New approaches for capturing and estimating variation in complex animal color patterns from digital photographs: application to the Eastern Box Turtle (Terrapene carolina)

Sample collection

Turtle samples of 55 turtles of the species Terrapene carolina were obtained from the Smithsonian Natural History Museum (n = 43) and from two nearby field sites known to have populations, Mason Neck Wildlife Refuge and The Clifton Institute (Virginia, USA; n = 12 in total). The samples selected from the Smithsonian were from locations in Virginia, Maryland and Washington D.C. All the individuals sampled at the Smithsonian Natural History Museum were preserved in ethanol. Field sampling was carried out to test for the influence of varying light conditions on the effectiveness of the color pattern capture method used in this work for animals sampled in the wild. In the field, searches were conducted early in the morning or later in the afternoon when temperatures were around 26° Celsius and 66% humidity (optimal average temperature and humidity to encounter box turtles in this area; E Maki, pers. obs., 2023). For this study we selected only individuals with a relative length >80 mm and a carapace width/length ratio <90%, since smaller individuals do not show the complexity of the pattern (E Maki, pers. obs., 2023). Younger turtles tend to be rounder in shape with a width measurement very close to the length measurement, adult length increases significantly more than their width as they grow (Adamovicz et al., 2018; Langtimm, Dodd & Franz, 1996; Way Rose & Allender, 2011). Males and females were identified based on the sexual dimorphism of the plastron, in which males have a slightly more concave plastron than females (Elghammer et al., 1979; Yahner, 1974; Biewer et al., 2024). Measurements were all taken in the field with a digital caliper.

Data collection

Turtle photographs

Photography took place in both controlled (museum) and field environments, but the methods used for taking the images were the same in order to compare the results obtained for the two different sampling conditions. All Smithsonian specimens were removed from the ethanol, dried slightly, and placed in a white bin next to an 18% gray color standard calibration card (brand: Digital Grey Kard) cut to 50 mm X 30 mm dimensions (Fig. 4). The gray color standard card was also placed next to the turtles sampled in the field (Fig. 4). As box turtles retract their head and stay still during encounters with humans, animals sampled in the field were always still. For each sampled animal (in the field or in the museum), photos were taken from five different viewpoints in order to capture variation in pattern across the entire carapace: top, front, back, left and right views (Fig. 4). Our approach is based on the idea that different body regions may experience distinct selective pressures (e.g., Allen et al., 2020; Glimm et al., 2021). Based on our previous work (Glimm et al., 2021), we hypothesize that different views of the shell of box turtles may show varying levels of morphological variation. Images of each turtle encountered in the field were taken at the time of encounter and in the location where the animal was found. The turtle shells were not cleaned of dirt or dust, though they did not have so much dirt as to occlude the pattern. All photos were taken in RAW format (.dng for the camera used) using a Google pixel 6 cellphone camera set to the default settings as follows: 1.2 µm pixel width, f/1.85 aperture, 82-degree field of view and 1/1.31 image sensor size. Each photo was taken from a distance of about 30 cm from the turtle using the natural light in the field or the fluorescent lighting at the Smithsonian for each specimen. The cellphone was held by hand without any tripod or holding device, except for images used for studying the influence of the angle at which images are taken (see below). One single person obtained the photos for all the individuals included in this study. For each view, two photos (for a total of 10 photos per turtle) were taken placing the camera as parallel to the view as possible. Since photos were obtained without holding devices and the distance from the animal was therefore a rough estimate, photos of each view were taken in duplicates to estimate the influence of the photo capture on variation in the studied measurements. Each duplicate photo was taken immediately after the initial photo without moving or adjusting the turtles. We tried to also maintain the camera position between the two pictures invariant.

