The evolution and function of pattern diversity in snakes

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1 Behavioral Ecology The official journal of the ISBE International Society for Behavioral Ecology Behavioral Ecology (2013), 24(5), doi: /beheco/art058 Original Article The evolution and function of pattern diversity in snakes William L. Allen, a Roland Baddeley, a Nicholas E. Scott-Samuel, a and Innes C. Cuthill b a School of Experimental Psychology, University of Bristol, 12a Priory Road, Bristol BS8 1TU, UK and b School of Biological Sciences, University of Bristol, Woodland Road, Bristol BS8 1UG, UK Received 3 December 2012; revised 17 May 2013; accepted 27 May 2013; Advance Access publication 5 July Species in the suborder Serpentes present a powerful model for understanding processes involved in visual signal design. Although vision is generally poor in snakes, they are often both predators and prey of visually oriented species. We examined how ecological and behavioral factors have driven the evolution of snake patterning using a phylogenetic comparative approach. The appearances of 171 species of Australian and North American snakes were classified using a reaction-diffusion model of pattern development, the parameters of which allow parametric quantification of various aspects of coloration. The main findings include associations between plain color and an active hunting strategy, longitudinal stripes and rapid escape speed, blotched patterns with ambush hunting, slow movement and pungent cloacal defense, and spotted patterns with close proximity to cover. Expected associations between bright colors, aggressive behavior, and venom potency were not observed. The mechanisms through which plain and longitudinally striped patterns might support camouflage during movement are discussed. The flicker-fusion hypothesis for transverse striped patterns being perceived as uniform color during movement is evaluated as theoretically possible but unlikely. Snake pattern evolution is generally phylogenetically conservative, but by sampling densely in a wide variety of snake lineages, we have demonstrated that similar pattern phenotypes have evolved repeatedly in response to similar ecological demands. Key words: aposematism, camouflage, flicker-fusion, reaction diffusion, Serpentes, Turing patterns. Introduction From the sleek black surface of the red-bellied black snake Pseudechis porphyriacus to the intricate kaleidoscope patterns of species such as the carpet python Morelia spilota and the high-contrast banding of the common coral snake (Micrurus fulvius), an extraordinary variety of snake coloration patterns have evolved. Several functions have been proposed to account for the different patterns observed on the visible surfaces of snakes, with the most common suggestions being camouflage through either background matching and/or disruption of form (Conant and Clay 1937; Camin and Ehrlich 1958; Beatson 1976; Jackson et al. 1976; Bechtel 1978; Vincent 1982; Sweet 1985; King 1987; Brodie 1989, 1992; King 1992; King 1993a; Lindell and Forsman 1996; Shine et al. 1998; Bowen 2003; Creer 2005; Wilson et al. 2006; Farallo and Forstner 2012; Isaac and Gregory 2013), aposematism (Campbell and Lamar 1989; Savage and Slowinski 1992; Brodie 1993; Brodie and Janzen 1995; Valkonen et al. 2011), and thermoregulation (Gibson and Falls 1979; Peterson et al. 1993; Lindell and Forsman 1996; Bittner et al. 2002). Address correspondence to W.L. Allen, who is now at Department of Anthropology, New York University, Rufus D. Smith Hall, 25 Waverley Place, New York, NY 10003, USA. will.allen@nyu.edu. The majority of these studies have only investigated coloration and color variation in a single species. This study assesses coloration diversity across the suborder Serpentes. The only previous broad comparative study of diversity in snake pattern appearance (Jackson et al. 1976) was conducted before the development of phylogenetic comparative methods (Felsenstein 1985; Harvey and Pagel 1991; Freckleton et al. 2002). Despite these revolutionary methodological advances, comparative approaches to understanding snake patterning have since received little attention (Wolf and Werner 1994; Forsman and Aberg 2008; Pyron and Burbrink 2009a). Jackson et al. (1976) classified 132 North American snake species and subspecies with distinctive appearances into 5 pigmentation pattern groups blotches, regular or irregular bands (here referred to as transverse stripes), longitudinal stripes, and unicoloredspeckled and used multiple discriminant analysis to identify the eco-behavioral variables such as escape behavior and habitat type, which best separated pattern types. Irregular transverse stripes and, to a lesser extent, blotched snakes relied on aggressive threat responses often backed up by a potent venom threat rather than flight when threatened (Creer 2005; Valkonen et al. 2011). In contrast, unicolored-speckled and longitudinally striped snakes were fast but otherwise poorly defended with venoms and threatening behavioral responses. These patterns have been suggested as suitable for a flight strategy because, unlike blotches, they do not The Author Published by Oxford University Press on behalf of the International Society for Behavioral Ecology. All rights reserved. For permissions, Downloaded please from journals.permissions@oup.com

2 1238 Behavioral Ecology provide reference points for a predator to use when tracking the snake s movement, allowing its motion away from the predator to go unnoticed until the tip of the tail passes by (Pough 1976; Brodie 1989, 1992). Snakes with regular transverse stripes had intermediate levels of defense and flight speed. The authors argued that this may be a compromise strategy providing disruptive camouflage when stationary, but a uniform color when moving, via flicker-fusion effects in their predators visual systems. That is, the stripes drift across the predator s visual field so fast that the variations in intensity ( flicker ) cannot be resolved (Pough 1976). The regular transverse stripe strategy included the venomous coral snakes (Micrurus and Micruroides), which are generally considered to have aposematic warning coloration (Campbell and Lamar 1989; Savage and Slowinski 1992; Brodie 1993) and serve as models for other species which are Batesian mimics (Brodie and Janzen 1995). As color was not measured, coral snakes and their mimics did not separate from other regularly banded snakes, so the ecological factors hypothesized to drive the evolution of aposematism were not investigated. Since the publication of Jackson et al s (1976) study, it has become accepted that comparative analyses need to account for phylogenetic nonindependence (Felsenstein 1985; Freckleton et al. 2002). In a preparatory study (Allen WL, unpublished data), Jackson et al s (1976) data were reanalyzed using Pagel s (1994) phylogenetically controlled tests of correlated discrete character evolution, implemented in Mesquite (Maddison and Maddison 2001), and