REPORT GENETICS
PRACTICUM PLANT
B
y
:
BRADFORD H
.
DEPARTEMENT OF BIOLOGY
ARIZONA STATE UNIVERSITY
APRIL
2024
I
.
REVIEW BIBLIOGRAPHY
T
h
e
ph
e
notypi
c
out
c
om
e
s of
c
ross
e
s
be
tw
ee
n in
d
ivi
d
u
a
ls
e
ss
e
nti
a
lly r
e
pr
e
s
e
nt th
e
pot
e
nti
a
l out
c
om
e
s of th
e
union of m
a
l
e a
n
d
f
e
m
a
l
e
g
a
m
e
t
e
s
,
b
ut th
e
s
e
out
c
om
e
s
ca
nnot
be de
finitiv
e
ly pr
ed
i
c
t
ed
.
T
h
e
r
e
sulting offspring from
a c
ross
a
r
e
not gu
a
r
a
nt
eed a
n
d ca
n only
be a
nti
c
ip
a
t
ed ba
s
ed
on pro
bab
iliti
e
s
.
T
o
de
t
e
rmin
e
th
e
lik
e
lihoo
d
of
o
b
s
e
rv
ed de
vi
a
tions from
e
xp
ec
t
ed
r
e
sults
,
a
st
a
tisti
ca
l t
e
st is
n
ece
ss
a
ry to
c
onv
e
rt th
e
s
e de
vi
a
tions into pro
bab
iliti
e
s of o
cc
urr
e
n
ce
b
y
c
h
a
n
ce
.
T
his t
e
st
,
known
a
s th
e C
hi
-
S
qu
a
r
e Te
st
,
r
e
quir
e
s
c
onsi
de
r
a
tion of s
a
mpl
e
siz
e a
n
d de
gr
ee
s of fr
eed
om
.
I
n th
e c
ont
e
xt of
pro
bab
ility
a
n
a
lysis
,
e
sp
ec
i
a
lly for qu
a
lit
a
tiv
e
tr
a
its
,
this
a
ppro
ac
h is
highly v
a
lu
ab
l
e
.
P
ro
bab
ility is qu
a
ntifi
ed be
tw
ee
n
0
a
n
d
1
,
wh
e
r
e
0
in
d
i
ca
t
e
s
a
n impossi
b
l
e e
v
e
nt
a
n
d
1
r
e
pr
e
s
e
nts
a ce
rt
a
in
e
v
e
nt
.
F
or
inst
a
n
ce
,
in th
e ca
s
e
of
a c
oin toss
,
th
e
pro
bab
ility of l
a
n
d
ing on
e
ith
e
r
h
ead
s or t
a
ils is
1
,
a
s
e
ith
e
r out
c
om
e
will o
cc
ur
.
T
h
e
ph
e
notypi
c
out
c
om
e
s r
e
sulting from
c
ross
e
s
a
r
e e
ss
e
nti
a
lly
a
r
e
fl
ec
tion of th
e
pro
bab
iliti
e
s
a
sso
c
i
a
t
ed
with th
e c
om
b
in
a
tion of
m
a
l
e a
n
d
f
e
m
a
l
e
g
a
m
e
t
e
s
,
a
n
d
th
e
y
ca
nnot
be de
finitiv
e
ly
c
onfirm
ed
.
T
h
e
r
e
sulting offspring from su
c
h
c
ross
e
s
ca
n only
be
pr
ed
i
c
t
ed ba
s
ed
on pro
bab
iliti
e
s r
a
th
e
r th
a
n
e
x
ac
t out
c
om
e
s
.
T
o
de
t
e
rmin
e
th
e
lik
e
lihoo
d
of o
b
t
a
ining sp
ec
ifi
c
in
d
ivi
d
u
a
ls from
a c
ross
,
a
st
a
tisti
ca
l
t
e
st is n
ece
ss
a
ry to tr
a
nsl
a
t
e de
vi
a
tions from
e
xp
ec
t
ed
v
a
lu
e
s into
pro
bab
iliti
e
s of th
e
s
e de
vi
a
tions o
cc
urring
b
y
c
h
a
n
ce
.
T
his t
e
st
,
known
a
s th
e C
hi
-
S
qu
a
r
e
t
e
st
(
X
²
t
e
st
),
is
c
ru
c
i
a
l for
a
n
a
lyzing g
e
n
e
ti
c da
t
a
,
e
sp
ec
i
a
lly wh
e
n s
a
mpl
e
siz
e
s
a
n
d de
gr
ee
s of fr
eed
om
a
r
e
signifi
ca
nt
.
F
or
e
x
a
mpl
e
,
g
e
n
e
ti
c e
xp
e
rim
e
nts som
e
tim
e
s yi
e
l
d
r
e
sults th
a
t
d
o not
m
a
t
c
h
Me
n
de
li
a
n r
a
tios
,
a
s s
ee
n in
a d
ihy
b
ri
d c
ross of smooth y
e
llow
p
ea
s with wrinkl
ed
gr
ee
n p
ea
s pro
d
u
c
ing
a
15
:
7
:
5
:
3
r
a
tio inst
ead
of th
e
e
xp
ec
t
ed
9
:
3
:
3
:
1
.
T
o v
e
rify if o
b
s
e
rv
ed
r
e
sults
a
lign with
Me
n
de
li
a
n
e
xp
ec
t
a
tions
,
th
e C
hi
-
S
qu
a
r
e
t
e
st
ca
n
be a
ppli
ed
to
de
t
e
rmin
e
if
de
vi
a
tions
a
r
e d
u
e
to r
a
n
d
om
c
h
a
n
ce
or oth
e
r f
ac
tors
.
Be
for
e
p
e
rforming this t
e
st
,
hypoth
e
s
e
s
a
r
e
formul
a
t
ed
to
a
ss
e
ss wh
e
th
e
r th
e
r
e
sults m
ee
t
e
xp
ec
t
a
tions
,
with on
e
hypoth
e
sis r
e
pr
e
s
e
nting th
e
e
xp
ec
t
ed e
v
e
nt
a
n
d
th
e
oth
e
r r
e
pr
e
s
e
nting
de
vi
a
tions from it
.
II
.
METHOD PRACTICUM
A
.
Ma
t
e
ri
a
l
A
n
d T
ool
T
h
e
m
a
t
e
ri
a
ls us
ed
in this pr
ac
ti
c
um
a
r
e
:
c
oins
a
n
d c
oins sh
ee
t
o
b
s
e
rv
a
tion
.
T
ools
W
hi
c
h us
ed
on pr
ac
ti
c
um
T
his is
:
c
oins
,
ca
l
c
ul
a
tors
a
n
d
st
a
tion
e
ry
.
B
.
W
ork
P
ro
ced
ur
e
A
singl
e c
oin w
a
s toss
ed
onto
a
m
e
t
a
l surf
ace
,
a
n
d
th
e
out
c
om
e
(
e
ith
e
r
a
num
be
r or im
a
g
e
)
w
a
s r
ec
or
ded
.
T
his pro
ce
ss w
a
s
r
e
p
ea
t
ed
50
tim
e
s
a
n
d
th
e
n
100
tim
e
s
.
T
h
e
r
e
sults w
e
r
e a
n
a
lyz
ed
using th
e c
hi
-
squ
a
r
e
m
e
tho
d
.
I
n
a
simil
a
r f
a
shion
,
th
e
pro
ced
ur
e
w
a
s r
e
p
ea
t
ed
using two
c
oins
,
whi
c
h w
e
r
e
toss
ed
simult
a
n
e
ously
.
T
h
e
s
a
m
e a
ppro
ac
h w
a
s
a
ppli
ed
wh
e
n using thr
ee c
oins
.
A
ll th
e
r
e
sults from th
e
s
e
tri
a
ls w
e
r
e
r
ec
or
ded
on
a
n o
b
s
e
rv
a
tion sh
ee
t
,
a
n
d
th
e da
t
a
w
a
s
a
n
a
lyz
ed a
s outlin
ed
in th
e
provi
ded
instru
c
tions
.
III
.
RESULTS AND DISCUSSION
A
.
Re
sults
Te
st
X
2
F
or t
e
st pro
bab
ility throwing thr
ee c
oin in
a
w
a
y
simult
a
n
e
ously
50
a
n
d
100
tim
e
s
.
T
h
e
r
e
sults of flipping
a c
oin
50
tim
e
s
.
T
h
e
o
b
s
e
rv
ed
fr
e
qu
e
n
c
i
e
s w
e
r
e
33
a
n
d
17
,
whil
e
th
e e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s w
e
r
e b
oth
25
.
T
h
e ca
l
c
ul
a
tion for th
e c
hi
-
squ
a
r
e
t
e
st is
a
s
follows
:
for th
e
out
c
om
e
33
,
th
e d
iff
e
r
e
n
ce be
tw
ee
n o
b
s
e
rv
ed a
n
d
e
xp
ec
t
ed
v
a
lu
e
s is squ
a
r
ed
,
r
e
sulting in
56
.
25
,
a
n
d
simil
a
rly
,
for th
e
out
c
om
e
17
,
th
e d
iff
e
r
e
n
ce a
lso r
e
sults in
56
.
25
.
S
umming th
e
s
e
v
a
lu
e
s giv
e
s
a
tot
a
l of
112
.
5
.
W
h
e
n
d
ivi
ded b
y th
e e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s
,
this yi
e
l
d
s
a c
hi
-
squ
a
r
e
v
a
lu
e
of
4
.
5
.
C
omp
a
ring this to
th
e c
hi
-
squ
a
r
e c
riti
ca
l v
a
lu
e
of
3
.
84
,
th
e
t
e
st r
e
sults in
d
i
ca
t
e
th
a
t th
e
c
hi
-
squ
a
r
e
v
a
lu
e e
x
ceed
s th
e c
riti
ca
l v
a
lu
e
,
l
ead
ing to th
e
r
e
j
ec
tion of
th
e
null hypoth
e
sis
a
n
d
sugg
e
sting th
a
t th
e
r
e
sults
a
r
e
not in
acc
or
da
n
ce
with th
e e
xp
ec
t
ed d
istri
b
ution
.
T
h
e
r
e
sults of throwing
a c
oin
100
tim
e
s w
e
r
e a
n
a
lyz
ed ba
s
ed
on
o
b
s
e
rv
ed a
n
d e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s
.
T
h
e
o
b
s
e
rv
ed
fr
e
qu
e
n
c
i
e
s w
e
r
e
41
a
n
d
59
,
whil
e
th
e e
xp
ec
t
ed
fr
e
qu
e
n
c
y w
a
s
50
for
eac
h out
c
om
e
.
T
his r
e
sult
ed
in v
a
lu
e
s of
72
.
25
for
b
oth o
b
s
e
rv
a
tions
,
summing to
144
.
5
.
T
h
e
fin
a
l
c
hi
-
squ
a
r
e
v
a
lu
e
s for
eac
h out
c
om
e
w
e
r
e
1
.
445
,
tot
a
ling
2
.
89
.
C
omp
a
ring this with th
e c
hi
-
squ
a
r
e c
riti
ca
l v
a
lu
e
of
3
.
84
,
th
e
r
e
sult shows th
a
t th
e ca
l
c
ul
a
t
ed c
hi
-
squ
a
r
e
v
a
lu
e
is l
e
ss
th
a
n th
e c
riti
ca
l v
a
lu
e
,
l
ead
ing to th
e acce
pt
a
n
ce
of th
e
hypoth
e
sis
a
n
d c
onfirming th
a
t th
e
t
e
st r
e
sults
a
lign with th
e e
xp
ec
t
ed
c
omp
a
rison
.
T
h
e
r
e
sults of throwing two
c
oins tog
e
th
e
r
50
tim
e
s
.
T
h
e
o
b
s
e
rv
ed
fr
e
qu
e
n
c
i
e
s for th
e
out
c
om
e
s
AA
,
AG
,
a
n
d GG
w
e
r
e
7
,
28
,
a
n
d
15
r
e
sp
ec
tiv
e
ly
,
whil
e
th
e e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s for th
e
s
e
out
c
om
e
s w
e
r
e
1
,
2
,
a
n
d
1
.
T
h
e ca
l
c
ul
a
tions for th
e c
hi
-
squ
a
r
e
st
a
tisti
c
involv
e
fin
d
ing th
e
squ
a
r
ed d
iff
e
r
e
n
ce
s
be
tw
ee
n o
b
s
e
rv
ed a
n
d
e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s
,
d
ivi
ded b
y th
e e
xp
ec
t
ed
fr
e
qu
e
n
c
y
.
F
or
AA
,
th
e
r
e
sult is
30
.
25
;
for
AG
,
it is
6
.
25
;
a
n
d
for
GG
,
it is
0
.
25
.
S
umming
th
e
s
e
v
a
lu
e
s giv
e
s
a c
hi
-
squ
a
r
e c
ount of
36
.
75
.
T
h
e c
riti
ca
l v
a
lu
e
from
th
e c
hi
-
squ
a
r
e
t
ab
l
e
for this
de
gr
ee
of fr
eed
om is
5
.
99
.
S
in
ce
th
e c
hi
-
squ
a
r
e c
ount
(
3
.
28
)
is l
e
ss th
a
n th
e c
riti
ca
l v
a
lu
e
(
5
.
99
),
th
e
r
e
sults
a
r
e
c
onsist
e
nt with th
e e
xp
ec
t
ed
out
c
om
e
s
.
T
h
e
r
e
sults of tossing two
c
oins
100
tim
e
s
,
th
e
o
b
s
e
rv
ed
fr
e
qu
e
n
c
i
e
s
(
O
)
for out
c
om
e
s
AA
,
AG
,
a
n
d GG a
r
e
19
,
50
,
a
n
d
31
,
r
e
sp
ec
tiv
e
ly
,
with
a
tot
a
l of
100
.
T
h
e e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s
(
E
)
for
eac
h out
c
om
e a
r
e ca
l
c
ul
a
t
ed a
s
25
,
50
,
a
n
d
25
.
T
h
e c
hi
-
squ
a
r
e
st
a
tisti
c
is
c
omput
ed b
y summing th
e
squ
a
r
ed d
iff
e
r
e
n
ce
s
be
tw
ee
n
o
b
s
e
rv
ed a
n
d e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s
,
d
ivi
ded b
y th
e e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s
.
T
h
e
v
a
lu
e
s
a
r
e
1
.
44
,
0
,
a
n
d
1
.
44
,
l
ead
ing to
a c
hi
-
squ
a
r
e
c
ount of
2
.
88
.
C
omp
a
ring this to th
e c
hi
-
squ
a
r
e
t
ab
l
e
v
a
lu
e
of
5
.
99
,
sin
ce
2
.
88
is l
e
ss th
a
n
5
.
99
,
th
e
r
e
sults
a
r
e c
onsist
e
nt with
e
xp
ec
t
a
tions
,
in
d
i
ca
ting no signifi
ca
nt
de
vi
a
tion
.
T
h
e
r
e
sults of throwing
50
tim
e
s with
3
c
oins
,
th
e
o
b
s
e
rv
ed
fr
e
qu
e
n
c
i
e
s for
eac
h out
c
om
e
(
AAA
,
AAG
,
AGG
,
GGG
)
a
r
e
0
,
9
,
20
,
17
,
a
n
d
4
r
e
sp
ec
tiv
e
ly
,
tot
a
ling
50
.
T
h
e e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s
a
r
e
ca
l
c
ul
a
t
ed a
s follows
:
for
AAA
,
it is
6
.
25
;
for
AAG
,
AGG
,
a
n
d GGG
,
it is
18
.
75
,
18
.
75
,
a
n
d
6
.
25
r
e
sp
ec
tiv
e
ly
.
T
h
e d
iff
e
r
e
n
ce
s
be
tw
ee
n
o
b
s
e
rv
ed
(
O
)
a
n
d e
xp
ec
t
ed
(
E
)
v
a
lu
e
s
a
r
e
th
e
n
c
omput
ed
,
yi
e
l
d
ing
squ
a
r
ed d
iff
e
r
e
n
ce
s of
7
.
5625
,
1
.
5625
,
3
.
0625
,
a
n
d
6
.
25
r
e
sp
ec
tiv
e
ly
.
T
h
e
s
e a
r
e
us
ed
to fin
d
th
e c
hi
-
squ
a
r
e
v
a
lu
e
s
,
r
e
sulting in
1
.
21
,
0
.
083
,
0
.
163
,
a
n
d
0
.
81
,
with
a c
hi
-
squ
a
r
e
st
a
tisti
c
of
2
.
266
.
G
iv
e
n th
a
t th
e c
hi
-
squ
a
r
e c
ount of
2
.
266
is l
e
ss th
a
n th
e c
hi
-
squ
a
r
e
t
ab
l
e
v
a
lu
e
of
7
.
82
,
th
e
r
e
sult in
d
i
ca
t
e
s th
a
t th
e
o
b
s
e
rv
ed
fr
e
qu
e
n
c
i
e
s
a
lign with th
e
e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s
,
de
monstr
a
ting no signifi
ca
nt
de
vi
a
tion from
e
xp
ec
t
a
tions
.
Da
t
a
from
100
tri
a
ls of throwing thr
ee c
oins tog
e
th
e
r is
pr
e
s
e
nt
ed
,
showing th
e
fr
e
qu
e
n
c
i
e
s of
d
iff
e
r
e
nt out
c
om
e
s
:
AAA
,
AAG
,
AGG
,
a
n
d GGG
,
with tot
a
ls of
0
,
10
,
38
,
37
,
a
n
d
15
r
e
sp
ec
tiv
e
ly
.
T
h
e
e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s for
eac
h out
c
om
e a
r
e
uniformly
ca
l
c
ul
a
t
ed a
s
12
.
5
.
T
h
e d
is
c
r
e
p
a
n
c
i
e
s
be
tw
ee
n o
b
s
e
rv
ed a
n
d e
xp
ec
t
ed
v
a
lu
e
s
a
r
e
th
e
n squ
a
r
ed a
n
d d
ivi
ded b
y th
e e
xp
ec
t
ed
v
a
lu
e
s
,
yi
e
l
d
ing r
e
sults of
0
.
5
,
0
.
007
,
0
.
007
,
a
n
d
0
.
5
.
S
umming th
e
s
e
v
a
lu
e
s giv
e
s
a c
hi
-
squ
a
r
e
st
a
tisti
c
of
1
.
014
.
C
omp
a
ring this
ca
l
c
ul
a
t
ed c
hi
-
squ
a
r
e
v
a
lu
e
to th
e
c
riti
ca
l v
a
lu
e
of
7
.
82
in
d
i
ca
t
e
s th
a
t th
e
o
b
s
e
rv
ed
r
e
sults
d
o not
signifi
ca
ntly
de
vi
a
t
e
from th
e e
xp
ec
t
ed
out
c
om
e
s
.
B
.
D
is
c
ussion
T
h
e C
hi
S
qu
a
r
e
(
X
²)
t
e
st is us
ed
to
a
ss
e
ss hypoth
e
s
e
s
ab
out th
e
a
lignm
e
nt
be
tw
ee
n o
b
s
e
rv
ed a
n
d e
xp
ec
t
ed e
v
e
nts or out
c
om
e
s
.
T
his
t
e
st is
c
ommonly
a
ppli
ed
in g
e
n
e
ti
c
s
,
for inst
a
n
ce
,
to
e
stim
a
t
e
th
e
pro
bab
ility of
ce
rt
a
in tr
a
its
a
pp
ea
ring in offspring from
a
g
e
n
e
ti
c c
ross
.
Ba
s
ed
on th
e
s
e
g
e
n
e
ti
c c
ross
e
s
,
tr
a
its th
a
t
a
r
e be
n
e
fi
c
i
a
l to hum
a
ns
,
su
c
h
a
s ri
ce
v
a
ri
e
ti
e
s th
a
t
a
r
e
tol
e
r
a
nt to m
a
rgin
a
l
e
nvironm
e
nts
,
ca
n
be
i
de
ntifi
ed
.
O
th
e
r hypoth
e
sis t
e
sts
be
si
de
s
C
hi
S
qu
a
r
e
in
c
lu
de
th
e
A
n
de
rson
-
Da
rling
,
K
olmogorov
-
S
mirnov
,
C
r
a
m
e
r
-
von
M
is
e
s
,
a
n
d
F
ish
e
r
'
s
c
umul
a
tiv
e
t
e
sts
.
