HYB: Punnett Square

Genetics is an extremely complex subject, which Tom and I have deliberate=
ly
over-simplified to help people get comfortable with the basics.  For thos=
e
who are interested in learning more, I present the Punnett Square.  This =
is
just a geometric device that helps us visualize all of the possibilites i=
n
a cross and compute the probabilities.   (I know, this is a lot like
insisting you learn your multiplication tables before programming a
spreadsheet -- but it WILL give you a good feel for the possibilities &
probabilities associated with a cross.)

For simplicity's sake (again!) I'll use the example from TWOI, p. 398. =

Start with two pieces of paper, one for notes and one for the chart.  Dra=
w
a chart with 6 columns and 6 rows, making each cell about an inch square.=
 =

This will become the Punnett Square.  Now  list the possible gametes that=

can be formed by the (Pl Pl pl pla) pod parent:

Pl Pl
Pl pl
Pl pla
Pl pl
Pl pla
pl pla

There are always six possibilities in the formation of gametes from a
tetraploid.   The number of combinations of four items, taken two at a
time, is six.  The first item can be paired with each of the other three;=

the second can also be paired with items 3 & 4; and items 3 & 4 make up t=
he
final pair.  (3 +2+1=3D6).   if you get more or less than six in a list l=
ike
this, you know you need to go back and re-figure it.  =


Write each combination and it's associated fraction (1/6) down the
left-hand side of the chart, so that there is one gamete per row.  In thi=
s
case, two of the combinations are duplicated so that 1/6 of the gametes a=
re
(Pl Pl), 2/6 are (Pl pl), 2/6 are (Pl pla) and 1/6 are (pl pla).  That's
why TWOI chart is a modified square with only four rows.  I prefer keepin=
g
the six rows because it simplifies the math.

Next, do the same for the (Pl pl pla pla) pollen parent:

Pl pl
Pl pla
Pl pla
pl pla
pl pla
pla pla

Now fill in the cell for row 1, column 1.  Copy the gamete from the pod
parent (from the left side of that row) and the gamete from the pollen
parent (from the top of  the column).  The first cell should now contain
"Pl Pl Pl pl".  Do the same for the other 36 cells. The frequency for any=

given cell is that of the pod parent multiplied by that of the pollen
parent.  1/6 x 1/6 =3D 1/36.  You only have to figure it once, past that =
you
can just count the cells.

When you've finished filling out the chart, you'll have enumerated the 36=

POSSIBILITIES of the cross.  Assuming that each of these possibilities ha=
s
an equal PROBABILITY of occuring, you can go on to analyze the genotypes.=
 =

Just count the number of times each one appears.

Pl Pl Pl pl
Pl Pl Pl pla
Pl Pl pl pla
Pl Pl pla pla
(etc.)

The number of boxes a genotype appears in, divided by 36 (the number of
boxes) gives you its frequency.  Now go on to talleying the pheotypes.  H=
ow
many have at least one Pl allele?  They will be selfs. How many have only=

pl and pla?  They will be plicatas.  (I'm skipping over genotypes rather
quickly, because when doing this for real problems it's easiest to assess=

only the genotypes associated with the favored phenotype.)

And I figure you want to get on to the fun part. =


"What if" you're breeding for plicatas but the best plant is a self... =

What are the odds that it carries only one Pl, which could be bred out in=

the next generation?  =


"What if" you're breeding for glaciatas....  There won't be any in the
first generation, but how would you select seedlings from this cross to
maximize the chances of getting glaciatas in the next generation?


O.K.  Fortunately for you, I just got the call I've been waiting for. =

Class dismissed!

Sharon McAllister
73372.1745@compuserve.com
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