nonphylogenetic chi-squared analyses in SPSS. Although chi-squared tests supported the associations described in Jackson et al s (1976) original study (e.g., between uniform coloration and docile behavior) because coloration and eco-morphological traits in snakes are generally quite conservative (King 1993b), none of the described associations were supported in phylogenetically controlled analyses, suggesting caution in interpreting the results of Jackson et al. (1976). Apparent snake pattern diversity may actually reflect only a few, early, radiations in color pattern followed by phylogenetic and/ or niche conservatism, with the resulting small effective sample size reducing the power for tests of adaptive hypotheses related to different ecological modes of life (Sahney et al. 2010). The aim of this study is to understand snake pattern diversity using modern comparative approaches and increase power by adding a phylogenetically diverse sample of Australian snakes to Jackson et al s (1976) original North American sample, and measuring ecological and pattern traits at a higher resolution. Importantly, the majority of Australian snakes come from the Elapidae and Boidae families, which each have only a few species in North America. The majority of North American species are colubrids, a group which has only a few species present in Australia, and the family Viperidae, which are not present in Australia. A full understanding of snake pattern diversity requires detailed pattern measurements (King 1992; King 1993a). However, the most common approach to snake pattern quantification is subjective categorical classifications based on researchers observations of whether, for example, a snake is blotched, uniform, longitudinal or transverse striped (Jackson et al. 1976), or an apparent mimic or nonmimic (Pyron and Burbrink 2009a). Categorical classification may be appropriate for answering specific questions, but it masks considerable variation within categories and reduces power to detect evolutionary patterns. Efforts have been made to establish continuous snake pattern measures. For example, Brodie (1989, 1992) quantified the stripedness of snakes by combining estimates of the completeness of longitudinal or transverse stripes, the contrast of longitudinal or transverse stripes, and the presence or absence of spots. Like King (1993b) or Westphal and Morgan s (2010) measures, this was suitable for purpose, but the choice of measures and how they are combined is arbitrarily driven by the researcher s perceptions rather than the unknown biologically relevant pattern traits (Tanaka and Mori 2007). The ideal representation of a camouflage or signaling pattern would be in terms of the receiver s perceptual representation of pattern in its natural context. However, cognitive representation of shape, pattern, and texture is not yet well enough understood for this to be achievable. One can model sets of colors (Endler and Mielke 2005) or color adjacency (Endler 2012), but whole patterns are a challenge (Allen and Higham 2013). An alternative approach, which we develop in this study, is to base pattern representation on a mathematical model of pattern development such as reaction-diffusion (R-D) systems (Turing 1952; Meinhardt 1982; Murray 2002). R-D models are useful for pattern classification for 2 main reasons. First, because they are developmentally inspired, they naturally lead to an understanding of patterning at multiple levels of explanation (Tinbergen 1963). Second, because parameters of the model correspond to visual attributes such as pattern shape, the spatial scale of pattern elements, pattern anisotropy, and pattern complexity, matching a synthetic R-D pattern to an image of snake patterning, as has been shown for field patterning (Allen et al. 2011), affords a parametric quantification of a pattern s appearance in detail. Methods Taxon sampling and tree reconstruction As no published phylogeny covers all the study species of potential interest (Lawson et al. 2005; Bryson et al. 2007; Wiens et al. 2008; Pyron and Burbrink 2009b; Zaher et al., 2009; Vidal et al. 2010; Pyron et al. 2011), we built a molecular phylogeny using up to 4 genes for each taxon: 2 mitochondrial (cytochrome b and ND4) and 2 nuclear (c-mos and RAG1). This combination has been shown to successfully resolve both recent and ancient radiations (Pyron et al. 2011). We based the species sample of Australian snakes on those in the appendix of Shine (1995), which lists 111 species, but notes that some poorly known and unstudied species are not present on the list. Lack of gene sequence data reduced the sample to 71 species. The North American snake sample was based on the species included in Ernst and Ernst (2003), which lists 131 species. Molecular sequence data were available for 91 of these species. We also included several subspecies that are characterized by different coloration, adding 6 subspecies of the common kingsnake Lampropeltis getula, 2 of the fox snake Pituophis melanoleucus, and 1 of the Western terrestrial garter snake Thamnophis elegans, for a total Australian and North American sample of 171 taxa. A number of other study species are divided into subspecies with different coloration patterns but either sequence data, images, or ecological and behavioral information that separated subspecies could not be identified, so we did not include them as separate taxonomic units. Although not a complete sample of North American and Australian snake fauna, the only obvious bias is toward more intensively studied and better understood species. Most currently recognized genera containing multiple species were sampled at least once. Genera not included were the shovel-nosed snakes Chionactis, patchnosed snakes Salvadora, black-headed snakes Tantilla, earth snakes

3 Allen et al. Snake dorsal patterns 1239 Virginia, and Australian tree snakes Dendrelaphis. We used BEAST (Drummond and Rambaut 2007) to infer trees. Details on the tree building procedure are available in electronic Supplementary Appendix 1. Accession numbers are listed in Supplementary Appendix 2, and the maximum clade credibility tree used in analyses is presented in Supplementary Appendix 3. Collection of snake images We obtained digital color photographs of the study species for classification by searching Google Image for each species scientific name and navigating specialist and general herpetological websites. Thanks to the enthusiasm, dedication, and openness of amateur and professional herpetologists in both North America and Australia, obtaining high-quality and well-labeled photographs for all the study species was not difficult. Photo selection criteria were that the image appeared well exposed and with a natural color balance. The snake s dorsal area had to be in view, though as it is common practice for field herpetologists to pose snakes for photography, this was normally the case. Occlusions of parts of the dorsal patterning due to a snake s body position or environmental features were allowed as long as the