Hello, today I am going to walk you through
a mass selection experiment. I will select
for length in Danio rerio, zebrafish. The
first thing I do is measure my zebrafish.
I arranged the zebrafish into a histogram
here. Using this data I calculate my mean
and standard deviation. I also do some research
and find that, for length in zebrafish, the
broad sense heritability is 0.85 and the realized
heritability is 0.67. My mean is 45 mm, with
a standard deviation of 3.2 mm. I am going
to select the top 10% to breed, and this proportion
tells me which I and Z values to use, as highlighted
on this table. In my research I also find
that zebrafish length is normally distributed,
so without breeding fish, I can calculate
the mean of the offspring. First I need to
find the truncation point, X sub T. This is
my cut-off point. The fish longer than X sub
T are the ones I will separate for breeding,
and are indicated by this shading. This is
also the top 10%. To find the truncation point,
we will use this formula. We already know
the mean, Z value and standard deviation,
so we can plug in those values and we get
that X sub T is 49.1 mm. We can label our
graph with that, and now I know to separate
all fish longer than 49.1 mm for breeding.
Next let’s find the mean of the selected
parent fish. We can find this with the following
formula. The mean of selected parents equals
the mean of the population plus the selection
differential. We don’t know the selection
differential, but we can find that as well,
using this formula, which says that the selection
differential is the selection intensity times
the standard deviation. We know both of those
values, so we can plug them in to find that
the selection differential is 5.6. Going back
to the formula for X sub S, we plug in mean
and selection differential, and find that
the mean of selected parents is 50.6. We can
add that to our graph. And the distance
between X sub s and X knot can be labeled
with the selection differential, since that
is how we found X sub s. Next I want to know
the response to selection. We can calculate
this using realized heritability, which is
equal to R over S. We can rearrange this formula
to say that the response to selection is the
realized heritability times the selection
differential, and we have both of these values.
When we plug them in, we find R to be 3.8
mm. We can add response to selection to our
graph, right here. Now I want to calculate
the mean of the offspring, X sub 1. To find
the mean of the offspring, we use the following
formula which says that the mean is equal
to the mean of the population plus the response
to selection. We know both of those values,
so we can plug them in and find the mean of
the offspring to be 48.8 mm. So, without doing
any breeding, I know what the mean of the
offspring will be. Can I keep repeating this
experiment to get a 1 meter long zebra fish?
Not practically. In existing mass selection
experiments, scientists saw a point at which
they could not breed the population past a
certain point, most notably they could not
make mice any smaller since the smallest mouse
was sterile. These limitations may come from
genes linked to the desired trait that result
in adverse effects to reproduction or mortality
rates.