T
h
e C
hi
S
qu
a
r
e
t
e
st is p
a
rti
c
ul
a
rly v
a
lu
ed
for
its suit
ab
ility in pr
ac
ti
ca
l
a
ppli
ca
tions wh
e
r
e
th
e da
t
a c
los
e
ly mirrors
r
ea
l
-
worl
d c
on
d
itions
.
T
o
c
on
d
u
c
t
a C
hi
S
qu
a
r
e
t
e
st
(
X
²),
th
e
pro
ce
ss st
a
rts with
formul
a
ting
a
hypoth
e
sis
,
whi
c
h s
e
rv
e
s
a
s
a
provision
a
l solution to th
e
r
e
s
ea
r
c
h pro
b
l
e
m
.
T
his hypoth
e
sis is th
e
n t
e
st
ed
using st
a
tisti
ca
l
m
e
tho
d
s
,
su
c
h
a
s th
e X
²
t
e
st
,
to v
e
rify if it
a
ligns with r
ea
l
-
worl
d da
t
a
.
T
wo hypoth
e
s
e
s
a
r
e
typi
ca
lly propos
ed
:
H
0
,
whi
c
h r
e
pr
e
s
e
nts th
e
hypoth
e
sis in lin
e
with th
e e
xp
ec
t
ed
out
c
om
e
,
a
n
d H
1
,
whi
c
h sugg
e
sts
a d
iff
e
r
e
nt out
c
om
e
.
Re
s
ea
r
c
h hypoth
e
s
e
s
a
r
e ca
t
e
goriz
ed
into on
e
-
w
a
y
a
n
d
two
-
w
a
y typ
e
s
.
T
h
e d
istin
c
tion li
e
s in th
e a
lt
e
rn
a
tiv
e
hypoth
e
sis
:
for on
e
-
w
a
y t
e
sts
,
H
1
might st
a
t
e
"
gr
ea
t
e
r th
a
n
,"
whil
e
for
two
-
w
a
y t
e
sts
,
it might st
a
t
e
"
not
e
qu
a
l to
."
F
ollowing th
e
hypoth
e
sis
formul
a
tion
,
th
e X
²
st
a
tisti
c
is
c
omput
ed a
n
d c
omp
a
r
ed
to
a c
riti
ca
l
v
a
lu
e
from th
e X
²
d
istri
b
ution t
ab
l
e
.
I
f th
e c
omput
ed X
²
v
a
lu
e
is low
e
r
th
a
n th
e c
riti
ca
l v
a
lu
e
,
th
e
initi
a
l hypoth
e
sis is
acce
pt
ed
,
in
d
i
ca
ting
a
signifi
ca
nt r
e
sult
.
C
onv
e
rs
e
ly
,
if th
e c
omput
ed
v
a
lu
e e
x
ceed
s th
e
c
riti
ca
l v
a
lu
e
,
th
e
initi
a
l hypoth
e
sis is r
e
j
ec
t
ed
,
th
e a
lt
e
rn
a
tiv
e
hypoth
e
sis is
acce
pt
ed
,
a
n
d
th
e
r
e
sult is
c
onsi
de
r
ed
not signifi
ca
nt
.
A
signifi
ca
nt r
e
sult impli
e
s th
a
t th
e
hypoth
e
sis is v
a
li
da
t
ed
through
s
a
mpl
e
t
e
sting
a
n
d
is
a
ppli
cab
l
e
to th
e b
ro
ade
r popul
a
tion
,
wh
e
r
ea
s
a
non
-
signifi
ca
nt r
e
sult sugg
e
sts th
a
t th
e
fin
d
ings from th
e
s
a
mpl
e
m
a
y
not g
e
n
e
r
a
liz
e
to th
e
popul
a
tion
.
A
100
%
c
onfi
de
n
ce
l
e
v
e
l impli
e
s ignoring th
e
risk of m
a
king
a
n
in
c
orr
ec
t
dec
ision
.
H
ow
e
v
e
r
,
ac
hi
e
ving su
c
h
a
l
e
v
e
l is not f
ea
si
b
l
e
beca
us
e
,
a
s not
ed b
y pr
e
vious r
e
s
ea
r
c
h
,
th
e
r
e
is
a
lw
a
ys
a
n
e
rror
m
a
rgin to
c
onsi
de
r
,
m
a
king
a
100
%
c
onfi
de
n
ce
l
e
v
e
l un
a
tt
a
in
ab
l
e
.
T
h
e
m
a
ximum
ac
hi
e
v
ab
l
e c
onfi
de
n
ce
l
e
v
e
l is
99
%
,
in
d
i
ca
ting
a
1
%
risk of
e
rror
,
whil
e
th
e c
ommonly us
ed c
onfi
de
n
ce
l
e
v
e
l is
95
%
,
c
orr
e
spon
d
ing
to
a
5
%
signifi
ca
n
ce
l
e
v
e
l
.
T
his
5
%
signifi
ca
n
ce
l
e
v
e
l is fr
e
qu
e
ntly
e
mploy
ed
in
a
gri
c
ultur
a
l r
e
s
ea
r
c
h
d
u
e
to its pr
ac
ti
ca
lity in
e
stim
a
ting
e
rror risks
a
sso
c
i
a
t
ed
with hypoth
e
s
e
s
.
Fac
tors influ
e
n
c
ing signifi
ca
n
ce
in
c
lu
de
hum
a
n
e
rror
d
uring o
b
s
e
rv
a
tions
,
non
-
norm
a
l
da
t
a
,
a
n
d
r
a
n
d
om
c
h
a
n
ce
.
I
n pr
ac
ti
ca
l
a
ppli
ca
tions of th
e C
hi
-
S
qu
a
r
e
t
e
st
,
r
ea
l
pl
a
nt o
b
j
ec
ts
a
r
e
oft
e
n su
b
stitut
ed
with
c
oins
d
u
e
to th
e
tim
e a
n
d
acc
ur
ac
y r
e
quir
ed
for pl
a
nt
e
xp
e
rim
e
nts
.
B
y tossing
c
oins
50
or
100
tim
e
s
,
a
n
d
with on
e
,
two
,
or thr
ee c
oins
a
t on
ce
,
six s
e
ts of
o
b
s
e
rv
a
tion
a
l
da
t
a a
r
e
g
e
n
e
r
a
t
ed a
n
d a
n
a
lyz
ed
using th
e C
hi
-
S
qu
a
r
e
t
e
st
.
T
h
e C
hi
-
squ
a
r
e
t
e
st r
e
sults for tossing
a c
oin
50
tim
e
s
,
with on
e
c
oin
,
two
c
oins
,
a
n
d
thr
ee c
oins
,
a
r
e
4
.
5
,
3
.
28
,
a
n
d
2
.
266
,
r
e
sp
ec
tiv
e
ly
,
c
omp
a
r
ed
to th
e
t
ab
l
e
v
a
lu
e
s of
3
.
84
,
5
.
99
,
a
n
d
7
.
82
.
F
or
a
singl
e c
oin
toss
,
th
e
r
e
sult is not signifi
ca
nt
beca
us
e
th
e ca
l
c
ul
a
t
ed C
hi
-
squ
a
r
e
v
a
lu
e e
x
ceed
s th
e
t
ab
l
e
v
a
lu
e
.
H
ow
e
v
e
r
,
for th
e
oth
e
r s
ce
n
a
rios
,
th
e
r
e
sults
a
r
e
signifi
ca
nt
a
s th
e ca
l
c
ul
a
t
ed
v
a
lu
e
s f
a
ll
be
low th
e
t
ab
l
e
v
a
lu
e
s
.
W
h
e
n tossing
a c
oin
100
tim
e
s
,
th
e C
hi
-
squ
a
r
e
v
a
lu
e
s
a
r
e
2
.
89
,
2
.
88
,
a
n
d
1
.
014
for on
e c
oin
,
two
c
oins
,
a
n
d
thr
ee c
oins
,
r
e
sp
ec
tiv
e
ly
,
a
ll of whi
c
h
a
r
e
signifi
ca
nt
a
s th
e
s
e
v
a
lu
e
s
a
r
e
sm
a
ll
e
r th
a
n th
e
c
orr
e
spon
d
ing t
ab
l
e
v
a
lu
e
s
.
IV
.
CONCLUSION
C
on
c
lusion
T
h
e
fin
d
ings from
P
r
ac
ti
c
um
E
v
e
nt
II
sugg
e
st th
a
t to
e
v
a
lu
a
t
e a
hypoth
e
sis r
e
g
a
r
d
ing
a
n
e
v
e
nt
,
th
e C
hi
-
S
qu
a
r
e
t
e
st
ca
n
be e
mploy
ed
to
a
lign th
e
or
e
ti
ca
l
e
xp
ec
t
a
tions with
ac
tu
a
l o
b
s
e
rv
a
tions
.
REPORT GENETICS
PRACTICUM PLANT
MONOHYBRID CROSS
B
y
:
BRADFORD H
.
DEPARTEMENT OF BIOLOGY
ARIZONA STATE UNIVERSITY
APRIL
2024
I
.
INTRODUCTION
A
.
Bac
kgroun
d Be
hin
d
Re
pro
d
u
c
tion is
a
fun
da
m
e
nt
a
l pro
ce
ss for living org
a
nisms
a
im
ed
a
t
e
nsuring th
e
ir surviv
a
l
.
D
iff
e
r
e
nt sp
ec
i
e
s h
a
v
e
uniqu
e
m
e
tho
d
s for
sust
a
ining th
e
ir
e
xist
e
n
ce
.
I
n pl
a
nts
,
r
e
pro
d
u
c
tion
ca
n o
cc
ur through
c
ross
b
r
eed
ing
be
tw
ee
n v
a
rious pl
a
nt sp
ec
i
e
s
.
Occa
sion
a
lly
,
th
e
offspring from su
c
h
c
ross
e
s
d
o not inh
e
rit th
e
s
a
m
e
g
e
n
e
ti
c
tr
a
its
a
s
th
e
ir p
a
r
e
nts
.
F
or inst
a
n
ce
,
in p
ea
pl
a
nts
,
offspring might h
a
v
e
wrinkl
ed
s
eed
s
e
v
e
n if
b
oth p
a
r
e
nts h
ad
roun
d
s
eed
s
.
Re
s
ea
r
c
h on
c
ross
b
r
eed
ing sugg
e
sts th
a
t v
a
ri
a
tions in offspring
a
ris
e
from th
e
c
om
b
in
a
tion of tr
a
its from
b
oth p
a
r
e
nts
.
Eac
h p
a
r
e
nt
'
s g
e
n
e
ti
c
m
a
t
e
ri
a
l
is
c
ontri
b
ut
ed
to th
e
offspring in
a
r
a
n
d
om m
a
nn
e
r
,
whi
c
h m
ea
ns th
e
offspring m
a
y not
a
lw
a
ys r
e
s
e
m
b
l
e
th
e
p
a
r
e
nts
.
W
hil
e
su
c
h g
e
n
e
ti
c
v
a
ri
a
tion
ca
n
be ad
v
a
nt
a
g
e
ous
,
it
ca
n
a
lso r
e
sult in signifi
ca
nt
d
r
a
w
bac
ks
.
II
.
REVIEW BIBLIOGRAPHY
T
h
e c
on
ce
pt of g
e
n
e
s w
a
s first intro
d
u
ced b
y
T
hom
a
s
H
unt
M
org
a
n
,
a
n
e
xp
e
rt in g
e
n
e
ti
c
s
a
n
d e
m
b
ryology
,
in
1911
.
M
org
a
n
propos
ed
th
a
t h
e
r
ed
it
a
ry su
b
st
a
n
ce
s
,
t
e
rm
ed
g
e
n
e
s
,
a
r
e
lo
ca
t
ed
in
sp
ec
ifi
c
positions on
c
hromosom
e
s
.
W
.
J
oh
a
ns
e
n l
a
t
e
r
de
s
c
ri
bed a
g
e
n
e a
s th
e
sm
a
ll
e
st unit of
a
n org
a
nism th
a
t
c
ont
a
ins h
e
r
ed
it
a
ry
inform
a
tion
,
situ
a
t
ed
in th
e
g
e
n
e
lo
c
us
.
Ge
n
e
s
a
r
e c
ompos
ed
of
prot
e
ins
a
n
d
nu
c
l
e
i
c ac
i
d
s
(
DNA a
n
d RNA
),
r
a
nging in siz
e
from
4
to
8
mi
c
rons
.
Acc
or
d
ing to
S
uryo
,
g
e
n
e
s poss
e
ss g
e
n
e
ti
c
inform
a
tion
,
p
e
rform
d
istin
c
t fun
c
tions
,
a
n
d
un
de
rgo
d
upli
ca
tion
d
uring mitosis
a
n
d
m
e
iosis
,
de
t
e
rmin
ed b
y th
e
s
e
qu
e
n
ce
of nitrog
e
n
ba
s
e
s
a
n
d
c
hromosom
e
p
a
rti
c
l
e
s
.
Ge
n
e
s pl
a
y s
e
v
e
r
a
l rol
e
s
,
in
c
lu
d
ing tr
a
nsmitting
inform
a
tion to th
e
n
e
xt g
e
n
e
r
a
tion
,
de
t
e
rmining inh
e
rit
ed
tr
a
its
,
a
n
d
r
e
gul
a
ting
de
v
e
lopm
e
nt
a
n
d
m
e
t
ab
olism
.
T
o f
ac
ilit
a
t
e
th
e de
s
c
ription
a
n
d
o
b
s
e
rv
a
tion of g
e
n
e
s
,
v
a
rious
t
e
rms
a
n
d
sym
b
ols
a
r
e
us
ed
.
D
omin
a
nt g
e
n
e
s
a
r
e
thos
e
th
a
t
ov
e
rsh
ad
ow th
e e
xpr
e
ssion of oth
e
r g
e
n
e
s
,
typi
ca
lly r
e
pr
e
s
e
nt
ed b
y
upp
e
r
ca
s
e
l
e
tt
e
rs
,
su
c
h
a
s
A
.
Rece
ssiv
e
g
e
n
e
s
a
r
e
thos
e
th
a
t
a
r
e
m
a
sk
ed b
y
d
omin
a
nt g
e
n
e
s
,
m
ea
ning th
e
ir tr
a
its
a
r
e
not
e
xpr
e
ss
ed
in
th
e
offspring
.
He
t
e
rozygous g
e
n
e
s r
e
sult from th
e c
om
b
in
a
tion of
g
e
n
e
s from
b
oth sp
e
rm
a
n
d e
gg
ce
lls
(
e
.
g
.,
Aa
).
H
omozygous
d
omin
a
nt
g
e
n
e
s
c
onsist of two
d
omin
a
nt g
e
n
e
s from
b
oth p
a
r
e
nts
,
su
c
h
a
s
AA
.
H
omozygous r
ece
ssiv
e
g
e
n
e
s
a
r
e
form
ed
from two r
ece
ssiv
e
g
e
n
e
s
from
b
oth p
a
r
e
nts
,
for
e
x
a
mpl
e
,
aa
.
H
omologous
c
hromosom
e
s
a
r
e
p
a
irs of
c
hromosom
e
s from
eac
h p
a
r
e
nt th
a
t
a
r
e
simil
a
r in sh
a
p
e
.
P
h
e
notyp
e
r
e
f
e
rs to th
e
o
b
s
e
rv
ab
l
e
tr
a
its in offspring
,
su
c
h
a
s h
e
ight
,
c
olor
,
a
n
d
sh
a
p
e
,
whil
e
g
e
notyp
e
r
e
f
e
rs to th
e
g
e
n
e
ti
c
m
a
k
e
up th
a
t
ca
nnot
be
s
ee
n
d
ir
ec
tly
,
su
c
h
a
s
AA
,
Aa
,
a
n
d aa
.
I
n
1842
,
G
r
e
gor
J
oh
a
nn
Me
n
de
l un
c
ov
e
r
ed
th
e
fun
da
m
e
nt
a
l prin
c
ipl
e
s of inh
e
rit
a
n
ce
through his
c
ross
-
b
r
eed
ing
e
xp
e
rim
e
nts
.
H
is fin
d
ings w
e
r
e
e
n
ca
psul
a
t
ed
in
Me
n
de
l
'
s
La
ws
I a
n
d II
.
Me
n
de
l
'
s
La
w
I a
ss
e
rts th
a
t
d
uring th
e
form
a
tion of g
a
m
e
t
e
s
,
a
ll
e
l
e
p
a
irs s
e
gr
e
g
a
t
e a
n
d
r
ec
om
b
in
e
with oth
e
r g
a
m
e
t
e
s
.
T
o v
e
rify this l
a
w
,
Me
n
de
l
c
on
d
u
c
t
ed a
monohy
b
ri
d c
ross
,
fo
c
using on
a
singl
e
tr
a
it
.
T
his typ
e
of
c
ross
e
x
a
min
e
s how
a
singl
e c
h
a
r
ac
t
e
risti
c
is inh
e
rit
ed
.
Me
n
de
l
'
s monohy
b
ri
d
c
ross
e
s
a
im
ed
to un
de
rst
a
n
d
th
e
p
a
tt
e
rn of tr
a
it inh
e
rit
a
n
ce
from
p
a
r
e
nts to offspring
.
T
h
e
r
e
sults of th
e
s
e e
xp
e
rim
e
nts
,
a
n
a
lyz
ed
in th
e
F
2
g
e
n
e
r
a
tion
,
de
monstr
a
t
ed a
1
:
2
:
1
r
a
tio
,
supporting th
e c
on
c
lusion
th
a
t g
e
n
e
s
a
r
e
p
a
ss
ed
from p
a
r
e
nts to th
e
ir prog
e
ny through g
a
m
e
t
e
s
.
III
.
METHOD PRACTICUM
A
.
Ma
t
e
ri
a
l
A
n
d T
ool
I
ngr
ed
i
e
nts us
ed
in this pr
ac
ti
c
um
a
r
e
:
soy
bea
n s
eed
s
,
pl
a
nting
m
ed
i
a
(
soil
)
a
n
d
o
b
s
e
rv
a
tion sh
ee
ts
.
T
h
e
tools us
ed
in this pr
ac
ti
c
um
a
r
e
:
s
eed b
ox
a
n
d
writing tools
.
B
.
W
ork
P
ro
ced
ur
e
T
h
e
s
eed
popul
a
tion
c
onsisting of
P
1
,
P
2
,
F
1
,
a
n
d F
2
w
a
s pl
a
nt
ed
in th
e
s
eedb
ox
c
ont
a
ining soil
.
T
h
e
soy
bea
n s
eed
s w
e
r
e
l
e
ft to grow
a
n
d
g
e
rmin
a
t
e
.
T
h
e
st
e
m
c
olors o
b
s
e
rv
ed
w
e
r
e
not
ed a
s
e
ith
e
r whit
e
or purpl
e
,
a
n
d b
oth st
e
m
a
n
d
s
eed c
olors w
e
r
e
r
ec
or
ded
.
IV
.
RESULTS AND DISCUSSION
A
.
Re
sults
1
.
C
rossov
e
r
I
n th
e
g
e
n
e
ti
c c
ross
be
tw
ee
n
G
ro
b
og
a
n
(
P
urpl
e
/
HH
)
a
n
d M
uri
a
(
G
r
ee
n
/
hh
),
th
e
r
e
sulting g
e
notyp
e
s w
e
r
e
o
b
s
e
rv
ed a
s follows
:
1
HH
,
2
H
h
,
a
n
d
1
hh
,
with ph
e
notyp
e
s showing
a
r
a
tio of
3
P
urpl
e
to
1
G
r
ee
n
.
U
sing
C
hi
-
squ
a
r
e a
n
a
lysis
,
th
e
o
b
s
e
rv
ed
num
be
rs w
e
r
e
15
P
urpl
e a
n
d
4
G
r
ee
n
,
with
e
xp
ec
t
ed
v
a
lu
e
s of
14
.
25
P
urpl
e a
n
d
4
.
75
G
r
ee
n
.
Ca
l
c
ul
a
ting th
e C
hi
-
squ
a
r
e
st
a
tisti
c
,
th
e
v
a
lu
e
s w
e
r
e
0
.
0044
for
P
urpl
e
a
n
d
0
.