For field-sampled animals, images often need to be taken without tripods or holding devices, and animal movement during photography can cause variations in the camera’s distance and angle relative to the subject. To estimate the influence of non-standardized image angle between the turtle and the camera on variation in the pattern measurements, the first three turtles encountered in the field on one random sampling day had images taken at different angles with three images for each view of each individual (instead of two as described above). To ensure that the different angles at which the images were taken were exactly the same across the tested individuals, the cellphone used to take the pictures was placed on a tripod (Amazon Basics) and a phone holder (SharingMoment) at 60 cm straight above each view of the turtle. To obtain different angles at which the photos were taken, each turtle was tilted using a protractor (Westcott). Photos were taken at 0-, 5-, and 10-degrees angles to simulate realistic variation that could happen when taking images of an animal without standardized camera placement. Angles were measured on the turtle by lining up the lowest edge of the carapace (around the middle point of the turtle) with the desired angle of the protractor. Turtles were then tilted to the left (-5, -10), right (+5, +10) and straight overhead (0) for the top view (five images in total for the top view, in triplicate). Turtles were tilted towards the camera (+5, +10) and (0) (camera on the ground parallel to the viewpoint) for the front, back, left, and right views (three images in total for the front, back, left and right views, in triplicate) (Fig. 5). When the camera is positioned as close to the ground as possible for the front, back, left, and right views, it limits the tilt to one direction. However, due to the nature of shooting from above, the camera is more likely to tilt to the left or right in the top view. Zero degrees were obtained when the photo was taken with the camera parallel to the top view of the turtle.

Finally, as organisms sampled in the field may have parts exposed to different light conditions, the gray standard card used for color calibration may not accurately reflect this variation. As such, we wanted to infer the influence of different lighting conditions between the gray standard calibration card and the study object. To do this a basketball hat was placed under three different lighting conditions (full shade, partial shade and full sun) and three photos each from the top and from the front were taken with an 18% color standard card being placed at different distances and lighting conditions from the hat (Fig. S1).

Step 1: Dynamic threshold for yellow detection

In the first pattern extraction step, we identified a “pre-pattern” as the set of pixels in each scute that were a threshold level more yellow than average for that scute. The threshold level is dynamic and adjusts to the overall yellow of each image because the average amount of yellow in an image varied due to lighting conditions, and also the yellow contrast between the pattern background and within the pattern foreground varied substantially from turtle to turtle.

The threshold yellow level was estimated using the red-minus-blue channel difference:

• the red-minus-blue value was calculated at each pixel as the difference of the red and green RGB channel values at that pixel: R − B

• The average red-minus-blue value was calculated for all pixels within the scute: mean(R − B)

• the threshold yellow level was 110% of the average red-minus-blue value (a scute pixel is marked as a pattern pixel if R − B >(1.1 ×mean(R − B)) at that pixel)

The average red-minus-blue value is unique to each image scute. By trial and error, the threshold parameter of 110% of each scute’s average red-minus-blue difference was determined to most closely capture the yellow pattern identified by eye. We test the effect of varying this threshold parameter on the captured pattern by measuring the sensitivity of pattern measures to the threshold in ‘Influence of the choice of threshold value’.

Step 2: Removal of spurious small objects

Once the set of pixels that were more yellow was identified by the formula described above, isolated pixels and groupings of pixels less than the threshold size of one mm² were removed. Depending on the spatial resolution of the image (i.e., pixels per mm), this threshold varied from 25 to 400 pixels. These pixels were identified as more yellow than average by the previous step, but were likely to be noise (or spurious non-pattern objects) since they were small and disconnected from larger yellow regions.

Step 3: Refinement of detected patterns

The third step of the pattern cleaning process was to fill small “holes” found within the identified yellow regions. Within connected yellow regions, isolated pixels often failed to meet the yellow threshold, possibly due to noise such as light scattering or glare. Gaps in the pattern objects were filled if they were smaller than one mm².

Step 4: Smoothing pattern edges

In a final fourth step, the edges of the yellow pattern were then smoothed, again with respect to the length scale of the image so that thin protrusions were removed, and contour fluctuations were smoothed and averaged at a fixed spatial scale for all scutes. This was achieved by having the boundary of the pattern eroded and then dilated with a 0.5 mm x 0.5 mm square structuring object. Erosion removes small amounts of the edge pixels of the pattern then dilation refills the pixels which results in a net zero effect except to remove thin and small size noise of the pattern along the edges. As an example, there may be a one-pixel wide (or otherwise thin) line that connects two pattern objects making it one object instead of two (Fig. 2B). The erosion and dilation steps will remove a very thin line connecting objects without changing the size of the objects.

The full pipeline for the analyzing digital images included MICA and GIMP to initially color calibrate the photos (see ‘Image processing’), the pattern was extracted in MATLAB as described here, the measures were computed in MATLAB (see ‘Pattern measurements’), and the analysis of the measurement data (e.g., CV calculations) was completed in Excel and R.

