QUESTION

Objective& Scope

The aim of this practical is for you to collect, analyse and interpret data on a colour-based sexual signal in the arthropod species Euremahecabe (the ‘grass yellow’ butterfly). Certain patches of dorsal wing colouration in males of this species are known to signal attractiveness, but others are not, and the same wing colour patches are also found in females (i.e. they are sexually homologous) but do not function as a signal in this sex. Together, we will mount a scientific investigation into the differences between the sexes, and of the scaling relationship between the size of the colour patches and the size of the overall wing. You will each use the digital image capture technology to take precise measurements of the size of the colour patches in one male and one female of this species. As a group, we will then pool the data, run an analysis, and discuss the possible conclusions. You will then each individually write up a single scientific report – written in the style of the journal Evolution, which you will submit as Assignment two (see the Unit Outline for further details on due dates etc. for internal versus external students).

By the end of this practical you will be able to:

• Explain the evolution of sexually selected traits such as bright colour signals;
• Explain the concepts of scaling relationships among different body parts, and be able to define the terms Allometry and Isometry;
• Use your dissecting microscope along with the Digilab and Motic Images software to take accurate and precise measurements of animal morphology;
• Run a simple statistical analysis (i.e., a linear regression) and know how to interpret the results;
• Prepare a scientific report in the style of a ready-to-submit manuscript aimed at the journal Evolution.

Exercise 4 Assignment 2 (25 %)

Background

Animal colouration serves a number of functions, including thermoregulation, crypsis (i.e., camouflage) and aposematism (i.e., the advertisement of toxicity). Displays of colour may also be used as a sexual signal, whereby they can signal gender or species identity, or an individual’s quality as a mate or sexual competitor. Usually in the case of mate quality signals among animals it is the males that signal to females, although females may also express the signal to a lesser degree as well.

When a particular colour patch is used as a sexual signal, theory tells us that it should be more costly for the animals to generate than other traits such as non-sexual colours, or other morphological structures (such as arms, legs, hair, etc.). These costs apply to many colour signals that require pigments which are metabolically expensive to synthesize or hard to get from the environment, and mean that only the highest quality individuals can afford to express the signal at its highest level. This, in turn, means that females can profitably use this trait as a reliable or ‘honest’ signal of male mate quality.

The sexual signalling systems still in use today are probably a tiny fraction of all signals which have been used at some time or another throughout the evolutionary history of the species. These have remained evolutionarily stable because they are honest, and hence, females get to mate with better quality males (on average) by paying attention to them.

Figure 4.2 Examples of isometric versus allometric colour patterns in Harlequin bugs. Isometry describes a 1:1 relationship between the size of the colour patches and the size of the body, that is, for every one unit of body size increase there is a corresponding one unit increase in colour patch size.

Aim

Your aim is to see whether the wing colouration of a tropical butterfly species (Euremahecabe) fits the predictions of what we should expect if the yellow markings function as an honest mate quality signal in males.

Assumptions

It is solid scientific practice to recognize the assumptions that go into constructing and testing particular hypotheses. In this case, we assume that:

(a)  The yellow patch functions entirely as a sexual signal, and that the size of this patch is an important component of male sexual attractiveness;

(b) The black markings have no sexual signal function, or function in a way that is independent of their relative size;

(c)  Males and females can freely allocate resources among different body structures during development, and allocating resources to wing colouration reduces the pool of resources that could be invested elsewhere;

(d) Producing yellow (from pteridines) is more costly than black (from melanin), that is, colouring an area of wing yellow takes more from the limited pool of resources than colouring that same area black. This is based on the fact that pteridine pigments require more resources to make than melanin.

Prediction(s) for testing

We will conduct this scientific investigation using the hypothetico-deductive approach. This is a specific application of the general scientific method which involves:

(a)  specifying a critical prediction from the hypothesis one wishes to test;

(b) collecting the data needed to test the prediction, and then;

(c) accepting or rejecting the hypothesis as an explanation for the problem.

Remember:

¹FemaleE. hecabetherefore only show yellow because it is strongly selected in males

Methods

You will each be given a sample of the wings from a single male and female butterfly. First, make an accurate line scientific drawing of a single fore- and hind-wing from your male specimen (showing the dorsal surface). You may also look at your wing under higher magnification to visualize the finer-scale structure of a wing scale.

