Analysis of Sampling Technique Used to Investigate Matching of Dorsal Coloration of Pacific Tree Frogs Hyla regilla with Substrate Color Madeleine van der Heyden, Kimberly Debriansky, and Randall Clarke Instructor: Edward Connor Abstract We conducted a preliminary study to estimate the sample size needed to achieve sufficient statistical power to test the hypothesis that the dorsal color of Pacific tree frog (Hyla regilla) tends to match the substrate color. The data were collected in a meadow near Beartrap Meadow in the Tahoe National Forest in July 2004. Twenty-three Pacific tree frogs were captured and photographed while walking a random zigzag path through the meadow. The decision regarding a substrate match was based on a two-out-of-three person agreement. It was determined that out of the 23 Pacific tree frogs encountered, 19 frogs did and 4 did not match the background color. The Binomial test was used for our statistical analysis and the Binomial parameter for the alternative hypothesis was set at p = 0.7. Our results indicated that we achieved sufficient statistical power with our sampling technique and that the Pacific tree frogs generally do match their substrate color.
Introduction The Pacific tree frog (Hyla regilla) is a small (1.9-5.1 cm) frog found mainly on the ground (despite its name) in a variety of plant communities from sea level to high mountains from southwest Canada to Baja California and from the Pacific Coast to western Montana. A black or dark brown eye stripe is nearly always present on the Pacific tree frog but its dorsal coloration is highly variable. The dorsal and leg colors range from green to tan, reddish, rust, copper, gray, cream, brown, black, or even blue. Some frogs have mixed colors such as green and copper or blue (Stebbins 2003). According to Stebbins, the Pacific tree frog is capable of changing from dark to light phase within a few minutes. However, Stebbins claims that the basic different color morphs do not change. Similarly, Resnick and Jameson (1963) claim that the color of Hyla regilla can increase or decrease in brightness in response to hormones, light, and temperatures but that this frog is fixed in hue, meaning that a green frog cannot change its color from green to brown. Resnick and Jameson report that the green color of the Pacific tree frog is genetically determined. They suggest that different alleles control the amount of guanine and carotenoid transcribed that result in the many different shades of a color. On the other hand, a study by Wente and Philips (2003) has shown that in the same Hyla regilla population both individuals that are able to change color and ones that are fixed color morphs are present. Wente and Philips (2003) also showed that color change requires days to weeks rather than minutes to hours. In nature, some animals are protected by cryptic coloration making them difficult to distinguish against their background so that visual detection by predators is decreased. Background matching, disruptive coloration and countershading are three ways of achieving crypsis. Matching dorsal surface and substrate color is believed to be important for the Pacific tree frog in order to escape detection of visual predators. According to Tuomi and Jormalainen (1999), the probability of being detected in a homogeneous habitat can be decreased by increasing the degree of crypsis against that background. In other words, a Pacific tree frog sitting in green grass can decrease the probability of being detected by being as green as the grass. Decreasing the probability of detection by a predator in heterogeneous habitats, on the other hand, is more difficult because the degree of crypsis of a given coloration and the probability of encountering a predator may vary spatially. Assuming a higher degree of crypsis decreases the probability of detection by a predator, we ultimately wanted to determine if the skin color of Hyla regilla in a given habitat generally matches the background color on which these anurans are located. However, prior to conducting the actual study, we needed to carry out a pilot study in order to estimate the sample size necessary to achieve sufficient statistical power to test the hypothesis that the dorsal color of Pacific tree frogs tends to match the substrate color. Methods Data Collection The study area was a meadow located northwest of Beartrap Meadow in the Sierra Nevada Mountains within the Tahoe National Forest about 5 miles north of Hwy. 49 between Bassetts and Yuba Pass on Forest Road 09 (Figure 1).
Figure 1. The light green dot on the map above indicates the approximate location of the study area in the Tahoe National Forest north of Highway 49 between Bassetts and the Yuba Pass. In order to conduct the study, a map was obtained from the Energetic Math Group. Drawn onto this map was the randomly walked route by the three observers searching for Pacific tree frogs. All three participants lined up in the shape of a comb and slowly walked straight lines randomly zigzagging the meadow (Figure 2).
