Behavioral
Ecology
The official journal of the
ISBE
International Society for Behavioral Ecology
Behavioral Ecology (2013), 24(5), 1237–1250. doi:10.1093/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. Cuthillb
aSchool of Experimental Psychology, University of Bristol, 12a Priory Road, Bristol BS8 1TU, UK and
bSchool 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 2013.
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. E-mail: [email protected].
© The Author 2013. Published by Oxford University Press on behalf of the
International Society for Behavioral Ecology. All rights reserved. For permissions,
please e-mail: [email protected]
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
1238
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,
Behavioral Ecology
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
Allen et al. • Snake dorsal patterns
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 www.wikipedia.org) were used to corroborate and supplement information. When printed information was
unavailable or unclear, we contacted experts in the field to supply
1239
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
= Du (θ )∇2u ) + u − u 3 − v ∂t
(1a)
∂v
= Dv ∇2v + γ (u − α − β )(1b)
∂t
Where Du(θ) is the anisotropic diffusion function:
Du (θ ) =
1
(2)
1 − δ u cos 2θ ′
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. Du and Dv 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 ((δu δx ) (δu δ y )))
−1
and δu is the magnitude of anisot-
ropy 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 – u3 – 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.
Behavioral Ecology
1240
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
Body girth
Sexual SVL dimorphism
Log (cm)a
Ordinal: broad (0), normal (1), slender (2)
Ordinal: mSVL > fSVL + 10% (0); mSVL = fSVL ± 10% (1); mSVL + 10% < fSVL (2)
Habitat type
Desert
Desert diverse
Grassland
Grassland diverse
Forest
Forest diverse
Aquatic
Aquatic diverse
Habitat generalism
Fossoriality
Arboreality
Ordinal: absent (0), present (1), preferentially present (2)b
Sum of all habitat type scores
Ordinal: remains above ground (0), occasional burrower (1), rarely above ground (2)
Ordinal: not arboreal (0), intermediate (1), arboreal (2)
Behavior
Activity time
Hunting strategy
Exposure amount
Ordinal: nocturnal (0), mainly nocturnal (1), intermediate (2), mainly diurnal (3), diurnal (4)
Ordinal: ambush hunter (0), flexible (1), active hunter (2)
Ordinal: always near cover (0), intermediate (1), frequently away from cover (2)
Antipredator defense
Aggressiveness
Venom potency
Escape speed
Cloacal excretions
Erratic movements
Death feigning
Ordinal: placid (0), occasionally aggressive (1), aggressive (2)
Ordinal: nonvenomous (0), venomous (1), and highly venomous (2)c
Ordinal: slow (0), normal (1), fast (2), very fast (3)
Ordinal: absent (0), present (1), present and highly pungent (2)
Dichotomous: absent (0), present (1)
Dichotomous: absent (0), present (1)
Diet
Invertebrate
Fish
Amphibians
Reptiles
Eggs
Birds
Mammals
Mainly interval: percentage of total diet, when quantitative data were unavailable, ordinal:
absent (0), occasional (1), preferred (2)d
Continent
North American/Australian
Dichotomous: North American (0), Australian (1)
aLog-transformed
prior to analysis to correct for a positive skew.
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.
cData on venom capability’s defensive usage are frequently unavailable, though all highly venomous snakes are likely to be potentially dangerous to predators.
dOrdinal 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.
bDiverse
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 Du and α. A set of axes showing the
current Du 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
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 = 0.005 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 = −0.99. 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.
Behavioral Ecology
1242
Plotting Du 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 Du 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 Du and α scores. Du 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 0.851 (spot score) to 0.923 (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 0.25. 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
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, www.californiaherps.com. (j) Unknown. (m) Jordan Vos. (l) Unknown.