You will then need to capture an image of all your wings (male and female), import into Motic Images, and calculate the area of the yellow and black colour patches, as well as overall wing area. As a class we will work through the calibration of your microscope and Motic software, so you can take accurate readings. You should measure each colour patch three separate times and average them for your final estimate (why?). You will enter your data into the class excel spreadsheet for analysis.

Results

Record the results of your measurements in the spreadsheet below, AND in an Excel spreadsheet at the computer at the teaching computer.

Statistical Analysis

We will run through the analysis together during the class, using the web-based package “Vassar Stats”, which is freely accessible from the homepage at:

http://faculty.vassar.edu/lowry/VassarStats.html.

Our main focus will be the relationship between wing size and colour patch size, and so we will use Regression to calculate the slope of the linear relationship between these two parameters. We will do this separately for males and females, and test whether the slope differs from a 1:1 (isometric) relationship in either sex.

A regression analysis is appropriate where you have one variable – the independent variable (e.g. wing area) that causes the variation in another variable – the dependent or predictor variable (e.g., colour patch area).If you expect (or observe) a straight line relationship between two variables of this nature then we can use a regression analysis to tell us the following things:

(1)  Is there a relationship between the two variables?

(2) How strong (or tight) is that relationship?

(3) What is the nature of the relationship? For example, is it a 1:1 relationship?

The nuts and bolts:

Prior to our analysis we first need to transform our variables so that they fulfill the statistical assumption of linearity. You can achieve this by taking the natural log of the data, as we demonstrated in the lab class. So, in Excel, you create another data column which contains the formula: = ln(xx), where xx = the cell you wish to transform, etc. Use the natural log transformation for both your dependent and independent variables.

Once your data are log-transformed, you are ready to run the regression. Go to the Vassarstats homepage and click on correlation and regression. There is info on this page that you may wish to read. Scroll down and click data import version, and when that loads up, scroll down until you see the form where you can paste your data from Excel. Paste it in and remember to remove the carriage return at the end of the data file (it would cause the analysis to crash). Paste so that your independent variable is the left column and your dependent variable is on the right, like this:

Then click on ‘Calculate’ and it will run a regression analysis on the data. If you scroll down, you will see an output that looks something like this (overleaf):

The things you need to take note of here are:

(1)  The t-value (in this case it is 7.43), the df (degrees of freedom) and the two-tailed P-value (which in this case is P<0.0001). A P-value that is less than 0.05 allows us to reject the hypothesis that there is no relationship between the variables, and to conclude that the two variables are, in fact, related. In the case of this analysis above, you would quote the result as “colour patch size was significantly related to wing size (t = 7.43, df = 8, P < 0.0001)”.

(2) The r² value, which tells you how much variation in the dependent variable (colour patch size) is explained by variation in the independent variable (wing size). In this case the r² value is 0.875, which means that 87.5 % of the variation in colour patch size is explained (= predicted) by variation in wing size. In this particular example we therefore have a strong relationship between our two variables.

(3) The slope, which tells you the gradient of the line of best fit for the relationship. In this case the value is 1.81, which tells us that for one unit increase in wing size, colour patch size increases ~ 1.8 units. This is of particular interest to us, as we wish to know whether the slope differs from 1.0, and in which direction.

In order to statistically test whether the slope of the colour patch: wing size relationship varies from 1.0, we need to make use of another aspect of the regression output, namely, the confidence limits for our slope, which are visible if you scroll a little further down the VassarStats output (Note: do not use the confidence limits for ‘rho’, which appear above the confidence limits for the regression slope):

In this case, the 95% confidence limits of our slope estimate are 1.25 – 2.37. This means that we can be 95% certain that the true value of our slope lies somewhere between 1.25 – 2.37. Remember that we don’t really know the true value of the regression slope, all we can do is estimate it using the data at hand, which are a sample of cases, containing measurement error (etc). And so we can conclude that the true value of our slope deviates from the isometric value of 1.0, and that we are (in all likelihood) dealing with a situation of positive allometry. In your discussion you would delve into the biological implications of this finding.

If, however, the 95% confidence limits had been 0.8 – 1.2, wewould then conclude that the scaling relationship is isometric.

Some additional notes:

–        Generate and present a scatterplot for your data, showing the relationship between your two variables. Graph the raw (untransformed) data.

