DOI: 10.5061/dryad.kprr4xh6t
title: Data for: A hypothesis for robust polarization vision: An example from the Australian Imperial Blue butterfly, Jalmenus evagoras

description: The Australian lycaenid butterfly, Jalmenus evagoras, has iridescent wings
 that are sexually dimorphic in both spectral reflection and degree of
 polarization, suggesting that these wing properties are likely to be
 important in mate recognition. We first describe the results of a field
 experiment showing that free-flying individuals of J. evagoras
 discriminate between visual stimuli that vary in polarization content in
 blue wavelengths but not in others. We then present detailed reflectance
 spectrophotometry measurements of the polarization content of male and
 female wings, showing that female wings exhibit blue-shifted reflectance,
 with a lower degree of polarization relative to male wings. Finally, we
 describe a novel method for measuring alignment of ommatidial
 arrays:  By measuring variation of depolarized eyeshine intensity
 from patches of ommatidia as a function of eye rotation, we show that a)
 individual rhabdoms contain mutually perpendicular microvilli; b) many
 rhabdoms in the array are rotated with respect to one another by as much
 as 45º; c) the rotated ommatidia are useful for robust polarization
 detection. By mapping the distribution of the ommatidial rotations in eye
 patches of J. evagoras, we show that males and females exhibit differences
 in the extent to which ommatidia are aligned. Both the number of rotated
 ommatidia suitable for robust polarization-detection, and the number of
 aligned ommatidia suitable for edge-detection, vary with respect to both
 sex and eye-patch elevation. Thus, J. evagoras exhibits finely-tuned
 ommatidial arrays suitable for perception of polarized signals, likely to
 match sex-specific life history differences in the utility of polarized
 signals.
description: POLARIZATION-DISCRIMINATION
 BEHAVIORAL EXPERIMENT:  Preferences of
 free-flying, patrolling individuals of <em>Jalmenus
 evagoras</em><em> </em>to approach robots with different
 wing treatments were recorded in 20-minute trials for each of the 3 color/
 polarization treatments, and measured in between 6-8 separate geographic
 field sites each, with each site consisting of patches of acacias occupied
 by larvae and pupae of <em>J. evagoras</em>. Specifically, ‘3M
 Red G280’ was tested in ten 20 min trials carried out in 6 sites, ‘3M
 Yellow R312’ was tested in 6 trials at 6 different sites, ‘3M+blue R374’
 was tested in 10 trials at 7 different sites. Sites were spaced no closer than
 300 m apart, with the farthest sites separated by over 40 km, to reduce
 the likelihood that individuals encountered at one site would also be
 present in subsequent trials at nearby sites. To further
 avoid the possibility of counting responses by the same individual
 butterflies more than once, we analyzed these results using site as the
 unit of replication, summing the total number of responses to polarized
 and depolarized models at each site for each treatment, and calculating
 one-sample student’s t-tests for the difference from zero of these total
 differences between polarized and depolarized responses across sites for
 each treatment. WING REFLECTANCE AND PERCEPTUAL ANALYSIS:
 Spectroscopic reflectance measurements were conducted
 for the dorsal forewings and hindwings of 12 female and 13 male
 <em>J. evagoras</em><em> </em>pinned museum
 specimens. The mean and standard error of the mean reflectance values were
 calculated and plotted. We used R package pavo (Maia et al. 2019) to
 generate coordinates in tetrahedral color space (Stoddard & Prum 2008) for
 each of the collected reflectance spectra. A tetrahedral color space is a
 chromaticity diagram that represents the gamut of all perceivable colors
 given a set of curves representing the sensitivity of the four
 photoreceptors of a tetrachromatic organism. Using the tetrahedral color
 space, we can then calculate coordinates that represent the perceived
 color of any given reflectance spectrum. We used sensitivity curves for
 each of the four photoreceptor types found in <em>J.
 evagoras</em> which indicated sensitivity from 300-700nm (Figure
 S2). Because reflectance spectra were recorded only from 350nm, we
 truncated the raw sensitivity curves to 350-700nm. Since we were primarily
 interested in the color of the wings themselves, rather than color in a
 particular context, we also assumed ideal lighting and background color
 (Maia et al. 2019).
 Coordinates in tetrahedral color space can be defined in a number of ways:
 cone-stimulations (absolute or relative values denoting estimated
 stimulation of each of the four photoreceptor types), hue and saturation
 (hue is denoted by azimuth and elevation of the color relative to the
 center of the tetrahedron, and saturation indicates the length of the
 vector from the center of the tetrahedron to the color), and finally the
 cartesian coordinates (x, y, z) of the color in the tetrahedral color
 space. Here we elected to use cartesian coordinates, because they have
 better statistical properties than the other measures (relative cone
 catches sum by definition to unity so are not independent, and the
 circular coordinate system for hue and saturation result in statistical
 complications). To test whether color significantly differed between males
 and females, we used the RRPP package in R (Collyer & Adams 2018),
 using multivariate response linear modeling of the effect of sex on the
 cartesian coordinates of each color in tetrahedral color space, as well as
 on the raw spectral data, for comparison. P-values from this combined
 analysis were corrected for multiple comparisons via the method of
 (Benjamini & Hochberg 1995). In
 addition, we summarize color contrasts between reflectance measurements of
 museum specimens and robot wing models. These contrasts were generated by
 computing the (un-weighted) Euclidean distance between colors in the
 tetrahedral color space. Colors that are perceptually more similar will
 generally have lower Euclidean distances. We chose this measure, rather
 than weighted Euclidean distances (JNDs; (Vorobyev & Osorio 1998; Maia et al.