majority was visible and the overall coloration pattern was clearly discernible. Photographs had to be labeled with a positive species identification that was accurate to the best of our knowledge, based on the appearance of the snake, prior knowledge, and other supplied information. Preference was given to snakes photographed outdoors in their natural habitat under apparently natural lighting conditions. We excluded photographs of snakes that had obviously been captive bred or were juvenile. As sexual dichromatism is comparatively rare and generally quite subtle in snakes (Shine and Madsen 1994) and sex information was not normally available, we did not aim to sample only males or females, or equal numbers of each. Neither did we try to sample snakes at particular stages in their sloughing cycle. In color polymorphic species, we made no attempt to either sample all morphs, or sample morphs in proportion to population size, though the sample size of species with distinct color morphs and those with particularly complex patterning was increased in order to get more reliable estimates of pattern and intraspecific pattern diversity. Nevertheless, some sampling bias toward more colorful or exaggerated individuals of a species may remain. In total, 828 images were used for the classification task. Up to 5 images that met the selection criteria were used. When more than 5 good images were available, they were selected randomly, except when pattern appeared to be highly variable when the sample size was increased to all available images which met selection criteria. The mean number of photos for each study species (or subspecies) was 4.83 (median 5, range 1 16). The 4 species for which there was just a single photo were 3 species of blindsnake (Ramphotyphlops) and the crowned snake Drysdalia coronata, all of which are uniformly colored. Snake ecological measures Our main sources of ecological information were Ernst and Ernst (2003) for North American snakes and Wilson and Swan (2008) and Cogger (1996) for Australian snakes. Greene (1988), Shine (1995), Conant and Collins (1998), Conant et al. (1999), Stebbins (2003), and numerous published papers and online species descriptions (www. reptile-database.org and were used to corroborate and supplement information. When printed information was unavailable or unclear, we contacted experts in the field to supply missing information. For a few Australian species, experts remained unsure of trait scores, leading to missing data. As data were unlikely to be missing at random (Rubin 1976; Nakagawa and Freckleton 2011), removing cases with missing data would lead to biased parameter estimates and reduce overall statistical power. Instead, because there was phylogenetic signal present in traits with missing data, we imputed missing trait values by calculating parsimony ancestral states in Mesquite (Garland and Ives 2000; Maddison and Maddison 2001). The ecological trait measures are summarized in Table 1; details on how they were selected and scored are available in Supplementary Appendix 1. A full table of the ecological and behavioral trait scores is presented in Supplementary Appendix 4. Pattern formation model In the simplest R-D models stripes are unoriented, forming labyrinth patterns (Meinhardt 1982). To produce consistently oriented stripes, as observed on many species of snake, R-D processes need to incorporate additional components such as prepatterns, specific boundary conditions, spatially varying reaction parameters (Meinhardt 1982; Lacalli et al. 1988; Murray and Myerscough 1991; Dillon et al. 1994), or, as chosen here, anisotropic diffusion (Kobayashi 1993; Shoji et al. 2003b). We applied the following R-D model: u = D t () θ 2 u ) + u 3 u u v (1a) v = 2 D v t + γ( u α β) (1b) v Where D u (θ) is the anisotropic diffusion function: D u () θ = 1 1 δ cos2θ Here, u and v are the concentration of 2 morphogens, an activator u and an inhibitor v. γ is a scaling factor to decrease calculation times. D u and D v are the diffusion coefficients. For v, the diffusion rate is held constant (i.e., it diffuses isotropically), whereas for u, it can be anisotropic, varying with direction according to Equation 2. In Equation 2, θ is the angle of gradient θ = ( tan ( ( δ δ ) ( δ δ ) )) 1 u x u y and δu is the magnitude of anisotropy for u. When δu is positive, diffusion is faster on the x axis, which results in transverse stripes forming perpendicular to the x axis, and when δu is negative, diffusion is faster on the y axis, resulting in longitudinal stripes forming perpendicular to the y axis. When δu = 0, diffusion of u is isotropic meaning that patterns will not be directional. The second part of the equations, u u 3 v and γ(u α β), is the reaction terms that describes the kinetics of the reaction between the 2 morphogens. The formation or direction of stripes does not critically depend on the choice of reaction terms (Shoji et al. 2002). However, spots, reverse spots, or irregular stripes are produced depending on the shape of nullclines of reaction terms (Shoji et al. 2003a). The shape of the nullcline depends on the upper and lower limits of activation level constraints, which can be manipulated by the β parameter in Equation 1b. When β is sufficiently positive, activator u forms into spots, and when β is sufficiently negative, inhibitor v forms into spots. When β is close to 0, blotches and labyrinth patterns form. u (2)

4 1240 Behavioral Ecology Table 1 Summary of the ecological and behavioral traits measured for each species. See main text and Supplementary Appendix 1 for further details on choice of factors, sources, and measurement criteria Category Trait Measure Body size SVL Log (cm) a Body girth Ordinal: broad (0), normal (1), slender (2) Sexual SVL dimorphism Ordinal: msvl > fsvl + 10% (0); msvl = fsvl ± 10% (1); msvl + 10% < fsvl (2) Habitat type Desert Ordinal: absent (0), present (1), preferentially present (2) b Desert diverse Grassland Grassland diverse Forest Forest diverse Aquatic Aquatic diverse Habitat generalism Sum of all habitat type scores Fossoriality Ordinal: remains above ground (0), occasional burrower (1), rarely above ground (2) Arboreality Ordinal: not arboreal (0), intermediate (1), arboreal (2) Behavior Activity time Ordinal: nocturnal (0), mainly nocturnal (1), intermediate (2), mainly diurnal (3), diurnal (4) Hunting strategy Ordinal: ambush hunter (0), flexible (1), active hunter (2) Exposure amount Ordinal: always near cover (0), intermediate (1), frequently away from cover (2) Antipredator defense Aggressiveness Ordinal: placid (0), occasionally aggressive (1), aggressive (2) Venom potency Ordinal: nonvenomous (0), venomous (1), and highly venomous (2) c Escape speed Ordinal: slow (0), normal (1), fast (2), very fast (3) Cloacal excretions Ordinal: absent (0), present (1), present and highly pungent (2) Erratic movements Dichotomous: absent (0), present (1) Death feigning Dichotomous: absent (0), present (1) Diet Invertebrate Mainly interval: percentage of total diet, when