Fluctuating Asymmetry Mandibles and Hind Tibia of Stag Beetles (Stag beetle report) - B PDF

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Fluctuating Asymmetry: Mandibles and Hind Tibia of Stag Beetles.

Introduction The Purpose of the study was to determine the similarities between Fluctuating Asymmetry of the Hind Tibia/Mandibles of the Stag Beetle and the effect of body size on Fluctuating Asymmetry. Fluctuating Asymmetry is a measure of the variation between the left and the right side of bilateral characters. Fluctuating Asymmetry can be used to estimate the effects of developmental accidents and can be a measure of genetic fitness (Leamy, Routman and Cheverud, 2002) (Thornhill and Gangestad, 2008). The greater the Fluctuating Asymmetry caues a reduction in genetic fitness. Male Stag Beetles who have a larger Fluctuating Asymmetry are less likely to find a willing mate hence Fluctuating Symmetry may act as a method of female Stag Beetles to determine genetic fitness. Fluctuating Asymmetry for Stag Beetles is elevated in areas of high radiation such as Chernobyl so can be used to measure the effect of long term radiation on morphology (Mller, 2002). Statistical analysis was conducted to either confirm or deny the following null or alternative hypotheses: Hypothesis 1: H0: The Fluctuating Asymmetry of the Hind Tibia does not exhibit variation between individuals. H1: The Fluctuating Asymmetry of the Hind Tibia exhibit variation between individuals. Hypothesis 2: H0: The Fluctuating Asymmetry of the Mandibles does not exhibit variation between individuals. H1: The Fluctuating Asymmetry of the Mandibles exhibit variation between individuals. Hypothesis 3: H0: The Fluctuating Asymmetry of the Hind Tibia and the Mandibles does not Increase with Body Length H1: The Fluctuating Asymmetry of the Hind Tibia and the Mandibles Increases with Body Length Hypothesis 4: Is the Fluctuating Asymmetry of the Hind Tibia or Mandibles greater? H0: The Fluctuating Asymmetry of the Hind Tibia and Mandibles are not significantly different.

H1: The Fluctuating Asymmetry of the Hind Tibia and Mandibles are significantly different

Methods From 20 Stag Beetles the Mandibles, Body length and hind Tibia were measured using a ruler to a 0.5mm accuracy. Two measurements for each beetle length and each Mandible and Hind Tibia were taken and then a mean calculated. The mean for each was then used to determine the Fluctuating Asymmetry. The Fluctuating Asymmetry values for the hind Tibia and Mandibles were then converted to absolute values to make each value positive.

Results

Figure 1. Histogram of Absolute Mandible Fluctuating Asymmetry of 20 Stag Beetles. A Histogram with a distribution curve representing the variability of the Fluctuating Asymmetry of the Mandibles from 20 Stag Beetles

Figure 2. Histogram of Absolute Hind Tibia Fluctuating Asymmetry of 20 Stag Beetles. A Histogram with a distribution curve representing the variability of the Fluctuating Asymmetry of the hind Tibia from 20 Stag Beetles Statis

Statistic

tic FA Mandible

Std.

Varianc

m

m

Statis

Mean Std.

Deviation

e

Statistic

Statistic

tic

Error

Statistic

Statistic

20

.04

.00

.04

.0191

.00285

.01275

.000

FA Tibia Abs

20

.04

.00

.04

.0121

.00288

.01286

.000

Valid N

20

Abs

(listwise)

To determine whether the first and second hypotheses can be accepted or rejected the histogram from Fig.1 and Fig.2 show that the spread of the data and hence whether the it is ‘varied’. Fig.1 the histogram shows a Table 1. Descriptive Statistics for the Absolute Fluctuating Asymmetry of the Mandibles and Hind Tibia

distribution curve and histogram which represents a loose bell curve which would indicate normally distributed data the spread of the data is relatively even and greatly varied. Utilizing Tab.1, the Standard Deviation for FA Mandible is 0.013 which in relation to the mean (0.019) and the range (0.04) is large and shows that the data is notably varied. Using a Shapiro-Wilk to test normality the Mandible Fluctuating Asymmetry (FA) was found to be normally distributed as well as varied (p=0.433) using a 95% confidence interval. The large variation around the mean and other statistics causes the rejection of the null hypothesis in favour of the alternative hypothesis. The histogram and distribution curve shown in Fig.2 demonstrates the variability of the FA of the Hind Tibia, the distribution curve shows a very slight peak and is incredibly shallow, demonstrating the Hind Tibia FA is wide spread though the greatest

frequency shows zero FA. The standard deviation (0.013) is large in comparison to the mean (0.012) and range (0.04). Using a Shapiro-Wilk test to determine normality. When using a 95% confidence interval the data is not normally distributed (p= 0.002). The large variation around the mean and other statistics causes the rejection of the null hypothesis 2 in favour of the alternative hypothesis.