Behavioral Ecology
1244
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, R2 = 0.029, F(2,169) = 5.119, P = 0.007
(Intercept)
Hunting strategy
0.739
0.190
0.888
0.084
0.832
2.262
0.407
0.025
0.078
0.085
0.086
0.086
0.008
−2.692
2.925
−2.726
0.994
0.008
0.004
0.007
−0.005
2.402
2.820
−3.167
0.996
0.018
0.006
0.002
Spot score, λ = 0, P(λ = 0) = 1, P (λ = 1) < 0.001, R2 = 0.147, F(4,139) = 8.011, P < 0.001
(Intercept)
Australian
Birds
Exposure amount
0.001
−0.229
0.251
−0.234
Longitudinal stripe score, λ = 0.682, P(λ = 0) < 0.001, P(λ = 1) < 0.001, R2 = 0.134, F(4,139) = 7.149, P < 0.001
(Intercept)
Escape speed
Exposure amount
SVL
−0.004
0.249
0.217
−0.256
0.667
0.104
0.077
0.081
Transverse stripe score excluding mimics, λ = 0.855, P (λ = 0) < 0.001, P (λ = 1) < 0.001, R2 = 0.100, F(4,135) = 5.013, P = 0.001
(Intercept)
Eggs
Erratic movement
Habitat generalism
−0.080
0.188
0.194
−0.160
1.007
0.074
0.081
0.068
−0.080
2.530
2.391
−2.340
0.937
0.013
0.018
0.021
Transverse stripe score including mimics, λ = 0.903, P (λ = 0) < 0.001, P (λ = 1) < 0.001, R2 = 0.078, F(3,140) = 5.943, P = 0.001
(Intercept)
Arboreality
Grassland diverse
−0.272
−0.221
−0.181
1.190
0.081
0.079
−0.229
−2.721
−2.298
0.819
0.007
0.023
0.069
0.080
0.079
0.071
0.078
−0.526
3.174
−2.906
−2.631
4.702
0.600
0.002
0.004
0.009
0.000
2.065
2.291
−3.055
3.963
0.041
0.023
0.003
0.000
0.370
−2.356
0.712
0.020
−0.138
−3.152
−2.471
2.449
0.891
0.002
0.015
0.016
−0.511
−2.124
2.732
−2.035
0.610
0.035
0.007
0.044
Blotch score, λ = 0, P (λ = 0) = 0, P (λ = 1) < 0.001, R2 = 0.221, F(5,138) = 9.756, P < 0.001
(Intercept)
Cloacal defense
Escape speed
Hunting strategy
SVL
−0.036
0.253
−0.230
−0.188
0.366
Cryptic color score excluding mimics, λ = 0, P (λ = 0) = 1, P (λ = 1) < 0.001, R2 = 0.134, F(4,162) = 7.998, P < 0.001
(Intercept)
Cloacal defense
Escape speed
Mammals
0.139
0.161
−0.205
0.268
0.067
0.070
0.067
0.068
Cryptic color score including mimics
No significant terms
Absolute pattern size score, λ = 0.835, P (λ = 0) < 0.001, P (λ = 1) < 0.001, R2 = 0.038, F(2,141) = 5.55, P = 0.004
(Intercept)
Habitat generalism
0.384
−0.171
1.038
0.073
Relative pattern size score
No significant terms
Complex pattern score, λ = 0.854, P (λ = 0) < 0.001, P (λ = 1) < 0.001, R2 = 0.140, F(4,139) = 7.55, P < 0.001
(Intercept)
Arboreality
Australian
SVL sexual dimorphism
−0.128
−0.228
−0.468
0.220
0.926
0.072
0.190
0.090
Pattern contrast score, λ = 0.806, P (λ = 0) < 0.001, P (λ = 1) < 0.001, R2 = 0.095, F(4,139) = 4.861, P < 0.001
(Intercept)
Arboreality
Escape speed
SVL
−0.488
−0.186
0.340
−0.197
0.954
0.088
0.124
0.097
Allen et al. • Snake dorsal patterns
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
1245
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
Behavioral Ecology
1246
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
Pattern traits
Continent
Morphology
Behavior
Antipredator
Diet
Habitat
Trait
λ
P(λ = 0)
P(λ = 1)
95% Confidence interval
Absolute pattern size
Blotch
Cryptic color
Longitudinal stripe
Plain
Relative pattern size
Spot
Transverse stripe
Australia
SVL
SVL sexual dimorphism
Girth
Activity time
Exposure amount
Hunting strategy
Erratic movement
Aggression
Cloacal defense
Death feigning
Escape speed
Venom potency
Eggs
Amphibians
Birds
Fish
Invertebrates