Pattern measurements

After the color pattern extraction steps, 19 pattern measurements were obtained (Table 1). These measurements were selected to quantify as many aspects of the color pattern as possible, including measures quantifying the general size, shape and number of objects in the pattern (E, PA, Ob, OA), color (H, S, B), contrast between the pattern and its background (ED, IC, RC, GC, BC, YC), and overall pattern distribution and organization (FA, PL, Sy, CR, OF, NO). Table 1 includes the descriptions of each measurement with their abbreviations and how they are calculated.

Table 1:

Description of the 19 pattern measurements used in this work.

For each measure, two examples are shown of relatively low and high measure values with the corresponding turtle pattern. *The convex hull is the smallest convex set that encloses all the pixels of the pattern, forming a convex polygon. In MATLAB, this is computed using bwconvhull.

Name	Definition and Formula	Purpose	Examples with low and high values among study turtles
Fractional area (FA)	The fractional area is calculated as the total number of yellow image pixels divided by the total number of pixels in the scute region: $FA=\frac{\Sigma \left(patternpixels\right)}{\Sigma \left(scutepixels\right)}$	Provides a measure of the fraction of space the pattern occupies in the scute. Based on the binary pattern image.
Mean eccentricity (E)	The eccentricity of the pattern objects is a value between 0 (a perfect circle) and 1 (a perfect line). It is calculated using stats.Eccentricity of the regionprops MATLAB subroutine as the ellipticity of the ellipse with the same second moments as the object. For an ellipse with major axis a and minor axis b, the ellipticity is $\sqrt{1-b^2/a^2}$.	Quantifies the mean shape of the region enclosing each of the pattern objects in a scute. Based on the binary pattern image.
Peak length (PL)	The peak length is the average distance between pattern objects (Miura, Komori & Shiota, 2000) computed by finding the skeletonization of the positive and negative of each image (valleys and peaks, respectively): $PL=\frac{2\cdot \Sigma \left(scutepixels\right)}{\left(\Sigma valleypixels\right)+\left(\Sigma peakpixels\right)}\cdot mm/pixel$	Provides a measure of the characteristic length scale of the image, roughly corresponding to the spacing of typical pattern objects. Based on the binary pattern image.
Perimeter/Area (PA)	The ratio of the perimeter and the area is the mean perimeter divided by the mean area of the pattern objects where the perimeter and area of objects is calculated using stats.Perimeter and stats.area of the regionprops MATLAB subroutine. $PA=\frac{meanobjectperimeter}{meanobjectarea}\cdot mm/pixel$	Quantifies aspects of the shape and area of the pattern objects. Larger wider patterns should have a lower value and longer and skinnier patterns have higher values. Based on the binary pattern image.
Hue (H)	The hue measures the color component of the pattern and has values that range from 0 to 1. For example, 0.00 = red, 0.33 = green, and 0.66 = blue. The image is converted from RGB to HSB in MATLAB and the hue is calculated as the mean of the hue values of all the pixels identified as pattern pixels.	Provides a single value that can easily quantify the color of the pattern. Based on the HSB of the image. Based on the HSB pixel color channels.
Saturation (S)	The saturation measures the color intensity of the pattern with values ranging from 0 (indicates no saturation or grayscale ) and 1 (indicates full saturation). The image is converted from RGB to HSB in MATLAB and then saturation is calculated as the mean of the saturation values of all the pixels identified as pattern pixels.	Provides a measure for which the overall saturation or intensity of the pattern color can be quantified in a single measurement. Based on the HSB pixel color channels.
Brightness (B)	The brightness of the pattern ranges from 0.0 (indicates very dark or black) to 1. 0 (indicates very bright or white color). The image is converted from RGB to HSB in MATLAB and then brightness is calculated as the mean of the brightness values of all the pixels identified as pattern pixels.	Provides a measure of the brightness of the color pattern. This is highly influenced by the amount of environmental light (Troscianko & Stevens, 2015). Based on the HSB pixel color channels.
Symmetry (Sy)	Symmetry is measured as the ratio of pixel overlap when a mirror-image copy of the pattern is overlaid onto the original image and rotated if needed. The symmetry index Sy is computed as the maximum pixel overlap over all rigid transformations (translations + rotations) of the mirror image copy. This algorithm was implemented in MATLAB via a brute-force method that searches over a discretization of all rigid transformations.	Provides a value between 0 and 1 that quantifies the axial symmetry of the pattern with respect to the center axis of the scute. Provides information about the mirror symmetry of the left and right half of the pattern. Based on the binary pattern image.
Euclidean distance of pixel color (ED)	The Euclidean distance measures the average distance between RGB pixel values from the identified pattern (pixels more yellow than average) and non-pattern (dark background of the scute). $ED=\sqrt{{\left(RC\right)}^2+{\left(GC\right)}^2+{\left(BC\right)}^2}$	Provides a single value that can quantify the contrast between the average values of the RGB between the pattern and non-pattern. Based on the RGB pixel color channels.