Figure 3. Body Length (mm) and Mandible Fluctuating Asymmetry of Stag Beetles. The relationship between the Body length and the dibl FA f 20 t b tl

Figure 4. Body Length and Hind Tibia Fluctuating Asymmetry of Stag Beetles. The relationship between body length and mandible FA of 20 stag beetles.

Fig.3 represents the relationship between the Mandible FA and the body length, the line of best fit shows there is a negative correlation between the body length and the Mandible FA though the data points are far isolated from the line of best fit. The R2 value for Mandible FA and body length is 0.123, the low R2 demonstrates a very loose relationship between the two variables and little evidence that one is proportional to the other. Using an ANOVA linear regression, and a 95% confidence interval the correlation is not significant as p=0.129. Therefore, there is no significant correlation between the Body length and the Mandible FA. Fig.4 shows the correlation between the Body length and the Hind Tibia FA. The Line of best fit indicates an inversely proportional relationship between

the Body length and the Hind Tibia FA, though the data visually does not seem to match the line of best fit hence a weak correlation. The weak correlation is confirmed by the small R2 value (0.039) which demonstrates that there is almost no correlation between the Body Length and the Hind Tibia FA. When a linear regression ANOVA was conducted on the variables (p=0.402), when using a 95% confidence interval indicated no significant correlation between Stag beetle body length and Hind Tibia FA. For both Mandible and Hind Tibia R2 and linear regression ANOVA allows the acceptance of the null hypothesis 3 and consequently FA does not increase with body size (body length).

Figure 5. Box Plots for Fluctuating Asymmetry of Stag Beetles Mandible and Hind Tibia. Box Plots representing the distribution of the Fluctuating Asymmetry data for 20 Stag Beetles.

F using Box plots. Comparing the spread of the FA for the Mandible and Hind Tibia shows the maximum (0.04) and minimum (0.00) for both variables are the same and consequently the Range (0.04). While the spread of the data is very different the median is higher for Mandible FA (0.018) with a smaller interquartile range than the Hind Tibia (0.011), the smaller interquartile Range and the larger mean indicates that the Mandible FA is greater on average. The Mean shown in Tab.1 for the Mandible FA (0.019) was greater than that of the Hind Tibia (0.012) further indicating that on average that the Mandible FA is greater than that of the Hind Tibia. To determine whether the Mandible FA is significantly greater than the Hind Tibia FA a Paired T test was conducted, and at a 90% confidence interval Mandible FA is significantly greater than that of the Hind Tibia as p=0.079. This allows the rejection of the null hypothesis 4 in favour of the alternative hypothesis.

Discussion The Results determined that FA of the Hind Tibia and Mandibles exhibits variation between individuals, FA for both protrusions are independent of the body size and FA is greater in the Mandibles than the Tibia.