Mammals
Reptiles
Aquatic
Aquatic diverse
Arboreality
Desert
Desert diverse
Forest
Forest diverse
Fossoriality
Grassland
Grassland diverse
Habitat generalism
0.894
0.477
0.880
0.722
0.971
0.974
0
0.926
0.976
0.971
0.942
0.896
0.945
0.851
0.874
0.917
0.803
0.895
1
0.98
1
0.952
0.755
0.616
0.900
0.880
0.951
0.968
0.930
0.810
0.698
0
0.542
0
0.751
0.965
0
0.751
0
<0.001
0.020
<0.001
<0.001
<0.001
<0.001
1
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
1
<0.001
<0.001
1
<0.001
1
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
1
<0.001
1
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
(0.554, 0.977)
(0.070, 0.850)
(0.712, 0.947)
(0.504, 0.859)
(0.927, 0.989)
(0.881, 0.992)
(NA, 0.752)
(0.725, 0.978)
(0.958, 0.988)
(0.927, 0.989)
(0.865, 0.975)
(0.777, 0.955)
(0.883, 0.973)
(0.609, 0.943)
(0.711, 0.951)
(0.800, 0.964)
(0.493, 0.923)
(0.796, 0.945)
(0.961, NA)
(0.954, 0.992)
(0.999, NA)
(0.828, 0.988)
(0.413, 0.910)
(0.328, 0.869)
(0.821, 0.945)
(0.747, 0.943)
(0.885, 0.980)
(0.907, 0.991)
(0.879, 0.961)
(0.647, 0.904)
(0.391, 0.887)
(NA, 0.134)
(0.191, 0.822)
(NA, 0.253)
(0.329, 0.904)
(0.918, 0.987)
(NA, 0.413)
(0.329, 0.904)
(NA, 0.595)
NA = not applicable.
Table 4 Phylogenetic correlations among standardized pattern traits
Blotch
Spot
Blotch
Longitudinal stripe
Transverse stripe
Contrast
Complex pattern
Cryptic color
Absolute pattern size
0.242
Longitudinal
stripe
Transverse
stripe
−0.487
−0.203
−0.487
0.031
−0.057
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
Contrast
−0.024
0.345
0.141
0.385
Complex
pattern
−0.148
−0.009
0.052
0.220
0.150
Cryptic color
0.006
−0.190
−0.070
−0.106
−0.529
0.183
Absolute
pattern size
Relative
pattern size
−0.161
−0.036
0.167
0.246
0.197
0.212
0.120
−0.214
−0.030
0.238
0.434
0.307
0.274
0.041
0.874
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.
Allen et al. • Snake dorsal patterns
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.
1247
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 0.28. 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
1248
of the European ratsnake Elaphe situla. However, this model was
unsuitable for our purpose of quantifying pattern appearance on
continuous scales, chiefly because it switches frequently between
pattern phenotypes such as longitudinal or transverse stripes with
small changes in parameter values.
It is interesting to visualize hypothetical evolutionary transitions
between pattern phenotypes in our R-D pattern space. Taking the
example of M. fulvius and Aspidites ramsayi (Figure 4j and m), M. fulvius is clearly highly conspicuous, whereas A ramsayi is much more
likely cryptic. These species occupy a similar position on pattern size
and transverse stripe score, but differ in their position on pattern
contrast, cryptic color, and pattern complexity. If the R-D model
has biological validity, then this shows how evolutionary and developmentally simple transitions in pigmentation deposition can lead
to coloration phenotypes with very different functions. Intriguingly,
estimates of λ (Table 3) are lower for blotch and spot pattern types,
suggesting that these may be pattern types in which evolutionary
transitions are easy and happen frequently, whereas acquiring or losing stripes or complex patterning is much more difficult.
