Welcome to Lab 4: Competition and
Natural Selection. Before we go through
the lab, let's highlight the main
concepts. What are the conditions
necessary for evolution by natural
selection to occur within a population?
What is fitness? What is relative fitness?
What are ways to estimate reproductive success?
What is the value of a statistical analysis?
First, you should be familiar with the
conditions necessary for a population to
evolve through the process of natural
selection. Let's go through them.
One, within a population
there must be phenotypic variation.
Two, the phenotype of interest must have a
genetic basis at least in part.
Three, some phenotypes will have a higher
probability of reproducing than other phenotypes.
You need to understand these
and be able to apply them to real-world scenarios.
The focus of natural selection
is all about the fitness of different phenotypes,
but what is fitness? How would
you define fitness if asked on an exam?
Today we are interested in relative fitness, or
the idea of how much an organism is
reproducing relative to others in the
population. Why do you think that is
important if a population is to evolve
through the process of natural selection?
Think about this and ask your TA if you still have questions.
In this lab you estimate reproductive
success using components of fitness.
This is a way to estimate reproductive
success without having to pollinate the
plants we are using, let them go to seed,
collect the seeds, plant the seeds,
wait for those to grow and then
see how many of those reproduce.
Now the big question we are asking revolves
around the third condition of natural selection.
Is there a difference in reproductive success
among different phenotypes? In the
context of the lab we are asking does
competition influence reproductive success?
As you do this lab, think about
what you learned in Lab 2 about
resources plants need to use as well.
Also think about ideas from the
population growth portion of the course.
Most populations exhibit logistic
population growth. Why don't populations
 seem to grow infinitely large?
In the laboratory, we have grown
Brassica rapa under different
types of competition, which we call
treatments. Brassica is a mustard,
but this particular variety has been
selectively bred to grow fast and
produce flowers within four weeks. There
are two color morphs - a green morph,
the dominant phenotype, and a
yellow-green morph, the recessive phenotype.
We know there is a single gene with two
alleles, big Y and little y, that produces the
color in these plants. The green plants
have at least one copy of the big Y allele,
and the yellow green plants have
two copies of the little y.
Their possible genotypes are as shown.
We have grown these plants under three treatments.
Treatment 1 - a single plant of each color morph is grown in separate pots.
We call these single green and single yellow.
As you can see there is no competition in this treatment.
Treatment 2 - we planted 1 green plant with 5 other green plants.
In another pot we planted 1 yellow plant with 5 other yellow plants.
This is our test of intramorph competition.
Treatment 3 - we planted 1 green plant with 5 yellow plants and 1 yellow plant
with 5 green plants. This is our test of intermorph competition.
Your mission is to determine -
is there a difference in reproductive success
for two different forms of Brassica
under different types of competition?
This is essentially our working hypothesis. These
are the steps we took to begin tackling the question.
Step 1 - We pick three
components of fitness to measure.
Recall from the pre-lab, you suggested
different traits in a plant one can measure
that would influence reproductive success,
for example plant height or number of leaves.
Step 2 - We then measured these traits    
for each of the treatments.
In Treatment 1 we measured all three
components of fitness for the single green
and the single yellow and recorded that data.
For Treatment 2, the intramorph competition treatment,
we randomly picked one green
plant and one yellow plant to measure
for all 3 components of fitness. For
Treatment 3, the intermorph treatment,
we measured all 3 components
for the green plant grown with a bunch
of yellow plants and then we did the same
thing for the yellow plant grown with a bunch
of green plants. This data is available in the
Excel file posted on Canvas under Lab 4 Assignment.
Now that you have your data, what does it
all mean? In the population growth lab we
had you collect data but we didn't do a
very sophisticated analysis with it.
For this lab we would like you to step that
up and to really look at the data
through the eyes of a scientist. For that
we'll have Dr. Pat Randolph
walk you through the spreadsheet.
For this lab what I have done is I've grabbed a data set
from Fall 2019 from one of the lab sections
and we're gonna use that to see is there
a difference in reproductive success of
the 2 morphs, the green morph and yellow-
green morph, under different types of competition.
And so what I want to do is
orient you to the spreadsheet so you
know how it's set up and then I want to
walk through how to calculate mean,
standard deviation, and standard error.
These are going to be important for the
data analysis side of things. So first
let's just orient you to the spreadsheet.
First of all, this first sheet here is
our Treatment 1, so this is our no
competition. So if you recall what that is
that's just a single green plant it's
grown all by itself and a single
yellow plant. This lab section selected
their 3 components of fitness to
be plant height, the number of flowers
and buds, and the buds are just flowers that
haven't opened up yet, and then root length.