–        But, run your statistics on the log-transformed data.

–        Report your statistical results in the way that others in evolution have done. So you would generally say verbally what you found, then give the precise, relevant statistical results in parentheses.

How to write formal scientific report?

There are a number of good ‘how to’ guides for writing scientific articles. We will run through this overview of the main parts of an article at the end of the lab class:

Marking scheme

The marking scheme for this assignment is below. Note that there is no word limit (only some scientific journals impose upper limits), but I would expect to have all the working bits and pieces of a good report you will need to produce 2000-2500 words. Similarly, there are no numerical limits on the number of cited references, but to cover the literature correctly you will need to cite at least 10-15. Any fewer and you will lose marks for the introduction and discussion – these are the sections where supporting scientific literature is referred to the most.

Usual late penalties apply (i.e. 5 % per day past the due date); see the unit outline.

Title & abstract                                                                                                     2 marks

–        Appropriate and informative title

–        Succinct and complete abstract (< 200 words)

Introduction                                                                                                         4 marks

–        Introduction well researched and logical in flow

–        Clearly stated aims & hypotheses

Methods                                                                                                                  3 marks

–        Methods complete and logical

–        Detailed enough so that it can be repeated

–        Explanation of statistics used

Results                                                                                                                     4 marks

–        Figures present (at back of manuscript), legends present and in house style

–        Appropriate statistics reported and correctly cited

–        Figures correctly cited

–        Appropriate tone & content

Discussion                                                                                                             4 marks

–        Clearly stated conclusion

–        Discussion well researched and logical in flow

–        Results tied to literature

Use of references                                                                                                 2 marks

–        Adequate number of references

–        Appropriate in-text referencing

Formatting (Evolution ‘house’ style)                                                          2 marks

–        Adhered to Evolution style

Grammar/spelling & simplicity/readability                                             4 marks           

–        Grammar fluid and succinct

–        Ideas flowed logically

–        Correct grammar, spelling and punctuation

Total: 25 marks

(25 % of overall assessment grade)

Formatting – EVOLUTION style

You are to format your report in the style requested for submissions to the journal Evolution. This means that you will need to follow the ‘guidelines for authors’ set out in the journal, or accessible on the Evolution webpage:

http://www.wiley.com/bw/submit.asp?ref=0014-3820&site=1

Useful literature

An example of the types of references that may prove useful for you are:

Bonduriansky R (2007) Sexual selection and allometry: a critical reappraisal of the evidence and ideas. Evolution 61: 838-849.

Cuervo JJ & Moller AP (2009) The allometric pattern of sexually size dimorphic feather ornaments and factors affecting allometry. Journal of Evolutionary Biology 22:1503-1515.

Kemp DJ (2008) Resource-mediated condition-dependence in sexually dichromatic butterfly wing colouration.Evolution 62:2346-2358.