In summary, this study first demonstrates that the method of
classifying animal patterns as outcomes of models of developmental pattern formation processes is effective as a general strategy for
making detailed descriptions of biological patterns when standardized images are unavailable (Allen et al. 2011). Second, the comparative analysis of snake patterning suggests that there is good
evidence for some previous hypotheses for the ultimate causes of
broad trends in snake pattern diversity, which had little support
when previous data were analyzed with phylogenetic comparative
methods. This includes how longitudinal stripes and uniform coloration are respectively associated with small, fast, exposed snakes,
and an active hunting strategy, suggesting these camouflage patterns function effectively during movement. Spots are found on
species that are frequently near cover and small speckled patterns
are more common on habitat generalists, suggesting these pattern
types provide good general-purpose camouflage. Blotched patterns
are associated with large, slow snakes that ambush hunt and can
defend themselves with unpleasant cloacal excretions, suggesting
that these patterns provide good camouflage while motionless in
typical ambush locations. Transverse striped snakes do not have a
clear overall pattern to their eco-behavioral associations; the idea
that transverse stripes achieve flicker-fusion during escape is plausible but requires focused empirical testing. Though analysis of
snake color was coarse, the expectation that bright colors would
be common on well-defended species to function as an aposematic
signal was not supported; the factors that lead to the evolution of
warning coloration in snakes await further investigation.
Supplementary material
Supplementary material can be found at http://www.beheco.
oxfordjournals.org/
Handling editor: Candy Rowe
References
Allen WL, Cuthill IC, Scott-Samuel NE, Baddeley R. 2011. Why the leopard got its spots: relating pattern development to ecology in felids. Proc R
Soc B. 278:1373–1380.
Allen WL, Higham JP. 2013. Analyzing visual signals as visual scenes. Am J
Primatol. 75:664–682.
Beatson RR. 1976. Environmental and genetical correlates of disruptive
coloration in the water snake, Natrix s. sipedon. Evolution. 30:241–252.
Behavioral Ecology
Bechtel HB. 1978. Color and pattern in snakes (Reptilia, Serpentes). J
Herpetol. 12:521–532.
Berlin B, Kay P. 1969. Basic color terms: their universality and evolution.
Berkeley (CA): University of California Press.
Bittner TD, King RB, Kerfin JM. 2002. Effects of body size and melanism on the
thermal biology of garter snakes (Thamnophis sirtalis). Copeia. 2002:477–482.
Bowen KD. 2003. Ontogenetic changes in the coloration of the northern
watersnake, Nerodia sipedon sipedon. J Herpetol. 37:729–731.
Brattstrom BH. 1955. The coral snake’mimic’problem and protective coloration. Evolution. 9:217–219.
Brodie E, Janzen F. 1995. Experimental studies of coral snake mimicry:
generalized avoidance of ringed snake patterns by free-ranging avian
predators. Funct Ecol. 9:186–190.
Brodie E. 1992. Correlational selection for color pattern and antipredator behavior in the garter snake Thamnophis ordinoides. Evolution.
46:1284–1298.
Brodie E. 1993. Differential avoidance of coral snake banded patterns by
free-ranging avian predators in Costa Rica. Evolution. 47:227–235.
Brodie ED 3rd. 1989. Genetic correlations between morphology and antipredator behaviour in natural populations of the garter snake Thamnophis
ordinoides. Nature. 342:542–543.
Bryson RW Jr, Pastorini J, Burbrink FT, Forstner MR. 2007. A phylogeny of
the Lampropeltis mexicana complex (Serpentes: Colubridae) based on mitochondrial DNA sequences suggests evidence for species-level polyphyly
within Lampropeltis. Mol Phylogenet Evol. 43:674–684.