Figure 2. The aerial photograph shows the study area called North of Beartrap Meadow with the zigzag path walked and all the Pacific tree frogs (numbered 1-23) captured along this pathway. The green dots represent the frogs that matched their background and the green dots with a black center symbolize the non-matching Hyla regilla. The study meadow was found to be particularly suitable for this study because it included a variety of habitats with substrates of different colors. Parts of the meadow were covered with lush dark green grass whereas other vegetated sections had a brownish color to
them because some plant stems and tips being rust to brown colored. Again other locations were open with exposed brown soil. Some areas were scattered with wood pieces and rocks. In certain areas, trees provided shade and, depending how much sunlight reached the ground, the color of he ground consequently appeared darker or lighter. A shallow pond was located in the southeastern corner of the meadow. The ground around this small pond was dark gray brown. Therefore, this heterogeneous study area provided a variety of background colors as well as Hyla regilla with a variety of skin colors. For the purpose of our study, we assessed both juvenile and mature frogs but excluded any new metamorphs. We defined metamorph as the stage when a frog first emerges out of the water and with its tail completely absorbed until its color changes from nearly black to being colorful. Metamorphs are very dark colored and about 1 cm in size. In order to avoid counting metamorphs, the length of each frog (head to tail) was measured. Any Pacific tree frogs with a body length of 1 cm or less were not included in this study. Whenever a Hyla regilla was spotted, it was quickly and carefully captured and photographed by a talented photographer who was hired specifically for this study. The location of each frog was carefully marked on the map (Figure 2). The photographer not only took a picture of the frog but also of the substrate which usually consisted of green grass, dark green leaves, bare brown ground, light brown wood chips, grey rocks, or dark brown mud. Flags were used to mark the location at which a frog was first spotted. This was necessary since the frogs, when approached, often jumped a few feet away in an attempt to escape. Figure 3. Six examples of dorsal coloration in Pacific tree frog. The frog on the top left is light green like the grass in which it was found. The frog in the top middle was found in typical wetland vegetation which was rust to green colored. The Hyla to the top right was detected on green overall vegetation with some plant leaves having a bluish shimmer. In the bottom row, the left frog was caught in an area with sparse grass and exposed beige colored soil, the frog in the middle was found in a shady area with lush dark green grass, and the nearly beige frog to the right was found on light brown exposed soil with rocks and beige wood chips nearby.
Each time a frog was captured, the three investigators took a good long look at the frog s skin color and pattern (Figure 3). A second good long look was taken at the substrate on which the frog had sat. Then each of the observers decided for him- or herself whether the frog did or did not match the background. The answer was either yes or no and once it was announced, the answer of the majority (either 2/3 or 3/3) was recorded. Statistical Analysis Under our null hypothesis, the probability of skin color substrate matches and nonmatches was p = 0.5 or, in other words, the skin color substrate matches were equally likely as non-matches. In that case, the odds of a color substrate match were the same as a non-match (odds =1.0). While strolling across the meadow, 23 frogs were encountered which are the 23 trials in our case. In order to conclude, at the α = 0.05 level, that the matching of the frog and substrate color was statistically significant and to be able to reject the null hypothesis that frogs are equally likely to match as not match the substrate, we had to observe 15 or more matches. The Binomial test (formula shown below) was used to calculate power relative to our alternative hypothesis and hence the sample size necessary to have a specified level of power. The alternative hypothesis had to be stated in terms of the Binomial parameter p. Assuming that color matching was more frequent than a 50/50 proposition, we set the Binomial parameter for the alternative hypothesis at p = 0.7 so that the probability of a skin color substrate match was 0.7 and that of a non-match 0.3. B n r n r ( n, r : p) = Cr p (1 p), where B(n, r : p) is the Binomial probability of getting r successes in n trials. To calculate the power (1-β) of this test, under the alternative hypothesis, the probability of being in the area of acceptance under the null hypothesis when the alternative hypothesis is true was calculated. The probability of getting 14, 13, 12, etc. matches in 23 trials with the Binomial parameter p = 0.7 was calculated. The sum of these values was the Type II error probability = β. Power is then just 1 - β. Results Out of 23 trials, 19 frogs matched the background and 4 did not match the substrate. The length of the frog was recorded to exclude metamorphs. The smallest frog was 1.2 cm and had well developed dorsal coloration. Table 1 shows the color assessments for each of the 23 frogs we encountered and whether the frog s color did or did not match the substrate color on which they were found. The descriptions of the two columns to the right show how substrate color varied as much as the dorsal color of the Pacific tree frogs.