0132
for
G
r
ee
n
,
tot
a
ling
0
.
0176
.
T
h
e c
omput
ed C
hi
-
squ
a
r
e
v
a
lu
e
(
0
.
0176
)
is l
e
ss th
a
n th
e c
riti
ca
l v
a
lu
e
from th
e C
hi
-
squ
a
r
e
t
ab
l
e
(
3
.
84
),
in
d
i
ca
ting th
a
t th
e
r
e
sults
a
r
e c
onsist
e
nt with
Me
n
de
l
'
s
F
irst
La
w
.
B
.
D
is
c
ussion
A
s
c
i
e
ntist
a
n
d
monk n
a
m
ed G
r
e
gor
J
oh
a
nn
Me
n
de
l un
c
ov
e
r
ed
th
e
prin
c
ipl
e
s of inh
e
rit
a
n
ce
in living org
a
nisms
.
T
h
e
s
e
prin
c
ipl
e
s
a
r
e
d
ivi
ded
into two p
a
rts
:
Me
n
de
l
'
s
La
w
I a
n
d Me
n
de
l
'
s
La
w
II
.
Me
n
de
l
'
s
La
w
I
,
a
lso known
a
s th
e
l
a
w of s
e
gr
e
g
a
tion
,
a
ss
e
rts th
a
t
d
uring th
e
form
a
tion of g
a
m
e
t
e
s
,
th
e
two
a
ll
e
l
e
s for
eac
h g
e
n
e
s
e
p
a
r
a
t
e
,
with
eac
h g
a
m
e
t
e
r
ece
iving only on
e a
ll
e
l
e
from
eac
h p
a
r
e
nt
.
T
o v
a
li
da
t
e
Me
n
de
l
'
s
La
w
I
,
a
monohy
b
ri
d c
ross w
a
s
c
on
d
u
c
t
ed
,
whi
c
h
e
x
a
min
e
s
th
e
inh
e
rit
a
n
ce
of
a
singl
e
tr
a
it
.
T
his typ
e
of
c
ross h
e
lps
de
t
e
rmin
e
how
tr
a
its
a
r
e
p
a
ss
ed
from p
a
r
e
nts to offspring
a
n
d
i
de
ntifi
e
s
d
omin
a
nt
a
n
d
r
ece
ssiv
e
g
e
n
e
s
.
U
n
de
rst
a
n
d
ing th
e
s
e
inh
e
rit
a
n
ce
p
a
tt
e
rns
ca
n gui
de
th
e de
v
e
lopm
e
nt of sup
e
rior pl
a
nt v
a
ri
e
ti
e
s
.
M
onohy
b
ri
d c
ross
e
s
a
r
e
be
n
e
fi
c
i
a
l
beca
us
e
th
e
y
ca
n l
ead
to th
e d
is
c
ov
e
ry of n
e
w v
a
ri
e
ti
e
s
through g
e
n
e
ti
c e
ngin
ee
ring
b
y pl
a
nt
b
r
eede
rs
.
B
y un
de
rst
a
n
d
ing
inh
e
rit
a
n
ce
p
a
tt
e
rns
,
b
r
eede
rs
ca
n s
e
l
ec
t f
a
vor
ab
l
e
g
e
n
e
s to
c
r
ea
t
e
n
e
w v
a
ri
e
ti
e
s th
a
t
e
nh
a
n
ce a
gri
c
ultur
a
l pro
d
u
c
tivity
,
improv
e
r
e
sist
a
n
ce
to p
e
sts
a
n
d d
is
ea
s
e
s
,
a
n
d ada
pt to v
a
rious
e
nvironm
e
nts
,
in
c
lu
d
ing m
a
rgin
a
l on
e
s
.
I
n pl
a
nt
b
r
eed
ing
,
s
e
v
e
r
a
l k
e
y f
ac
tors signifi
ca
ntly imp
ac
t th
e
out
c
om
e
of
c
rossing pl
a
nts
,
prim
a
rily
c
hromosom
e
s
,
DNA
,
a
ll
e
l
e
s
,
lo
c
i
,
g
e
notyp
e
,
a
n
d
ph
e
notyp
e
.
T
h
e
s
e e
l
e
m
e
nts
a
r
e
intri
ca
t
e
ly
c
onn
ec
t
ed
.
C
hromosom
e
s
a
r
e
thr
ead
-
lik
e
stru
c
tur
e
s of g
e
n
e
ti
c
m
a
t
e
ri
a
l foun
d
in
th
e
nu
c
l
e
us of
e
uk
a
ryoti
c ce
lls
,
a
n
d
th
e
y
c
ont
a
in lo
c
i
,
whi
c
h
a
r
e
sp
ec
ifi
c
lo
ca
tions o
cc
upi
ed b
y g
e
n
e
s
.
Ge
n
e
s
,
a
s
de
s
c
ri
bed b
y
W
.
J
oh
a
ns
e
n
,
a
r
e
th
e
sm
a
ll
e
st units of h
e
r
ed
ity lo
ca
t
ed
within lo
c
i on
c
hromosom
e
s
.
W
h
e
n g
e
n
e
s
a
r
e
lo
ca
t
ed a
t th
e
s
a
m
e
lo
c
us on
homologous
c
hromosom
e
s
,
th
e
y
a
r
e
r
e
f
e
rr
ed
to
a
s
a
ll
e
l
e
s
.
Ge
n
e
s
de
t
e
rmin
e
th
e
tr
a
its of living org
a
nisms
,
a
n
d d
uring r
e
pro
d
u
c
tion
,
th
e
c
om
b
in
a
tion of p
a
r
e
nt
a
l g
e
n
e
s r
e
sults in offspring with
a
g
e
n
e
ti
c
m
a
k
e
up
,
or g
e
notyp
e
,
d
iff
e
r
e
nt from th
e
p
a
r
e
nts
.
Ge
notyp
e
s
a
r
e
usu
a
lly
de
not
ed
with sym
b
ols wh
e
r
e
upp
e
r
ca
s
e
l
e
tt
e
rs r
e
pr
e
s
e
nt
d
omin
a
nt tr
a
its
a
n
d
low
e
r
ca
s
e
l
e
tt
e
rs r
e
pr
e
s
e
nt r
ece
ssiv
e
tr
a
its
.
Rece
ssiv
e
tr
a
its m
a
y not
be e
xpr
e
ss
ed
if th
e
y
a
r
e
ov
e
rsh
ad
ow
ed b
y
d
omin
a
nt tr
a
its
,
m
a
king th
e
visi
b
l
e
tr
a
it
,
or ph
e
notyp
e
,
d
omin
a
nt
.
F
or
e
x
a
mpl
e
,
in p
ea
pl
a
nt
c
ross
e
s
,
mor
e
offspring
e
xhi
b
it y
e
llow s
eed
s
c
omp
a
r
ed
to gr
ee
n s
eed
s
,
showing
a
ph
e
notypi
c
r
a
tio of
3
:
1
,
whil
e
th
e
g
e
notypi
c
r
a
tio is
1
:
2
:
1
.
P
r
ac
ti
ca
l
e
xp
e
rim
e
nts w
e
r
e c
on
d
u
c
t
ed
to
a
n
a
lyz
e
monohy
b
ri
d
c
ross
e
s in pl
a
nts using soy
bea
n v
a
ri
e
ti
e
s
.
T
h
e G
ro
b
og
a
n v
a
ri
e
ty s
e
rv
ed
a
s th
e P
1
p
a
r
e
nt
,
whil
e
th
e M
uri
a
v
a
ri
e
ty w
a
s th
e P
2
p
a
r
e
nt
.
T
o
pro
d
u
ce
th
e F
1
g
e
n
e
r
a
tion
,
s
eed
s from
a c
ross
be
tw
ee
n th
e G
ro
b
og
a
n
a
n
d M
uri
a
v
a
ri
e
ti
e
s w
e
r
e
utiliz
ed
.
F
or th
e F
2
g
e
n
e
r
a
tion
,
s
eed
s
de
riv
ed
from
F
1
c
ross
e
s w
e
r
e
us
ed
.
T
h
e G
ro
b
og
a
n v
a
ri
e
ty
,
r
e
l
ea
s
ed
in
2008
,
is
c
h
a
r
ac
t
e
riz
ed b
y
a de
t
e
rmin
a
t
e
growth typ
e
,
purpl
e
hypo
c
otyl
a
n
d
e
pi
c
otyl
,
gr
ee
nish l
ea
f
c
olor
,
a
n
d b
rown st
e
m f
ea
th
e
r
c
olor
.
I
ts flow
e
rs
a
r
e
purpl
e
,
s
eed c
o
a
t is y
e
llow
,
a
n
d
m
a
tur
e
po
d
s turn
b
rown
.
T
h
e
s
eed
s
'
hilum
c
olor is
b
rown
,
with l
a
n
ce
ol
a
t
e
l
ea
v
e
s
.
T
h
e
flow
e
ring
p
e
rio
d
is
be
tw
ee
n
30
a
n
d
32
da
ys
,
with po
d
s m
a
turing in
a
pproxim
a
t
e
ly
76
da
ys
.
P
l
a
nts r
eac
h
a
h
e
ight of
50
-
60
c
m
,
with s
eed
w
e
ight
a
v
e
r
a
ging
18
gr
a
ms p
e
r
100
s
eed
s
,
a
n
d
yi
e
l
d a
v
e
r
a
g
e
s
2
.
77
tons
p
e
r h
ec
t
a
r
e
,
with
a
pot
e
nti
a
l of
3
.
40
tons p
e
r h
ec
t
a
r
e
.
T
h
e
v
a
ri
e
ty h
a
s
a
prot
e
in
c
ont
e
nt of
43
.
9
%
a
n
d a
f
a
t
c
ont
e
nt of
18
.
4
%
.
I
t
ada
pts w
e
ll to
v
a
rious
e
nvironm
e
nt
a
l
c
on
d
itions
,
thriving in r
a
iny s
ea
sons
a
n
d
w
e
ll
-
irrig
a
t
ed a
r
ea
s
.
T
h
e c
l
a
ssifi
ca
tion
de
t
a
ils for th
e M
uri
a
v
a
ri
e
ty
a
r
e a
s follows
:
it
h
a
s roun
d
,
y
e
llow
,
ov
a
l
-
c
olor
ed
s
eed
s
a
n
d
t
a
ll pl
a
nts r
eac
hing
40
-
50
c
m in h
e
ight
.
T
h
e
w
e
ight of
1
,
000
gr
a
ins is
125
gr
a
ms
,
with
a
prot
e
in
c
ont
e
nt of
35
-
36
%
a
n
d a
yi
e
l
d
of
1
.
72
tons p
e
r h
ec
t
a
r
e
.
T
his v
a
ri
e
ty
e
xhi
b
its r
e
sist
a
n
ce
to rust
a
n
d
l
ea
f
d
is
ea
s
e
s
.
I
n th
e
pr
ac
ti
c
um
,
s
eed
s
from
P
1
,
P
2
,
F
1
,
a
n
d F
2
w
e
r
e
pl
a
nt
ed
,
with
10
s
eed
s
eac
h for
P
1
,
P
2
,
a
n
d F
1
,
a
n
d
20
s
eed
s for
F
2
.
T
h
e
s
e
s
eed
s w
e
r
e
pl
aced
in
a
s
eed b
ox
within
a
s
c
r
ee
n hous
e a
n
d
monitor
ed
for on
e
w
ee
k
,
d
uring whi
c
h th
e
y
w
e
r
e
r
e
gul
a
rly w
a
t
e
r
ed
.
A
ft
e
r
a
w
ee
k
,
st
e
m
c
olor w
a
s
a
ss
e
ss
ed
,
r
e
v
ea
ling th
a
t
P
1
pl
a
nts h
ad
purpl
e
st
e
ms
,
P
2
pl
a
nts h
ad
gr
ee
n st
e
ms
,
a
n
d F
1
pl
a
nts
a
lso h
ad
purpl
e
st
e
ms
.
T
his in
d
i
ca
t
e
s th
a
t th
e
purpl
e
c
olor in
P
1
ca
n
be de
not
ed a
s
HH
,
gr
ee
n
c
olor in
P
2
a
s hh
,
a
n
d
th
e
purpl
e c
olor in
F
1
a
s
H
h
,
following
Me
n
de
l
'
s first l
a
w
.
F
or th
e F
2
pl
a
nts
,
out of
19
o
b
s
e
rv
ed
,
15
h
ad
purpl
e
st
e
ms
a
n
d
4
h
ad
gr
ee
n st
e
ms
.
T
h
e
da
t
a
w
a
s th
e
n
a
n
a
lyz
ed
using th
e C
hi
-
S
qu
a
r
ed
t
e
st with
a c
riti
ca
l v
a
lu
e
of
3
.
84
.
V
.
CONCLUSION
C
on
c
lusion
F
rom this pr
ac
ti
ca
l
e
v
e
nt
III
,
it
ca
n
be c
on
c
lu
ded
th
a
t
a
monohy
b
ri
d c
ross fo
c
us
e
s on
a
singl
e
tr
a
it wh
e
n
e
x
a
mining inh
e
rit
a
n
ce
.
T
h
e F
1
g
e
n
e
r
a
tion shows only
d
omin
a
nt tr
a
its
,
whil
e
th
e F
2
g
e
n
e
r
a
tion
d
ispl
a
ys
a c
om
b
in
a
tion of
d
omin
a
nt
a
n
d
r
ece
ssiv
e
tr
a
its with
a
g
e
notyp
e
r
a
tio of
1
:
2
:
1
a
n
d a
ph
e
notyp
e
r
a
tio of
3
:
1
.
T
his is illustr
a
t
ed
b
y th
e
pr
e
v
a
l
e
n
ce
of purpl
e
st
e
ms
,
whi
c
h
a
r
e a d
omin
a
nt tr
a
it for
soy
bea
n st
e
m
c
olor
.
T
h
e
ph
e
notyp
e
r
a
tio o
b
s
e
rv
ed d
uring th
e
e
xp
e
rim
e
nt w
a
s
dee
m
ed
signifi
ca
nt
,
a
s th
e C
hi
-
S
qu
a
r
e
t
e
st r
e
v
ea
l
ed
th
e ca
l
c
ul
a
t
ed X
²
v
a
lu
e
(
0
.
0176
)
w
a
s l
e
ss th
a
n th
e X
²
t
ab
l
e
v
a
lu
e
(
3
.
84
).
REPORT GENETICS
PRACTICUM PLANT
DIHYBRID CROSS
B
y
:
BRADFORD H
.
DEPARTEMENT OF BIOLOGY
ARIZONA STATE UNIVERSITY
APRIL
2024
I
.
INTRODUCTION
A
.
Bac
kgroun
d Be
hin
d
Re
pro
d
u
c
tion is
a
n
a
tur
a
l pro
ce
ss for living org
a
nisms
a
im
ed a
t
pr
e
s
e
rving th
e
ir sp
ec
i
e
s
.
Eac
h org
a
nism h
a
s uniqu
e
m
ec
h
a
nisms for
this pr
e
s
e
rv
a
tion
.
I
n pl
a
nts
,
r
e
pro
d
u
c
tion
ca
n o
cc
ur through
c
ross
b
r
eed
ing
be
tw
ee
n
d
iff
e
r
e
nt sp
ec
i
e
s
.
Occa
sion
a
lly
,
th
e
offspring
from su
c
h
c
ross
e
s
d
o not sh
a
r
e
th
e
s
a
m
e
g
e
n
e
ti
c c
omposition
a
s th
e
ir
p
a
r
e
nts
.
F
or inst
a
n
ce
,
p
ea
pl
a
nts m
a
y pro
d
u
ce
offspring with wrinkl
ed
s
eed
s
e
v
e
n if th
e
p
a
r
e
nts h
ad
roun
d
s
eed
s
.
Re
s
ea
r
c
h on
c
ross
b
r
eed
ing
in
d
i
ca
t
e
s th
a
t th
e
v
a
ri
a
tions in offspring
a
ris
e
from th
e
mix of tr
a
its
from
b
oth p
a
r
e
nts
.
S
in
ce
p
a
r
e
nt
a
l g
e
notyp
e
s
c
ontri
b
ut
e
th
e
ir g
a
m
e
t
e
s
in
de
p
e
n
de
ntly
,
th
e
r
e
sulting offspring
ca
n
d
iff
e
r from th
e
ir p
a
r
e
nts
.
T
h
e
s
e d
iff
e
r
e
n
ce
s
ca
n som
e
tim
e
s
be be
n
e
fi
c
i
a
l
b
ut m
a
y
a
lso
ca
us
e
h
a
rm to pl
a
nts
a
n
d
oth
e
r living org
a
nisms
.
II
.
REVIEW BIBLIOGRAPHY
W
h
e
n g
e
n
e
s
a
n
d a
ll
e
l
e
s un
de
rgo
c
rossov
e
r
,
th
e
y p
a
ir
in
de
p
e
n
de
ntly with th
e
ir p
a
rtn
e
rs
,
following
a
st
a
n
da
r
d
l
a
w known
a
s
th
e
l
a
w of in
de
p
e
n
de
nt
a
ssortm
e
nt
,
or
Me
n
de
l
'
s
Sec
on
d La
w
.
T
his
prin
c
ipl
e a
ss
e
rts th
a
t wh
e
n two in
d
ivi
d
u
a
ls h
a
v
e
multipl
e
p
a
irs of tr
a
its
,
th
e
s
e
tr
a
its
a
ssort in
de
p
e
n
de
ntly of on
e a
noth
e
r
,
m
ea
ning th
a
t
a
ll
e
l
e
s
for
d
iff
e
r
e
nt tr
a
its
d
o not influ
e
n
ce eac
h oth
e
r
.
Re
s
ea
r
c
h into
Me
n
de
l
'
s
Sec
on
d La
w is
c
ommonly
c
on
d
u
c
t
ed
using
D
rosophil
a
m
e
l
a
nog
a
st
e
r
,
a
sp
ec
i
e
s of fruit fly th
a
t h
a
s
bee
n
a
k
e
y mo
de
l org
a
nism in g
e
n
e
ti
c
s for
ov
e
r
a ce
ntury
.
T
hom
a
s
H
unt
M
org
a
n first i
de
ntifi
ed
s
e
x link
a
g
e a
n
d
g
e
n
e
ti
c
r
ec
om
b
in
a
tion using th
e
s
e
fruit fli
e
s
.
T
h
e
y
a
r
e
f
a
vor
ed
in
g
e
n
e
ti
c
stu
d
i
e
s
d
u
e
to th
e
ir sm
a
ll siz
e
,
d
istin
c
t s
e
xu
a
l
d
imorphism
,
short g
e
n
e
r
a
tion tim
e
,
a
n
d
minim
a
l sp
ace
r
e
quir
e
m
e
nts for
m
a
int
e
n
a
n
ce
.
D
rosophil
a
m
e
l
a
nog
a
st
e
r
,
c
ommonly known
a
s th
e
fruit fly
,
is
c
l
a
ssifi
ed
within th
e
phylum
A
rthropo
da
,
c
l
a
ss
I
ns
ec
t
a
,
or
de
r
D
ipt
e
r
a
,
su
b
or
de
r
C
y
c
lorrh
a
ph
a
,
s
e
ri
e
s
Aca
lyptr
a
t
a
,
f
a
mily
D
rosophili
dae
,
a
n
d
g
e
nus
D
rosophil
a
.
T
his sp
ec
i
e
s is r
e
l
a
tiv
e
ly lightw
e
ight
d
u
e
to its sm
a
ll
siz
e
,
y
e
t it poss
e
ss
e
s
a
ro
b
ust
e
xosk
e
l
e
ton
a
n
d
int
e
gum
e
nt
.
T
h
e
int
e
gum
e
nt
,
whi
c
h
c
ov
e
rs th
e e
ntir
e b
o
d
y of th
e
fly
,
c
ont
a
ins num
e
rous
n
e
rv
e
s s
e
nsitiv
e
to stimuli su
c
h
a
s light
,
pr
e
ssur
e
,
soun
d
,
t
e
mp
e
r
a
tur
e
,
win
d
,
a
n
d
o
d
ors
.
