Biol 217 Evolution
Spring 2010
Quantitative Variation
in
Helianthus annus (Sunflower) Seed Stripes
Quantitative variation within and among groups is at the base of all studies of
evolutionary change. In order to discuss changes in populations we need to develop a
language and a set of concepts that allow us to describe and compare characteristics of
populations. These skills involve understanding the distribution of characters in two
broad categories: measures of central tendency; and, ways of describing the
distribution of values around these measures of centrality. In this lab we will measure
the extent of variation in a natural population within and among groups using the
common sunflower (Helianthus annus) seed as the subject of our investigation. The
language and concepts that we begin to explore today are the basis for making
comparisons between different populations that exist at the same time and for examining
changes in a population at different times.
Stripe variation in the common sunflower (Helianthus annus)
We will use histograms to represent the distribution of a population with respect to a
particular character. In a histogram the character being discussed is represented on one
axis while the number of individuals in the population with that value of the character are
represented on the other axis.
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Spring 2010
In this graph we see a representation of the following hypothetical data:
#Stripes
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
#Seeds
5
3
25
65
68
24
74
32
25
12
8
14
10
5
2
Part 1 – Collecting data
Each student will receive three envelopes of BURPEE S Mammoth sunflower seeds.
First, take a few minutes to spread them out and look at the ways they vary. In this first
part of the activity you will divide up your sunflower seeds based on the number of
stripes that they have. We will probably have some class discussion of how to score
stripes. Keep them in separate piles based upon the number of stripes and photograph
your results.
Part 2 – Representing your data
Record the number of seeds in each category (number of stripes). Then place them in test
tubes arranged in a rack to create a histogram-like representation of your data. Compare
your population to several other group’s populations. Then write 2-3 sentences describing
your population with respect to the number of stripes.
Part 3 – Measures of central tendency
Calculate the mean, median and mode for your population. Show where each of these
occurs by laying a piece of paper at the base of your test tubes and marking where each of
these measures occur. Compare your results with a couple of other groups and write a
sentence or 2 describing your population.
mean = (∑ x)/n
where x is a value and n is the number of values
This statistic is also commonly referred to as the average. It is computed by adding each
of the values in the distribution and dividing by the number of values in the distribution.
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Median: the middle value
The median of a distribution can be found by putting the numbers in ascending order and
taking the number in the middle, e.g. if the distribution has five values ( 5, 5, 4, 2, 1),
then the third value is the median (4). If there is more than one middle value, then the
mean of the two values is used.
Mode: the most frequent value
The mode is simply the value which occurs more often, e.g. the mode of this distribution,
8, 7 ,5 ,5, 5, 3, 1 is five.
Mode
Rat Weight
Media n
7.5
5
Number of rats
10
Mean
2.5
1
2
3
4
6
5
7
8
9
10
Weight (g)
Part 4 – Measures of distribution
Enter your data into the JMP statistics program and have it calculate the standard
deviation, skewness, and kurtosis values for your population distribution.
Standard Deviation = √[∑ (x - "frequency mean")2/(n - 1) ]
where x is a value and n is the number of values
The standard deviation is a measure of the spread of a distribution. It is calculated by
first calculating the mean of the distribution. Then, the difference between each value
and the mean should be squared and all of those numbers added up. That value is divided
by the total number of values minus one in the distribution and the square root of that
number is the standard deviation.
The standard deviation of a distribution indicates where most of the values are found. If
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Spring 2010
you look at the values between the mean and one standard deviation above the mean 32%
of the population values are represented (assuming that the population is normally
distributed). We can extend this understanding of how the standard deviation describes a
distribution to arrive at the following conclusions:
68% of the population falls within ±1 SD of the mean
95% of the population falls within ±2 SD of the mean
99.7% of the population falls within ±3 SD of the mean
This is shown graphically on the figure below.
Shell Length
MEAN
40
20
NUMBER
30
10
10
20
30
40
Shell Length
± 1-
68%
± 2-
95%
± 3-
99.7%
Skewness = (1/ns3)∑(x - "frequency mean")3
where s is the std. deviation, x and n as before
Skewness is a statistic that describes the relative sizes of the tails of the distribution. A
negative skewness value implies that the left tail of the distribution is longer. A positive
skewness value implies that the right tail of the distribution is longer.
The calculation is similar to calculations for the standard deviation. After finding the
frequency mean, the cubes of the differences between the each of the values and the mean
are summed. Then, that number is divided by the number of values in the distribution
and the cube of the standard deviation.
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Fruit Weight
30
NUMBER
20
10
1
2
3
4
5
6
7
8
9
10
Fruit Weight
A positively skewed distribution. The red line represents a symmetrical distribution for
reference. Note that in a positively skewed distribution the mean will be greater than the
median population value.
Kurtosis = (1/ns4)∑(x - "frequency mean")4 - 3
s, n and x as before
Kurtosis is a statistic that describes how sharp the peak of the distribution is. A negative
score indicates platykurtosis (a relatively flat peak), while a positive score indicates
leptokurtosis (a relatively sharp peak).
mesokurtic
"normal"
platykurtic
300
100
leptokurtic
10
20
30
X
5
Number
200
Biol 217 Evolution
Spring 2010
Part 5 – Multidimensional variation
Using the seeds from within one category of stripe number, make three additional sets of
measurements on your seeds. For example, if you looked at all 19 seeds that had 11
stripes (hypothetical data), you also could measure seed weight, buoyancy, seed length,
oil extraction, etc. to examine intraclass variation.
Lab Write up (Individual)
In addition to submitting your JMP file electronically, your write up should include:

Your definition for the character stripe number. Include two photos of an
individual seed (i.e., one picture of each flat side) and clearly mark the stripes
that you counted in your analysis.

Your raw data for variation with respect to stripe number in your population
in tabular form. Include a photograph of the histogram made by arranging
your seeds in test tubes of equal size.

A clearly labeled graph of the distribution of your population on which you
have indicated the mean, median, mode (with reference to the histogram) and
the calculated values for standard deviation, skew and kurtosis.

A clearly labeled graph of the distribution of the full class’s population.

A short description of your data (not simply listing the statistics but describing
it as you might to a friend who was not familiar with statistics) and
comparison of your data to another group’s data. Do you think they are both
samples from the same population? Why or why not?

Discuss why central tendency may not be such an important factor for natural
historian with a Darwinian perspective.

A definition of the three other characters that you measured. A description of
your findings on interclass variation including a histogram of your results.
Show a scatter plot with a linear regression line for the most correlated of two
of your three quantitative traits that you measured on seeds with the same
number of stripes.

A brief discussion of how this detailed information about variation is relevant
to evolution. Sunflowers are an important economic crop. How has natural
and artificial selection contributed to the variation that you have observed?
Several references and one pedigree are presented below that may help you to
think about this problem.
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This is a modified version of a lab developed by John Jungck at Beloit College. Several of
the figures were taken from the Biometrics module by Daniel Hornbach published the
BioQUEST Library.
See http://bioquest.org/biostat for additional information about these statistics.
A more detailed explanation of how to calculate these statistics can be found in Biometry
by Sokal and Rohlf, which is the text for the Beloit College Biometrics course. Chapter
4, Desriptive Statistics, gives a good explanation of the first four statistics. Chapter 2 is
on frequency distributions and may be of some help.
Tang et al. (2006) reported the above data and three loci model for the inheritance of
sunflower seed characteristics.
Considerable variation exists in seed characteristics of different cultivars of sunflower. A
sample of this variation from a seed company in China is illustrated below.
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Newfield.com source: Ningxia Newfield Foods Co., Ltd., China
http://www.newfield.com.cn/english/products/sunflowerseeds.htm
References:
Bert, P.F., I. Jouan, D. Tourvielle de Labrouche, F. Serre, J. Philippon, P. Nicolas, and F.
Vear. (2003). Comparative genetic analysis of quantitative traits in sunflower
(Helianthus annuus L.). 2. Characterization of QTL involved in
developmental and agronomic traits. Theoretical and Applied Genetics
107:181–189.
Smith, J. Stephen C., Eric Hoeft, Glenn Cole, Henry Lu, Elizabeth S. Jones, Steven J.
Wall, and Donald A. Berry. (2009). Genetic Diversity among U.S. Sunflower
Inbreds and Hybrids: Assessing Probability of Ancestry and Potential for
Use in Plant Variety Protection. Crop Science 49: 1295-1303.