The histogram in Fig.1 and the distribution curve demonstrated there was variation in the Mandible FA as the data expressed normal distribution (Shapiro-Wilk) and in relation to the mean the standard deviation (0.013) was large and represented over 25% of the range (0.04) of the FA. The large variation exhibited allowed the rejection of the null hypothesis 1 and acceptance of the alternative hypothesis: Mandible FA exhibited variation between individuals. The histogram shown in Fig.2 and the distribution curve showed that Hind Tibia FA was varied though less so than the Mandible FA, Using Shapiro-Wilk the data was not normally distributed. Hind Tibia FA standard deviation (0.013) was also large in relation to the mean (0.012). The null hypothesis 2 was rejected in favour of the alternative hypothesis therefore Hind Tibia FA exhibited variation between individuals. Fig.3 and Fig.4 show the relationship of the Mandible and Hind Tibia respectively and the body length of the Stag Beetle. In both cases there is a negative correlation between the Body length and the FA indicating that body length has a negative effect on FA for both Mandible and Hind Tibia. But when a linear regression is conducted the R2 value for both Mandible and Hind Tibia showed a very little correlation between Mandible FA and Body length. Using linear regression ANOVA there was found to be no statistically significant correlation between Body length and Mandible and Hind Tibia FA. The Null hypothesis 3 is accepted: Body length has no statistically significant effect on Mandible and Hind Tibia FA. Fig,5 represents the spread of the FA for both Mandible and Hind Tibia this indicated a slightly larger FA for the Mandible than the Hind Tibia as the median was greater with a more concentrated interquartile range. The mean FA was also larger for the Mandible than the Hind Tibia. A paired sample T-test conducted demonstrated that mean Mandible FA was significantly greater than that of the mean Hind Tibia FA at a 90% confidence interval consequently the null hypothesis 4 was rejected in favour of the alternative hypothesis. Though the result is significant as the p value = 0.079 when the confidence interval is 95% the result would be defined as insignificant and the null hypothesis would have to be accepted. There are forms of selection that act on the Mandibles and the Hind Tibia. One form of selection is sexual selection that acts on the Mandibles, which are anterior protrusions prominent in the male Stag Beetles, shown in Fig.6. The sexual dimorphism Represented in Fig.6 hints that the Mandibles are sexually selected. The Mandibles are under intrasexual selection as they are used by the Male Stag Beetle to compete and gain to access females for copulation. As in the case with many other intrasexual selected characteristics larger and stronger mandibles may consequently allow the male to win more combat and hence gain greater access to females, this also becomes an advantage in gaining mates as the Mandible becomes a secondary sexual characteristic and sexually selected causing the males with greater mandibles to obtain more mating’s with females (Goyens et al., 2015) (Mills et al., 2015). Due to the

sexual dimorphism of the large Mandibles the average male’s combined mandible mass is 0.12g in relation to their total mass of 1.34g, this heavily shifts the males centre of mass anteriorly (Goyens, Dirckx and Aerts, 2014). The shift in the centre of mass of requires the body of the male stag beetle to be stabilised. The stabilisation of the Stag beetle may be subject to selection that causes a more muscular hind tibia to counteract the weight of the mandibles. The anterior tibia in the male stag beetle are strongly correlated with the mandible length the selection may also act on the Hind tibia (Tomkins, Kotiaho and LeBas, 2005). Stabilizing selection may also be acting on the Mandibles to counteract the Sexual selection in order to prevent the Mandibles enlarging too greatly and causing too great a handicap and death before a successful mating.

Figure 6. Photo of a male (a) and a female (b) Cyclommatus metallifer (Stag Beetle) from: (Goyens et al., 2015)

The method of measuring FA could have been more refined by using a more accurate method of measuring the samples using a ruler with a smaller scale and a microscope. FA could have been measured on other protrusions such as the forelimb tibia which has been linked to the development of the mandible. Other methods of measuring body size could have been used such as the mass of the Stag beetle to determine the effect on FA.

Bibliography

Goyens, J., Van Wassenbergh, S., Dirckx, J. and Aerts, P. (2015). “Cost of flight and the evolution of stag beetle weaponry”. Journal of The Royal Society Interface, 12(106), pp.20150222-20150222. Mills, M., Nemri, R., Carlson, E., Wilde, W., Gotoh, H., Lavine, L. and Swanson, B. (2015). “Functional mechanics of beetle mandibles: Honest signaling in a sexually selected system”. Journal of Experimental Zoology Part A: Ecological Genetics and Physiology, 325(1), pp.3-12. Goyens, J., Dirckx, J. and Aerts, P. (2014). “Costly sexual dimorphism in Cyclommatus metallifer stag beetles”. Functional Ecology, 29(1), pp.3543. Mills, M., Nemri, R., Carlson, E., Wilde, W., Gotoh, H., Lavine, L. and Swanson, B. (2015). Functional mechanics of beetle mandibles: Honest signaling in a sexually selected system. Journal of Experimental Zoology Part A: Ecological Genetics and Physiology, 325(1), pp.3-12. Leamy, L., Routman, E. and Cheverud, J. (2002). “An epistatic genetic basis for fluctuating asymmetry of mandible size in mice”. Evolution, 56(3), p.642. Thornhill, R. and Gangestad, S. (2008). “The evolutionary biology of human female sexuality”. Oxford: Oxford University Press, pp.162-168. Mller, A. (2002). “Developmental Instability and Sexual Selection in Stag Beetles from Chernobyl and a Control Area”. Ethology, 108(3), pp.193204. Word Count: 1900...