T
o
d
istinguish
be
tw
ee
n m
a
l
e a
n
d
f
e
m
a
l
e
fli
e
s
,
on
e ca
n
o
b
s
e
rv
e
s
e
v
e
r
a
l
c
h
a
r
ac
t
e
risti
c
s
:
f
e
m
a
l
e
fli
e
s h
a
v
e a
sm
a
ll
,
point
ed
abd
om
e
n
,
wh
e
r
ea
s m
a
l
e
fli
e
s h
a
v
e a
roun
ded abd
om
e
n with
da
rk
m
a
rkings
a
t th
e
tip
.
Add
ition
a
lly
,
m
a
l
e
s typi
ca
lly h
a
v
e
only
5
abd
omin
a
l
s
e
gm
e
nts
a
n
d
3
b
l
ac
k strip
e
s on th
e
surf
ace
,
whil
e
f
e
m
a
l
e
s h
a
v
e
7
s
e
gm
e
nts
a
n
d
5
b
l
ac
k strip
e
s
.
III
.
METHOD PRACTICUM
A
.
Ma
t
e
ri
a
l
A
n
d T
ool
T
h
e
m
a
t
e
ri
a
ls us
ed
in this pr
ac
ti
c
um
a
r
e
D
rosophil
a
m
e
l
a
nog
a
st
e
r
fli
e
s
,
fly m
ed
i
a
,
c
l
ea
r pl
a
sti
c
,
c
hloroform
,
c
otton
a
n
d
o
b
s
e
rv
a
tion sh
ee
ts
.
T
h
e
tools us
ed
in this pr
ac
ti
c
um
a
r
e c
l
ea
r
b
ottl
e
s
,
Pe
tri
d
ish
d
ish
e
s
a
n
d
writing ut
e
nsils
.
B
.
W
ork
P
ro
ced
ur
e
F
li
e
s of th
e
sp
ec
i
e
s
D
rosophil
a
m
e
l
a
nog
a
st
e
r w
e
r
e c
hos
e
n for
m
a
ting
ba
s
ed
on two sp
ec
ifi
c
tr
a
its
.
O
n
ce
pup
ae de
v
e
lop
a
pproxim
a
t
e
ly
6
-
7
da
ys
a
ft
e
r m
a
ting
,
a
ll p
a
r
e
nt
c
ross
e
s
a
r
e
d
is
ca
r
ded be
for
e
th
e
pup
ae ca
n tr
a
nsform into im
a
go
.
T
h
e
r
e
sulting first
-
g
e
n
e
r
a
tion
(
F
1
)
c
ross
e
s
a
r
e
th
e
n o
b
s
e
rv
ed
.
I
f
multipl
e
ph
e
notyp
e
s
a
r
e
pr
e
s
e
nt
,
th
e c
ross
ca
n
be c
ontinu
ed
,
a
s
som
e
of th
e
f
e
m
a
l
e
s us
ed
m
a
y not
be
virgin
.
T
h
e
o
b
s
e
rv
ed da
t
a
is
a
n
a
lyz
ed
using th
e C
hi
S
qu
a
r
e
(
X
²)
t
e
st
.
III
.
RESULTS AND DISCUSSION
Re
sults
1
.
C
ross
Re
sults
I
n
a c
ross
be
tw
ee
n
Eb
ony
(
♀
)
a
n
d D
umpy
(
♂
),
wh
e
r
e
Eb
ony is r
e
pr
e
s
e
nt
ed a
s
PP
for wing l
e
ngth
a
n
d TT
for
b
rown
b
o
d
y
c
olor
,
a
n
d D
umpy is r
e
pr
e
s
e
nt
ed a
s pp for wing l
e
ngth
a
n
d
tt for whit
e b
o
d
y
c
olor
,
th
e
r
e
sulting offspring
'
s g
e
notyp
e
s
a
r
e
a
n
a
lyz
ed
using
a P
unn
e
tt squ
a
r
e
.
F
or
a c
ross of
P
p
T
t x
P
p
T
t
,
th
e
g
a
m
e
t
e
s
a
r
e PT
,
P
t
,
PT
,
a
n
d P
t
.
T
h
e P
unn
e
tt squ
a
r
e
shows th
e
following g
e
notyp
e d
istri
b
ution
:
PPTT
,
PPT
t
,
P
p
TT
,
P
p
T
t
,
PP
tt
,
P
ptt
,
pp
TT
,
a
n
d
pp
T
t
.
I
n th
e
s
ec
on
d
g
e
n
e
r
a
tion
,
th
e
ph
e
notypi
c
r
a
tio o
b
s
e
rv
ed
is
209
:
79
:
68
:
23
,
with th
e e
xp
ec
t
a
tion r
a
tio
be
ing
9
:
3
:
3
:
1
.
I
n
Tab
l
e
4
.
3
,
th
e C
hi
S
qu
a
r
e
t
e
st r
e
sults for th
e F
2
de
s
ce
n
da
nts
a
r
e
pr
e
s
e
nt
ed
.
Ob
s
e
rv
ed
fr
e
qu
e
n
c
i
e
s for th
e
c
h
a
r
ac
t
e
risti
c
s w
e
r
e
209
,
71
,
68
,
a
n
d
23
,
tot
a
ling
371
.
T
h
e
e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s w
e
r
e ca
l
c
ul
a
t
ed a
s
208
.
6875
,
69
.
5625
,
69
.
5625
,
a
n
d
23
.
1875
,
r
e
sp
ec
tiv
e
ly
.
T
h
e
squ
a
r
ed d
iff
e
r
e
n
ce
s
be
tw
ee
n o
b
s
e
rv
ed a
n
d e
xp
ec
t
ed
v
a
lu
e
s w
e
r
e
0
.
097
,
2
.
066
,
2
.
441
,
a
n
d
0
.
0351
,
whi
c
h wh
e
n
d
ivi
ded b
y th
e e
xp
ec
t
ed
v
a
lu
e
s
,
g
a
v
e
th
e
r
e
sults
0
.
000468
,
0
.
0296
,
0
.
035
,
a
n
d
0
.
001513
.
S
umming th
e
s
e
v
a
lu
e
s r
e
sult
ed
in
a C
hi
S
qu
a
r
e
st
a
tisti
c
of
0
.
0666
.
W
ith
a C
hi
S
qu
a
r
e
t
ab
l
e
v
a
lu
e
of
7
.
82
,
th
e c
omput
ed
st
a
tisti
c
is l
e
ss th
a
n th
e
t
ab
l
e
v
a
lu
e
,
in
d
i
ca
ting th
a
t th
e
o
b
s
e
rv
ed
r
e
sults
a
r
e
not
signifi
ca
ntly
d
iff
e
r
e
nt from th
e e
xp
ec
t
ed
v
a
lu
e
s
a
n
d
thus
a
lign
with th
e a
nti
c
ip
a
t
ed
r
a
tio
.
C
.
D
is
c
ussion
A d
ihy
b
ri
d c
ross involv
e
s m
a
ting two in
d
ivi
d
u
a
ls
c
onsi
de
ring two
d
iff
e
r
e
nt tr
a
its
.
T
his typ
e
of
c
ross
de
monstr
a
t
e
s
th
a
t
Me
n
de
l
'
s s
ec
on
d
l
a
w is v
a
li
d
,
whi
c
h st
a
t
e
s th
a
t g
e
n
e
s on
d
iff
e
r
e
nt
c
hromosom
e
s s
e
gr
e
g
a
t
e
in
de
p
e
n
de
ntly
,
r
e
sulting in four
ph
e
notypi
c
out
c
om
e
s in
a
9
:
3
:
3
:
1
r
a
tio
.
T
his shows th
a
t
a
ll
e
l
e
s
with
d
iff
e
r
e
nt g
e
n
e c
h
a
r
ac
t
e
risti
c
s
d
o not int
e
r
ac
t
.
W
h
e
n
e
x
a
mining two
d
istin
c
t tr
a
its
d
uring
a c
ross
,
d
iff
e
r
e
nt r
a
tio
c
omp
a
risons
a
r
e
o
b
s
e
rv
ed
.
Add
ition
a
lly
,
th
e
g
e
n
e
ti
c
m
a
k
e
up of
th
e
offspring will
d
iff
e
r from th
e
ir p
a
r
e
nts
.
F
or inst
a
n
ce
,
c
rossing
p
ea
pl
a
nts with roun
d
y
e
llow s
eed
s
a
n
d
gr
ee
n wrinkl
ed
s
eed
s
pro
d
u
ce
s offspring with roun
d
y
e
llow
,
roun
d
gr
ee
n
,
wrinkl
ed
y
e
llow
,
a
n
d
wrinkl
ed
gr
ee
n s
eed
s
,
following
a
9
:
3
:
3
:
1
r
a
tio
.
D
ihy
b
ri
d c
ross
e
s
a
n
d Me
n
de
l
'
s s
ec
on
d
l
a
w
a
r
e c
los
e
ly link
ed
.
Be
si
de
s p
ea
s
,
this m
e
tho
d
is us
ed
in oth
e
r pl
a
nts to
de
v
e
lop n
e
w
v
a
ri
e
ti
e
s with
de
sir
ab
l
e
tr
a
its
,
su
c
h
a
s high iron
c
ont
e
nt in ri
ce
for
a
n
e
mi
a
suff
e
r
e
rs
,
d
is
ea
s
e
-
r
e
sist
a
nt
c
orn
,
a
n
d ea
rly
-
m
a
turing
,
high
-
yi
e
l
d
ing
c
hili p
e
pp
e
rs
.
S
imil
a
rly
,
c
rossing t
a
ll
,
oil
-
pro
d
u
c
ing
j
a
troph
a
pl
a
nts yi
e
l
d
s high
-
yi
e
l
d
ing v
a
ri
e
ti
e
s suit
ab
l
e
for f
e
n
ce
pl
a
nting
.
T
h
e D
rosophil
a
m
e
l
a
nog
a
st
e
r
,
c
ommonly us
ed
for
d
ihy
b
ri
d c
ross
e
s
,
e
xhi
b
its s
e
v
e
r
a
l
d
istin
c
tiv
e c
h
a
r
ac
t
e
risti
c
s
.
T
h
e
s
e
fli
e
s
a
r
e
sm
a
ll
,
m
ea
suring
be
tw
ee
n
3
-
5
mm
,
with
a
wing v
e
in
(
c
ost
a
l v
e
in
)
th
a
t is split n
ea
r th
e b
o
d
y
a
n
d a
g
e
n
e
r
a
lly f
ea
th
e
r
-
sh
a
p
ed a
rist
a
with
7
-
12
b
r
a
n
c
h
e
s
.
T
h
e
post
e
rior
c
rossv
e
in is
usu
a
lly str
a
ight
,
a
n
d
th
e
ir
e
y
e
s
a
r
e
r
ed
.
Ma
l
e a
n
d
f
e
m
a
l
e
fli
e
s
d
iff
e
r in s
e
v
e
r
a
l w
a
ys
:
f
e
m
a
l
e
s h
a
v
e a
sm
a
ll
,
point
ed abd
om
e
n
,
whil
e
m
a
l
e
s
'
abd
om
e
ns
a
r
e
roun
ded a
n
d da
rk
a
t th
e
tip
.
Add
ition
a
lly
,
m
a
l
e
s h
a
v
e
only
5
abd
omin
a
l s
e
gm
e
nts
c
omp
a
r
ed
to
th
e
7
in f
e
m
a
l
e
s
.
Ma
l
e
s
a
lso poss
e
ss
10
s
e
x
c
om
b
s on th
e
upp
e
r
si
de
of th
e
ir front l
e
gs
,
c
onsisting of short
,
stiff h
a
irs
.
Fe
m
a
l
e
s
,
on
th
e
oth
e
r h
a
n
d
,
h
a
v
e
5
b
l
ac
k lin
e
s on th
e
ir
abd
om
e
n
,
wh
e
r
ea
s
m
a
l
e
s only h
a
v
e
3
.
D
rosophil
a
m
e
l
a
nog
a
st
e
r fli
e
s
a
r
e
pr
e
f
e
rr
ed
for
c
ross
-
b
r
eed
ing
e
xp
e
rim
e
nts for s
e
v
e
r
a
l r
ea
sons
:
th
e
y
a
r
e ea
sily
o
b
t
a
in
ab
l
e
,
m
a
int
e
n
a
n
ce
is str
a
ightforw
a
r
d a
n
d
in
e
xp
e
nsiv
e
,
th
e
ir
lif
e c
y
c
l
e
is short
,
it is simpl
e
to
d
istinguish
be
tw
ee
n m
a
l
e
s
a
n
d
f
e
m
a
l
e
s
,
th
e
y pro
d
u
ce a
l
a
rg
e
num
be
r of offspring in on
e
lif
e
c
y
c
l
e
,
a
n
d
th
e
y h
a
v
e
num
e
rous mut
a
nts
.
Add
ition
a
lly
,
th
e
y h
a
v
e a
sm
a
ll num
be
r of
c
hromosom
e
s
b
ut th
e
ir siz
e
is r
e
l
a
tiv
e
ly l
a
rg
e
.
Ma
l
e D
rosophil
a d
o not
e
xhi
b
it
d
iffi
c
ulty
d
uring
c
ross
-
b
r
eed
ing
.
T
h
e
initi
a
l stu
d
y on
D
rosophil
a
m
e
l
a
nog
a
st
e
r w
a
s
c
on
d
u
c
t
ed b
y
T
hom
a
s
H
unt
M
org
a
n
,
who
c
ross
ed a
whit
e
-
e
y
ed
m
a
l
e
with
a
r
ed
-
e
y
ed
f
e
m
a
l
e
,
r
e
sulting in
a
ll offspring h
a
ving r
ed e
y
e
s
,
in
d
i
ca
ting
th
a
t r
ed e
y
e
s
a
r
e d
omin
a
nt
a
n
d
whit
e e
y
e
s
a
r
e
r
ece
ssiv
e
.
W
h
e
n
c
rossing
D
rosophil
a
m
e
l
a
nog
a
st
e
r
,
o
b
s
e
rv
ab
l
e d
iff
e
r
e
n
ce
s
a
mong
offspring
a
r
e
oft
e
n
d
u
e
to mut
a
tions
,
whi
c
h
a
r
e c
h
a
ng
e
s in th
e
DNA
s
e
qu
e
n
ce ca
us
ed b
y
e
xt
e
rn
a
l f
ac
tors
.
M
ut
a
tions
,
de
riv
ed
from th
e La
tin wor
d
"
mut
a
tus
,"
a
r
e
de
fin
ed a
s inh
e
rit
ed c
h
a
ng
e
s in g
e
n
e
ti
c
m
a
t
e
ri
a
l
.
T
h
e
pro
ce
ss of
mut
a
tion is
ca
ll
ed
mut
a
g
e
n
e
sis
,
a
n
d
th
e
org
a
nisms with mut
a
tions
a
r
e
known
a
s mut
a
nts
,
whil
e
th
e a
g
e
nts
ca
using mut
a
tions
a
r
e
ca
ll
ed
mut
a
g
e
ns
.
T
h
e c
h
a
r
ac
t
e
risti
c
s of mut
a
nts in
D
rosophil
a
m
e
l
a
nog
a
st
e
r
a
r
e de
t
a
il
ed
in su
b
s
e
qu
e
nt stu
d
i
e
s
.
T
h
e
"
D
umpy
"
mut
a
tion r
e
sults in wings th
a
t
a
r
e
short
e
r th
a
n usu
a
l
,
oft
e
n
a
pp
ea
ring
a
s if th
e
y w
e
r
e c
ut off
,
a
n
d
th
e c
h
e
st h
a
ir is un
e
v
e
n
.
T
h
e
s
e
wings
a
r
e
position
ed a
t
a
90
-
de
gr
ee a
ngl
e
from th
e b
o
d
y
wh
e
n in th
e
ir st
a
n
da
r
d
position
.
T
h
e
"
Se
pi
a
"
mut
a
tion
ca
us
e
s th
e
e
y
e
s to r
a
ng
e
in
c
olor from
c
ho
c
ol
a
t
e b
rown to
b
l
ac
k
d
u
e
to
da
m
a
g
e
on sp
ec
ifi
c c
hromosom
e
s
. "
C
lot
"
fli
e
s h
a
v
e
m
a
roon
-
c
olor
ed e
y
e
s th
a
t
da
rk
e
n to
b
rown with
a
g
e
. "
Eb
ony
"
fli
e
s
a
r
e
n
ea
rly
b
l
ac
k with
a da
rk
c
olor
acc
umul
a
ting on th
e
ir
b
o
d
i
e
s
d
u
e
to
a de
f
ec
t in th
e
ir
b
l
ac
k pigm
e
nt
.
T
h
e
"
C
urly
"
mut
a
tion
ca
us
e
s th
e
wings to
be c
urly
,
a
r
e
sult of
a d
omin
a
nt g
e
n
e
mut
a
tion th
a
t
pro
d
u
ce
s this
ab
norm
a
lity
. "
W
hit
e
"
fli
e
s h
a
v
e
whit
e e
y
e
s
d
u
e
to
da
m
a
g
e
to th
e
g
e
n
e
r
e
sponsi
b
l
e
for pro
d
u
c
ing r
ed
pigm
e
nt
,
whi
c
h
norm
a
lly shoul
d
not pro
d
u
ce a
ny r
ed
pigm
e
nt
.
T
h
e
"
E
y
e
missing
"
mut
a
tion r
e
sults in
e
y
e
s
a
pp
ea
ring
a
s
d
ots
d
u
e
to
a
mut
a
tion on
th
e
thir
d c
hromosom
e
,
pr
e
v
e
nting th
e ce
lls from forming
e
y
e
s
a
s
th
e
y shoul
d
.
T
h
e
"
C
l
a
r
e
t
"
mut
a
tion is
c
h
a
r
ac
t
e
riz
ed b
y
b
urgun
d
y or
ru
b
y
-
r
ed e
y
e
s
. "
M
ini
a
tur
e
s
"
h
a
v
e
v
e
ry short wings
a
n
d a
r
e
un
ab
l
e
to fly
d
u
e
to
a
r
ece
ssiv
e
mut
a
tion in th
e
“
v
e
stigi
a
l g
e
n
e
”
on th
e
s
ec
on
d c
hromosom
e
. "
Ta
xi
"
mut
a
nts h
a
v
e
wings th
a
t
a
r
e
str
e
t
c
h
ed
out
,
m
a
king th
e
m mor
e
fun
c
tion
a
l for flying or p
e
r
c
hing
. "
B
l
ac
k
"
fli
e
s h
a
v
e
th
e
ir
e
ntir
e b
o
d
i
e
s
c
olor
ed b
l
ac
k
d
u
e
to
da
m
a
g
e
on
sp
ec
ifi
c c
hromosom
e
s
.
T
o inv
e
stig
a
t
e
th
e c
ross
b
r
eed
ing of
D
rosophil
a
m
e
l
a
nog
a
st
e
r fli
e
s
,
a
simul
a
tion
-
ba
s
ed
pr
ac
ti
ca
l
e
xp
e
rim
e
nt w
a
s
c
on
d
u
c
t
ed
.
T
h
e
simul
a
tion involv
ed c
rossing
Eb
ony fli
e
s
,
whi
c
h
h
a
v
e
long wings
a
n
d a b
rown
b
o
d
y
c
olor
,
with
D
umpy fli
e
s
,
c
h
a
r
ac
t
e
riz
ed b
y wings th
a
t
a
r
e
two
-
thir
d
s of th
e
ir
b
o
d
y l
e
ngth
a
n
d a
whit
e b
o
d
y
c
olor
.
T
h
e
r
e
sults from this simul
a
tion in
c
lu
ded
209
fli
e
s with long wings
a
n
d a b
rown
b
o
d
y
,
71
fli
e
s with wings
two
-
thir
d
s of th
e
ir
b
o
d
y l
e
ngth
a
n
d a b
rown
b
o
d
y
,
68
fli
e
s with
long wings
a
n
d a
whit
e b
o
d
y
,
a
n
d
23
fli
e
s with wings two
-
thir
d
s
of th
e
ir
b
o
d
y l
e
ngth
a
n
d a
whit
e b
o
d
y
.
T
his
da
t
a
sugg
e
sts th
a
t
long wings
a
n
d b
rown
b
o
d
i
e
s
a
r
e d
omin
a
nt tr
a
its ov
e
r wings two
-
thir
d
s of th
e b
o
d
y l
e
ngth
a
n
d
whit
e b
o
d
i
e
s
.
