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HYB: Punnett Square Question

Lurkers:  either hit the DELETE key or brace yourself for a stroll across

Donald's questions require some rather technical answers this time.  I've
found myself writing at a level that beginning hybridizers usually consider
far too complex and those who are comfortable with iris genetics dismiss as
greatly over-simplified. IOW, I don't expect to please ANYONE but my goal
is just to impart a comfortable, working knowledge of the fertile families
and how they interact.   Those who are interested in learning more can
peruse articles in back issues of the ASI yearbook.

Message text written by Donald Eaves:

>>The AAAB chart, like the ABBB chart I talked you through earlier should
>>help you understand why we call the unbalanced types "relatively
>>instead of dismissing them as sterile.
My biggest sticking point.  How do I read this in the square?  Or a chart
for that matter?  I know some of the theory here, but this I can't get to
gel for me.

It's not something that jumps off the page and grabs your attention, but if
you are already aware that the unbalanced types exhibit some fertility you
can see from the chart the types of viable gametes they are capable of
producing and better imagine their potential uses.  To fully understand HOW
all this can happen, though, you need to move on to the study of chromosome
conjugation. More about this later....

>>The AABB chart should be enlightening, to say the least.  [Hint: 
>>the underlying assumption of the Punnett Square that does not accurately
>>represent amphidiploid genetics.
Well, I would say here it demonstrates the flaw in the quantum approach.
A 36 seed pod yielding a perfect statistical result would half, or 18, AABB
types, the other half would consist of 1 AAAA, 1 BBBB, 8 AAAB and 8
ABBB types (if I did the square correctly).  If the idea was crossing AABB
X AABB would result in offspring designated AABB in the system, then it
would be incorrect 1/2 the time.

Actually, in this case it is the underlying assumption of random
recombination that is incorrect so that the ratios of the Punnett square
over-simplify the situation and the quantum model would more accurately
depict the real world.  But the Punnett Square holds valuable lessons if we
just take the process chromosome conjugation into account.   So I ask you
to read on....

As I understand the amphidiploid aspect, the Punnett Square would have
to be modified to accomodate the pairing.  The formula 3+2+1 = 3D6
does not work with the amphidiploid.  If AABB is a tetraploid
then you would have to think of A-A B-B as the amphidiploid counterpart,
where A-A transmit together rather than separately.  I didn't try to see if
if I could extend the square to accommodate a tetra x amphdiploid.

Not exactly.  First, the Punnett Square itself was developed for the
analysis of tetraploids so if we attempt to modify it for amphidiploids we
find ourselves with a model that's so simple it provides little insight. 
Second, our modern arilbreds are amphidiploidlike hybrids -- not true
amphidiploids.  To make the most of it, we just need to interpret the
square in light of other knowledge.  

In using it conventionally to analyze the recombination of alleles at a
single locus, situations arise in which there are linkage effects --
something the assumption of independent recombination does not accommodate.
 In theory, at least, linkage effects are measureable so the square's
recombination ratios can be modified by linkage factors. 

In iris, of course, we don't have sufficient data to compute those numbers
but we can make some intuitive use of the concept and in this case extend
it a bit to look at other factors that could affect the distribution of

So your next "homework assignment" is to re-examine those charts thinking
about the effects of chromosome conjugation at meiosis.  Here are the
general answers, so all you'll really have to do is match them to charts
and convince yourself that each match is correct and the explanation fits.

Autotetraploids.  Because all sets are homologous, the assumption of random
recombination is valid -- subject to linkage effects described above at the
chromosome level.  [Hint:  modern TBs are now so many generations from
species that we tend to treat them as autotetraploids but among the  arils
only I. hoogiana and I. stolonifera are true autotetrapoids.]   

Allotetraploids.  Homologous chromosomes pair, others are distributed
somewhat at random.  The result is reduced fertility, but viable gametes
are produced in the expected ratio. [Hint:  applies to most types of
tetraploid arils and arilbreds.]

Amphidiploids.  Because there are two different types of homologous sets,
the chromosomes conjugate in a diploid-like manner.  Of course, we're
discussing amphidiploidlike hybrids, not true amphidiploids so it gets a
bit more complicated -- but in general we can expect viable gametes from
AABB-type arilbreds to be ABs and viable gametes from OORR-type arils ORs. 

A nice, neat system -- but in the world of arils & arilbreds there's always
a lurking "GOTCHA!" 

Cultivars that seems to be fully functional halfbreds have not been
produced merely by intercrossing available halfbreds, but also by
outcrosses and backcrosses over decades of concerted effort to broaden the
gene pool.  We have many breeders we treat as if they are amphidiploids,
but we really do not know exactly where they fit on the
amphidiploid-allotetraploid continuum. 

When one of these looks like a halfbred and breeds like a halfbred, we
confidently cross it with halfbreds and expect to get more halfbreds. 
Selective Fertilization [another subject entirely] makes it so.  But down
through the years many hybridizers have  "mixed up the genes to see what
happens" and I have tested cultivars that appear to function more like
allotetraploid halfbreds than amphidiploids.  

I had one very special cultivar that I didn't introduce because test
crosses couldn't determine whether it was a relatively fertile quarterbred
or less-than-fully-fertile halfbred and many that I eliminated from
consideration because they simply didn't fit into the current
classification system.  But it does NOT have to be registered and
introduced to be used for breeding <sly G>.

Bottom line:  the Punnett Square you've constructed for the AABB type
halfbred has a dual purpose.  For work within this fertile family and for
most other purposes, you can ignore all possibilities except type AB
gametes.   But when something unexpected happens in a cross between an
assumed amphidiploidlike halfbred and another type, the full chart can be
used to assess the possible explanations. In that case, it becomes a very
useful tool for determining the type of plant you are working with and
deciding what further tests you want to make with it.

Oh, I charted.  You wouldn't believe the amount of paper! 

Ah, but I would!  Been there.  Done that.  Plus pedigree charts and
quantum/chromosome set comparison charts.  Off-season charting can focus
bloom-season efforts on the most productive crosses and shave years off of
a program.

So this
feel for the fertility thing is still my sticking point, though I have
ideas of the area.  Fortunately, I am able to take advantage of information
others have worked out, both from this list and other sources.  Not
quite the same as really understanding, but useful until I can get hold
of the concept.

You have obviously cleared the first hurdle:  the realization that
fertility is not a simple matter when working with arilbreds.

We may have paid too little attention to the second:  learning to identify
and work with the fertile family of modern halfbreds.  By doing do, one can
avoid even thinking about such fertility questions as you have posed -- but
will also miss out on much of the fun!

You've already experimented at the third stage:  working between fertile
families to produce unbalanced types -- and I assume you're trying trying
to learn as much as possible from both the successes and failures of those

The current discussion is the fourth and, IMO final stage:  using the
unbalanced types with both members of the fertile families and with other
unbalanced types in pursuit of new breakthroughs.  Here, the REAL fun

Sharon McAllister

Old school buds here:

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