quantitative data were unavailable, ordinal: Fish Amphibians Reptiles Eggs Birds Mammals absent (0), occasional (1), preferred (2) d Continent North American/Australian Dichotomous: North American (0), Australian (1) a Log-transformed prior to analysis to correct for a positive skew. b Diverse type habitats indicate heterogeneous habitats, for example, forest diverse includes woodland, chaparral, and scrubland, whereas forest is more visually homogeneous closed-canopy forest. Prior to analysis, scores are divided by the sum of all habitat type scores to indicate strength of preference for each habitat type. c Data on venom capability s defensive usage are frequently unavailable, though all highly venomous snakes are likely to be potentially dangerous to predators. d Ordinal data converted to percentages (see Supplementary Appendix 4). Occasional scores given 50% weighting. Analyses were repeated giving occasional scores 10% weighting with no effect on pattern of associations. To represent snake patterns with a complex edge-enhanced appearance (Osorio and Srinivasan 1991), a contrasting ring was added around the perimeter of pattern elements in each of the simple patterns by dilating the negative of the image and adding the altered pixels to the original using functions in the Image Processing Toolbox in MATLAB (Natick, Massachusetts: The MathWorks Inc.). The synthetic snake images displayed to observers were scaled (0 1) images of activator concentration u, with lighter areas indicating areas of higher activator density. Classification task We recruited 5 observers to perform the classification task of identifying which synthetic R-D pattern had a visual appearance most similar to that of the dorsal pattern displayed on the snake in each of the 828 images. To enable observers to make their classification decisions straightforwardly, a custom graphical user interface (GUI) was written in MATLAB using the GUIDE layout editor (Figure 1). The observer could change the current synthetic snake by selecting from 1 of the 9 pattern types displayed at the bottom of the screen (Figure 2). The set of 9 could be manipulated by clicking buttons to increase or decrease D u and α. A set of axes showing the current D u and α value was displayed to facilitate observers navigation around pattern space and ability to return to different patterns. Observers could switch between simple and complex patterns via a button press. In addition to classifying the pattern, observers were also asked which colors were present on the snake. Color categories were the 11 basic color terms (Berlin and Kay 1969): black, white, gray, brown, blue, green, red, yellow, pink, purple, and orange. As color could not be measured accurately in this large sample of uncalibrated images taken in uncontrolled conditions, either objectively using spectral measurements (Endler 1990) or transformed camera pixel values (Stevens et al. 2007), or subjectively using, for example, color chips, this approach offers a way of capturing the rough properties of a snake s spectral reflectance. As human perception of surface reflectance in digital images adjusts to estimates of scene illumination (color constancy; Land 1971) and because we selected

5 Allen et al. Snake dorsal patterns 1241 Figure 1 Screenshot of the MATLAB GUI used to classify the snake patterns interactively. Top left is the image containing the snake to classify, and beneath this, the current classification selection. The 9 options for the current combination of Du and α are below this. Top right are buttons enabling navigation between different combinations of Du and α, selection of plain, simple or complex patterns, colors, contrast, and classification satisfaction. Figure 2 Example of the 9 basic patterns for 1 combination of Du and α. Here, Du = and α = 1.6. Spot and reverse spot patterns are formed by manipulating β, and longitudinal and transverse stripes are formed by manipulating diffusion anisotropy δu. In total, there are 50 combinations of Du and α, for a total of 450 different potential base patterns. photographs that did not have a strong color cast, judgments will be largely unaffected by the color of the illuminant when the image was taken. Observers were required to make a judgment on a 5-point scale of how high the contrast between pattern elements was (but told to ignore this question if the snake was plain) and rate how satisfied they were with the accuracy of their classification on a 5-point scale from poor to excellent. Observers pressed a button to indicate they were finished with their classification. If any questions were unanswered, an error message was produced. Otherwise, parameters were reset and the next snake image for classification was displayed. Observers worked at their own pace, taking breaks as desired. The entire process typically took 5 h and was spread over a few days. Pattern measures for analysis Each classification was recorded as follows: Du and α scores were those that underlied the classification pattern. Whether each trial was judged to be plain, patterned, complexly patterned, or containing each color was initially scored as yes (1) or no (0). Because only 213 of 4140 classifications were for reverse-spotted patterns (negative β values forming patterns with light spots on a dark background, lower left patterns in Figure 2), these were grouped together with spotted patterns (positive β values, upper right patterns in Figure 2). Spot scores for each classification were either not-spotted (0), intermediate spots (1), or regular spots (2), depending on the value of β. Transverse stripe scores were either absent (0) when δu = 0, intermediate (1) when δu = 0.495, and present (2) when δu = 0.99, and longitudinal stripe scores were either absent (0) when δu = 0, intermediate (1) when δu = 0.495, and present (2) when δu = As the basal pattern type in the model (central pattern in Figure 2), blotch scores of 2 were given if all the other pattern type (spot, reverse spot, longitudinal, and transverse stripe) scores were 0, 1 if the sum of other pattern type scores was 1, and 0 if the sum of other pattern type scores was 2. To determine species scores for all variables in the classification task, we took the median classification of each example snake image, with the contribution of each observer s score weighted by their normalized classification confidence score. This was done so that if an observer was not confident with their classification choice, it had less influence on the average classification for each image. To obtain species average measures, the mean of the weighted medians was taken. Blotch, spot, transverse stripe, and longitudinal stripe scores were multiplied by the patterned score so that species which were mainly classed as plain, but occasionally classed as patterned, had lower scores than those always classified as patterned. Thus, these pattern type scores reflect the overall frequency of blotches, spots, transverse, or longitudinal stripes in each species coloration on a scale of 0 1.