T
h
e
r
e
sults w
e
r
e
v
e
rifi
ed
using th
e C
hi
-
S
qu
a
r
e
t
e
st
,
with th
e
formul
a
provi
ded
to
de
t
e
rmin
e
th
e
st
a
tisti
ca
l signifi
ca
n
ce
.
G
iv
e
n th
e de
gr
ee
s of
fr
eed
om
,
th
e C
hi
-
S
qu
a
r
e
v
a
lu
e
w
a
s
c
omp
a
r
ed
to th
e c
riti
ca
l v
a
lu
e
from th
e
t
ab
l
e
.
S
in
ce
th
e ca
l
c
ul
a
t
ed C
hi
-
S
qu
a
r
e
v
a
lu
e
w
a
s mu
c
h
sm
a
ll
e
r th
a
n th
e
t
ab
l
e
v
a
lu
e
,
th
e
null hypoth
e
sis w
a
s
acce
pt
ed
,
in
d
i
ca
ting th
a
t th
e
o
b
s
e
rv
ed
r
a
tios
a
lign with th
e
or
e
ti
ca
l
e
xp
ec
t
a
tions
.
Va
ri
ab
ility in th
e
r
e
sults
ca
n
be a
ttri
b
ut
ed
to th
e
r
a
n
d
om n
a
tur
e
of th
e c
ross
b
r
eed
ing
e
v
e
nts
.
IV
.
CONCLUSION
A
.
C
on
c
lusion
T
h
e c
on
c
lusion from this pr
ac
ti
ca
l
e
v
e
nt
IV
is th
a
t
a d
ihy
b
ri
d c
ross
involv
e
s m
a
ting two in
d
ivi
d
u
a
ls
c
onsi
de
ring two
d
istin
c
t tr
a
its
.
D
ihy
b
ri
d
c
ross
e
s
de
monstr
a
t
e
th
e
v
a
li
d
ity of
Me
n
de
l
'
s s
ec
on
d
l
a
w
,
whi
c
h st
a
t
e
s
th
a
t g
e
n
e
s lo
ca
t
ed
on
d
iff
e
r
e
nt
c
hromosom
e
s s
e
gr
e
g
a
t
e
in
de
p
e
n
de
ntly
,
r
e
sulting in four
d
iff
e
r
e
nt ph
e
notyp
e
s in
a
9
:
3
:
3
:
1
r
a
tio
.
A
n
e
x
a
mpl
e
of
a
d
ihy
b
ri
d c
ross is o
b
s
e
rv
ed
in th
e
fruit fly
D
rosophil
a
m
e
l
a
nog
a
st
e
r
.
REPORT GENETICS
PRACTICUM PLANT
DEVIATION LAW MENDEL
B
y
:
BRADFORD H
.
DEPARTEMENT OF BIOLOGY
ARIZONA STATE UNIVERSITY
MAY
2024
I
.
INTRODUCTION
A
.
Bac
kgroun
d Be
hin
d
L
iving org
a
nisms
e
xhi
b
it
a
r
e
m
a
rk
ab
l
e
l
e
v
e
l of
d
iv
e
rsity
,
with
offspring n
e
v
e
r
be
ing i
de
nti
ca
l to th
e
ir p
a
r
e
nts
.
T
his
c
on
ce
pt is
a
m
a
jor
fo
c
us of g
e
n
e
ti
c
stu
d
i
e
s
.
Ge
n
e
ti
c
knowl
ed
g
e e
xplor
e
s th
e
inh
e
rit
a
n
ce
p
a
tt
e
rns of living things
,
oft
e
n using pro
bab
ility th
e
ory to pr
ed
i
c
t
out
c
om
e
s
.
H
ow
e
v
e
r
,
a
ft
e
r stu
d
ying g
e
n
e
ti
c
pro
bab
ility
,
it
'
s
c
l
ea
r th
a
t
e
xp
ec
t
ed
out
c
om
e
s might not
a
lw
a
ys o
cc
ur
.
F
or inst
a
n
ce
,
c
l
a
ssi
c
Me
n
de
li
a
n r
a
tios su
c
h
a
s
1
:
2
:
1
for
a
monohy
b
ri
d c
ross
a
n
d
9
:
3
:
3
:
1
for
a
d
ihy
b
ri
d c
ross
a
r
e
not gu
a
r
a
nt
eed
in
e
v
e
ry
ca
s
e
.
De
vi
a
tions from th
e
s
e
e
xp
ec
t
ed
r
a
tios
,
known
a
s
de
vi
a
tions from
Me
n
de
li
a
n r
a
tios
,
oft
e
n
o
cc
ur
,
in
d
i
ca
ting th
a
t not
a
ll offspring
c
onform to
Me
n
de
li
a
n
pr
ed
i
c
tions
.
II
.
REVIEW BIBLIOGRAPHY
Me
n
de
l
'
s s
ec
on
d
l
a
w
a
ss
e
rts th
a
t wh
e
n two in
d
ivi
d
u
a
ls h
a
v
e
multipl
e
p
a
irs of tr
a
its
,
th
e
s
e
tr
a
its
a
r
e
inh
e
rit
ed
in
de
p
e
n
de
ntly r
a
th
e
r
th
a
n
be
ing
de
p
e
n
de
nt on
eac
h oth
e
r
.
I
n oth
e
r wor
d
s
,
a
ll
e
l
e
s for
d
iff
e
r
e
nt tr
a
its
d
o not influ
e
n
ce
on
e a
noth
e
r
.
T
his prin
c
ipl
e
l
ead
s to
d
istin
c
t inh
e
rit
a
n
ce
p
a
tt
e
rns
.
Acc
or
d
ing to
Me
n
de
l
'
s r
e
s
ea
r
c
h
,
a
monohy
b
ri
d c
ross r
e
sults in
a
ph
e
notypi
c
r
a
tio of
12
:
1
if in
c
ompl
e
t
e
d
omin
a
n
ce
is pr
e
s
e
nt
,
a
n
d
3
:
1
in th
e ca
s
e
of
c
ompl
e
t
e d
omin
a
n
ce
.
I
n
a
d
ihy
b
ri
d c
ross
,
th
e F
2
g
e
n
e
r
a
tion typi
ca
lly
d
ispl
a
ys
a
9
:
3
:
3
:
1
ph
e
notypi
c
r
a
tio
.
De
spit
e
this
,
som
e
inh
e
rit
a
n
ce
p
a
tt
e
rns
d
o not
c
onform to
Me
n
de
li
a
n r
a
tios
,
a
n
d
r
e
s
ea
r
c
h
e
rs m
a
y o
b
s
e
rv
e
v
a
ri
a
tions su
c
h
a
s
9
:
3
:
4
,
9
:
7
,
12
:
3
:
1
,
9
:
6
:
1
,
a
n
d
15
:
1
.
T
h
e
s
e de
vi
a
tions
,
upon
c
los
e
r
e
x
a
min
a
tion
,
oft
e
n
a
lign with
Me
n
de
l
'
s prin
c
ipl
e
s wh
e
n th
e
num
be
rs
a
r
e c
om
b
in
ed
in
sp
ec
ifi
c
w
a
ys
,
l
ead
ing to wh
a
t is known
a
s
Me
n
de
li
a
n ps
e
u
d
o
-
de
vi
a
tion
.
Ge
n
e
int
e
r
ac
tions
ca
n l
ead
to n
e
w ph
e
notypi
c
out
c
om
e
s or r
e
sult in
a
lt
e
r
ed e
xpr
e
ssion p
a
tt
e
rns
,
a
ph
e
nom
e
non known
a
s
e
pist
a
sis
.
T
his
o
cc
urs wh
e
n th
e
int
e
r
ac
tion
be
tw
ee
n g
e
n
e
s pro
d
u
ce
s ph
e
notypi
c
v
a
ri
a
tions th
a
t
de
vi
a
t
e
from
Me
n
de
li
a
n inh
e
rit
a
n
ce
p
a
tt
e
rns
.
E
pist
a
sis
ca
n m
a
nif
e
st in
d
iff
e
r
e
nt forms
:
d
omin
a
nt
e
pist
a
sis
(
with
a
12
:
3
:
1
r
a
tio
),
r
ece
ssiv
e e
pist
a
sis
(
with
a
9
:
3
:
4
r
a
tio
),
d
omin
a
nt
-
r
ece
ssiv
e e
pist
a
sis
(
with
a
13
:
3
r
a
tio
),
d
omin
a
nt
d
upli
ca
t
e e
pist
a
sis
(
with
a
15
:
1
r
a
tio
),
r
ece
ssiv
e d
upli
ca
t
e e
pist
a
sis
(
with
a
9
:
7
r
a
tio
),
a
n
d d
upli
ca
t
e
g
e
n
e
s with
c
umul
a
tiv
e e
ff
ec
ts
(
with
a
9
:
6
:
1
r
a
tio
).
T
h
e c
on
ce
pt of
a
t
a
vism w
a
s intro
d
u
ced b
y
W
.
Ba
t
e
son
a
n
d RC
P
unn
e
tt
.
Ge
n
e
int
e
r
ac
tions th
e
ms
e
lv
e
s
d
o not
a
lt
e
r th
e
ph
e
notyp
e b
ut
r
e
sult in ph
e
notyp
e
s th
a
t
e
m
e
rg
e
from th
e
int
e
rpl
a
y of two p
a
irs of non
-
a
ll
e
li
c
g
e
n
e
s
.
D
omin
a
nt
e
pist
a
sis o
cc
urs wh
e
n on
e
g
e
n
e
suppr
e
ss
e
s
th
e e
xpr
e
ssion of
a
noth
e
r g
e
n
e
.
I
n this
c
ont
e
xt
,
th
e
g
e
n
e
r
e
sponsi
b
l
e
for m
a
sking th
e e
xpr
e
ssion of
a
noth
e
r non
-
a
ll
e
li
c
g
e
n
e
is r
e
f
e
rr
ed
to
a
s
th
e e
pist
a
ti
c
g
e
n
e
,
whil
e
th
e
suppr
e
ss
ed
g
e
n
e
is known
a
s th
e
hypost
a
ti
c
g
e
n
e
.
I
n th
e F
2
g
e
n
e
r
a
tion
,
this r
e
sults in
a
ph
e
notypi
c
r
a
tio
of
12
:
3
:
1
.
T
h
e c
ryptom
e
ry ph
e
nom
e
non w
a
s initi
a
lly i
de
ntifi
ed
wh
e
n pur
e
r
ed
str
a
ins of
L
in
a
ri
a
m
a
ro
cca
n
a
flow
e
rs w
e
r
e c
ross
ed
with pur
e
whit
e
str
a
ins
,
r
e
sulting in purpl
e
flow
e
rs in th
e F
1
g
e
n
e
r
a
tion
.
W
h
e
n th
e
s
e F
1
purpl
e
flow
e
rs w
e
r
e
int
e
r
c
ross
ed
,
th
e
r
e
sulting offspring in
c
lu
ded
purpl
e
,
r
ed
,
a
n
d
whit
e
flow
e
rs in
a
r
a
tio of
9
:
3
:
4
.
D
omin
a
nt r
ece
ssiv
e
e
pist
a
sis o
cc
urs through th
e
int
e
r
ac
tion of two g
e
n
e
s with
d
iff
e
r
e
nt
a
ll
e
l
e
s wh
e
r
e
on
e
g
e
n
e
m
a
sks th
e e
ff
ec
t of th
e
oth
e
r
.
T
his int
e
r
ac
tion
pro
d
u
ce
s two
d
istin
c
t ph
e
notypi
c
tr
a
its
,
l
ead
ing to
a
13
:
3
r
a
tio in th
e F
2
g
e
n
e
r
a
tion
.
D
omin
a
nt
d
upli
ca
t
e
s
,
or polym
e
ry
,
is
c
h
a
r
ac
t
e
riz
ed b
y th
e
a
pp
ea
r
a
n
ce
of
a
sp
ec
ifi
c
tr
a
it in th
e
offspring of h
e
t
e
rozygous
c
ross
e
s
d
u
e
to th
e
influ
e
n
ce
of multipl
e
g
e
n
e
s
a
t
d
iff
e
r
e
nt lo
c
i
,
whi
c
h pro
d
u
ce
th
e
s
a
m
e
tr
a
it
.
T
h
e
ph
e
notypi
c
r
a
tio for this ph
e
nom
e
non in th
e F
2
g
e
n
e
r
a
tion is
15
:
1
.
T
h
e c
ryptom
e
ry ph
e
nom
e
non w
a
s initi
a
lly i
de
ntifi
ed
wh
e
n pur
e
r
ed
str
a
ins of
L
in
a
ri
a
m
a
ro
cca
n
a
flow
e
rs w
e
r
e c
ross
ed
with
pur
e
whit
e
str
a
ins
,
r
e
sulting in purpl
e
flow
e
rs in th
e F
1
g
e
n
e
r
a
tion
.
W
h
e
n th
e
s
e F
1
purpl
e
flow
e
rs w
e
r
e
int
e
r
c
ross
ed
,
th
e
r
e
sulting
offspring in
c
lu
ded
purpl
e
,
r
ed
,
a
n
d
whit
e
flow
e
rs in
a
r
a
tio of
9
:
3
:
4
.
D
omin
a
nt r
ece
ssiv
e e
pist
a
sis o
cc
urs through th
e
int
e
r
ac
tion of two
g
e
n
e
s with
d
iff
e
r
e
nt
a
ll
e
l
e
s wh
e
r
e
on
e
g
e
n
e
m
a
sks th
e e
ff
ec
t of th
e
oth
e
r
.
T
his int
e
r
ac
tion pro
d
u
ce
s two
d
istin
c
t ph
e
notypi
c
tr
a
its
,
l
ead
ing
to
a
13
:
3
r
a
tio in th
e F
2
g
e
n
e
r
a
tion
.
D
omin
a
nt
d
upli
ca
t
e
s
,
or polym
e
ry
,
is
c
h
a
r
ac
t
e
riz
ed b
y th
e a
pp
ea
r
a
n
ce
of
a
sp
ec
ifi
c
tr
a
it in th
e
offspring of
h
e
t
e
rozygous
c
ross
e
s
d
u
e
to th
e
influ
e
n
ce
of multipl
e
g
e
n
e
s
a
t
d
iff
e
r
e
nt lo
c
i
,
whi
c
h pro
d
u
ce
th
e
s
a
m
e
tr
a
it
.
T
h
e
ph
e
notypi
c
r
a
tio for
this ph
e
nom
e
non in th
e F
2
g
e
n
e
r
a
tion is
15
:
1
.
III
.
METHOD PRACTICUM
A
.
Ma
t
e
ri
a
l
A
n
d T
ool
I
ngr
ed
i
e
nts
W
hi
c
h us
ed
on pr
ac
ti
c
um
T
his is
:
po
c
k
e
t pl
a
sti
c a
n
d
c
olor
b
uttons
.
T
h
e
tools us
ed
in this pr
ac
ti
c
um
a
r
e
:
o
b
s
e
rv
a
tion sh
ee
ts
a
n
d
writing tools
.
B
.
W
ork
P
ro
ced
ur
e
A
pl
a
sti
c ba
g
c
ont
a
ining
c
olor
ed b
uttons w
a
s sh
a
k
e
n until th
e c
olors
w
e
r
e
mix
ed
.
O
n
e b
utton w
a
s th
e
n r
a
n
d
omly s
e
l
ec
t
ed
,
a
n
d
th
e
out
c
om
e
w
a
s r
ec
or
ded
.
T
h
e b
uttons w
e
r
e
s
e
l
ec
t
ed a
tot
a
l of
90
tim
e
s
a
n
d
160
tim
e
s
,
with
eac
h inst
a
n
ce d
o
c
um
e
nt
ed
on
a
n o
b
s
e
rv
a
tion sh
ee
t
.
T
h
e
da
t
a
w
a
s
a
n
a
lyz
ed
using
a c
hi
-
squ
a
r
e
t
e
st
,
a
n
d
th
e
po
c
k
e
t w
a
s l
abe
l
ed
with
a c
o
de
.
IV
.
RESULTS AND DISCUSSION
Re
sults
Te
st
X
2
F
or proof
de
vi
a
tion l
a
w
Me
n
de
l
.
Rece
ssiv
e e
pist
a
sis
(
9
:
3
:
4
)
a
n
a
lysis with
a
tr
ea
tm
e
nt of
90
x
.
T
h
e
o
b
s
e
rv
ed
v
a
lu
e
s for y
e
llow
,
gr
ee
n
,
a
n
d
r
ed
w
e
r
e
56
,
20
,
a
n
d
14
r
e
sp
ec
tiv
e
ly
,
tot
a
ling
90
.
T
h
e
e
xp
ec
t
ed
v
a
lu
e
s w
e
r
e ca
l
c
ul
a
t
ed
to
be
50
.
625
for y
e
llow
,
16
.
875
for
gr
ee
n
,
a
n
d
22
.
5
for r
ed
.
T
h
e
squ
a
r
ed d
iff
e
r
e
n
ce
s
be
tw
ee
n o
b
s
e
rv
ed
a
n
d e
xp
ec
t
ed
v
a
lu
e
s w
e
r
e
28
.
891
,
9
.
766
,
a
n
d
72
.
25
,
r
e
sp
ec
tiv
e
ly
,
l
ead
ing to
a c
hi
-
squ
a
r
e
v
a
lu
e
of
4
.
36
.
G
iv
e
n th
a
t th
e c
hi
-
squ
a
r
e c
ount
is l
e
ss th
a
n th
e c
hi
-
squ
a
r
e
t
ab
l
e
v
a
lu
e
of
5
.
99
,
th
e
r
e
sults
a
r
e
c
onsi
de
r
ed
signifi
ca
nt
a
n
d c
onsist
e
nt with
e
xp
ec
t
a
tions
.
I
n th
e a
n
a
lysis
of th
e e
pist
a
sis r
ece
ssiv
e
(
9
:
3
:
4
)
with
160
x tr
ea
tm
e
nt
,
th
e
o
b
s
e
rv
ed
fr
e
qu
e
n
c
i
e
s for
b
l
ac
k
,
y
e
llow
,
a
n
d
pink w
e
r
e
91
,
24
,
a
n
d
45
,
r
e
sp
ec
tiv
e
ly
,
tot
a
ling
160
.
T
h
e e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s w
e
r
e ca
l
c
ul
a
t
ed
to
be
90
for
b
l
ac
k
,
30
for y
e
llow
,
a
n
d
40
for pink
.
T
h
e de
vi
a
tions
be
tw
ee
n
o
b
s
e
rv
ed a
n
d e
xp
ec
t
ed
v
a
lu
e
s w
e
r
e
squ
a
r
ed a
n
d d
ivi
ded b
y th
e
e
xp
ec
t
ed
v
a
lu
e
s to
de
t
e
rmin
e
th
e c
hi
-
squ
a
r
e
v
a
lu
e
s
:
0
.
011
for
b
l
ac
k
,
1
.
2
for y
e
llow
,
a
n
d
0
.
625
for pink
.
S
umming th
e
s
e
v
a
lu
e
s giv
e
s
a c
hi
-
squ
a
r
e c
ount of
1
.
836
.
C
omp
a
ring this to th
e c
hi
-
squ
a
r
e
t
ab
l
e
v
a
lu
e
of
5
.
99
,
th
e
r
e
sult in
d
i
ca
t
e
s th
a
t th
e
o
b
s
e
rv
ed da
t
a a
lign with th
e
e
xp
ec
t
ed
out
c
om
e
s
,
a
s th
e c
hi
-
squ
a
r
e c
ount is l
e
ss th
a
n th
e
t
ab
l
e
v
a
lu
e
.
T
h
e da
t
a
for
d
omin
a
nt
e
pist
a
sis
(
12
:
3
:
1
)
with
a
90
x tr
ea
tm
e
nt is
pr
e
s
e
nt
ed
.
Ob
s
e
rv
ed
v
a
lu
e
s for
c
ho
c
ol
a
t
e
,
y
e
llow
,
a
n
d
gr
ee
n
a
r
e
65
,
19
,
a
n
d
6
,
r
e
sp
ec
tiv
e
ly
,
summing to
90
.
E
xp
ec
t
ed
v
a
lu
e
s
a
r
e ca
l
c
ul
a
t
ed a
s
67
.