SOLUTION

Abstract
The butterflies of Lepidoptera species exhibit vibrant colors which are thought to function as a sexual signal for attracting females of the same species. A butterfly Euremahecabe found in Australia was investigated whether the color patches on the male wings are responsible for sexual signaling. Literature tells that producing color from the pigments is more expensive for the animal as compared to other sexual signals.  A statistical analysis involving linear regression can profitably be employed to check if there exists anyconnection between size of the butterfly wings and the size of the yellow patch found on the wings. Separate data was collected for males and females. Digital image capture technology was used to take precise measurements and software like Digilab and Motic images were also employed. The linear regression analysis found a strong relationship between the wing size and the patch size but on the contrary the slope depicted negative Allometry. An Isometric 1:1 relation could not be found. The yellow patch size does not increase corresponding to the wing size. Hence it was found that theyellow color area on the wings of male butterfly is not more than the female wings and hence the hypothesis was also rejected which stated that the yellow color patch function as sexual signals in male butterfly of Euremahecabe.
Introduction
A small butterfly named Euremahecabe (Linnaeus, 1758) belonging to class pieridae is commonly found in Asia or Africa (Woodhall, 2005). Yata, 1995 recognized 18 sub species. Only Euremahecabe occurs in the Australian sub region. Wet and dry season forms are recognized by Jones, 1992. This species is found all through the year in Afrotropical, oriental and Australian region (Yata, 1995). These butterflies fly close to the ground over grass and therefore also called common grass yellow. Although it is an odd name because the larvae of this species does not eat grass. The morphology of the adult butterfly is similar in males and females, which means they are sexually homologous. The dorsal surface of wings is yellow with black edges while ventral surface is yellow with black spots. There are certain color patches present at the dorsal wings of these butterflies which are known to signal attractiveness but this characteristic is present only in the male member of the species (Ghiradella et al., 1972; Rutowski1977). The problem here which needs to be addressed is to determine difference between two sexes and to define the relationship between wing size and size of the color patches on the wings.
Research shows that Animals use colors to perform a number of functions. Some use it for thermoregulation while others use it for their defense in either hiding from the prey called camouflage or display toxicity called aposematic behavior. Colors are also used by animals as a sexual signal to guide the opposite sex of the same species (Andersson, 1994). Usually the male member practices color for sexual signaling (Andersson, 1994). Theory suggests that production of color as a sexual signal is more expensive for an animal as compared to other morphological structures like arms, legs or hair ((Muma andWeatherhead, 1989; Hill, 1993). The pigments required to synthesize the color are metabolically very expensive for the animal and therefore only high quality males can synthesize such pigments to display sexual signal. Thus production of color for sexual signaling is an indication of a dependable and honest male mate quality. Out of the many sexual signals displayed by animals, color signals occupy a small proportion and also they have remained constant in the evolutionary history and as a result only better quality males catch attention from the female members of the species (Common and Waterhouse, 1982).
The butterfly in question, Euremahecabe displays two colors, yellow and black. The yellow color on the wings is due to the presence of pigment pteridines and black color comes from the pigment melanin (Silberglied and Taylor, 1978). The present study will investigate whether the yellow color patches in the male Euremahecabe functions primarily as sexual signal for male mate quality and to find out the relationship between size of the color patch and wing size.
The hypothesis to be tested is whether the yellow color patches on the male butterfly has any contribution towards sexual signaling and to determine if the wing size of the butterfly has any relationship with the size of yellow color patch present on the wing.
There are many assumptions which led to the creation and testing of this hypothesis. It was already assumed that yellow patches function as sexual signal while the black patches are devoid of any such quality. During the process of development into an adult butterfly, both the sexes can use their available resources to develop any bodily structure and using these resources for color signals is very expensive (Common and Waterhouse, 1982). Investing the resources for color preparation reduces the overall resources that can be used somewhere else. The production of yellow color is more expensive as compared to black. This is because the pigment pteridine responsible for yellow coloration requires more resources as compared to pigment melanin responsible for black coloration. This means displaying yellow wing color extracts more resources from the already limited supply of resources.
It has been predicted that the yellow color patches in male butterfly,Euremahecabe functions as sexual attractiveness signals and the size of the wing is related to the size on yellow patches on it.Also the yellow color area on the wings of male butterfly is more as compared to the female wings. A hypothetical- deductive approach is to be carried out to scientifically investigate the hypothesis and to test whether the prediction is true or false. If the prediction does not hold true then the hypothesis will summarily be rejected and vice versa.
Methods
