The Dihybrid Punnett Square – An Alternative Way
The Punnett square is the most firmly established tool used in explaining dihybrid crosses. In the example below I have used
Mendel’s cross between round, yellow seeded (RRYY) and wrinkled, green seeded varieties (rryy). The dihybrid has the
genotype RrYy and makes four kinds of gamete, RY, Ry, rY and ry.
The 16 different ways 4 kinds of gamete can combine at fertilisation are usually shown in the checkerboard diagram named
after the geneticist R. C. Punnett.
Independent assortment is often illustrated using Mendel’s dihybrid cross with peas, using two contrasting seed traits: round vs
wrinkled, and yellow vs green peas.
The 4 different kinds of gamete are conventionally written in the order RY, Ry, rY, ry. The 16 different fertilization events yield
9 different genotypes and 4 phenotypes, in a pattern that depends on the order in which the gametes are written along the top
and side of the square.
The conventional order in which the gametes are written is one of 24 possible sequences, so what’s so special about this one?
The answer is probably nothing, but the convention seems to have been set in stone ever since Punnett published his work
early in the 20th century.
There is, however, one way of writing the sequence of gametes that is arguably more informative than the traditional one, and
is shown in Fig. 1, together with the traditional one for comparison.
RY
Ry
ry
rY
RY
RRYY
RRYy
RrYy
RrYY
Rryy
Ry
RRYy
RRyy
Rryy
RrYy
RrYY
rrYy
ry
RrYy
Rryy
rryy
rrYy
rrYy
rryy
rY
RrYy
RrYy
rrYy
rrYY
RY
Ry
rY
ry
RY
RRYY
RRYy
RrYY
RrYy
Ry
RRYy
RRyy
RrYy
rY
RrYY
RrYy
ry
RrYy
Rryy
Traditional
Alternative
Fig. 1
The alternative Punnett is, I believe, considerably more useful than the conventional one, for several reasons:


It is easier to count and therefore check the phenotypes and genotypes.
Most important, it is easier to see that the 9:3:3:1 ratio is actually the product of two independent 3:1 ratios (12/16 to
4/16) for colour and shape, respectively (Fig. 2).
Martin Hanson
Colour: 12 yellow : 4 green
Shape: 12 round : 4 wrinkled
= 3:1

= 3:1
Fig. 2
The 3:1 ratios are independent of each other, as Fig. 3 shows:
 Of the yellow seeds, ¾ are round and ¼ are wrinkled.
 Of the green seeds, ¾ are round and ¼ are wrinkled.
 Of the round seeds, ¾ are yellow and ¼ are green.
 Of the wrinkled seeds, ¾ are yellow and ¼ are green.
Yellow seeds:
9 round : 3 wrinkled
= 3:1
Green seeds:
3 round : 1 wrinkled
Round seeds:
9 yellow: 3 green
= 3:1
= 3:1
Wrinkled seeds:
3 yellow: 1 green
= 3:1
Fig. 3
The concept of independence in the segregation of chromosomes is, I believe, one of the most difficult to grasp in
Level 2 genetics, so any visual tool that makes it clearer is surely worth adopting.

As students are younger than their teachers, they should have more adaptable brains. What would constitute change
for teachers would be a first-time experience for students, who would easily cope.
Yes, but why change?
One could (and many no doubt will) argue that the conventional Punnett has served for over a century, so why change? The
British still do it this way, and the leading American textbook Biology by Campbell, Reece et al still uses the traditional one, so
why should New Zealand step out of line?
I think that we need a more robust justification than “it’s the way it’s always done, here and overseas”. It strikes me that here is
a chance for New Zealand teachers to put some real flesh on that over-used phrase “professional development”.
Summary of pros and cons:
Arguments for
Arguments Against
Makes the phenotypes easier to count
“Teachers have enough to worry about as it is”
As a consequence, the otherwise concealed 3:1 monohybrid ratios
can be clearly seen
Teachers would have to briefly leave their comfort zone.
Even more important, the independence of the two 3:1 ratios is
clearly evident.
“So what? My students find the present arrangement hard enough,
without having to change”.
If instituted nationally, it would give real substance to the phrase
“professional development”
“My grandmother was a bio teacher in the 1930s and what was good
enough for her is good enough for me.”
The acid test is, or should be, the students. Just ask a class of Level 2 students who have not yet been taught dihybrid genetics,
and show them the above two Punnett squares, and ask them to vote on which shows a clearer pattern.
It would be an interesting and, I suspect, revealing experiment.
Martin Hanson