5
,
16
.
875
,
a
n
d
5
.
625
for
c
ho
c
ol
a
t
e
,
y
e
llow
,
a
n
d
gr
ee
n
.
T
h
e
squ
a
r
ed
d
iff
e
r
e
n
ce
s
be
tw
ee
n o
b
s
e
rv
ed a
n
d e
xp
ec
t
ed
v
a
lu
e
s
d
ivi
ded b
y th
e
e
xp
ec
t
ed
v
a
lu
e
s yi
e
l
d
0
.
092
for
c
ho
c
ol
a
t
e
,
0
.
267
for y
e
llow
,
a
n
d
0
.
025
for gr
ee
n
.
S
umming th
e
s
e
v
a
lu
e
s giv
e
s
a c
hi
-
squ
a
r
e
v
a
lu
e
of
0
.
384
.
W
ith
a ca
l
c
ul
a
t
ed c
hi
-
squ
a
r
e
v
a
lu
e
of
0
.
835
a
n
d a c
riti
ca
l v
a
lu
e
of
5
.
99
,
th
e
r
e
sults
a
r
e c
onsist
e
nt with
e
xp
ec
t
a
tions
,
in
d
i
ca
ting th
a
t th
e
o
b
s
e
rv
ed da
t
a a
ligns w
e
ll with th
e
hypoth
e
siz
ed d
istri
b
ution
.
I
n th
e
t
ab
l
e
showing
d
omin
a
nt
e
pist
a
sis
(
12
:
3
:
1
)
with
a
tot
a
l of
160
tr
ea
tm
e
nts
,
th
e
o
b
s
e
rv
ed a
n
d e
xp
ec
t
ed
num
be
rs for y
e
llow
,
gr
ee
n
,
a
n
d
r
ed
ph
e
notyp
e
s
a
r
e
r
ec
or
ded
.
T
h
e
o
b
s
e
rv
ed
num
be
rs
a
r
e
128
,
19
,
a
n
d
13
r
e
sp
ec
tiv
e
ly
,
whil
e
th
e e
xp
ec
t
ed
num
be
rs
a
r
e
120
,
30
,
a
n
d
10
.
T
h
e c
hi
-
squ
a
r
e ca
l
c
ul
a
tions involv
e de
t
e
rmining th
e
squ
a
r
ed d
iff
e
r
e
n
ce
s
be
tw
ee
n o
b
s
e
rv
ed a
n
d e
xp
ec
t
ed
v
a
lu
e
s
,
d
ivi
ded b
y th
e e
xp
ec
t
ed
v
a
lu
e
s
.
F
or y
e
llow
,
this yi
e
l
d
s
0
.
533
,
for gr
ee
n
4
.
033
,
a
n
d
for r
ed
0
.
9
.
S
umming th
e
s
e
v
a
lu
e
s r
e
sults in
a c
hi
-
squ
a
r
e c
ount of
5
.
466
.
T
his
v
a
lu
e
is
c
omp
a
r
ed
to th
e c
hi
-
squ
a
r
e
t
ab
l
e
v
a
lu
e
of
5
.
99
,
in
d
i
ca
ting th
a
t
th
e
o
b
s
e
rv
ed
r
e
sults
a
r
e c
onsist
e
nt with
e
xp
ec
t
a
tions
,
a
s th
e c
hi
-
squ
a
r
e c
ount is l
e
ss th
a
n th
e
t
ab
l
e
v
a
lu
e
.
T
h
e d
omin
a
nt
-
r
ece
ssiv
e e
pist
a
sis
(
13
:
3
)
with
90
o
b
s
e
rv
a
tions
,
c
h
a
r
ac
t
e
risti
c
s w
e
r
e
r
ec
or
ded
for y
e
llow
a
n
d
gr
ee
n tr
a
its
.
T
h
e
o
b
s
e
rv
ed c
ounts w
e
r
e
86
for y
e
llow
a
n
d
4
for gr
ee
n
,
tot
a
ling
90
.
T
h
e
e
xp
ec
t
ed c
ounts w
e
r
e ca
l
c
ul
a
t
ed a
s
73
.
125
for y
e
llow
a
n
d
16
.
875
for
gr
ee
n
.
T
h
e c
hi
-
squ
a
r
e
t
e
st w
a
s p
e
rform
ed
using th
e
formul
a
(
|
O
-
E
|
-
1
/
2
)²,
l
ead
ing to
a c
hi
-
squ
a
r
e
v
a
lu
e
of
331
.
53
.
T
h
e c
hi
-
squ
a
r
e c
ounts
for y
e
llow
a
n
d
gr
ee
n w
e
r
e
2
.
267
a
n
d
9
.
823
r
e
sp
ec
tiv
e
ly
,
r
e
sulting in
a
tot
a
l
c
hi
-
squ
a
r
e
v
a
lu
e
of
12
.
09
.
W
ith th
e c
hi
-
squ
a
r
e
t
ab
l
e
v
a
lu
e a
t
3
.
84
,
th
e ca
l
c
ul
a
t
ed c
hi
-
squ
a
r
e e
x
ceed
s th
e
t
ab
l
e
v
a
lu
e
,
in
d
i
ca
ting th
a
t th
e
hypoth
e
sis is r
e
j
ec
t
ed
or
d
o
e
s not
a
lign with
e
xp
ec
t
a
tions
.
T
h
e
r
e
sults of th
e d
omin
a
nt
-
r
ece
ssiv
e e
pist
a
sis
(
13
:
3
)
tr
ea
tm
e
nt
a
n
a
lyz
ed
with
160
s
a
mpl
e
s
.
T
h
e
o
b
s
e
rv
ed c
h
a
r
ac
t
e
risti
c
s in
c
lu
de
whit
e
a
n
d c
ho
c
ol
a
t
e
tr
a
its
,
with fr
e
qu
e
n
c
i
e
s of
132
a
n
d
28
,
r
e
sp
ec
tiv
e
ly
.
T
h
e
e
xp
ec
t
ed
v
a
lu
e
s for whit
e a
n
d c
ho
c
ol
a
t
e
tr
a
its w
e
r
e
130
a
n
d
30
.
T
h
e
c
hi
-
squ
a
r
e ca
l
c
ul
a
tion involv
ed c
omp
a
ring o
b
s
e
rv
ed a
n
d e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s
,
yi
e
l
d
ing
a c
hi
-
squ
a
r
e
v
a
lu
e
of
0
.
092
.
T
his v
a
lu
e
is
be
low
th
e c
riti
ca
l thr
e
shol
d
of
3
.
84
,
in
d
i
ca
ting th
a
t th
e
o
b
s
e
rv
ed
r
e
sults
a
r
e
c
onsist
e
nt with th
e
hypoth
e
sis
.
T
h
e
r
e
sults of
a
g
e
n
e
ti
c d
upli
ca
t
e e
xp
e
rim
e
nt with
a c
umul
a
tiv
e
e
ff
ec
t r
a
tio of
9
:
6
:
1
un
de
r
90
x tr
ea
tm
e
nt
.
Ob
s
e
rv
a
tions w
e
r
e
r
ec
or
ded
for
b
l
ac
k
,
whit
e
,
a
n
d
y
e
llow tr
a
its with tot
a
ls
a
s follows
:
b
l
ac
k
,
53
;
whit
e
,
18
;
a
n
d
y
e
llow
,
19
,
summing up to
90
.
E
xp
ec
t
ed
v
a
lu
e
s w
e
r
e
ca
l
c
ul
a
t
ed a
s
50
.
625
for
b
l
ac
k
,
33
.
75
for whit
e
,
a
n
d
5
.
625
for y
e
llow
.
T
h
e c
hi
-
squ
a
r
e
v
a
lu
e
s for th
e de
vi
a
tions
be
tw
ee
n o
b
s
e
rv
ed a
n
d
e
xp
ec
t
ed c
ounts w
e
r
e c
omput
ed
,
yi
e
l
d
ing
5
.
64
for
b
l
ac
k
,
248
.
0625
for
whit
e
,
a
n
d
178
.
890625
for y
e
llow
,
tot
a
ling
432
.
59375
.
W
h
e
n th
e
s
e
w
e
r
e d
ivi
ded b
y th
e e
xp
ec
t
ed
v
a
lu
e
s
a
n
d
summ
ed
,
th
e c
hi
-
squ
a
r
e
st
a
tisti
c
( ²)
ca
m
e
to
39
.
264189
.
S
in
ce
th
e ca
l
c
ul
a
t
ed c
hi
-
squ
a
r
e
v
a
lu
e
𝑋
e
x
ceed
s th
e c
riti
ca
l
c
hi
-
squ
a
r
e
v
a
lu
e
of
5
.
99
,
th
e
r
e
sults in
d
i
ca
t
e
th
a
t
th
e d
iff
e
r
e
n
ce
s o
b
s
e
rv
ed a
r
e
not signifi
ca
nt
a
n
d d
o not
a
lign with th
e
e
xp
ec
t
ed
r
a
tios
.
T
h
e
t
ab
l
e d
ispl
a
ys th
e
r
e
sults of
a
g
e
n
e
ti
c d
upli
ca
tion
e
xp
e
rim
e
nt with
a c
umul
a
tiv
e e
ff
ec
t r
a
tio of
9
:
6
:
1
un
de
r
a
tr
ea
tm
e
nt of
160
.
T
h
e
o
b
s
e
rv
ed
fr
e
qu
e
n
c
i
e
s for
b
l
ac
k
,
whit
e
,
a
n
d
y
e
llow tr
a
its w
e
r
e
106
,
44
,
a
n
d
10
,
r
e
sp
ec
tiv
e
ly
,
with
a
tot
a
l of
160
.
T
h
e e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s w
e
r
e ca
l
c
ul
a
t
ed a
s
90
for
b
l
ac
k
,
60
for whit
e
,
a
n
d
10
for
y
e
llow
.
T
h
e
squ
a
r
ed d
iff
e
r
e
n
ce
s
be
tw
ee
n o
b
s
e
rv
ed a
n
d e
xp
ec
t
ed
fr
e
qu
e
n
c
i
e
s w
e
r
e
256
for
b
l
ac
k
,
256
for whit
e
,
a
n
d
0
for y
e
llow
,
summing up to
512
.
T
h
e c
hi
-
squ
a
r
e
v
a
lu
e
s
ca
l
c
ul
a
t
ed
w
e
r
e
2
.
84
for
b
l
ac
k
,
4
.
26
for whit
e
,
a
n
d
0
for y
e
llow
,
giving
a
tot
a
l
c
hi
-
squ
a
r
e
of
7
.
10
.
S
in
ce
th
e c
hi
-
squ
a
r
e ca
l
c
ul
a
t
ed
(
7
.
10
)
is gr
ea
t
e
r th
a
n th
e c
hi
-
squ
a
r
e
t
ab
l
e
v
a
lu
e
(
5
.
99
),
th
e
r
e
sults in
d
i
ca
t
e
th
a
t th
e
out
c
om
e
s
a
r
e
not
signifi
ca
nt
a
n
d d
o not m
ee
t th
e e
xp
ec
t
ed
r
e
sults
.
Tab
l
e
5
.
9
shows th
e
r
e
sults of
a
r
ece
ssiv
e d
upli
ca
t
e e
pist
a
sis
t
e
st with
a
90
x tr
ea
tm
e
nt
.
T
h
e
o
b
s
e
rv
ed
num
be
rs w
e
r
e
51
y
e
llow
a
n
d
39
gr
ee
n
,
tot
a
ling
90
.
T
h
e e
xp
ec
t
ed
v
a
lu
e
s w
e
r
e ca
l
c
ul
a
t
ed a
s
50
.
625
for y
e
llow
a
n
d
39
.
375
for gr
ee
n
.
T
h
e d
iff
e
r
e
n
ce
s
be
tw
ee
n th
e
o
b
s
e
rv
ed
a
n
d e
xp
ec
t
ed
v
a
lu
e
s w
e
r
e
squ
a
r
ed
,
ad
just
ed
,
a
n
d
summ
ed
to o
b
t
a
in
a
c
hi
-
squ
a
r
e
v
a
lu
e
.
T
h
e ca
l
c
ul
a
t
ed c
hi
-
squ
a
r
e
v
a
lu
e
w
a
s
0
.
020
,
whi
c
h is
l
e
ss th
a
n th
e c
riti
ca
l v
a
lu
e
of
5
.
99
.
T
h
e
r
e
for
e
,
th
e
r
e
sults
a
r
e
c
onsi
de
r
ed
to
a
lign with
e
xp
ec
t
a
tions
,
in
d
i
ca
ting th
a
t th
e
fin
d
ings
a
r
e
c
onsist
e
nt with th
e
hypoth
e
sis
.
I
n
Tab
l
e
5
.
10
,
whi
c
h
de
t
a
ils th
e
r
ece
ssiv
e d
upli
ca
t
e e
pist
a
sis
with
a
9
:
7
r
a
tio un
de
r
160
x tr
ea
tm
e
nt
,
th
e
o
b
s
e
rv
ed
fr
e
qu
e
n
c
i
e
s
a
r
e a
s
follows
:
G
r
ee
n
,
94
;
B
l
ac
k
,
66
;
T
ot
a
l
,
160
.
E
xp
ec
t
ed
v
a
lu
e
s
a
r
e
90
for
G
r
ee
n
a
n
d
70
for
B
l
ac
k
.
Ca
l
c
ul
a
ting th
e c
hi
-
squ
a
r
e
v
a
lu
e
s
,
th
e
formul
a
us
ed
is
(
|
O
-
E
|
-
1
/
2
)² /
E
,
r
e
sulting in
12
.
25
for
G
r
ee
n
a
n
d
20
.
25
for
B
l
ac
k
,
whi
c
h sums up to
32
.
5
.
W
h
e
n th
e
in
d
ivi
d
u
a
l
c
hi
-
squ
a
r
e
v
a
lu
e
s
a
r
e d
ivi
ded b
y th
e
ir r
e
sp
ec
tiv
e e
xp
ec
t
ed
v
a
lu
e
s
,
th
e
r
e
sulting v
a
lu
e
s
a
r
e
0
.
136
for
G
r
ee
n
a
n
d
0
.
289
for
B
l
ac
k
,
with
a
tot
a
l
c
hi
-
squ
a
r
e c
ount
of
0
.
425
.
T
his
c
ount is l
e
ss th
a
n th
e c
hi
-
squ
a
r
e
t
ab
l
e
v
a
lu
e
of
5
.
99
,
in
d
i
ca
ting th
a
t th
e
o
b
s
e
rv
ed
r
e
sults
a
r
e c
onsist
e
nt with th
e e
xp
ec
t
ed
v
a
lu
e
s
.
I
n th
e
stu
d
y
,
th
e
o
b
s
e
rv
ed c
h
a
r
ac
t
e
risti
c
s w
e
r
e
r
ec
or
ded a
s
follows
:
81
b
l
ac
k
a
n
d
9
pink out of
a
tot
a
l of
90
s
a
mpl
e
s
.
T
h
e e
xp
ec
t
ed
num
be
rs w
e
r
e ca
l
c
ul
a
t
ed
with th
e
formul
a
for
a d
omin
a
nt
d
upli
ca
t
e
e
pist
a
sis r
a
tio of
15
:
1
,
yi
e
l
d
ing
84
.
375
for
b
l
ac
k
a
n
d
5
.
625
for pink
.
T
h
e
c
hi
-
squ
a
r
e ca
l
c
ul
a
tion for th
e
o
b
s
e
rv
ed
v
e
rsus
e
xp
ec
t
ed
v
a
lu
e
s
r
e
sult
ed
in
a c
hi
-
squ
a
r
e c
ount of
1
.
568
.
C
omp
a
ring this to th
e c
hi
-
squ
a
r
e
t
ab
l
e
v
a
lu
e
of
3
.
84
shows th
a
t th
e ca
l
c
ul
a
t
ed c
hi
-
squ
a
r
e
is l
e
ss
th
a
n th
e
t
ab
l
e
v
a
lu
e
,
in
d
i
ca
ting th
a
t th
e e
xp
e
rim
e
nt
'
s r
e
sults
a
r
e
c
onsist
e
nt with th
e e
xp
ec
t
ed
out
c
om
e
s
.
I
n th
e
o
b
s
e
rv
ed e
xp
e
rim
e
nt
,
c
h
a
r
ac
t
e
risti
c
s w
e
r
e
not
ed a
s follows
:
B
l
ac
k with
a c
ount of
151
,
P
ink
with
a c
ount of
9
,
a
n
d
th
e
tot
a
l
a
mount
be
ing
160
.
T
h
e e
xp
ec
t
ed
num
be
rs w
e
r
e ca
l
c
ul
a
t
ed a
s
150
for
B
l
ac
k
a
n
d
10
for
P
ink
.
U
sing th
e
s
e
v
a
lu
e
s
,
th
e c
hi
-
squ
a
r
e
st
a
tisti
c
w
a
s
c
omput
ed
,
yi
e
l
d
ing
0
.
25
for
eac
h
c
olor wh
e
n
c
omp
a
ring o
b
s
e
rv
ed a
n
d e
xp
ec
t
ed
v
a
lu
e
s
.
T
h
e c
om
b
in
ed
c
hi
-
squ
a
r
e
v
a
lu
e
for th
e
two
ca
t
e
gori
e
s w
a
s
0
.
0283
.
S
in
ce
th
e
ca
l
c
ul
a
t
ed c
hi
-
squ
a
r
e
v
a
lu
e
of
0
.
0283
is l
e
ss th
a
n th
e
t
ab
l
e
v
a
lu
e
of
3
.
84
,
th
e
r
e
sults in
d
i
ca
t
e
th
a
t th
e e
xp
e
rim
e
nt
'
s out
c
om
e
s
a
lign with th
e
e
xp
ec
t
ed d
istri
b
ution
.
B
.
D
is
c
ussion
A de
vi
a
tion from
Me
n
de
l
'
s l
a
ws
ca
n
be
s
ee
n in th
e
un
e
qu
a
l r
a
tio
of g
e
notyp
e
s
a
n
d
ph
e
notyp
e
s o
b
s
e
rv
ed
in
d
ihy
b
ri
d c
ross
e
s
c
omp
a
r
ed
to
Me
n
de
li
a
n r
a
tios
.
De
spit
e
th
e
s
e d
iff
e
r
e
n
ce
s
,
th
e
ov
e
r
a
ll
c
omp
a
rison
r
e
m
a
ins
c
onsist
e
nt
e
v
e
n wh
e
n
d
iff
e
r
e
nt g
e
n
e
s
a
r
e e
xpr
e
ss
ed
,
a
ph
e
nom
e
non known
a
s ps
e
u
d
o
-
de
vi
a
tion
.
T
h
e
s
e de
vi
a
tions
a
ris
e
from
int
e
r
ac
tions
be
tw
ee
n g
e
n
e
s
,
whi
c
h
ca
n l
ead
to v
a
ri
a
tions from
Me
n
de
li
a
n
e
xp
ec
t
a
tions
.
T
h
e ad
v
a
nt
a
g
e
of stu
d
ying su
c
h
de
vi
a
tions is
th
a
t th
e
y
ca
n
be
utiliz
ed
to i
de
ntify
a
n
d de
v
e
lop sup
e
rior tr
a
its
.
Ad
v
a
n
ce
s in g
e
n
e
ti
c
knowl
ed
g
e
sugg
e
st th
a
t it is possi
b
l
e
to
c
r
ea
t
e
n
e
w pl
a
nt v
a
ri
e
ti
e
s with
e
nh
a
n
ced c
h
a
r
ac
t
e
risti
c
s
b
y l
e
v
e
r
a
ging th
e
s
e
de
vi
a
tions
.
F
or inst
a
n
ce
,
r
e
s
ea
r
c
h h
a
s shown th
a
t tr
a
nsform
ed bea
n
pl
a
nts
ca
n pro
d
u
ce
tr
a
nsg
e
ni
c
pl
a
nts with
Me
n
de
li
a
n inh
e
rit
a
n
ce
p
a
tt
e
rns
.
