left to right, in each image: Four-eye butterflyfish (C. capistratus), butter hamlet (H. unicolor), black hamlet (H. nigricans) and barred hamlet (H. puella), seen 45° from below (first two columns, left). Detail of ventral appearance (last two columns, right) significant that once we completed photographing and the bar was left for few minutes above a dead coral head, two hamlets, a blue and a butter, came immediately to inspect our setup and vigorously displayed against the "intruding" hamlets on the bar without interrupting their territorial displays even when we approached to try and recover the bar.
Following Caves and Johnsen (2018)'s guidelines, high-resolution photographs were cropped to 1024 × 1024 pixels and saved separately for each RGB channel. The angular width of each scene was obtained by scaling with an object of known actual size in the photograph and by selecting a biologically significant viewing distance. For the photographs of live models and mimics in their natural habitat ( Figure 6, main text), we measured the sizes of corals or rocks appearing in the images, while for the bottom-up images of the mounted individuals ( Figure A4) we measured the hamlets' interorbital distances, to derive image width.