Intensity contrast (IC)	The intensity contrast was measured for the RGB image converted to gray scale as the difference of the mean intensity of the pattern (pixels more yellow than average) and non-pattern (dark background of the scute) pixels. IC = Mean Pattern Intensity − Mean Non-Pattern Intensity	Provides a measure that quantifies the difference in intensity between the pattern and non-pattern. Based on the grayscale image.
Number of Objects (Ob)	The number of objects is the total number of objects composing the pattern identified by the pattern recognition algorithm. In the MATLAB subroutine, bwlabel was used to number the objects. Ob = number of objects	Quantifies the number of objects in each pattern. Provides a number that can determine how interconnected the patterns are. It can also be used as a building block for other measurements. Based on the binary pattern image.
Average object area (OA)	The average object area was calculated as the mean of the area for each of the identified pattern objects. The area of each object was calculated using stats.Area of the regionprops MATLAB subroutine. $OA=mean\left(objectarea\right)\cdot {\left(mm/pixel\right)}^2$	Provides a mean measure of the size of the objects composing the color pattern. Quantifies the average overall size of the pattern objects. Based on the binary pattern image.
Red contrast (RC)	Difference of the average red pixels of the identified pattern (pixels more yellow than average) versus the non-pattern (dark background) pixels, where the red value of a pixel was the value of the red RGB channel. $RC=mean\left(\begin{array}{c}\hfill redof\hfill \\ \hfill pattern\hfill \\ \hfill pixels\hfill \end{array}\right)-mean\left(\begin{array}{c}\hfill redof\hfill \\ \hfill non-pattern\hfill \\ \hfill pixels\hfill \end{array}\right)$	Provides a quantification of contrast present in the red pixels between the identified pattern and the non-pattern (dark background of the scute). Based on the RGB pixel color channels.
Blue contrast (BC)	Difference of the average blue pixels of the identified pattern (pixels more yellow than average) versus the non-pattern (dark background) pixels, where the blue value of a pixel was the value of the blue RGB channel. $BC=mean\left(\begin{array}{c}\hfill blueof\hfill \\ \hfill pattern\hfill \\ \hfill pixels\hfill \end{array}\right)-mean\left(\begin{array}{c}\hfill blueof\hfill \\ \hfill non-pattern\hfill \\ \hfill pixels\hfill \end{array}\right)$	Provides a quantification of contrast present in the blue pixels between the identified pattern and the non-pattern (dark background of the scute). Based on the RGB pixel color channels.
Green contrast (GC)	Difference of the average green pixels of the identified pattern (pixels more yellow than average) versus the non-pattern (dark background) pixels, where the green value of a pixel was the value of the green RGB channel. $GC=mean\left(\begin{array}{c}\hfill greenof\hfill \\ \hfill pattern\hfill \\ \hfill pixels\hfill \end{array}\right)-mean\left(\begin{array}{c}\hfill greenof\hfill \\ \hfill non-pattern\hfill \\ \hfill pixels\hfill \end{array}\right)$	Provides a quantification of contrast present in the green pixels between the identified pattern and the non-pattern (dark background of the scute). Based on the RGB pixel color channels.
Yellow contrast (YC)	Difference of the average yellow pixels of the identified pattern (pixels more yellow than average) versus the non-pattern (dark background) pixels, where the yellow value of a pixel was defined as the minimum of the red and green RGB pixel values: $YC=mean\left(\begin{array}{c}\hfill yellowof\hfill \\ \hfill pattern\hfill \\ \hfill pixels\hfill \end{array}\right)-mean\left(\begin{array}{c}\hfill yellowof\hfill \\ \hfill non-pattern\hfill \\ \hfill pixels\hfill \end{array}\right)$	Provides a quantification of contrast present in the yellow pixels (combination red and green pixels) between the identified pattern and the non-pattern (dark background of the scute). Based on the RGB pixel color channels.
Centrality ratio (CR)	The centrality ratio is the ratio of the average distance of pattern versus non-pattern pixels from the center of the scute, where the center is the centroid $\left(Cx,Cy\right)$. $CR=\frac{\text{mean}\left(\begin{array}{c}\hfill \text{pattern pixel}\hfill \\ \hfill \text{distances to centroid}\hfill \end{array}\right)}{\text{mean}\left(\begin{array}{c}\hfill \mathrm{non}-\text{pattern pixel}\hfill \\ \hfill \text{distances to centroid}\hfill \end{array}\right)}$	Provides a measure to quantify on average how close the pattern pixels are to the center of the scute in comparison to the non-patten pixels. Based on the binary pattern image.
Occupation factor (OF)	The number of pixels of the pixelated convex hull* is divided by the total number of scute pixels. $OF=\frac{\left(\Sigma \left(ConvexHull\right)\right)}{\left(\Sigma \left(scute\right)\right)}$	Provides another measure to quantify the fraction of the scute area that the pattern covers in comparison to the overall pixels, but specifically focuses on the convex hull of the pattern. Based on the binary pattern image.
Normalized offset (NO)	The normalized offset is measured as the distance of the pattern center from the scute center normalized by the scute radius which is computed as the square root of the scute area. $NO=\frac{\sqrt{{\left(Px-Cx\right)}^2+{\left(Py-Cy\right)}^2}}{\sqrt{\Sigma \left(scutepixels\right)}}$, where (Px, Py) is the centroid of the pattern pixels and (Cx, Cy) is the centroid of the scute pixels.	Provides a measure to quantify how far off center the pattern is in relation to the center of the scute. Based on the binary pattern image.