D
iff
e
r
e
nt typ
e
s of
de
vi
a
tions from
Me
n
de
li
a
n prin
c
ipl
e
s
in
c
lu
de d
omin
a
nt
e
pist
a
sis
,
r
ece
ssiv
e e
pist
a
sis
,
r
ece
ssiv
e d
omin
a
nt
e
pist
a
sis
,
d
upli
ca
t
e
/
polym
e
ri
c d
omin
a
nt
e
pist
a
sis
,
d
upli
ca
t
e
r
ece
ssiv
e
e
pist
a
sis
,
g
e
n
e
s with
c
umul
a
tiv
e e
ff
ec
ts
,
a
n
d
v
a
rious g
e
n
e
int
e
r
ac
tions
.
T
h
e
ph
e
nom
e
non of
a
t
a
vism w
a
s initi
a
lly
de
s
c
ri
bed b
y
W
.
Ba
t
e
son
a
n
d R
.
C
.
P
unn
e
t
.
T
his involv
e
s g
e
n
e
int
e
r
ac
tions th
a
t
d
o not
a
lt
e
r th
e
ph
e
notyp
e d
ir
ec
tly
b
ut inst
ead
l
ead
to ph
e
notyp
e
s r
e
sulting from th
e
c
oop
e
r
a
tion
be
tw
ee
n two p
a
irs of non
-
a
ll
e
li
c
g
e
n
e
s
.
F
or inst
a
n
ce
,
d
iff
e
r
e
nt
c
om
b
typ
e
s in
c
hi
c
k
e
ns
,
su
c
h
a
s w
a
lnut
,
ros
e
,
p
ea
,
a
n
d
singl
e
,
e
xhi
b
it
a
r
a
tio of
9
:
3
:
3
:
1
.
E
pist
a
sis
,
a
noth
e
r ph
e
nom
e
non
,
o
cc
urs wh
e
n
on
e
g
e
n
e
m
a
sks th
e e
ff
ec
t of
a
noth
e
r non
-
a
ll
e
li
c
g
e
n
e
.
T
h
e
g
e
n
e
th
a
t
m
a
sks is r
e
f
e
rr
ed
to
a
s th
e e
pist
a
ti
c
g
e
n
e
,
whil
e
th
e
g
e
n
e
whos
e e
ff
ec
t
is m
a
sk
ed
is
ca
ll
ed
th
e
hypost
a
ti
c
g
e
n
e
.
T
his l
ead
s to
a
n
F
2
ph
e
notyp
e
r
a
tio of
12
:
3
:
1
,
a
s s
ee
n in th
e
inh
e
rit
a
n
ce
of fruit
c
olor in pumpkins
,
wh
e
r
e d
omin
a
nt whit
e
m
a
sks y
e
llow
a
n
d
gr
ee
n
c
olors
.
C
ryptom
e
ry
,
d
is
c
ov
e
r
ed b
y
C
orr
e
ns
,
o
cc
urs wh
e
n
c
rossing r
ed a
n
d
whit
e L
in
a
ri
a
m
a
ro
cca
n
a
flow
e
rs pro
d
u
ce
s purpl
e
flow
e
rs in th
e F
1
g
e
n
e
r
a
tion
,
a
n
d
su
b
s
e
qu
e
nt
F
2
c
ross
e
s yi
e
l
d
purpl
e
,
r
ed
,
a
n
d
whit
e
flow
e
rs in
a
9
:
3
:
4
r
a
tio
.
D
omin
a
nt r
ece
ssiv
e e
pist
a
sis involv
e
s int
e
r
ac
tions
be
tw
ee
n two
d
iff
e
r
e
nt
a
ll
e
l
e
s wh
e
r
e
on
e a
ll
e
l
e c
ov
e
rs th
e
oth
e
r
,
r
e
sulting in
a
n
F
2
r
a
tio of
13
:
3
.
A
n
e
x
a
mpl
e
of this is s
ee
n in th
e
inh
e
rit
a
n
ce
of f
ea
th
e
r
c
olor in pur
eb
r
ed c
hi
c
k
e
ns
,
wh
e
r
e d
omin
a
nt whit
e c
olor m
a
sks th
e
r
ece
ssiv
e c
olor
.
T
h
e
ph
e
nom
e
non of
d
upli
ca
t
e
s or polym
e
ry o
cc
urs wh
e
n
a
c
h
a
r
ac
t
e
risti
c e
m
e
rg
e
s from h
e
t
e
rozygous
c
ross
e
s
d
u
e
to th
e
influ
e
n
ce
of oth
e
r g
e
n
e
s
.
T
his h
a
pp
e
ns wh
e
n two or mor
e
g
e
n
e
s
a
t
d
iff
e
r
e
nt lo
c
i
e
xhi
b
it th
e
s
a
m
e
tr
a
it
.
F
or inst
a
n
ce
,
in th
e
inh
e
rit
a
n
ce
of fruit sh
a
p
e
in
Ca
ps
e
ll
a
,
th
e
tri
a
ngul
a
r sh
a
p
e
is
d
omin
a
nt whil
e
th
e
ov
a
l sh
a
p
e
is
r
ece
ssiv
e
.
D
uring
c
ross
e
s
,
th
e
tri
a
ngul
a
r sh
a
p
e
pr
ed
omin
a
t
e
s
beca
us
e
th
e C a
n
d D
g
e
n
e
s m
a
sk th
e c a
n
d d
g
e
n
e
s
.
T
hus
,
c
rossing
ccD
_
a
n
d
C
_
dd
g
e
n
e
s r
e
sults in th
e e
xpr
e
ssion of th
e
tri
a
ngul
a
r tr
a
it
.
C
ompl
e
m
e
nt
a
ry g
e
n
e
int
e
r
ac
tion
,
first
de
s
c
ri
bed b
y
W
.
Ba
t
e
son
a
n
d
R
.
C
.
P
unn
e
tt
,
o
cc
urs wh
e
n g
e
n
e
s work tog
e
th
e
r to pro
d
u
ce a
tr
a
it
;
if
on
e
g
e
n
e
is missing
,
th
e
tr
a
it
d
o
e
s not
a
pp
ea
r fully
.
F
or
e
x
a
mpl
e
,
in
T
rifolium r
e
p
e
ns
,
high
HCN c
ont
e
nt r
e
quir
e
s th
e
pr
e
s
e
n
ce
of
b
oth
L
a
n
d H
g
e
n
e
s
,
whil
e
low
HCN c
ont
e
nt r
e
sults from th
e
pr
e
s
e
n
ce
of hh or
ll
H
_
g
e
n
e
s
.
T
h
e
ph
e
nom
e
non of g
e
n
e d
upli
ca
tion with
c
umul
a
tiv
e
e
ff
ec
ts involv
e
s
d
iff
e
r
e
nt
a
ll
e
l
e
s wh
e
r
e a d
omin
a
nt g
e
n
e ca
n m
a
sk
a
r
ece
ssiv
e
tr
a
it in
c
ross
e
s
,
r
e
sulting in
a
ph
e
notyp
e
r
a
tio of
9
:
6
:
1
.
F
or
e
x
a
mpl
e
,
th
e
inh
e
rit
a
n
ce
of pumpkin fruit sh
a
p
e
s
,
whi
c
h in
c
lu
de d
is
c
,
roun
d
,
a
n
d
ov
a
l
,
involv
e
s
d
omin
a
nt
C a
n
d L
g
e
n
e
s
a
n
d
r
ece
ssiv
e c a
n
d
l
g
e
n
e
s
.
C
rossing
B
_
ll g
e
n
e
s typi
ca
lly pro
d
u
ce
s
d
is
c
-
sh
a
p
ed
fruit
,
e
v
e
n
though roun
d
is th
e e
xp
ec
t
ed
sh
a
p
e
.
A
pr
ac
ti
c
um
c
on
d
u
c
t
ed
without using physi
ca
l o
b
j
ec
ts
,
su
c
h
a
s pl
a
nts
,
oft
e
n
de
m
a
n
d
s
c
onsi
de
r
ab
l
e
tim
e a
n
d
pr
ec
ision
,
p
a
rti
c
ul
a
rly wh
e
n
a
ss
e
ssing
de
vi
a
tions from
Me
n
de
l
'
s inh
e
rit
a
n
ce
p
a
tt
e
rns
.
T
o
add
r
e
ss
this
,
a
simul
a
tion involving
c
olor
ed b
uttons is
e
mploy
ed
,
ba
s
ed
on th
e
a
ssumption th
a
t
de
vi
a
tions from
Me
n
de
l
'
s
La
w will
be
pr
e
s
e
nt in
proportions
c
onsist
e
nt with th
e
or
e
ti
ca
l pr
ed
i
c
tions
.
T
h
e
simul
a
tion
involv
e
s s
e
l
ec
ting
b
uttons
90
a
n
d
160
tim
e
s
,
r
e
sp
ec
tiv
e
ly
.
T
h
e
r
e
sulting
da
t
a
is th
e
n
a
n
a
lyz
ed
using th
e C
hi
S
qu
a
r
e
t
e
st to
c
omp
a
r
e ac
tu
a
l
out
c
om
e
s with th
e
or
e
ti
ca
l
e
xp
ec
t
a
tions r
e
g
a
r
d
ing
de
vi
a
tions from
Me
n
de
l
'
s
La
w
.
T
h
e C
hi
S
qu
a
r
e
t
e
st r
e
sults for
c
olor
ed b
utton s
e
l
ec
tion
in th
e
simul
a
tion show th
a
t th
e
hypoth
e
sis initi
a
lly hol
d
s tru
e
,
in
d
i
ca
ting signifi
ca
nt fin
d
ings wh
e
n th
e ca
l
c
ul
a
t
ed C
hi
S
qu
a
r
e
v
a
lu
e
is
sm
a
ll
e
r th
a
n th
e
t
ab
l
e
v
a
lu
e
.
C
onv
e
rs
e
ly
,
if th
e ca
l
c
ul
a
t
ed C
hi
S
qu
a
r
e
v
a
lu
e e
x
ceed
s th
e
t
ab
l
e
v
a
lu
e
,
th
e
r
e
sults
a
r
e dee
m
ed
insignifi
ca
nt
.
T
h
e
r
a
tio o
b
s
e
rv
ed
in th
e e
pist
a
ti
c
r
ece
ssiv
e
s
ce
n
a
rio
a
ligns with th
e
e
xp
ec
t
ed
9
:
3
:
4
r
a
tio
.
F
or oth
e
r
de
vi
a
tions from
Me
n
de
l
'
s l
a
ws
,
th
e C
hi
S
qu
a
r
e
t
e
st
da
t
a d
o not show signifi
ca
nt
d
iff
e
r
e
n
ce
s
,
a
lthough som
e
insignifi
ca
nt r
e
sults
a
r
e
not
ed
in
ca
s
e
s of
d
omin
a
nt r
ece
ssiv
e e
pist
a
sis
a
n
d d
upli
ca
t
e
g
e
n
e de
vi
a
tions
.
T
h
e
s
e
v
a
ri
a
tions
a
r
e a
ttri
b
ut
ed
to th
e
r
a
n
d
om s
e
l
ec
tion of
b
uttons
,
whi
c
h intro
d
u
ce
s v
a
ri
ab
ility in th
e c
olor
d
istri
b
ution
,
r
e
fl
ec
ting th
e
pro
bab
ilisti
c
n
a
tur
e
of th
e e
v
e
nts
.
IV
.
CONCLUSION
A
.
C
on
c
lusion
T
h
e
fin
d
ings from this pr
ac
ti
ca
l
e
v
e
nt r
e
v
ea
l s
e
v
e
r
a
l
de
vi
a
tions from
Me
n
de
l
'
s
La
w
,
in
c
lu
d
ing v
a
rious typ
e
s of g
e
n
e
int
e
r
ac
tions
.
T
h
e
s
e de
vi
a
tions
a
r
e
ca
t
e
goriz
ed a
s
d
omin
a
nt
e
pist
a
sis
(
with
a
12
:
3
:
1
r
a
tio
),
r
ece
ssiv
e e
pist
a
sis
(
or
mo
d
ifying g
e
n
e
) (
with
a
9
:
3
:
4
r
a
tio
),
d
omin
a
nt
-
r
ece
ssiv
e e
pist
a
sis
(
inhi
b
iting
g
e
n
e
) (
with
a
13
:
3
r
a
tio
),
d
omin
a
nt
d
upli
ca
t
e e
pist
a
sis
(
polym
e
ry
) (
with
a
15
:
1
r
a
tio
),
a
n
d
r
ece
ssiv
e d
upli
ca
t
e e
pist
a
sis
(
c
ompl
e
m
e
nt
a
ry f
ac
tors
) (
with
a
9
:
7
r
a
tio
).
Add
ition
a
lly
,
th
e
r
e
is th
e
g
e
n
e d
upli
ca
t
e e
ff
ec
t with
a c
umul
a
tiv
e
p
a
tt
e
rn
(
with
a
9
:
6
:
1
r
a
tio
).
REPORT GENETICS
PRACTICUM PLANT
CALCULATION OF ALLEL FREQUENCY
,
GENOTYPE
FREQUENCY
,
MEASUREMENT PROPERTIES QUALITATIVE AND
QUANTITATIVE
B
y
:
BRADFORD H
.
DEPARTEMENT OF BIOLOGY
ARIZONA STATE UNIVERSITY
MAY
2024
I
.
INTRODUCTION
A
.
Bac
kgroun
d Be
hin
d
L
if
e
forms
ca
n r
e
pro
d
u
ce
through two prim
a
ry m
e
tho
d
s
:
a
s
e
xu
a
l
a
n
d
s
e
xu
a
l r
e
pro
d
u
c
tion
.
A
s
e
xu
a
l r
e
pro
d
u
c
tion typi
ca
lly r
e
sults in
offspring with low g
e
n
e
ti
c d
iv
e
rsity
.
I
n
c
ontr
a
st
,
s
e
xu
a
l r
e
pro
d
u
c
tion
l
ead
s to offspring with
a
high
e
r
de
gr
ee
of g
e
n
e
ti
c
v
a
ri
a
tion
.
T
his
in
c
r
ea
s
ed d
iv
e
rsity o
cc
urs
beca
us
e
th
e
g
e
n
e
s
a
n
d a
ll
e
l
e
s from
eac
h
p
a
r
e
nt s
e
p
a
r
a
t
e a
n
d
r
ec
om
b
in
e
r
a
n
d
omly with thos
e
of th
e
ir p
a
rtn
e
r
,
un
a
ff
ec
t
ed b
y oth
e
r g
e
n
e
s
a
n
d a
ll
e
l
e
s
.
T
his prin
c
ipl
e
is known
a
s th
e
l
a
w of in
de
p
e
n
de
nt
a
ssortm
e
nt
,
e
n
ca
psul
a
t
ed
in
Me
n
de
l
'
s first
a
n
d
s
ec
on
d
l
a
ws
.
O
ffspring from
a
s
e
xu
a
l r
e
pro
d
u
c
tion
,
or
c
loning
,
form
a
popul
a
tion with
a
wi
de
r
a
ng
e
of in
d
ivi
d
u
a
l
a
n
d
g
e
n
e
ti
c d
iv
e
rsity
.
Acc
or
d
ing to th
e Ha
r
d
y
-
We
in
be
rg prin
c
ipl
e
,
th
e
s
e
offspring
e
xhi
b
it
d
iv
e
rs
e
qu
a
ntit
a
tiv
e a
n
d
qu
a
lit
a
tiv
e
tr
a
its
,
a
n
d
th
e
fr
e
qu
e
n
c
i
e
s of
a
ll
e
l
e
s
a
n
d
g
e
notyp
e
s r
e
m
a
in st
ab
l
e
,
a
ssuming no
e
volution
a
ry influ
e
n
ce
s
.
II
.
REVIEW BIBLIOGRAPHY
P
opul
a
tion g
e
n
e
ti
c
s is
a
su
b
fi
e
l
d
of g
e
n
e
ti
c
s th
a
t fo
c
us
e
s on
stu
d
ying g
e
n
e
s within popul
a
tions
.
T
his involv
e
s m
a
th
e
m
a
ti
ca
lly
a
n
a
lyzing th
e
g
e
n
e
ti
c
v
a
ri
a
tions
ca
us
ed b
y inh
e
rit
a
n
ce a
t th
e
popul
a
tion l
e
v
e
l
.
A
popul
a
tion
c
onsists of
a
group of org
a
nisms of th
e
s
a
m
e
sp
ec
i
e
s
.
A
ll m
e
m
be
rs of
a
sp
ec
i
e
s sh
a
r
e a c
ommon g
e
n
e
pool
,
whi
c
h in
c
lu
de
s th
e
tot
a
l s
e
t of
a
ll
e
l
e
s or g
e
n
e
ti
c
inform
a
tion foun
d
in
in
d
ivi
d
u
a
ls th
a
t int
e
r
b
r
eed
within th
a
t popul
a
tion
.
T
h
e Ha
r
d
y
-
We
in
be
rg
La
w
,
de
v
e
lop
ed
in
de
p
e
n
de
ntly
b
y
E
nglish m
a
th
e
m
a
ti
c
i
a
n
G
o
d
fr
e
y
Ha
rol
d Ha
r
d
y
a
n
d Ge
rm
a
n physi
c
i
a
n
W
ilh
e
lm
We
in
be
rg
,
de
s
c
ri
be
s how
g
e
n
e
fr
e
qu
e
n
c
i
e
s r
e
m
a
in
c
onst
a
nt in
a
popul
a
tion un
de
rgoing r
a
n
d
om
m
a
ting
,
a
llowing pr
ed
i
c
tions
ab
out
a
ll
e
l
e
fr
e
qu
e
n
c
i
e
s within th
a
t
popul
a
tion
.
Ha
r
d
y
-
We
in
be
rg
'
s l
a
w
a
ss
e
rts th
a
t g
e
n
e
fr
e
qu
e
n
c
i
e
s within
a
popul
a
tion
ca
n st
a
y
c
onst
a
nt
a
n
d ac
hi
e
v
e e
quili
b
rium
ac
ross on
e
g
e
n
e
r
a
tion
.
F
or this
e
quili
b
rium to
be
m
a
int
a
in
ed
,
ce
rt
a
in
c
on
d
itions
must
be
s
a
tisfi
ed
:
m
a
ting must o
cc
ur r
a
n
d
omly
,
th
e
r
e
must
be
no
n
a
tur
a
l s
e
l
ec
tion
,
th
e
popul
a
tion siz
e
must
be
l
a
rg
e
,
th
e
r
e
shoul
d be
no
mut
a
tions
,
a
n
d
no migr
a
tion shoul
d
t
a
k
e
pl
ace
.
I
n g
e
n
e
r
a
l t
e
rms
,
th
e
Ha
r
d
y
-
We
in
be
rg l
a
w
ca
n
be e
xpr
e
ss
ed a
s follows
:
if th
e
fr
e
qu
e
n
c
y of
a
ll
e
l
e A
is
de
not
ed b
y p
a
n
d
th
e
fr
e
qu
e
n
c
y of
a
ll
e
l
e a
is
de
not
ed b
y q
,
th
e
n th
e
r
e
sults of
a c
ross
be
tw
ee
n two h
e
t
e
rozygous in
d
ivi
d
u
a
ls
(
Aa
×
Aa
)
will pro
d
u
ce
:
homozygous
d
omin
a
nt
AA
=
p
×
p
=
p
²,
h
e
t
e
rozygous
2
Aa
=
2
p
×
q
=
2
pq
,
a
n
d
homozygous r
ece
ssiv
e aa
=
q
×
q
=
q
².
He
n
ce
,
th
e
formul
a ca
n
be
writt
e
n
a
s p
² (
AA
) +
2
pq
(
Aa
) +
q
² (
aa
) =
1
.
S
in
ce
(
p
+
q
)² =
1
,
it follows th
a
t p
+
q
=
1
,
a
n
d
th
e
r
e
for
e
p
=
1
–
q
.
III
.
METHOD PRACTICUM
A
.
Ma
t
e
ri
a
l
A
n
d T
ool
T
h
e
m
a
t
e
ri
a
ls us
ed
in this pr
ac
ti
c
um
a
r
e
:
pl
a
sti
c ba
gs
c
ont
a
ining
soy
bea
ns
,
pl
a
sti
c ba
gs
c
ont
a
ining
c
olor
ed b
uttons
,
pl
a
sti
c ba
gs
c
ont
a
ining nuts l
a
n
d A
n
d
sh
ee
t o
b
s
e
rv
a
tion
.