6 1242 Behavioral Ecology Plotting D u against α (Figure 3) showed that most variation was along a single dimension that corresponded to a measure of pattern element size, with increasing values of both variables creating larger patterns. Consequently, principal components analysis (PCA) was used to reduce D u and α to a single dimension. The first component accounted for 86.71% of variance (eigenvalue = 1.51). The remaining 13.29% of variance had an eigenvalue of 0.20 and was strongly correlated with longitudinal stripe score (R = 0.840, P < 0.001) so we decided to use the original longitudinal stripe score in analyses rather than the second component. We used classical multidimensional scaling (MDS) to assess the similarities and dissimilarities of the Euclidian distances between vectors of species 11 average color scores to explore the possibility of reducing the number of color categories. The first dimension gave low scores to species that were often classified as having colors traditionally considered as components of snake warning coloration (black MDS coefficient = 0.634, white = 0.246, red = 0.226, and yellow = 0.219) and high scores to species that were classified as having colors commonly considered cryptic (brown = 0.634, gray = 0.171, and green = 0.08). Other colors, as well as being very uncommon, were not strongly associated with position on this dimension (blue = 0.047, pink = 0.043, purple = 0.005, and orange = 0.036). Therefore, rather than analyzing each color separately, we included this dimension as a factor in our analysis to describe how cryptic or conspicuously colored each species was. Phylogenetic analyses To assess how snake patterning is related to the ecological and behavioral measures, we conducted phylogenetic generalized least squares (PGLS) analyses (Grafen 1989; Freckleton et al. 2002) in the caper package (Orme et al. 2012) for R (R Development Core Team). All variables were standardized before analysis. Minimal adequate linear regression models for Figure 3 Median pattern classifications of each species D u and α scores. D u and α scores for non-longitudinally striped species are strongly correlated and both describe pattern size. Principal component analysis was used for dimension reduction; the line shows the first component. each of the response measures (plain patterning score, longitudinal stripe score, transverse stripe score, spot score, blotch score, pattern size score, complex pattern score, and cryptic color score) were constructed by first eliminating all terms from the full model with P > 0.5, then using backward elimination of ecological measures until only traits with P < 0.05 remained. Model diagnostics were checked for linear regression assumptions. In no instances were there outliers necessitating removal. The cryptic color and transverse stripe models were constructed both with and without the 5 study species (Cemophora coccinea, Lampropeltis mexicana, Lampropeltis pyromelana, Lampropeltis zonata, and Rhinocheilus lecontei), which are putative mimics of the coral snakes Micruroides euryxanthus and M. fulvius (Pyron and Burbrink 2009a) because eco-behavioral variables may relate to the color pattern per se or the pattern-venom association (i.e., aposematism). Where predictor variables were scored in a categorical fashion, we analyzed their possible effects in a 2-step process. In the primary analysis, they were treated as linear contrasts because, for all factors considered, any predicted effect was expected to be monotonic. For example, for the 3-point scale from nonvenomous (0) to highly venomous (2), if there is any relationship with color, it is likely to be continuously increasing or decreasing. However, even if not predicted by theory or expected from previous studies, it would be unwise to ignore possible nonmonotonic relationships so, in a secondary analysis (Supplementary Appendix 7), these were modeled as polynomial contrasts to allow for nonlinear relationships. These results should be considered exploratory, as stimuli for future studies or development of new functional hypotheses. Results Intraclass correlation coefficients for all of the pattern classification measures ranged from (spot score) to (pattern contrast score), indicating that observers were making very similar classifications, that they were able to navigate the pattern space effectively to find the most appropriate pattern, and that they were using similar criteria to judge similarity. No single observer appeared to be classifying particular patterns dramatically differently from the others. This suggests that pattern space was perceptually well defined and without distant areas of pattern space that produced perceptually similar patterns. Participants classified 28 species as always being plain, 85 species were always classified as having a pattern, and the remaining 58 species were sometimes classified as plain and sometimes as patterned. These species included species with pattern polymorphisms and those with indistinct patterns. The number of species with scores more than 0.25 for each of the weighted pattern measures were: longitudinal stripes (17), transverse stripe (60), blotch (36), and spot (61). Forty-four species had weighted complex pattern scores more than A table of classification results is available in Supplementary Appendix 5. Figure 4 gives examples of the median classifications of several species and their position within a simplified snake pattern space. The summary results of PGLS analyses are presented in Table 2. The full model selection processes are reported in Supplementary Appendix 6. Having a plain integument was associated with an active hunting strategy. Species with longitudinal stripes were generally small, fast, and often exposed to visually hunting predators. Species frequently classified as having regular spotted patterns were more common in North America, frequently near cover, and

7 Allen et al. Snake dorsal patterns 1243 Figure 4 Examples of a selection of the snake images classified (photos), synthetic patterns based on classification scores for image (beneath corresponding photo), and the position of each example in a simplified representation of snake pattern space (plainness, color, complexity, and contrast not shown). Top left panel: spotted snakes. (a) Western hog-nosed snakes, Heterodon nasicus. (b) Cottonmouth, Agkistrodon contortrix. (c) Brown snake, Storeria dekayi. (d) Narrow-headed garter snake, Thamnophis rufipunctatus. Top right, blotched snakes. (i) Stimson s python, Antaresia stimsoni. (q) Speckled kingsnake, Lampropeltis getula holbrooki. Bottom left: longitudinally striped snakes. (o) Aquatic garter snake, Thamnophis atratus. (p) Northwestern garter snake, Thamnophis ordinoides. Bottom left: transverse striped snakes. (j) Eastern coral snake, M. fulvius. (m) Woma, Aspidites ramsayi. (t) DeVis banded snake Denisonia devisi. Examples e, f, g, h, n, r, s, and u are not of a specific snake, but included to illustrate the range of pattern space. (a) G.A. Hammerson. (b) Unknown. (c) J.D. Willson. (d) Tom Brennan. (i) David Fischer. (q) Mike Pingleton. (o and p) Gary Nafis, (j) Unknown. (m) Jordan Vos. (l) Unknown.