DOI: 10.7717/peerj.19690/table-1

Measurement noise analysis

In this study, we investigate how various factors, such as the angle at which photos are taken, different images of the same subject, and the placement of the color calibration standard card influence the variation in pattern measurements. Regardless of the factor being tested, the influence of these factors was assessed using the coefficient of variation (CV) of pairwise differences. The CV in this study corresponds to the pairwise difference of the image measurements obtained from the two (or three for the angle testing) pictures of the same view on the same animal. CVs were calculated for each measurement separately. CV calculated for three pictures per view used the standard CV formula $\frac{\sigma }{\mu }$, where σ is the standard deviation and μ is the mean of the measurements. With only two images, however, the standard deviation underestimates variability. The pairwise difference divided by the mean offers a more accurate measure of relative variability between the two values. For consistency, we refer to this relative difference calculation as “CV” in two-image comparisons, which was computed using this equation: ${\displaystyle PairwiseDifference=CV=\left|\frac{image1-image2}{mean\left(image1\&2\right)}.\right|}$

This analysis allows inferring the robustness of each pattern measurement under the different tested sampling conditions. Coefficients of variation above 10% were considered to indicate substantial variation in that measurement.

A p-value was computed to test whether pattern measurements differed significantly between images from the field and those from the museum (‘Variation in pattern measurements due to sample source’), and again to assess whether the coefficient of variation (CV) of any measurement was significantly correlated with the consensus score (‘Categorization and complexity of pattern’). Because T-tests, F-tests, and CV correlations were conducted independently across 19 measurements, p-values were adjusted using the Benjamini–Hochberg procedure to control the false discovery rate.

The absence of standardized lighting for field turtles could greatly affect the hue, saturation and brightness (HSB) (Table 1, Table S1) if the standard is not exposed to the same lighting conditions as the turtle, leading to variations in HSB between photographs (Table S1). To test the influence of the placement of the gray standard in comparison to the object of interest, we used images taken of a hat with the gray color standard placed at different distances from the hat. Images (two viewpoints and three photos taken per viewpoint) were then color calibrated following the same methods described above and values of HSB were measured on the images to infer the influence of different lighting between color standard and object of interest on HSB using CVs as described above.