A laboratory experiment was carried out to test the hypothesis. Each student was given the samples of butterfly wings for analysis. Samples of both the male and female butterfly were provided. Students were first instructed to make a drawing of the wings of male butterfly. Both the fore and hind wing was drawn from the dorsal side. Microscope was also provided to see the detailed and magnified structure of the wing. To get accurate measurement of animal morphology, Digilab and Motic images software were used. Students were instructed to use this software accurately. Images of all wings of both the sexes of butterflies were taken and imported into Motic Images. Overall wing area and the black and yellow color patch area on the wing were calculated. In order to reduce inaccuracy in the measurement, three separate readings were taken to measure the area of each color patch. Average reading of the three dimensions was considered final. The same procedure was carried on to take the readings of female wing and the data was collected separately for male and female wings. The data collected was filled in an excel spreadsheet for analysis. The Final step was to determine how the size of the wing is related to the color patch size present on it. A simple statistical analysis or linear regression was carried on to calculate the results. “Vassar Stats” is an online tool which can be used to test data for regression analysis. The graph obtained as an output can easily describe how the two variables are related to each other. The linear regression analysis generates three kinds of results namely, Isometric, Positive Allometry and Negative Allometry. Isometric is a 1:1 relationship which holds that for every one unit increase in one variable, there is corresponding increase of one unit in the other variable. Positive Allometry shows >1:1 relation and Negative Allometry shows <1:1 relationship. In the present study, the two variables to be tested are wing size and color patch size. The wing size is the independent variable while the color patch size is the dependent variable. The linear regression was carried out separately for male and female wings to test if there is any deviation from a 1:1 isometric relationship.
Statistical Procedure
Before using the data for statistical analysis, the dependent and independent variables were first transformed to fulfill statistical assumptions of linearity. Natural log of the data was taken. In the excel spreadsheet, a new data column containing formula ln(xx) was created where xx is the cell to be transformed. Regression can be run after the data has been log transformed. Vassar Stats webpage allows regression to be run. By Clicking on Correlation and Regression, a page opens up and after scrolling down click data import version. A form opens up and data from the excel sheet was pasted into that form. Carriage return at the end of data file was removed. Data was pasted in such a way that wing size was assigned X axis on left side and the color patch size was allotted Y axis on right side. By clicking on calculate button, Regression was run and output was obtained after further scrolling down. The output is the results obtained which is to be analyzed and interpreted to form a conclusion.
Results
The following results were obtained after running regression for the collected data.
The t-test was carried on using the slope of regression line and the standard error. The t-value comes out to be 7.33. The degrees of freedom (df)which is equal to the number of observation minus 2 is calculated as 15. Finally the P value is calculated from the t-test score and degrees of freedom. The two-tailed P value is calculated as <0.0001. The significance level is 0.05. If the P value comes out to be less than significance level, then null hypothesis can’t be accepted. This confirms that the two testing variables are related to each other and hence there is a considerable relation between the wing size and color patch size.
Ther2 value is the coefficient of determination and is used to predict how a change in the independent variable can affect the dependent variable to change. If the points lie closer to the line, it means a better fit.r2 value is calculated as 0.7815 which means that the wing size is
78.1 % good in predicting the color patch. A higher value means that it is easier to predict one variable from another.Therefore the dependent and independent variable represent strong relation with each other.
The slope gives the steepness of the line. It is formed by change in Y when there is a change in X. Slope is calculated by dividing units of Y axis with those of X axis. If the units of X and Y increases simultaneously then the slope is positive but on the contrary if the values do not change corresponding to one another then slope is negative. Slope value came out as 0.650 which indicates that the units of X and Y axis does not change consistently. When the X axis increases by one unit, there is only 0.65 unit increases in the Y axis. This is of particular interest to us, as we wish to know whether the slope differs from 1.0, and in which direction. If the wing size increases by one unit then the color patch size does not increase by one unit rather color patch size increases by only 0.65 units. The slope of the line will deviate from 1.0 in the negative side.
By further scrolling down the Vassar Stats output, we come across the confidence limits for slope. This is predominantly essential because these limits test statistically if the slope of color patches and wing size varies from 1.0. The 0.95 confidence intervals are 0.4602 – 0.84 which means that the slope will lie between these two intervals. The values are less than 1 and the data shows negative allometry.