8 1244 Behavioral Ecology Table 2 Regression results for the best supported phylogenetically informed generalized least-squares models explaining variation in pattern classification scores. Model λ estimates phylogenetic signal in the model residuals Pattern trait Fixed effect Coefficient Standard error t P-value Plain score, λ = 0.855, P(λ = 0) < 0.001, P(λ = 1) < 0.001, R 2 = 0.029, F(2,169) = 5.119, P = (Intercept) Hunting strategy Spot score, λ = 0, P(λ = 0) = 1, P (λ = 1) < 0.001, R 2 = 0.147, F(4,139) = 8.011, P < (Intercept) Australian Birds Exposure amount Longitudinal stripe score, λ = 0.682, P(λ = 0) < 0.001, P(λ = 1) < 0.001, R 2 = 0.134, F(4,139) = 7.149, P < (Intercept) Escape speed Exposure amount SVL Transverse stripe score excluding mimics, λ = 0.855, P (λ = 0) < 0.001, P (λ = 1) < 0.001, R 2 = 0.100, F(4,135) = 5.013, P = (Intercept) Eggs Erratic movement Habitat generalism Transverse stripe score including mimics, λ = 0.903, P (λ = 0) < 0.001, P (λ = 1) < 0.001, R 2 = 0.078, F(3,140) = 5.943, P = (Intercept) Arboreality Grassland diverse Blotch score, λ = 0, P (λ = 0) = 0, P (λ = 1) < 0.001, R 2 = 0.221, F(5,138) = 9.756, P < (Intercept) Cloacal defense Escape speed Hunting strategy SVL Cryptic color score excluding mimics, λ = 0, P (λ = 0) = 1, P (λ = 1) < 0.001, R 2 = 0.134, F(4,162) = 7.998, P < Cryptic color score including mimics (Intercept) Cloacal defense Escape speed Mammals No significant terms Absolute pattern size score, λ = 0.835, P (λ = 0) < 0.001, P (λ = 1) < 0.001, R 2 = 0.038, F(2,141) = 5.55, P = Relative pattern size score (Intercept) Habitat generalism No significant terms Complex pattern score, λ = 0.854, P (λ = 0) < 0.001, P (λ = 1) < 0.001, R 2 = 0.140, F(4,139) = 7.55, P < (Intercept) Arboreality Australian SVL sexual dimorphism Pattern contrast score, λ = 0.806, P (λ = 0) < 0.001, P (λ = 1) < 0.001, R 2 = 0.095, F(4,139) = 4.861, P < (Intercept) Arboreality Escape speed SVL

9 Allen et al. Snake dorsal patterns 1245 predators of birds. Transverse stripes were rare on species living in grasslands or an arboreal lifestyle. When coral snake mimics are removed from the sample, transverse stripes are predicted by erratic movement, habitat specialism, and egg consumption. Blotched patterns were associated with an ambush hunting strategy, slow movement, large body size, and pungent cloacal defense. The association predicted by Jackson et al. (1976) and Creer (2005) between both these pattern phenotypes and aggressive behavior was not supported (aggression term in final blotch model: r = 0.027, standard error = 0.077, t = 0.302, P = 0.76; aggression term in final transverse stripe model: r = 0.023, standard error = 0.076, t = 0.302, P = 0.76). The model of complex patterning showed a positive association toward species where females grow longer than males, those which live in North America and those which are more terrestrial. Higher contrast between the colors and tones of pattern elements was observed on small terrestrial snakes and those that can move rapidly away from threats. Habitat generalists generally had patterns with smaller elements in absolute terms, but none of the predictors were associated with the size of pattern elements relative to snout-vent length (SVL). When mimics were included in the analysis, no predictors were related to the cryptic color score. However, when mimics were removed, the minimal adequate color model included main effects of escape speed, mammalian predation, and cloacal defense, with snakes that are slow, predate on mammals, and described as having highly pungent cloacal defenses generally having more cryptic colors. Table 3 shows λ estimates for all the pattern and eco-behavioral traits, indicating whether a trait evolves on the snake tree in accordance with a Brownian motion model of trait evolution (λ = 1) or with no detectable phylogenetic signal (λ = 0). This shows that most traits measured are relatively conservative, with λ values at or near 1. Exceptions include spot and blotch scores, which are more evolutionarily labile. Some pattern traits were related to each other; correlations after accounting for phylogeny are presented in Table 4. These show that blotched, transverse striped, and to a lesser extent, longitudinally striped snakes are generally high contrast. Transverse stripes are also likely to be complex, probably the result of classifications of coral snakes and their mimics. Spot patterns are generally lower contrast, simpler, smaller, and more cryptically colored than other pattern types. Discussion By analyzing snake patterns in terms of a biologically plausible mathematical model of snake pattern development, we obtained detailed classifications of large numbers of snake patterns. The parameters of the pattern development model corresponded to visual attributes of patterning such as anisotropy, pattern size, and complexity. Conceptually, in our model, diversity in patterning evolves through changes in parameter values. The parameter values were associated with ecological and behavioral variables to understand the drivers of diversity in snake patterning in a phylogenetic context. Like Jackson et al. (1976), we found that pattern diversity was mainly related to behavior rather than habitat choice. Jackson et al. (1976) reported that dorsal patterns were associated with 2 broad antipredator strategies in snakes. Plain and longitudinally striped snakes had limited defensive ability and instead relied on rapid flight from threats to escape predation. In contrast, they found that transverse striped and blotched snakes were generally aggressive and well defended to respond to attacks. Similar patterns of association were observed in this study for plain and longitudinally striped snakes but not blotched and transverse striped snakes. The latter conclusions of Jackson et al. (1976) are, therefore, not robust to increasing the sample to include Australian species, controlling for phylogeny and using more detailed measures of pattern. Species with higher longitudinal stripe scores were generally small snakes frequently exposed to danger, but able to move away from threats rapidly (though they were not found to be particularly placid or poorly