Tang, Shunxue, Alberto Leon, William C. Bridges, and Steven J. Knapp. (2006).
Quantitative Trait Loci for Genetically Correlated Seed Traits are Tightly
Linked to Branching and Pericarp Pigment Loci in Sunflower. Crop Science
46: 721-734.
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Other related references of possible use for your analysis and report:
Angadi, S. V., and M. H. Entz. (2002). Water Relations of Standard Height and
Dwarf Sunflower Cultivars. Crop Science 42: 152-159.
Lambrides, C. J., S. C. Chapman, and R. Shorter. (2004). Genetic Variation for Carbon
Isotope Discrimination in Sunflower: Association with Transpiration
Efficiency and Evidence for Cytoplasmic Inheritance. Crop Science 44: 16421653.
Lenardon, S. L., M. E. Bazzalo, G. Abratti, C. J. Cimmino, M. T. Galella, M. Grondona,
F. Giolitti, and A. J. León. (2005). Screening Sunflower for Resistance to
Sunflower chlorotic mottle virus and Mapping the Rcmo-1 Resistance Gene.
Crop Science 45: 735-739.
Robinson, R. G., L. A. Bernat, H. A. Geise, F. K. Johnson, M. L. Kinman, E. L. Mader,
R. M. Oswalt, E. D. Putt, C. M. Swallers, and J. H. Williams. (1967). Sunflower
Development at Latitudes Ranging from 31 to 49 Degrees. Crop Science 7:
134-136.
Ruiz, Ricardo Adolfo, and Gustavo Angel Maddonni. (2006). Sunflower Seed Weight
and Oil Concentration under Different Post-Flowering Source-Sink Ratios.
Crop Science 46: 671-680.
Tang, Shunxue, Adam Heesacker, Venkata K. Kishore, Alberto Fernandez, El Sayed
Sadik, Glenn Cole, and Steven J. Knapp. (2003). Genetic Mapping of the Or5
Gene for Resistance to Orobanche Race E in Sunflower. Crop Science 43:
1021-1028.
de la Vega, Abelardo J., and Scott C. Chapman. (2006). Defining Sunflower Selection
Strategies for a Highly Heterogeneous Target Population of Environments.
Crop Science 46: 136-144.
Yu, Ju-Kyung, Shunxue Tang, Mary B. Slabaugh, Adam Heesacker, Glenn Cole, Martin
Herring, John Soper, Feng Han, Wen-Chy Chu, David M. Webb, Lucy
Thompson, Keith J. Edwards, Simon Berry, Alberto J. Leon, Martin Grondona,
Christine Olungu, Nele Maes, and Steven J. Knapp. (2003). Towards a
Saturated Molecular Genetic Linkage Map for Cultivated Sunflower. Crop
Science 43: 367-387.
Yue, Bing, Xiwen Cai, Brady A. Vick, and Jinguo Hu. (2009). Genetic Diversity and
Relationships among 177 Public Sunflower Inbred Lines Assessed by TRAP
Markers. Crop Science 49: 1242-1249.
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Notes to Teaching Assistants:
[Intro to JMP: columns, variables, distributions, changing axes, looking at moments.
Have them enter their data into JMP and generate a graph of the distribution of their
population. Print it. [print preview}
Put their print out on paper in front of test tubes
Rough time estimates:
10-15 minutes intro to measures of distribution
10-15 minute intro to JMP
Half hour collecting data
Half hour: They enter data, do calculations, print graphs.
Class discussion: [put up some data on board as well as some of the means and see if that
is a useful way to describe populations for comparisons.]
Range
Standard deviation mean ±1 SD is 68% of population; ±2SD is 95% of population; ±3SD
is 99.7% of pop.
Skewedness +skew is shifted left or pulled right (mean is greater than the median) –skew
is shifted right or pulled left (mean is less that the median)
Kurtosis – is platykurtic (flat); + is leptokurtic (pointy); and 0 is mesokurtic (normal).
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