To test the effect of noise in the angle of photography, we tested angles of −5, −10, 0, 5 and 10 degrees from baseline to measure the coefficient of variation as the angle is varied (Fig. 5).

Sensitivity analysis and threshold selection

The pattern identification algorithm uses a non-uniform threshold where values vary from image to image. We found that a (110%) threshold on the minimum red and blue difference (see ‘Color pattern identification algorithm’) created the most accurate pattern recognition results based on human visual comparison (Fig. 6). This threshold can be adjusted to add more or less total area (“thickness”) to the pattern as it increases or decreases the number of pixels identified as “more yellow” than average (Fig. 6). To test the influence of the threshold on the pattern identified by the algorithm, we changed the threshold from 110% by +/−5% (115% and 105%) and +/−20% (130% and 90%) (Fig. 6). These specific percent increases and decreases were chosen to demonstrate how much the fractional area changes with small and large changes to the threshold. We chose to focus on fractional areas since we found it to be the least sensitive measurement to variation (see ‘Results’). As such, although this is a conservative measure, if a threshold was found to affect this measurement, it could be assumed that it would affect all the other measurements even more. Each threshold was then run across all the images in the study. Fractional area measures were then analyzed using CV to determine the variation between the original threshold of 110% and each of the four test thresholds (90%, 105%, 115%, 130%) and the percent change between the test thresholds and the optimal thresholds, generating a framework of how sensitive to changes our algorithm is.

Citizen science: color pattern categorization to describe complexity

The color calibrated top view of 98 individuals was presented to 31 volunteers of different genders and similar age to obtain an estimate of the color pattern complexity as seen by the human eye. Color pattern complexity was inferred based on the consensus value obtained across the volunteers on categorization of the observed patterns. The volunteers were all undergraduate students at George Mason University who responded to an advertisement asking for participants for a project to categorize the color pattern of different individuals of box turtles. No remuneration or any other benefits was offered to participants and no information on the participants was collected. Images (one top view image per individual) were uploaded to a google drive folder where participants could see but not edit the images. An Excel file with the individual/picture ID listed was also available on the Google drive. Volunteers were instructed to work alone (no volunteer knew the identity of others), to download the Excel file on their computer, and choose up to four categories per individual of the nine categories presented (Table 2). In a pilot study, initial categories were suggested to 10 volunteers, and respondents could also add their own pattern categories if they felt that a better classification could be found for a certain pattern. For the follow-up analysis, the most frequent categories write-ins were added and unused categories were subtracted resulting in the nine categories listed in Table 2. Volunteers looked at the images on their own devices (cell phones or computers) and were instructed to carry out the categorization only on the basis of the pattern. Volunteers were provided with the descriptions for each pattern as in Table 2. Although the use of different devices from volunteer to volunteer may affect some aspects of coloration and as such some aspects of the patterns may be more or less visible, we asked volunteers to focus on broad pattern categorization.

Consensus values were then obtained for the pattern of each turtle by calculating a consensus score based on the diversity (low consensus) or uniformity (high consensus) of the categories selected by volunteers. We first quantified the consensus for each category for each turtle using a consensus proportion method (also known as a majority voting method) by determining whether students more frequently assigned a 0 (category does not apply) or a 1 (category does apply) for that category, with the proportion reflecting the level of agreement among students for that category and that turtle. For example, if six students assigned a ‘0’ and four students assigned a ‘1’ for a category for a single turtle, the consensus for that category was 60%. For a binary assignment as we used, the proportion of the most frequent assignment (the proportion of ‘0’s or ‘1’s, whichever is higher) is a value from 0.5 to 1.0 (low to high category consensus). Since volunteers could choose up to four categories, and the categories were not mutually exclusive, the consensus score was computed independently for each category in this way. Then, the overall consensus score across all categories, for each turtle, was computed as the arithmetic mean of the nine individual consensus proportions for each category. A complete lack of consensus (for example, a random volunteer assignment of ‘0’s and ‘1’s) would predict an overall consensus close to 0.5 and complete consensus (every volunteer agrees on whether a category applies for every category) would have an overall consensus score of 1.0.