 2013)) because we do not have good estimates for
 the required parameters (weber fraction, photoreceptor densities) for
 <em>J. evagoras</em>. DEGREE OF POLARIZATION:
 We also measured the polarization content of reflected
 light at both λ=360 nm and 450 nm. We computed the Degree of Polarization
 (DoP) of male and female specimens as well as of the mock wings, defined
 as
 |<em>I<sub>H</sub></em>-<em>I<sub>V</sub></em>|/(<em>I<sub>H</sub></em>+<em>I<sub>V</sub></em>), with <em>I<sub>H</sub></em> and <em>I<sub>V</sub></em> calculated by taking the total intensity of a polarization image, at a range of angles of incident light <strong>θ </strong>and detection angles <strong>φ</strong>. We analyzed DoP as a function of the combined angle between <strong>θ </strong>and <strong>φ (</strong>which we termed “angular contrast” and can be thought of as the obliquity of the viewing angle with respect to the source of illumination). The relationship between angular contrast and DoP in blue and UV appeared to be non-linear, so we tested various linear and polynomial mixed-effects models that analyzed the relationship between these two variables and Sex. The relationship between DoP in UV and angular contrast was best described by a 2<sup>nd</sup> order polynomial (Table S2), whereas for DoP in blue, a 3<sup>rd</sup> order polynomial provided the best fit (Table S2). The significance of the orthogonal polynomial terms of angular contrast, Sex, and their interactions were evaluated using parametric bootstrapping and model comparison: First, a maximal mixed effects linear model was fitted that considered Sex, the orthogonal polynomial terms of Angular contrast, and their 1st order interactions as fixed effect terms, accounting for repeated measurement of individuals by fitting random intercepts for individuals. Then, to calculate the significance of each of these fixed effect terms, 'smaller' models were constructed that lacked each of these terms and were compared via parametric bootstrapping against 'larger' models that included these terms (but no higher order terms). Effect subtraction proceeded hierarchically from interaction to individual fixed effects. Larger and smaller models compared in this way thus differ only by the term of interest.             The maximal model, containing all of the fixed effects and their interactions, described above, was the best fit, most parsimonious model, and therefore was selected to generate model fits and confidence bands using the ‘effects’ package in R (Halekoh & Højsgaard 2014; Fox 2003). Confidence bands, where included, denote smoothed means and standard errors. Parametric bootstrapping was done using the 'Pbmodcomp' function of the 'pbkrtest' package in R  All mixed effects models were fit using maximum likelihood with the 'lmer' function of package 'lme4' (Bates et al. 2015) in R (Version 3.4.1, R Core Team 2017). R-squared values for testing model fits were made using the r.squaredGLMM function of the ‘MuMIn’ package (Bartoń 2020) and the R2 function in the semEff package (Murphy 2020).  ANALYSIS OF SEX AND ELEVATION ON EDGE AND POLARIZATION DETECTION: The effects of Sex and Elevation (along the ‘forward-facing’ part of the eye, azimuth of ~10º) within the eye on the percent of putative edge detectors and polarization detectors (ED and PD respectively, as well as the more specific “ED-only” and “PD-only” metrics, see Results for metric definitions) were investigated using mixed effects linear models followed by parametric bootstrapping and model comparison in a similar fashion to the polynomial mixed-effects model workflow above.             The maximal model, that considered Sex, Elevation, and their 1st order interaction as fixed effect terms, accounting for repeated measurement of individuals by fitting random intercepts for individuals within the effect of Elevation, was the best fit, most parsimonious model, and therefore was selected to generate model fits and confidence bands using the ‘effects’ package in R (Fox 2003). Confidence bands, where included, were generated using the Kenward-Roger coefficient-covariance matrix to compute effect standard errors, as implemented in the ‘effects’ package. Parametric bootstrapping was done using the 'Pbmodcomp' function of the 'pbkrtest' package in R (Halekoh & Højsgaard 2014). All mixed effects models were fit using maximum likelihood with the 'lmer' function of package 'lme4' (Bates et al. 2015) in R (Version 3.4.1, R Core Team 2017). Plots are made using the ggplot2 package in R (Wickham et al. 2016), and manually edited in Inkscape (version 0.92.4).  
description: R version 4.0.3