A graph for the dependent and independent variables was formed using the raw or untransformed data. The wing area or the independent variable was plotted on the X axis while the dependent variable or yellow patch size was plotted on the Y axis. The corresponding X and Y values were marked on the graph and output was produced. The graph clearly depicts that for one unit increase in independent variable (wing size), the dependent variable (yellow patch) does not increase by one unit. The graph shows negative Allometry<1:1 relationship. The prediction does not hold true and the results show that the males do not have larger yellow wing area. Along with this the hypothesisthat yellow wing color is used as a sexual signal by males to attract females is also rejected.
Discussion
The study aimed to scientifically investigate the function of yellow color patches in the butterfly Euremahecabe. Theory tells that animals display bright colors to attract the opposite gender of their species. Usually the males employ body structures to attract the females because production of color as a sexual signal is potentially expensive with limited resources. The pigments required to produce color use a lot of resources and only better quality males can afford to use already limited resources for color production. It was hypothesized that the male butterfly, Euremahecabe uses the yellow wing coloration as a sexual signal and hence displays a better male mate quality. A logical prediction made to test the hypothesis was that male members of the species have large yellow wing area than females. Data was collected and statistical procedures were carried out to test the prediction. Data was collected separately for male and female wings and recorded in excel spreadsheet. Regression analysis was carried on after taking natural log of the parameters. The two- tailed P value came out to be <0.0001 which means that wing size and yellow patches on it are related to each other. The r2 value of 0.781 explains that wing size is 78.1 % good in predicting the color patch size. The slope was calculated between the X and Y axis. Two different slopes were formed for male and female wing analysis. The slope value of 0.65 tells that the slope will deviate from 1.0 in the negative side. The 0.95 confidence intervals of 0.4602 – 0.84 illustrate that slope lies between these two units.The slope did not show isometric 1:1 relationship, but the slope deviates on the negative side and show negative allometry<1:1 relationship. The results of statistical analysis clearly deny the prediction that males have larger yellow wing area than females. At the same time size of the wing and size of the yellow patch show negative allometry. The yellow patch size does not increase corresponding to the wing size. As the prediction does not hold true, consequently the hypothesis will also be rejected which stated that the yellow wing color in the male member of Euremahecabe function as sexual signal of male mate quality. This holds true with the literature as well which tells that formation of color as a sexual signal is very much expensive for an animal because of the limited pool of resources. The animal can profitably use other body parts to attract the female and conserve the resources to use it somewhere else. The implications of the statistical analysis help to understand the problem better.
The P value and the slope value clearly stated that the independent and dependent variables are negatively related. The two variables do not follow an isometric 1:1 relationship and hence the yellow color patch does not function as a sexual signal in male members. The potential future research directions can be based on investigating other body structures of the male butterfly that can function as sexual signals for attracting the females of the same species. The other body structures such as legs, arms etc. can also function as signals and they use fewer resources than those consumed in displaying bright colors.
References
1.    Andersson, S., 1994. Sexual Selection in Animals. Princeton University Press, Princeton, NJ.
2.    Bonduriansky R (2007) Sexual selection and allometry: a critical reappraisal of the evidence and ideas. Evolution 61: 838-849.
3.    Cameron, A.C., Windmeijer, F.A.G., (1997).”An R-squared measure of goodness of fit for some common nonlinear regression models.” Journal of Econometrics, Volume 77, Issue 2, April 1997, Pages 329-342.
4.    Common, I.F.B., Waterhouse, D.F., 1982. Butterflies of Australia: Field Edition. Angus and Robertson Publishers, London.
5.    Cuervo JJ & Moller AP (2009) Theallometric pattern of sexually size dimorphic feather ornaments and factors affecting allometry. Journal of Evolutionary Biology 22:1503-1515.
6.    http://faculty.vassar.edu/lowry/VassarStats.html.
7.    Graham, S.M., Watt, W.B., Gall, L.F., 1980. Metabolic resource allocation vs. mating attractiveness: adaptive pressures on the ‘‘alba’’ polymorphism of Colias butterflies. Proceedings of the National Academy of Sciences of the USA 77, 3615e3619.
8.    Kemp DJ (2008) Resource-mediated condition-dependence in sexually dichromatic butterfly wing coloration. Evolution 62:2346-2358.
9.    Muma, K.E., Weatherhead, P.J., 1989. Male traits expressed in females: direct or indirect selection? Behavioral Ecology and Sociobiology 25, 23e31.
10.    N. Nagelkerke, “A Note on a General Definition of the Coefficient of Determination,” Biometrika, vol. 78, no. 3, pp. 691–692, 1991.
11.    Rutowski, R.L., 1977. The use of visual cues in sexual and species discrimination by males of the small sulphur butterfly Euremalisa (Lepidoptera, Pieridae). Journal of Comparative Physiology 115, 61e74.
12.    Rutowski, R.L., Macedonia, J.M., Morehouse, N., Taylor-Taft, L., 2005. Pterin pigments amplify iridescent ultraviolet signal in males of the orange sulphur butterfly, Coliaseurytheme. Proceedings of the Royal Society of London B 272, 2329e2335.
13.    Stavenga, D.G., Stowe, S., Siebke, K., Zeil, J., Arakawa, K., 2004. Butterfly wing colors: scale beads make pierid wings brighter. Proceedings of the Royal Society of London B 271, 1577e1584.
14.    Steel, R. G. D. and Torrie, J. H., Principles and Procedures of Statistics, New York: McGraw-Hill, 1960, pp. 187, 287.

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