Camin JH, Ehrlich PR. 1958. Natural selection in water snakes (Natrix sipedon L.) on islands in Lake Erie. Evolution. 12:504–511.
Campbell JA, Lamar WW. 1989. The venomous reptiles of Latin America.
Ithaca (NY): Comstock Pub. Associates.
Clark RW. 2004. Timber rattlesnakes (Crotalus horridus) use chemical cues to
select ambush sites. J Chem Ecol. 30:607–617.
Clark RW. 2006. Fixed videography to study predation behavior of an
ambush foraging snake, Crotalus horridus. Copeia 2006:181–187.
Cogger HG. 1996. Reptiles and amphibians of Australia. 6th ed. Sydney
(Australia): Reed.
Conant R, Clay WM. 1937. A new subspecies of water snake from islands
in Lake Erie. MI: University of Michigan Museum of Zoology.
Conant R, Collins JT. 1998. Field guide to reptiles and amphibians. Boston
(MA): Houghton Mifflin Harcourt.
Conant R, Stebbins RC, Collins JT. 1999. Reptiles and amphibians. Boston
(MA): Houghton Mifflin Harcourt.
Creer D. 2005. Correlations between ontogenetic change in color pattern
and antipredator behavior in the Racer, Coluber constrictor. Ethology
111:287–300.
Dillon R, Maini PK, Othmer HGG. 1994. Pattern formation in generalized
Turing systems. J Math Biol. 32:345–393.
Drummond AJ, Rambaut A. 2007. BEAST: Bayesian evolutionary analysis
by sampling trees. BMC Evol Biol. 8:1–8.
Endler JA. 1978. A predator’s view of animal color patterns. Evol Biol.
11:319–364.
Endler JA. 1990. On the measurement and classification of colour in studies of animal colour patterns. Biol J Linn Soc. 41:315–352.
Endler JA. 2012. A framework for analysing colour pattern geometry: adjacent colours. Biol J Linn Soc. 107:233–253.
Endler JA, Mappes J. 2004. Predator mixes and the conspicuousness of
aposematic signals. Am Nat. 163:532–547.
Endler JA, Mielke P. 2005. Comparing entire colour patterns as birds see
them. Biol J Linn Soc. 86:405–431.
Ernst CH, Ernst EM. 2003. Snakes of the United States and Canada.
Washington (DC): Smithsonian Books.
Farallo VR, Forstner MR. 2012. Predation and the maintenance of color
polymorphism in a habitat specialist squamate. PLoS One. 7:e30316.
Felsenstein J. 1985. Phylogenies and the comparative method. Am Nat.
125:1–15.
Forsman A, Aberg V. 2008. Associations of variable coloration with niche
breadth and conservation status among Australian reptiles. Ecology.
89:1201–1207.
Freckleton RP, Harvey PH, Pagel M. 2002. Phylogenetic analysis and comparative data: a test and review of evidence. Am Nat. 160:712–726.
Garland Jr T, Ives AR. 2000. Using the past to predict the present: confidence intervals for regression equations in phylogenetic comparative
methods. Am Nat. 155:346–364.
Gibson AR, Falls JB. 1979. Thermal biology of the common garter snake
Thamnophis sirtalis (L.). II. The effects of melanism. Oecologia. 43:99–109.
Allen et al. • Snake dorsal patterns
Grafen A. 1989. The phylogenetic regression. Philos Trans R Soc Lond B
Biol Sci. 326:119–157.
Granit R, Harper P. 1930. Comparative studies on the peripheral and central retina: II. Synaptic reactions in the eye. Am J Physiol. 95:211–228.
Greene HW. 1988. Antipredator mechanisms in reptiles. In: Biology of
the reptilia: Ecology B: defense and life history. Vol. 16. New York: Alan
R. Liss Inc. p. 1–152.
Hall JR, Cuthill IC, Baddeley R, Shohet AJ, Scott-Samuel NE. 2013.