defended with venoms, as suggested by Jackson et al. (1976)). Nevertheless, these associations suggest a pattern phenotype especially suited to flight as a primary defense. With a few possible exceptions, such as the black mamba Dendroaspis polylepis (Spawls et al. 1995), even relatively fast snakes are unlikely to be able to outrun their major predators over extended periods (Mosauer 1935; Jayne 1986), so if a snake chooses to flee when threatened, it must either use tactics that cause a predator to lose track of it or reach a refuge where it can no longer be captured. Snake species whose habitat and behavior requires them to generally have to travel further to reach a safe retreat may find patterning which makes tracking difficult for predators especially advantageous. Previously, it has been proposed that longitudinal stripes achieve this in 2 ways: first, by reducing the probability of initial or subsequent detection while stationary through camouflage with disruptive elements; and second, if detected, by making it difficult for predators to track while the snake is fleeing by not providing reference points on the body (Brattstrom 1955; Jackson et al. 1976; Brodie 1989, 1992). With regard to a disruptive camouflage function for longitudinal stripes, because few elements intersect with the body outline the camouflage principle is likely to be surface disruption rather than disruption of outline (Stevens et al. 2009). However, as the pattern elements run parallel to the true outline of the snake, it is not obvious how this design would effectively disguise form. The principal camouflage mechanism may, therefore, be background matching, though quite what backgrounds longitudinal stripes would be effective against is unclear. As for the argument that having pattern elements that do not vary along the primary axis of forward movement removes features that can be tracked (in contrast to blotched, transverse striped, and spotted patterns), this idea is plausible. However, the advantage longitudinal stripes might have over plain patterns, other than a separate improvement in camouflage against certain backgrounds, is less obvious. Perhaps, predator attention is focused on stripes and so away from other potential reference points that proceed with the snake s forward movement (Brattstrom 1955)? Longitudinal stripes may also make tracking more difficult by creating misleading local motion detection signals in directions different from the global heading of the snake (Hu et al. 2009), especially if only segments of the snake are seen at 1 time, as in the barber pole illusion (Wallach 1935), an instance of the aperture problem (Hildreth 1984). Just as we found, Jackson et al. (1976) also noted the association between plain patterning and active hunting and interpreted this in terms of movement camouflage. Like longitudinally striped snakes, a plain snake moving forward would be devoid of any trackable reference points. Unlike longitudinally striped snakes, plain snakes lack patterns that may cause a misleading motion signal during movement. Perhaps, a plain strategy is adapted to favor improved crypsis, whereas motionless compared with longitudinal stripes or

10 1246 Behavioral Ecology Table 3 Single trait λ estimates showing the degree of phylogenetic signal present in each trait. A trait with λ = 0 contains no phylogenetic signal, i.e., it is extremely labile. When λ = 1, the trait is phylogenetically conservative, conforming to a Brownian motion model of trait evolution Trait λ P(λ = 0) P(λ = 1) 95% Confidence interval Pattern traits Absolute pattern size <0.001 <0.001 (0.554, 0.977) Blotch <0.001 (0.070, 0.850) Cryptic color <0.001 <0.001 (0.712, 0.947) Longitudinal stripe <0.001 <0.001 (0.504, 0.859) Plain <0.001 <0.001 (0.927, 0.989) Relative pattern size <0.001 <0.001 (0.881, 0.992) Spot 0 1 <0.001 (NA, 0.752) Transverse stripe <0.001 <0.001 (0.725, 0.978) Continent Australia <0.001 <0.001 (0.958, 0.988) Morphology SVL <0.001 <0.001 (0.927, 0.989) SVL sexual dimorphism <0.001 <0.001 (0.865, 0.975) Girth <0.001 <0.001 (0.777, 0.955) Behavior Activity time <0.001 <0.001 (0.883, 0.973) Exposure amount <0.001 <0.001 (0.609, 0.943) Hunting strategy <0.001 <0.001 (0.711, 0.951) Antipredator Erratic movement <0.001 <0.001 (0.800, 0.964) Aggression <0.001 <0.001 (0.493, 0.923) Cloacal defense <0.001 <0.001 (0.796, 0.945) Death feigning 1 < (0.961, NA) Escape speed 0.98 <0.001 <0.001 (0.954, 0.992) Venom potency 1 < (0.999, NA) Diet Eggs <0.001 <0.001 (0.828, 0.988) Amphibians <0.001 <0.001 (0.413, 0.910) Birds <0.001 <0.001 (0.328, 0.869) Fish <0.001 <0.001 (0.821, 0.945) Invertebrates <0.001 <0.001 (0.747, 0.943) Mammals <0.001 <0.001 (0.885, 0.980) Reptiles <0.001 <0.001 (0.907, 0.991) Habitat Aquatic <0.001 <0.001 (0.879, 0.961) Aquatic diverse <0.001 <0.001 (0.647, 0.904) Arboreality <0.001 <0.001 (0.391, 0.887) Desert 0 <0.001 <0.001 (NA, 0.134) Desert diverse <0.001 <0.001 (0.191, 0.822) Forest 0 1 <0.001 (NA, 0.253) Forest diverse <0.001 <0.001 (0.329, 0.904) Fossoriality <0.001 <0.001 (0.918, 0.987) Grassland 0 1 <0.001 (NA, 0.413) Grassland diverse <0.001 <0.001 (0.329, 0.904) Habitat generalism 0 1 <0.001 (NA, 0.595) NA = not applicable. Table 4 Phylogenetic correlations among standardized pattern traits Blotch Longitudinal stripe Transverse stripe Contrast Complex pattern Cryptic color Absolute pattern size Relative pattern size Spot Blotch Longitudinal stripe Transverse stripe Contrast Complex pattern Cryptic color Absolute pattern size maybe plain snakes do not move quickly enough to make motion confusion caused by longitudinal stripes effective. Blotched patterns are typically used by large and slow ambush hunters and those with pungent cloacal defenses. Blotched patterns may be especially cryptic whereas motionless in typical ambush sites. As well as choosing sites where potential prey have left chemical cues (Clark 2004), snakes favor ambush sites in cover, whether this is under boulders (Tsairi and Bouskila 2004), in leaf litter, or around fallen branches (Clark 2006), all microhabitats likely to have irregularly shaped background objects or patterns of shadowing in which blotched patterns should be especially effective.