The consensus values were used as an indication of complexity of the pattern. The stronger the consensus, the less complex the color pattern was considered. To infer which pattern measurements may best reflect the complexity of the pattern, we ran a correlation analysis using the corresponding value of each pattern measurement (as the average over the two (n = 2) top view images) for each turtle versus the consensus score. The correlation test was run for the turtle images for which we had both consensus scores and statistical measures, a total of 53 turtle images (n = 43 from the Smithsonian Natural History Museum and n = 10 from field sites). Although we had collected statistical measures for 55 turtles (see ‘Sample collection’), the 98 top views presented to the volunteers inadvertently excluded two of these individuals so that there were only 53 turtles for which we had both consensus scores and statistical measures. The correlation test was run for a total of 19 statistical measures in R (R Core Team, 2024) using the corr.test function (Pearson’s correlation).

Variation in pattern measurements

We developed algorithms to identify the color pattern and compute the pattern measurements describing the different aspects of the pattern. We tested which of the pattern measurements are more or less variable within and across individuals (3.1) and more or less strongly influenced by variation in sampling conditions (3.2, 3.4, 3.5) or algorithm threshold (3.3). We also measure how variation depends on pattern characterization (3.6). As an estimate of the measurement noise, we use the coefficient of variation (CV) calculated on multiple images of the same view for the same individual.

Variation in pattern measurements across and within individuals

Across individuals: To assess the measurement variation across all studied individuals, we calculate the mean of the pattern measurements obtained for each individual as the value of the pattern measurement for that turtle and measure the variation of those values across the 55 individuals as CV=σ/μ. The coefficient of variation across all the 55 individuals indicate that three measures (blue contrast, yellow contrast, and average area of objects) were more variable across turtles (blue contrast CV = 0.985, yellow contrast CV = 0.890, average area of objects CV = 0.645; Fig. 7). Three measures (mean eccentricity, centrality ratio, and symmetry) were instead the least variable across the 19 measurements (mean eccentricity CV = 0.078, centrality ratio CV = 0.144, and symmetry CV = 0.149; Fig. 7). Full table can be found in Table S2A.

Within individuals: When looking at the CV obtained on the two images taken on the same view of the same individual, six measures had high CVs (higher than 10%): average area and number of objects, yellow, blue, and green contrast, and normalized offset (Fig. 8) while the other measurements had low CVs (CVs < 10%, Fig. 8). This suggests that the majority of the measures are stable when taking repeated images of the same individual without changing the angle or lighting conditions (see below). Additionally, the variation across each measurement for the two photos taken of each individual is similar across the different viewpoints (Table S2B).

Comparing the within-turtle variability and the across-turtle variability as a ratio is a measure of the extent to which high across-turtle variability may be due to noise (Table S2C). The overall variation attributable to measurement noise was 10 to 30% for most (16 out of 19) measures.

Variation in pattern measurements due to sample source

Field versus museum sampling: To compare how the field sampling versus more controlled conditions (Smithsonian specimens) may influence the variation observed for the different pattern measurements, we ran a T-test (difference in means), F-test (difference in variances), and a second F-test (difference in CVs) across each individual and viewpoint per measurement comparing the field vs the museum data. Overall, we found similar means across views and pattern measurements independently of where the turtles were sampled (T-test, Table S3) though occasionally the top view showed a significant difference (T-test with significance p < 0.05) (Table 3). Comparing the museum and field samples, the variation of the measures (F-test computed on the SD, Table S3) was significantly different for the hue, brightness and red contrast (Table 3). The coefficient of variation of the measures (F-test computed on the CV, Table S3) was significantly different for the hue and the occupation factor (Table 3). With the exception of the occupation factor, all measures identified for significant variation for any of the three tests were related to color, especially hue.