Table 1. Matches between frogs and substrate, body length of frog, frog color, and substrate color Frog # Match Body length Frog color Substrate color * (cm) 1 no 1.2 copper, yellow, green sparse light green grass and beige soil 2 yes 1.8 light green light green plants 3 yes 2.0 light green light green plants 4 no 2.0 light green light green and brown plants 5 yes 1.8 beige green light green plants 6 yes 1.6 green with copper back light green and brown 7 yes 1.6 green faint leopard pattern sparse light green grass 8 yes 1.8 leopard pattern and green sparse light green grass and beige soil 9 yes 2.0 leopard pattern and green tall light green grass 10 no 2.1 green with copper back light green plants 11 yes 1.9 green light green plants 12 yes 2.2 green light green plants 13 no 2.4 darker green lush dark green grass, shady area 14 yes 2.2 darker green lush dark green grass, shady area 15 yes 1.8 dark green dark green grass, shady area 16 yes 2.3 green, beige leopard green brown plants 17 yes 3.3 blue, green lush dark blue green plants, shady area 18 yes 2.5 bright green lush light green 19 yes 2.0 green copper broken brown and green light plants 20 yes 2.4 green, copper, beige stripe beige logs, rocks, green brown plants 21 yes 2.0 green, copper stripe beige logs, green brown plants 22 yes 1.8 mud gray exposed gray soil 23 yes 1.6 dark exposed gray soil * 19 matches and 4 non-matches The probability of 14 matches was 0.109, that of 13 matches 0.065, etc. Table 2 shows the values calculated using the Binomial Distribution function. The probability of a Type II error (β) was 0.227, the sum of the tabulated values. Consequently the power of the test used was determined to be 0.773. Table 2: Values calculated from using the Binomial Distribution function r Probability of r, given Binomial parameter of p = 0.7 14 0.109 13 0.065 12 0.033 11 0.014 10 0.005 9 0.001 8 0.000 7 0.000 β 0.227 (β - Type II error probability) 1- β 0.773 (Power: 1-β)
Figure 3. A Pacific tree frog that matches the grass and soil substrate so well that it cannot be easily detected upon visual inspection. The dorsal coloration of the majority of frogs matched the background as shown on this image. Figure 3 illustrates one example of the extent of color matching between Pacific tree frogs and the substrate. The dorsal surface color of Hyla regilla generally matched the background color. Discussion We found that our technique of sampling frogs in the study meadow was adequate to assess the color matching of Pacific tree frogs and the substrate on which they were found. With a sample size of 23 frogs, 15 or more matches would lead to rejection of the null hypothesis that apparent substrate matching was no more likely than not matching the substrate at the α = 0.05 level. We sampled 23 frogs, 19 of which matched the substrate and 4 frogs did not match the substrate. The null hypothesis was rejected in favor of the alternative hypothesis that Pacific tree frogs tend to match the substrate color. We also determined that the power of our test relative to the alternative hypothesis that tree frogs should match the substrate 70% of the time was 0.773 for a sample size of only 23 frogs! Never was a green frog found on beige soil. The four frogs that did not match the substrate were only slightly more detectable that the other 19 frogs. Since we used eyes and our own judgment to determine whether a frog did or did not match the substrate, our entire study may be biased. Wente and Philips (2003) used a
spectraradiometer to measure the reflectance of the dorsal surface of each frog. It would be interesting to see if the results of our study would have been different had we used a more sophisticated method to measure the frog skin color. We conclude that the dorsal coloration of Pacific tree frog generally matches the background color even in a heterogeneous habitat. However, from this study we cannot tell whether the color of the frogs changes over time or not. We also cannot say if there are three different morphs present in this population as suggested by Wente and Philips (2003). Perhaps some frogs that were caught were fixed green or brown morphs. If such morphs would have been placed into a habitat with a different background color, they would most likely been detected and eliminated by visual predators. Perhaps we also encountered morphs that actually can change color, but because it may take days or weeks to change color as suggested by Wente and Philips (2003), we would have never been able to differentiate such morphs from fixed morphs. References Resnick, L. E. and D. L. Jameson. 1963. Color polymorphism in Pacific Tree frogs. Science. 142:1081-1083 Stebbins, R.C. 2003. A Field Guide to Western Reptiles and Amphibians, 3 rd ed. Boston, MA: Houghton Mifflin Company. Tuomi, J. and V. Jormalainen. 1999. Optimization of cryptic coloration in heterogeneous habitats. Biological Journal of the Linnean Society 67: 151-161. Wente, W. H. and J. B. Philips. 2003. Fixed green and brown color morphs and a novel colorchanging morph of the Pacific tree frog Hyla regilla. The American Naturalist. 162: 461-473.