Camouflage, detection and identification of moving targets. Proc R Soc
B. 280:20130064.
Harvey PH, Pagel M. 1991. The comparative method in evolutionary biology. Oxford: Oxford University Press.
Hildreth EC. 1984. The measurement of visual motion. Cambridge (MA):
MIT Press.
Hinman KE, Throop HL, Adams KL, Dake AJ, McLauchlan KK, McKone
MJ. 1997. Predation by free-ranging birds on partial coral snake mimics:
the importance of ring width and color. Evolution 51:1011.
Hu DL, Nirody J, Scott T, Shelley MJ. 2009. The mechanics of slithering
locomotion. Proc Natl Acad Sci U S A. 106:10081–10085.
Isaac LA, Gregory PT. 2013. Can snakes hide in plain view? Chromatic and
achromatic crypsis of two color forms of the western terrestrial Garter
snake (Thamnophis elegans). Biol J Linn Soc. 108:756–772.
Jackson JF, Ingram W, Campbell HW. 1976. The dorsal pigmentation pattern of snakes as an antipredator strategy: a multivariate approach. Am
Nat. 110:1029–1053.
Jarvis JR, Taylor NR, Prescott NB, Meeks I, Wathes CM. 2002. Measuring
and modelling the photopic flicker sensitivity of the chicken (Gallus
g. domesticus). Vision Res. 42:99–106.
Jayne BC. 1986. Kinematics of terrestrial snake locomotion. Copeia
1986:915–927.
Kelly D. 1974. Spatio-temporal frequency characteristics of color-vision
mechanisms. J Opt Soc Am. 64:983–990.
King RB. 1987. Color pattern polymorphism in the Lake Erie water snake,
Nerodia sipedon insularum. Evolution. 41:241–255.
King RB. 1992. Lake Erie water snakes revisited: morph-and age-specific
variation in relative crypsis. Evol Ecol. 6:115–124.
King RB. 1993a. Color-pattern variation in lake erie water snakes: prediction and measurement of natural selection. Evolution. 47:1819.
King RB. 1993b. Color pattern variation in Lake Erie water snakes: inheritance. Can J Zoolog. 71:1985–1990.
Kobayashi R. 1993. Modeling and numerical simulations of dendritic crystal growth. Physica D. 63:410–423.
Lacalli TC, Wilkinson DA, Harrison LG. 1988. Theoretical aspects of
stripe formation in relation to Drosophila segmentation. Development.
104:105–113.
Land JJ. 1971. The retinex theory of color vision. J Opt Soc Am. 61:1–11.
Lawson R, Slowinski JB, Crother BI, Burbrink FT. 2005. Phylogeny of the
Colubroidea (Serpentes): new evidence from mitochondrial and nuclear
genes. Mol Phylogenet Evol. 37:581–601.
Lindell LE, Forsman A. 1996. Sexual dichromatism in snakes: support for
the flicker-fusion hypothesis. Can J Zoolog. 74:2254–2256.
Maddison W, Maddison D. 2001. Mesquite: a modular system for evolutionary analysis. Version 2.75. http://mesquiteproject.org
Meinhardt H. 1982. Models of biological pattern formation. London:
Academic Press.
Mosauer W. 1935. How fast can snakes travel? Copeia 1935:6–9.
Murray JD. 2002. Mathematical biology. New York: Springer.
Murray JD, Myerscough MR. 1991. Pigmentation pattern formation on
snakes. J Theor Biol. 149:339–360.
Nakagawa S, Freckleton RP. 2011. Model averaging, missing data and
multiple imputation: a case study for behavioural ecology. Behav Ecol
Sociobiol. 65:103–116.
Niskanen M, Mappes J. 2005. Significance of the dorsal zigzag pattern of Vipera latastei gaditana against avian predators. J Anim Ecol.
74:1091–1101.
Orme CDL, Freckleton RP, Thomas GH, Petzoldt T, Fritz SA, Isaac NJB.
2012. Caper: comparative analyses of phylogenetics and evolution in R.
Meth Ecol Evol. 3:145–151.