T
ools
W
hi
c
h us
ed
on
pr
ac
ti
c
um th
e
s
e a
r
e
:
ba
l
a
n
ce
s
,
ca
l
c
ul
a
tors
a
n
d
st
a
tion
e
ry
B
,
W
ork
P
ro
ced
ur
e
Te
st
1
F
or inst
a
n
ce
,
a
popul
a
tion is
c
onsi
de
r
ed
st
ab
l
e
wh
e
n it
c
onsists of
in
d
ivi
d
u
a
ls with r
ed
(
GG
),
whit
e
(
gg
),
a
n
d
pink
(
G
g
)
ph
e
notyp
e
s
.
A
s
a
mpl
e
of
200
in
d
ivi
d
u
a
ls is r
a
n
d
omly s
e
l
ec
t
ed
from this popul
a
tion
.
T
h
e c
olors of th
e
s
e
l
ec
t
ed
in
d
ivi
d
u
a
ls
a
r
e
r
ec
or
ded
,
a
n
d
th
e
fr
e
qu
e
n
c
i
e
s of th
e
g
e
notyp
e
s
a
n
d
th
e a
ll
e
l
e
s
G a
n
d
g
a
r
e
th
e
n
ca
l
c
ul
a
t
ed
.
Te
st
2
T
wo po
c
k
e
ts
,
eac
h pr
e
p
a
r
ed
in th
e
s
a
m
e
m
a
nn
e
r
,
w
e
r
e
fill
ed
with two
typ
e
s of
c
olor
ed b
uttons
.
B
uttons w
e
r
e
r
a
n
d
omly
d
r
a
wn from
eac
h
po
c
k
e
t
,
a
n
d
th
e c
olor of
eac
h
b
utton
d
r
a
wn w
a
s r
ec
or
ded
.
T
his pro
ce
ss
w
a
s r
e
p
ea
t
ed
100
tim
e
s
.
T
h
e
fr
e
qu
e
n
c
y of g
e
notyp
e
s
a
n
d a
ll
e
l
e
s w
a
s
th
e
n
ca
l
c
ul
a
t
ed
.
T
h
e
r
e
sulting
da
t
a
w
a
s
e
nt
e
r
ed
into th
e a
v
a
il
ab
l
e
l
abe
ls
,
a
n
d a C
hi
-
S
qu
a
r
e
t
e
st
(
X
²)
w
a
s us
ed
for
a
n
a
lysis
.
Te
st
3
T
h
e
stu
d
y involv
ed
o
b
s
e
rving
b
oth qu
a
ntit
a
tiv
e a
n
d
qu
a
lit
a
tiv
e
c
h
a
r
ac
t
e
risti
c
s of p
ea
nut l
a
n
d
.
I
n
d
ivi
d
u
a
ls w
e
r
e
r
a
n
d
omly s
e
l
ec
t
ed
from
th
e a
v
a
il
ab
l
e
p
ea
nut l
a
n
d
popul
a
tion
a
n
d
w
e
igh
ed
.
T
his pro
ce
ss w
a
s
r
e
p
ea
t
ed
100
tim
e
s
.
Ob
s
e
rv
a
tions in
c
lu
ded c
olor
a
n
d
w
e
ight
,
a
n
d
th
e
r
e
sults w
e
r
e
pr
e
s
e
nt
ed
in
a
gr
a
ph
.
IV
.
RESULTS AND DISCUSSION
A
.
Re
sults
1
.
E
xp
e
rim
e
nt
1
T
h
e a
ll
e
l
e
fr
e
qu
e
n
c
i
e
s w
e
r
e ca
l
c
ul
a
t
ed a
s follows
:
th
e
fr
e
qu
e
n
c
y of
a
ll
e
l
e
q w
a
s
de
t
e
rmin
ed a
n
d
th
e
fr
e
qu
e
n
c
y of
a
ll
e
l
e
p w
a
s th
e
n
\(
p
=
1
-
0
.
43
=
0
.
57
\).
T
h
e
g
e
notyp
e
fr
e
qu
e
n
c
i
e
s w
e
r
e c
omput
ed a
s
:
GG
=
\( (
0
.
57
)^
2
\
tim
e
s
100
\
%
=
32
.
49
\
%
\),
G
g
= \(
2
\
tim
e
s
(
0
.
57
\
tim
e
s
0
.
43
) \
tim
e
s
100
\
%
=
49
.
02
\
%
\),
a
n
d
gg
= \( (
0
.
43
)^
2
\
tim
e
s
100
\
%
=
18
.
49
\
%
\).
T
h
e
r
a
tio of g
e
notyp
e
s
GG
:
G
g
:
gg w
a
s
32
.
49
:
49
.
02
:
18
.
49
,
simplifying to
2
:
3
:
1
.
T
h
e C
hi
-
S
qu
a
r
e
t
e
st
ca
l
c
ul
a
tions show
ed
o
b
s
e
rv
ed
v
a
lu
e
s
(
O
)
of
33
,
129
,
a
n
d
38
for
GG
,
G
g
,
a
n
d
gg
,
r
e
sp
ec
tiv
e
ly
,
with
e
xp
ec
t
ed
v
a
lu
e
s
(
E
)
of
50
for
GG
,
100
for
G
g
,
a
n
d
50
for gg
.
T
h
e C
hi
-
S
qu
a
r
e
v
a
lu
e
s w
e
r
e ca
l
c
ul
a
t
ed a
s
5
.
78
for
GG
,
8
.
41
for
G
g
,
a
n
d
2
.
88
for gg
,
tot
a
ling
17
.
07
.
W
ith
a c
riti
ca
l v
a
lu
e
of
5
.
99
,
th
e C
hi
-
S
qu
a
r
e c
ount of
17
.
07
in
d
i
ca
t
e
s th
a
t th
e
o
b
s
e
rv
ed
r
e
sults
a
r
e
not signifi
ca
nt
,
m
ea
ning th
e
y
d
o not fit th
e e
xp
ec
t
ed
v
a
lu
e
s
.
2
.
E
xp
e
rim
e
nt
2
I
n
a
popul
a
tion wh
e
r
e
th
e
g
e
notyp
e
fr
e
qu
e
n
c
i
e
s
a
r
e de
not
ed a
s
HH
=
28
,
HK
=
46
,
a
n
d
sis
=
26
,
th
e a
ll
e
l
e
fr
e
qu
e
n
c
y
ca
l
c
ul
a
tion
be
gins
b
y
de
t
e
rmining th
e a
ll
e
l
e
fr
e
qu
e
n
c
y for
a
ll
e
l
e
q
.
B
y using th
e e
qu
a
tion q
²
=
0
.
26
,
th
e
v
a
lu
e
of q is foun
d
to
be
√
0
.
26
,
whi
c
h
e
qu
a
ls
a
pproxim
a
t
e
ly
0
.
509
.
C
ons
e
qu
e
ntly
,
a
ll
e
l
e
p is
ca
l
c
ul
a
t
ed a
s
1
–
0
.
509
,
r
e
sulting in
0
.
491
.
T
h
e
g
e
notyp
e
fr
e
qu
e
n
c
i
e
s
a
r
e
th
e
n
ca
l
c
ul
a
t
ed a
s
follows
:
HH
=
p
² = (
0
.
491
)² ×
100
%
=
24
.
1
%
,
HK
=
2
pq
=
2
×
0
.
491
×
0
.
509
×
100
%
=
50
%
,
a
n
d
sis
=
q
² = (
0
.
509
)² ×
100
%
=
25
.
9
%
.
T
h
e
r
e
for
e
,
th
e
g
e
notyp
e
r
a
tio
HH
:
HK
:
sis is
a
pproxim
a
t
e
ly
24
:
50
:
26
,
simplifying to roughly
1
:
2
:
1
.
A c
hi
-
squ
a
r
e
t
e
st
c
omp
a
ring o
b
s
e
rv
ed
a
n
d e
xp
ec
t
ed
v
a
lu
e
s shows th
a
t th
e ca
l
c
ul
a
t
ed c
hi
-
squ
a
r
e
v
a
lu
e
(
0
.
72
)
is l
e
ss th
a
n th
e c
riti
ca
l v
a
lu
e
(
5
.
99
),
in
d
i
ca
ting th
a
t th
e
o
b
s
e
rv
ed
fr
e
qu
e
n
c
i
e
s
a
r
e c
onsist
e
nt with
Me
n
de
li
a
n inh
e
rit
a
n
ce
p
a
tt
e
rns
.
B
.
D
is
c
ussion
T
h
e
out
c
om
e
s of r
a
n
d
om m
a
ting
d
o not
a
lt
e
r th
e
c
h
a
r
ac
t
e
risti
c
s of
a
sp
ec
ifi
c
popul
a
tion
.
P
opul
a
tion
c
ounts
ba
s
ed
on
r
a
n
d
om s
a
mpling
ca
n
be de
t
e
rmin
ed
using th
e Ha
r
d
y
-
We
in
be
rg
prin
c
ipl
e
,
whi
c
h in
d
i
ca
t
e
s th
a
t g
e
n
e
fr
e
qu
e
n
c
i
e
s in
a
popul
a
tion
ca
n
st
a
y
c
onst
a
nt
a
n
d
m
a
int
a
in
e
quili
b
rium
ac
ross g
e
n
e
r
a
tions
.
T
his
prin
c
ipl
e
impli
e
s th
a
t in
a ba
l
a
n
ced
popul
a
tion
,
g
e
n
e a
n
d
g
e
notyp
e
fr
e
qu
e
n
c
i
e
s r
e
m
a
in un
c
h
a
ng
ed
from on
e
g
e
n
e
r
a
tion to th
e
n
e
xt
.
T
his st
ab
ility is typi
ca
lly o
b
s
e
rv
ed
in l
a
rg
e
popul
a
tions wh
e
r
e
m
a
ting o
cc
urs r
a
n
d
omly
a
n
d
no
e
xt
e
rn
a
l f
ac
tors influ
e
n
ce
g
e
n
e
fr
e
qu
e
n
c
i
e
s
.
F
or g
e
n
e
fr
e
qu
e
n
c
y st
ab
ility
,
ce
rt
a
in
c
on
d
itions must
be
m
e
t
:
r
a
n
d
om m
a
ting
,
no n
a
tur
a
l s
e
l
ec
tion
,
a
l
a
rg
e
popul
a
tion
siz
e
,
no mut
a
tions
,
a
n
d
no migr
a
tion
.
T
h
e Ha
r
d
y
-
We
in
be
rg l
a
w
ca
n
be
summ
a
riz
ed
with th
e
following formul
a
:
if th
e
fr
e
qu
e
n
c
y of
a
ll
e
l
e A
is r
e
pr
e
s
e
nt
ed b
y p
a
n
d a
ll
e
l
e a b
y q
,
th
e
n th
e
fr
e
qu
e
n
c
i
e
s
of
d
iff
e
r
e
nt g
e
notyp
e
s from
a
h
e
t
e
rozygous
Aa
×
Aa c
ross
a
r
e
:
homozygous
d
omin
a
nt
(
AA
) =
p
²,
h
e
t
e
rozygous
(
Aa
) =
2
pq
,
a
n
d
homozygous r
ece
ssiv
e
(
aa
) =
q
².
C
ons
e
qu
e
ntly
,
th
e e
qu
a
tion p
² (
AA
)
+
2
pq
(
Aa
) +
q
² (
aa
) =
1
hol
d
s tru
e
,
with p
+
q
=
1
,
thus p
=
1
–
q
.
P
opul
a
tion g
e
n
e
ti
c
s in
c
lu
de
s s
e
v
e
r
a
l k
e
y
c
on
ce
pts su
c
h
a
s
a
ll
e
l
e
fr
e
qu
e
n
c
y
,
g
e
notyp
e
fr
e
qu
e
n
c
y
,
a
n
d b
oth qu
a
lit
a
tiv
e a
n
d
qu
a
ntit
a
tiv
e
tr
a
its
.
A
ll
e
l
e
s
a
r
e
v
a
ri
a
tions of g
e
n
e
s foun
d a
t th
e
s
a
m
e
position on
a c
hromosom
e b
ut p
e
rform opposit
e
fun
c
tions
.
F
or
inst
a
n
ce
,
th
e T a
ll
e
l
e a
n
d
th
e
t
a
ll
e
l
e b
oth influ
e
n
ce
pl
a
nt h
e
ight
,
with th
e T a
ll
e
l
e
promoting t
a
lln
e
ss
a
n
d
th
e
t
a
ll
e
l
e
l
ead
ing to
short
e
r pl
a
nts
.
A
pl
a
nt with th
e T
t g
e
notyp
e
will
be
t
a
ll
beca
us
e
th
e
T a
ll
e
l
e
is
d
omin
a
nt ov
e
r th
e
t
a
ll
e
l
e
.
A
ll
e
l
e
fr
e
qu
e
n
c
y r
e
f
e
rs to th
e
proportion of
a
p
a
rti
c
ul
a
r
a
ll
e
l
e
within
a
popul
a
tion
,
whi
c
h
ca
n
be
de
riv
ed
from th
e
fr
e
qu
e
n
c
y of
a
known g
e
notyp
e
.
I
n
a
n
e
quili
b
rium
popul
a
tion
,
knowing th
e
fr
e
qu
e
n
c
y of
a
homozygous g
e
notyp
e
a
llows for th
e ca
l
c
ul
a
tion of
a
ll
e
l
e
fr
e
qu
e
n
c
i
e
s
.
T
h
e
g
e
notyp
e
of
a
n
in
d
ivi
d
u
a
l r
e
pr
e
s
e
nts th
e
sp
ec
ifi
c
g
e
n
e a
rr
a
ng
e
m
e
nt
,
whil
e
th
e
ph
e
notyp
e
is th
e
o
b
s
e
rv
ab
l
e e
xpr
e
ssion of th
a
t g
e
notyp
e
.
F
or
e
x
a
mpl
e
,
TT a
n
d
tt
a
r
e
homozygous g
e
notyp
e
s
,
with
TT be
ing
homozygous
d
omin
a
nt
a
n
d
tt homozygous r
ece
ssiv
e
,
whil
e T
t is
a
h
e
t
e
rozygous
d
omin
a
nt g
e
notyp
e
,
wh
e
r
e
th
e d
omin
a
nt
T a
ll
e
l
e
m
a
sks th
e
r
ece
ssiv
e
t
a
ll
e
l
e
.
Ge
notyp
e
fr
e
qu
e
n
c
y is th
e c
ount of
eac
h g
e
notyp
e
within
a
popul
a
tion
.
Ge
n
e
s or ph
e
notyp
e
s
e
xhi
b
it
d
istin
c
t
c
h
a
r
ac
t
e
risti
c
s
,
whi
c
h
ca
n
be ca
t
e
goriz
ed
into qu
a
lit
a
tiv
e a
n
d
qu
a
ntit
a
tiv
e
tr
a
its
.
Q
u
a
lit
a
tiv
e
tr
a
its r
e
f
e
r to
c
h
a
r
ac
t
e
risti
c
s th
a
t
ca
nnot
be
m
ea
sur
ed
a
n
d
inst
ead
r
e
fl
ec
t th
e
qu
a
lity of th
e
o
b
j
ec
t
,
whil
e
qu
a
ntit
a
tiv
e
tr
a
its
a
r
e
m
ea
sur
ab
l
e a
ttri
b
ut
e
s th
a
t in
d
i
ca
t
e
th
e a
mount of th
e
o
b
j
ec
t
,
su
c
h
a
s
b
o
d
y w
e
ight or h
e
ight
.
P
r
ac
ti
ca
l work h
a
s
bee
n
c
on
d
u
c
t
ed
to t
e
st th
e Ha
r
d
y
-
We
in
be
rg prin
c
ipl
e
,
ca
l
c
ul
a
t
e a
ll
e
l
e
fr
e
qu
e
n
c
i
e
s
,
a
n
d de
t
e
rmin
e b
oth qu
a
ntit
a
tiv
e a
n
d
qu
a
lit
a
tiv
e
tr
a
its
within popul
a
tions
.
T
his involv
ed
thr
ee e
xp
e
rim
e
nts
:
th
e
first us
ed
200
b
uttons of thr
ee c
olors
(
r
ed
,
whit
e
,
pink
)
to
de
t
e
rmin
e
g
e
notyp
e a
n
d a
ll
e
l
e
fr
e
qu
e
n
c
i
e
s for
G a
n
d
g
a
ll
e
l
e
s
,
whi
c
h w
e
r
e
th
e
n
a
n
a
lyz
ed
using
a C
hi
-
squ
a
r
e
t
e
st
;
th
e
r
e
sults show
ed
th
a
t th
e
e
xp
e
rim
e
nt
a
l
da
t
a
w
a
s not signifi
ca
nt
a
s th
e ca
l
c
ul
a
t
ed C
hi
-
squ
a
r
e
v
a
lu
e e
x
ceeded
th
e
t
ab
l
e
v
a
lu
e
.
T
h
e
s
ec
on
d
t
e
st us
ed a
simil
a
r
m
e
tho
d b
ut with two
c
olors
a
n
d
100
b
uttons
,
r
e
v
ea
ling signifi
ca
nt
r
e
sults sin
ce
th
e ca
l
c
ul
a
t
ed C
hi
-
squ
a
r
e
v
a
lu
e
w
a
s l
e
ss th
a
n th
e
t
ab
l
e
v
a
lu
e
.
T
h
e
thir
d
t
e
st involv
e
s using p
ea
nuts
a
s o
b
j
ec
ts to o
b
s
e
rv
e
th
e
ir qu
a
lit
a
tiv
e a
n
d
qu
a
ntit
a
tiv
e
prop
e
rti
e
s
.
Pea
nuts
a
r
e
pr
e
p
a
r
ed
,
a
n
d
th
e
n
100
nuts
a
r
e
s
e
l
ec
t
ed
.
Eac
h nut is w
e
igh
ed
in
d
ivi
d
u
a
lly
be
for
e
moving on to th
e
n
e
xt on
e
.
A
ft
e
r
a
ll
100
nuts
a
r
e
w
e
igh
ed
,
th
e
y
a
r
e ca
t
e
goriz
ed b
y w
e
ight
,
a
n
d a
gr
a
ph is
c
r
ea
t
ed
.
T
h
e
r
e
sulting
c
h
a
rt shows th
a
t th
e
high
e
st w
e
ight
a
mong th
e
p
ea
nuts is
0
.
5
gr
a
ms
,
with
23
p
ea
nuts f
a
lling into this
ca
t
e
gory
,
whil
e
th
e
sm
a
ll
e
st w
e
ight is
0
.
8
gr
a
ms
,
r
e
pr
e
s
e
nt
ed b
y
3
p
ea
nuts
.
T
his
pr
ac
ti
ca
l
e
x
e
r
c
is
e a
ims to v
a
li
da
t
e
th
e a
ssumptions of th
e Ha
r
d
y
-
We
in
be
rg
La
w
.
H
ow
e
v
e
r
,
a
pplying th
e Ha
r
d
y
-
We
in
be
rg
La
w to
popul
a
tions is
c
h
a
ll
e
nging
beca
us
e
not
a
ll popul
a
tions m
ee
t th
e
c
on
d
itions r
e
quir
ed b
y th
e
l
a
w
.
Fac
tors su
c
h
a
s n
a
tur
a
l
d
is
a
st
e
rs
,
mut
a
tions
,
a
n
d
pr
ede
t
e
rmin
ed
m
a
rri
a
g
e
s
ca
n
a
ff
ec
t th
e a
ppli
cab
ility
of th
e Ha
r
d
y
-
We
in
be
rg
La
w
.
V
.
CONCLUSION AND SUGGESTION
A
.
C
on
c
lusion
T
h
e
pr
ac
ti
ca
l
e
v
e
nt
VI
in popul
a
tion g
e
n
e
ti
c
s l
ead
s to
c
on
c
lusions involving
c
on
ce
pts su
c
h
a
s
Ha
r
d
y
-
We
in
be
rg
e
quili
b
rium
,
g
e
n
e
fr
e
qu
e
n
c
y
,
a
ll
e
l
e
fr
e
qu
e
n
c
y
,
qu
a
lit
a
tiv
e
tr
a
its
,
a
n
d
qu
a
ntit
a
tiv
e
tr
a
its
.
