Measuring natural selection on the milkweed (Asclepias syriaca)
using the methods of Lande and Arnold (1983).
Briefly, we set out to see if we could detect the action of natural selection on milkweed
by obtaining an estimate of fitness, and the measurement of traits that might be the targets
of natural selection.
We measured both the number of fruits produced per plant as a measure of female
reproductive success which is a component of fitness.
We also measured the total number of inflorescences. Since the plants are
hermaphrodites, they have the capacity to be a male (paternal) parent as well. The
number of inflorescences can be considered a component of male fitness but rather than
use the absolute number of inflorescences as a measure of male fitness I did the
following:
Note that I determined the male component of fitness in the following way (called
MALEREPRO in the Excel spreadsheet).
Milkweed is self-incompatible and each seed produced has a maternal parent and a
paternal parent. The maternal parent is easy since the fruit remains attached to the
maternal plant, so we can just count fruits to determine the maternal component of fitness
(FEMALEREPRO). For the paternal/male component, I divided the number of
inflorescences each plant produced by the total number of inflorescences in our sample
(there were 744 inflorescences). We also know that the total number of fruits produced in
our sample was 872. We'll assume that on average each plant as a male parent could have
fertilized fruits as a function of the proportion of inflorescences it produced in the
population (this assumes there is a linear relationship between the number of
inflorescences a plant produces and male fitness).
For example, a plant with two inflorescences has 2/744 chance of siring a fruit, therefore
on average the number of fruits it sired as a male was 872 x 2/744 = 3.52 fruits and this
would be its male component of fitness or male reproductive success.
If a plant produced 0 inflorescences then it has a 0/744 chance of siring fruits,
and so on average it sires 872 x 0/ 744 = 0 fruits (and so on for various numbers of
inflorescences).
Since males and females make one genetic contribution to each fruit, the total fitness of
each plant was calculated as:
the number of fruits produced as a female + male fitness (estimated as above).
Following Lande and Arnold, I then converted this to relative fitness by simply
calculating the mean number of fruits in the sample and then divided each by this mean
(called RELFIT (relative fitness) in the Excel spreadsheet).
For all other characters, they are simply listed in the spread sheet in units of cm or in
counts for number of leaves. In the analyses I carried out, I standardized the characters by
first calculating the standard deviation of each character, and then dividing each data
point by the standard deviation of that character (I have not provided that data in the
spread sheet since you don’t need it).
This is what I did for the analysis presented below. You can carry this out on the raw data
if you like. It won't change the values of the correlations you will carry out, but it is not
necessary for you to do it.
So for example, the standard deviation of plant height was = 24.78, so I divided each
height by this value.
ANALYSES FOR YOU TO PERFORM
The idea will be to produce tables for milkweed just like the tables in Lande and Arnold.
1a So calculate the mean and standard deviation for each morphological character.
(Height, Number leaves, leaf length, leaf width)
1b Following the Lande and Arnold paper, you should also calculate the correlation
coefficient between each pair of morphological characters (see hand out on using SAS to
do this).
Construct and enter these values in a table like Table 1 in Lande and Arnold.
2) For the purposes of description it would be interesting to draw histograms the
distributions of all traits and note and comment on their shapes.
3) You should also then plot Relative fitness (on Y-axis) against each of the four
morphological traits and calculate the correlation of Relative fitness against each of
these. So this will give four plots or graphs and the corresponding correlations for each.
4) I will provide the analysis for the multiple regressions (that is, the information for a
second table, corresponding to Table 2 of Lande and Arnold). The analysis is presented
below.
Briefly, I analysed the data using the statistical program known as SAS. I can provide
the raw output file as well as the programming code I used later if anyone wants to know
how to do this.
In the multiple regression of relative fitness against each of the morphological
characters the analysis provides an estimate of the selection gradient, whether it is
negative or positive and a t-test and associated p-value indicating whether it is
statistically significant. The table below is comparable to table 2 of Lande and Arnold
and can be interpreted following their interpretation of their data in table 2. Include the
table in your write-up.
Table of Standardized selection coefficients (S') and gradients (β') including quadratic
(γ') terms.
(Note that I have only carried out the analysis on the standardized data, not on the raw
data, which in any case, gives comparable results).
I've provided estimates of the selection differential (S') and the selection gradient (β') and
the quadratic term (γ') for the standardized data.
β'
S'
γ'
Height
0.71***
0.46 +/- 0.04***
0.11 +/- 0.03***
#Leaves
0.28***
0.01 +/- 0.04ns
0.03 +/- 0.02ns
Leaf length
0.38***
0.05 +/- 0.04ns
0.03 +/- 0.03ns
Leaf width
0.44***
0.08 +/- 0.04ns
-0.05 +/- 0.02*
R2 = 0.59***
*** P < 0.001, * P < 0.05, ns = not statistically significant
Your Write up is due October 14th.
So your task is to prepare a write up of the field experiment we conducted.
The write up should be structured as follows:
1. Introduction - not more than two paragraphs stating the objectives of the study and
providing a little background on the approach of measuring natural selection in the field
(following Lande and Arnold 1983).
2. Materials and Methods - describe the field work that was conducted and the analyses
carried out.
3. Results - present the results of the analysis essentially modeling the tables you prepare
following tables 1 and 2 in Lande and Arnold. But, you will also include 4 graphs (or
figures) of relative fitness plotted against each character as well as graphs of the
distribution of traits that you should comment on before getting into the Lande and
Arnold analysis. The written portion of the results should simply describe the contents of
the Tables and graphs as in any scientific publication.
4. Discussion - briefly discuss your results, by interpreting them following the
interpretations in the Lande and Arnold paper. You can also provide a critique or
problems associated with our particular analysis.