And if we call the components are
our proxies of reproductive success, so
we're not measuring the number of
offspring directly we have these proxies here.
The group name here is just the
individuals that collected the data, you
don't need to worry about that for this
lab but that's what this row is all about.
We have three sheets here so the
first sheet labeled Table 1a is our no
competition treatment, so Treatment 1.
Table 1b if I click on that, is our
intramorph competition. So if we recall
'intra' means within, so that's green plants
competing with green or the yellow
plants competing with the yellow plants.
And so there's data collected
here. And then Table 1c is the intermorph
competition, 'inter' meaning
between, and  so we have a single green
competing with a bunch of yellow or
yellow plant competing with a bunch of
green and that's what we mean
by intermorph competition, so two different
morphs or phenotypes. Let's go back to
Table 1a. Okay so here are the data for
the no competition and what I want to do
is walk through now how to calculate
mean, standard deviation, and standard
error using a spreadsheet, using Excel.
And again I strongly recommend you use a
spreadsheet to do these calculations.
Everyone here should have access to
Office365 for free through your UC
Davis account, and so I just suggest you
use Excel it's just easiest and we're
all familiar with that. So to calculate
mean what I'm gonna do is I want to
calculate the average value of plant
height for the green plant here. So to do
that in Excel whenever I want to do a
formula, first I want to highlight where
I want to put that value, and then I'm
gonna put in an equal sign. So the equals
tells the spreadsheet I'm gonna do a
formula of some form. And Excel is kind of nice,
it has a command for average so if I 
just type average or start typing average,
average pops up so just click on
that. Then you'll see this parenthesis here
and so inside the parentheses is where I
want to put the data I want the average for.
So what I'm gonna do is highlight
the cells here that I want the average for,
I hit return and voila, there it is
so magically I've calculated the average.
And so what's nice about Excel is it did
that quickly and accurately, and what's
really nice is I can copy this formula
into all the cells here. And so to do that
I'm gonna grab this little corner, see that
little green box right there, gonna grab
that with my cursor let's drag that all
the way down and there it is I've
calculated the average for all
components of fitness you know within
just a few seconds and so that's the
power of a spreadsheet, it allows us to do
this very quickly and accurately.
Standard deviation we want that value too.
So to do that again we type in equals,
again that's telling Excel I'm doing
some sort of formula. Excel has a command for
standard deviation its STDEV just gonna
click on that and just like I did with
the average I'm just gonna highlight the
cells I'm interested in, hit return and
voila there it is. And just like with the
average I can just copy that formula
all the way down and I've calculated
standard deviation for all those values.
So the pound sign here, the number sign
maybe hashtag is more of a familiar term
to you, this just means there's no data
there. You can leave those it doesn't
mean anything, you can clean it up just
whatever you like to do, it doesn't matter.
Okay so standard error, so we're gonna need
standard error for graphs we want you
to do, and quite often on graphs you'll see
standard error bars, we'll discuss that later.
Excel does not have a command
for standard error, but standard error is your
standard deviation divided by
the square root of your sample size
and that formula is in your lab manual.
So to calculate this, so I'm gonna put
an equal sign there that's saying I'm doing a
formula. I'm gonna highlight the cell for
the standard deviation, I want to divide
that by the square root of my sample
size. So what's my sample size? So if I look
at the green plant here for plant height, I have
1 2 3 4 5 6 7 8 9 10 11 12 data points,
so my sample size is 12. But I
want to take the square root of that and
one way to do that is raise that to 1/2 
that's one way you take the square root,
hit return and there it is the
standard error. There other ways to
calculate the square root of 12, Excel
has a command for square root or you can
just plug that number in a calculator,
get that value, and plug it in the
formula. I just do it this way it's
easier for me, at least I find it easier.
And just like with the other
calculations I can just copy that all
the way down and voila I've calculated
the standard error.
And since I'm kind of picky, I like to clean things
up a little bit, I'm gonna get rid of those pound signs.
One way to do that is go under edit, clear,
clear contents that just cleans that up.
I'll do the same thing with the other
set of pound signs. You don't have to do this,
again this is just me
being picky and then I have a nice clean
data set with the mean, standard
deviation, and standard error. So we want
you to do that for the intramorph
competition data set and the intermorph
competition data set. That's important
because you're gonna be using these
values the mean, standard deviation, and
standard error in deciding - is there a difference
in reproductive success between the green plant
and the yellow-green plant
for the different components
of fitness under different types of competition?
That's it for this video.
Make sure to check out the next video on
how to do t-tests. As always, if you have
any questions please contact your TA.
