The (autosomal) monohybrid
cross experiments as presented
here can also be regarded as
corresponding to the tests of a
restricted, simple model. In this
model however no particular
attention was given to combinations
of hereditary factors, which would
be or is closer to reality, nor to any
specific relation of hereditary
factors to the germ- and pollen
cells. So, a logical next step would
indeed be than to execute further
experiments that do include these
features to see whether the found
laws of development, as Mendel
called them, still remain valid and
also find sufficient proof than.
      
So Mendel executed a dihybrid
cross between plants of a
pure-breeding line producing seeds
that have a green colour and a
wrinkled shape and plants of a
pure-breeding line producing seeds
that have a yellow colour and a
round shape.
       
x --»
P1 P2 F1
yellow green yellow
round wrinkled round
      
Then Mendel raised a next
generation of plants which he
crossed mutually. The seeds he
found showed, often even in one
pod, a great variety.
     
x --»
F1 F1
      
From 15 plants he got 556 seeds.
315 were round and yellow
101 ,, wrinkled ,, yellow
108 ,, round ,, green
32 ,, wrinkled ,, green
( So a ratio of  9 : 3 : 3 : 1   -24- )
The next year Mendel raised the
F2 generation using all these seeds.
 * Eleven seeds from the 315 round
and yellow seeds did not grew into
a plant and from the others three
plants bore no seeds. Mendel
harvested (from these F2 plants):
from 38 plants: round and yellow
,, 65     ,,    : round yellow and green
,, 60     ,,    : round yellow and wrinkled yellow
,, 138     ,,    : round yellow and green and wrinkled yellow and green seeds.
Let the phenotypic characteristics
of the seeds be indicated as
follows:
wrinkled a
green b
       
Round A
Yellow B
           
wrinkled a
Yellow B
       
Round A
green b
than there are from these 301
plants raised from the F1 round and
yellow seeds:
38 -  AB
65 -  ABb
60 -  AaB
138 -  AaBb
 * From the 101 wrinkled yellow
seeds 96 plants bore seeds. From
28 plants:  wrinkled yellow aB
68     ,,    :  wrinkled yellow aBb
 and green
                   seeds were harvested.
 * From the 108 round green seeds
102 plants with seeds were raised:
35 plants  gave round green Ab
67     ,,      gave round and Aab
 wrinkled green
                   seeds.
 * The 32 wrinkled green seeds 
produced 30 plants that all bore
again wrinkled green seeds - ab.
     
Gathered all together the following 
table can be drawn up:
38 plants with the mark AB
35 ,, ,, ,, ,, Ab
28 ,, ,, ,, ,, aB
30 ,, ,, ,, ,, ab
65 ,, ,, ,, ,, ABb
68 ,, ,, ,, ,, aBb
60 ,, ,, ,, ,, Aab
67 ,, ,, ,, ,, Aab
138 ,, ,, ,, ,, AaBb
In this table three groups can be
discerned.
The first group joins the marks:
AB, Ab, aB and ab.
Mendel observed that in following
generations of these seeds those
characteristics remained constant
and so unchanged.
All these forms are represented
on average 33 times.
(38+35+28+30=131:4=32,75)
The second group joins the marks:
ABb, aBb, AaB and Aab.
In following generations some
characteristics remained constant
and others hybrid, varying only
with respect to the phenotypic
features of the hybrid.
These forms are represented on
average 65 times.
(65+68+60+67=260:4=65)
The third group joins the mark
AaBb and their offspring behaved
exactly as the hybrids from which
they were derived. This form is
represented 138 times.
It becomes clear now that the ratio
between these three groups is
1 : 2 : 4  
and those numbers 33 : 65 : 138
do indeed come very close to the
theoretical 33 : 66 : 132 ratio.
So the development progression
has nine (32) forms. Four of them
are represented only once and
remain constant in both phenotypic
characteristics. Forms AB and ab,
are also the same as the forms of
the parental generation and forms
Ab and aB represent the remainder
of the possible combinations
between A, a, B and b. The second
group consists also out of  four 
forms that occur twice and are each
constant in one phenotypic
characteristic but than hybrid in the
other (ABb --» AB & Ab;
aBb --» ab & aB; AaB --» AB & aB
and Aab --» ab & Ab). One form
occurs four times and is hybrid for
both phenotypic characteristics. So
the offspring of the hybrids (F1)
will develop, with regard to two
phenotypic characteristics,
according to the following
expression:
AB + Ab + aB + ab
+ 2ABb + 2aBb+ 2AaB + 2Aab 
+ 4AaBb.
This development series is
apparently a combination
progression for A, a, B and b that
is produced fully by combining:
A + 2Aa + a
and
B + 2Bb + b
Thus, the laws of development
found in the monohybrid crosses
continue in dihybrid crosses. And
they do also in trihybrid crosses, as
Mendel experienced, A + 2Aa + a
and B + 2Bb + b and C + 2Cc + c
and this all than regardless of all
other phenotypic characters one
could distinguish.
In fact Mendel experimented
hybrid crosses up till the seven
pairs of phenotypic characteristics
presented already earlier.
     
Let, generalizing now, n be the
number of all phenotypic
characteristics, or of all genetic
factors for that matter, that one
could recognize in two living beings
which can have progeny together.
Than the number of possible forms
-combination possibilities- in the
development progression is 3n and
the full number of possible
individuals belonging to such a
development progression with
regard to the combination
possibilities is 4n. The number of
combination possibilities, that will
remain constant, than is 2n.
      
     
           
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