11 Allen et al. Snake dorsal patterns 1247 An argument for the transverse stripe strategy put forward in Jackson et al. (1976) and Pough (1976) was that these patterns are disruptive while the snake is motionless, but if a snake chooses to flee, the stripes merge to form a uniform pattern devoid of trackable reference points because the temporal frequency of pattern elements exceeds the critical fusion frequency (CFF) of the predator s vision. In support of this hypothesis, they showed how slower transverse striped snakes have more stripes, as would be necessary to achieve sufficient temporal frequency for flicker-fusion, and larger snakes have more stripes, suggestive because the Granit Harper law states that as stimulus area increases, so does CFF (Granit and Harper 1930; Rovamo and Raninen 1988). Our results are inconclusive on this theory, though the association between transverse striping and erratic movement suggests camouflage that functions in conjunction with movement (Hall et al. 2013). Patterns of relationships that would be more indicative, for example, between transverse striping and rapid escape speed, were not observed. Proper evaluation of this hypothesis would require detailed empirical work to assess whether CFF is exceeded during escape under natural predation conditions. Though there are physiological upper limits on CFF due to photoreceptor recovery rates, a number of variables influence CFFs including brightness, spectral composition, stimulus size, and viewing eccentricity (Kelly 1974; Jarvis et al. 2002). Although human observers field observations of snake patterns fusing are suggestive (Pough 1976; Shine and Madsen 1994), direct evidence for this idea is lacking (Stevens 2007) and what matters is the CFF of the normal predator(s), not that of humans. The hypothesis also rests on the assumption that the predator is unable to track forward progress at any point during attack. The idea of transverse stripes fusing in predators perceptions during escape needs to be treated with caution until after it has been empirically assessed with respect to snake speed and predator vision in natural viewing conditions (Pough 1976; Endler 1978; Ruxton et al. 2004; Stevens 2007). With regard to spotted patterns, these were more common on American species, those which predated birds and those which were frequently near cover. Interpretation of this pattern of associations is not straightforward, but taken in conjunction with the findings that small patterns were more common on habitat generalists and that spot patterns were generally small (Table 4), it is likely that spot and speckle patterns provide a good general-purpose background matching camouflage pattern, effective when hiding against a wide variety of backgrounds. We are unaware of any evidence that would suggest spots are especially effective at hiding from avian vision so this association awaits interpretation. It is also unclear why species with complex patterns (Osorio and Srinivasan 1991) are associated with a less arboreal lifestyles. Similarly, confident explanations for why complex patterning is associated with species where females grow larger than males, and why there is generally lower contrast between pattern elements in arboreal species, are also hard to provide at this time. High-contrast patterns are probably found on faster species because of the influence of pattern contrast on speed perception, though the exact effect is unclear because increased contrast can increase or decrease perceived speed (e.g., Thompson 1982; Scott-Samuel et al. 2011). It is also worth pointing out that if highcontrast patterns cause misperception of speed, then this will have influenced the reports of snakes speed on which the escape speed measure was based. Proper evaluation of this theory will require new comparative data on snake locomotion speeds taken with standardized methods (Jayne 1986). The reason for the associations between high-contrast pattern and both small body size and decreasing arboreality await further investigation. The associations with the color measure showed that, after removing coral snake mimics, more cryptic colors are used by slower species, those which prey on mammals and those which possess strong cloacal defense. This does not support our expectation that blacks, whites, reds, and yellows would be used by aggressive and venomous snakes as components of an aposematic coloration strategy. There is now a considerable amount of evidence suggesting that some snakes color patterns function as warning signals (Savage and Slowinski 1992; Brodie 1993; Brodie and Janzen 1995; Hinman et al. 1997), rather than these color patterns having no functional difference from similar patterns with cryptic colors, as suggested by Brattstrom (1955). However, selection in aposematic species does not necessarily favor increased conspicuousness (Endler and Mappes 2004), rather distinctiveness may be key (Sherratt and Beaty 2003; Stevens and Ruxton 2012). Evidence is emerging that apparently cryptic snake patterns, which do not contain traditionally conspicuous colors, can also have an aposematic function, for example, the zig-zag patterns on European vipers (Wüster et al. 2004; Niskanen and Mappes 2005; Valkonen et al. 2011). If snakes are commonly aposematic without being conspicuously colored, given that coral snakes and other conspicuously colored dangerous snakes such as Pelamis platurus are uncommon in our sample, an association across the 171 species in our sample between color, venom potency, and aggressiveness may not necessarily be expected. That conspicuous colors are rarer on snakes, which feed on mammalian prey, is interesting. Pyron and Burbrink (2009a) noted a similar result, finding that coral snake mimicry was common in species that feed on ectothermic prey. The most obvious general difference between mammals and other prey categories (except eggs) in this context is reduced color vision, though if the function of bright colors is to deter predation on snakes rather than improve hunting success, this association is in the opposite direction to that predicted if color was being utilized to communicate to predators but remain cryptic from prey. The functional significance of this relationship merits further investigation. In general, the developmental model performed well, allowing detailed aspects of patterning and pattern variation within and between species to be captured. Several study species received relatively low confidence scores from observers. Observer feedback and the patterns of these species suggested that they were taxa with either very complex patterns which the model could only roughly approximate, and those which included multiple features such as both spots and stripes, for example, the timber rattlesnake Crotalus horridus, which has irregularly shaped transverse stripes and a single longitudinal stripe. Instead, depending on the aspects of patterning observers considered most important, patterns were classified as either of 1 or the other type, but because of intraspecific and interobserver variation, this ambiguity meant that mean classifications reflected the general pattern well. For example, the mountain garter snake Thamnophis elegans has spots, blotches, and longitudinal stripes to varying extents between individuals and mean classifications resulted in a spot score of 0.52, blotch score of 0.21, and a longitudinal stripe score of The model also has some difficulty in discriminating between snakes with regularly sized and shaped transverse stripes and snakes with more irregular transverse stripes (compare M. fulvius and Aspidites ramsayi; Figure 4j and m). Murray and Myerscough s (1991) cell chemotaxis model of snake pattern development can more accurately reproduce the visual appearance of some complex snake patterns such as the diamond patterns of the eastern diamondback Crotalus adamanteus and the double spot