Osorio D, Srinivasan MV. 1991. Camouflage by edge enhancement in animal coloration patterns and its implications for visual mechanisms. Proc
R Soc B. 244:81–85.
Pagel M. 1994. Detecting correlated evolution on phylogenies: a general
method for the comparative analysis of discrete characters. Proc R Soc
B. 255:37–45.
1249
Peterson CR, Gibson AR, Dorcas ME. 1993. Snake thermal ecology: the causes and consequences of body-temperature variation.
In: Snakes: ecology and behavior. New York: McGraw-Hill. p.
241–314.
Pough FH. 1976. Multiple cryptic effects of crossbanded and ringed patterns of snakes. Copeia 1976:834–836.
Pyron RA, Burbrink FT. 2009a. Body size as a primary determinant
of ecomorphological diversification and the evolution of mimicry
in the lampropeltinine snakes (Serpentes: Colubridae). J Evol Biol.
22:2057–2067.
Pyron RA, Burbrink FT. 2009b. Neogene diversification and taxonomic
stability in the snake tribe Lampropeltini (Serpentes: Colubridae). Mol
Phylogenet Evol. 52:524–529.
Pyron RA, Burbrink FT, Colli GR, de Oca AN, Vitt LJ, Kuczynski CA,
Wiens JJ. 2011. The phylogeny of advanced snakes (Colubroidea), with
discovery of a new subfamily and comparison of support methods for
likelihood trees. Mol Phylogenet Evol. 58:329–342.
Rovamo J, Raninen A. 1988. Critical flicker frequency as a function of
stimulus area and luminance at various eccentricities in human cone
vision: a revision of Granit-Harper and Ferry-Porter laws. Vision Res.
28:785–790.
Rubin DB. 1976. Inference and missing data. Biometrika 63:581–592.
Ruxton GD, Sherratt, TN, Speed MP. 2004. Avoiding attack: the evolutionary ecology of crypsis, warning signals, and mimicry. Oxford: Oxford
University Press.
Sahney S, Benton MJ, Ferry PA. 2010. Links between global taxonomic
diversity, ecological diversity and the expansion of vertebrates on land.
Biol Lett. 6:544–547.
Savage JM, Slowinski JB. 1992. The colouration of the venomous coral
snakes (family Elapidae) and their mimics (families Aniliidae and
Colubridae). Biol J Linn Soc. 45:235–254.
Scott-Samuel NE, Baddeley R, Palmer CE, Cuthill IC. 2011. Dazzle camouflage affects speed perception. PLoS One. 6:e20233.
Sherratt TN, Beatty CD. 2003. The evolution of warning signals as reliable
indicators of prey defense. Am Nat. 162:377–389.
Shine R, Ambariyanto, Harlow PS, Mumpuni. 1998. Ecological divergence
among sympatric colour morphs in blood pythons, Python brongersmai.
Oecologia 116:113–119.
Shine R, Madsen T. 1994. Sexual dichromatism in snakes of the genus Vipera:
a review and a new evolutionary hypothesis. J Herpetol. 28:114–117.
Shine R. 1995. Australian snakes: a natural history. Ithaca: Cornell
University Press.
Shoji H, Iwasa Y, Kondo S. 2003a. Stripes, spots, or reversed spots in twodimensional Turing systems. J Theor Biol. 224:339–350.
Shoji H, Iwasa Y, Mochizuki A, Kondo S. 2002. Directionality of
stripes formed by anisotropic reaction-diffusion models. J Theor Biol.
214:549–561.
Shoji H, Mochizuki A, Iwasa Y, Hirata M, Watanabe T, Hioki S, Kondo
S. 2003b. Origin of directionality in the fish stripe pattern. Dev Dyn.
226:627–633.
Spawls S, Branch B, Branch WR. 1995. The dangerous snakes of Africa:
natural history, species directory, venoms and snakebite. Sanibel Island
(FL): Ralph Curtis-Books.