Influence of the choice of threshold value

Since the threshold was chosen arbitrarily (“by eye”) to capture the pattern, we investigated the effect of changing the threshold by a small and large percentage (Table 4). Increasing the threshold by 5% or 20% decreases the area of the pattern identified, while decreasing (−5%, −20%) the threshold increases the area of the pattern identified (Fig. 6 and Table 4). Figure 6 shows the comparison between the pattern captured by the algorithm at the default 110% threshold (110% more yellow than average in the studied view) to what can be seen by the human eye and in comparison to the increased or decreased thresholds across all five viewpoints. At 110% threshold (our standard in this study), the algorithm captures a large portion of the pattern as seen by the human eye with limited false negative and false positive pattern area. When the threshold is lowered, the fractional area of the pattern is increased since a lower threshold for identifying a pixel as “more yellow than average” is a less strict criterion and leads to the identification of more pattern pixels, and when the threshold is increased, the criterion becomes more strict and the fractional area of the pattern is decreased. The impact of the threshold on the value of the fractional area is shown in Table 4. Increasing or decreasing the threshold by 5% of the average value resulted in a modest change in the fractional area of 3–7%. Changing the threshold by 20% in either direction had a larger impact of 12–27% on the fractional area. Variation between the new thresholds and the preferred were found to be fairly consistent across views with the top scutes having less variation. For our criterion that a CV greater than 10% indicates substantial variation, a threshold variation of 5% did not result in substantial variation while a variation of 20% did result in substantial variation. Figure 6 visually presents the changes in thresholds for one of the studied turtles.

Placement of the color standard

Placement of the color standard at different distances from the object of interest (Fig. S1) resulted in significant variation (CV > 10%) in the brightness measurements. Specifically, adjusting the position of the color standard when taking photos from above and in front led to CVs of 47% and 38%, respectively. This highlights the substantial variability in color measurements that can occur when the color standard is not exposed to the same lighting conditions as the object of interest.

Influence of the angle at which pictures are taken

Due to the curved shape of the turtle carapace, we tested how small variation in the angle at which the pictures of the animal are taken influences each pattern measurement for each view. We found that out of the seven pattern measurements, the measurements with the highest variation in relation to the CV were the normalized offset, intensity ratio, average area of objects and the Euclidean distance while the three measurements with the lowest variation were the mean eccentricity, occupation factor and centrality ratio (Fig. 9). For added context, the measured coefficient of variation for the average area of objects was comparable to that already measured for within individual turtle variation (Table S4 right-most column), but the normalized offset, Euclidean distance and intensity ratio that were substantially elevated due to angle variation.

When looking at the CV measures for the different viewpoints, there is a clear difference between the top view and the others (front, back, left, and right) (Table S4). For the measures with the highest CVs, the top view generally has the lowest CV with most measurements being under 15%, while for the other viewpoints more than half of the measurements have a CV over 30% (Table S4).

Categorization and complexity of pattern

We used a consensus score—agreement in categorization of each individual turtle pattern across 31 volunteers—as a measure of pattern complexity, with lower consensus scores suggesting a more complex pattern and vice versa. We found that for the full set of 98 turtles that were categorized, the consensus scores ranged from 66% to 87%, suggesting that the complexity of the pattern varied across turtles since this is a broad range of complexity scores. For the subset of 53 turtles for which we had both consensus scores and the measurements used in this work (see ‘Citizen science: color pattern categorization to describe complexity’), the consensus scores similarly ranged from 67% to 87% (Fig. 10). Across all the 98 studied individuals, the categories “Patchy” and “Blotchy” had the lowest average consensus scores of 67% and the category “Single-Spotted” had the highest consensus score of 91%. Thus according to this chosen conceptualization of “complexity”, patchy and blotchy patterns have the highest complexity and single-spotted patterns have the lowest complexity.

A correlation analysis was performed between the 19 pattern measurements and the consensus score for 53 turtles to determine which measurement(s) may best describe complexity in color pattern in box turtles. Correlation values above 30% were observed for two pattern measurements. The largest correlations were found between the consensus score and the average object area and the eccentricity (Fig. 11). Since we are using higher consensus scores as a measure of lower complexity, this would be interpreted as bigger and less rounded objects being correlated with patterns that are easier to characterize and lower complexity. The largest negative correlation (−0.28) was found between the consensus score and occupation factor (Fig. 11). This would be interpreted as a higher occupation factor score being correlated with higher complexity. Although the fractional area was also negatively correlated with consensus (−0.16), this correlation was not nearly as strong, suggesting there is an interaction with the contour of the objects since the occupation factor is based on the convex hull of pattern objects. For the 19 measures, none of the correlations were significant after adjusting the p-values using the Benjamini–Hochberg correction to control the false positive rate. Cook’s distance was run between the measurements and the consensus scores to look for outliers skewing the results. A Cook’s distance (>1) indicates that one individual influenced the significant results. The Cook’s distance was small for these results signifying they are not too influenced by outliers.