Stebbins RC. 2003. A field guide to western reptiles and amphibians.
Boston: Houghton Mifflin Harcourt.
Stevens M, Párraga CA, Cuthill IC, Partridge JC, Troscianko TS. 2007.
Using digital photography to study animal coloration. Biol J Linn Soc.
90:211–237.
Stevens M, Ruxton GD. 2012. Linking the evolution and form of warning
coloration in nature. Proc R Soc B. 279:417–426.
Stevens M, Winney IS, Cantor A, Graham J. 2009. Outline and surface
disruption in animal camouflage. Proc R Soc B. 276:781–786.
Stevens M. 2007. Predator perception and the interrelation between different forms of protective coloration. Proc R Soc B. 274:1457–1464.
Sweet SS. 1985. Geographic variation, convergent crypsis and mimicry in
gopher snakes (Pituophis melanoleucus) and western rattlesnakes (Crotalus viridis). J Herpetol. 19:55–67.
Tanaka K, Mori A. 2007. Quantitative evaluation of individual snake coloration by use of principal components analysis with variable selection.
Curr Herpetol. 26:117–137.
Thompson P. 1982. Perceived rate of movement depends on contrast.
Vision Res. 22:377–380.
Tinbergen N. 1963. On aims and methods of ethology. Z Tierpsychol.
20:410–433.
1250
Tsairi H, Bouskila A. 2004. Ambush site selection of a desert snake (Echis
coloratus) at an oasis. Herpetologica 60:13–23.
Turing AM. 1952. The chemical basis of morphogenesis. Philos T R Soc
B. 237:37–72.
Valkonen J, Niskanen M, Björklund M, Mappes J. 2011. Disruption or aposematism? Significance of dorsal zigzag pattern of European vipers. Evol
Ecol. 25:1047–1063.
Vidal N, Dewynter M, Gower DJ. 2010. Dissecting the major American
snake radiation: a molecular phylogeny of the Dipsadidae Bonaparte
(Serpentes, Caenophidia). C R Biol. 333:48–55.
Vincent JWJ. 1982. Color pattern variation in Crotalus lepidus lepidus
(Viperidae) in Southwestern Texas. Southwest Nat. 27:263.
Wallach H. 1935. Uëber visuell wahrgenommene Bewegungsrichtung.
Psych Fo. 20:325–380.
Westphal MF, Morgan TJ. 2010. Quantitative genetics of pigmentation
development in 2 populations of the common garter snake, Thamnophis
sirtalis. J Hered. 101:573–580.
Wiens JJ, Kuczynski CA, Smith SA, Mulcahy DG, Sites JW Jr, Townsend
TM, Reeder TW. 2008. Branch lengths, support, and congruence:
Behavioral Ecology
testing the phylogenomic approach with 20 nuclear loci in snakes. Syst
Biol. 57:420–431.
Wilson D, Heinsohn R, Wood J. 2006. Life-history traits and ontogenetic
colour change in an arboreal tropical python, Morelia viridis. J Zool.
270:399–407.
Wilson S, Swan G. 2008. A complete guide to reptiles of Australia. 2nd ed.
Sydney (Australia): Reed.
Wolf M, Werner YL. 1994. The striped colour pattern and striped/
non-striped polymorphism in snakes (Reptilia: Ophidia). Biol Rev.
69:599–610.
Wüster W, Allum CS, Bjargardóttir IB, Bailey KL, Dawson KJ, Guenioui J,
Lewis J, McGurk J, Moore AG, Niskanen M, et al. 2004. Do aposematism
and Batesian mimicry require bright colours? A test, using European
viper markings. Proc R Soc B. 271:2495–2499.
Zaher H, Grazziotin FG, Cadle JE, Murphy RW, Moura-Leite JC,
Bonatto SL. 2009. Molecular phylogeny of advanced snakes (Serpentes,
Caenophidia) with an emphasis on South American Xenodontines:
a revised classification and descriptions of new taxa. Pap Avul Zool.
49:115–153.