Experimental studies on the duration of life. IX. New life tables for Drosophila. X. The duration of life of Drosophila melanogaster in the complete absence of food


Pearl, R.; Parker, S.L.

American Naturalist, 58: 71-80, 193-218

1924


In the first of these Studies we presented life tables for wild type and quintuple flies. These tables were based upon the collected data then available from the control portions of experiments in which these two sorts had been used. In the period which has elapsed since the publication of these pioneer life tables for Drosophila our work has been greatly extended, and in a number of particulars refined. Especially we have come to use in all the experimental work stocks which are more homogeneous genetically. Thus, for a long-lived stock we now use, instead of a random sample of a mass culture of wild type flies as was formerly the case, a random sample of our line 107, which is an inbred, long-lived "pure" strain. The origin of this line we have described in the second of these Studies. By "pure" we mean, of course, only that it is a highly inbred and homozygous strain. Similarly, we have come to use for a short-lived stock in experimental work pure vestigial strains, the study of Gonzalez having shown that it is this mutant gene alone which is chiefly responsible for (or invariably associated with) the observed brachybioty of quintuple flies.

EXPERIMENTAL
STUDIES
ON
THE
DURATION
OF
LIFE.
IX.
NEW
LIFE
TABLES
FOR
DROSOPHILA
1
RAYMOND
PEARL
AND
SYLVIA
L.
PARKER
IN
the
fi
rst
of
these
Studies
(27)
we
presented
life
tables
for
wild
type
and
quintuple
fl
ies.
These
tables
were
based
upon
the
collected
data
then
available
from
the
control
portions
of
experiments
in
which
these
two
sorts
had
been
used.
In
the
period
which
has
elapsed
since
the
publication
of
these
pioneer
life
tables
for
Dro-
sophila
our
work
has
been
greatly
extended,
and
in
a
number
of
particulars
refined.
Especially
we
have
come
to
use
in
all
the
experimental
work
stocks
which
are
more
homogeneous
genetically.
Thus,
for
a
long-lived
stock
we
now
use,
instead
of
a
random
sample
of
a
mass
cul-
ture
of
wild
type
fl
ies
as
was
formerly
the
case,
a
random
sample
of
our
line
107,
which
is
an
inbred,
long-lived
"pure"
strain.
The
origin
of
this
line
we
have
described
in
the
second
of
these
Studies
(32).
By
"pure"
we
mean,
of
course,
only
that
it
is
a
highly
inbred
and
homo-
zygous
strain.
Similarly,
we
have
come
to
use
for
a
short-lived
stock
in
experimental
work
pure
vestigial
strains,
the
study
of
Gonzalez
(62)
having
shown
that
it
is
this
mutant
gene
alone
which
is
chiefly
responsible
for
(or
invariably
associated
with)
the
observed
brachybioty
of
quintuple
fl
ies.
It
seems
desirable
now
to
present
new
life
tables
for
these
genetically
more
homogeneous
groups,
in
order
that
they
may
be
at
hand
for
reference
in
connection
with
further
studies
shortly
to
be
published.
Furthermore,
we
have
not
hitherto
published
any
Drosophila
life
tables
with
age
reckoned
on
a
"centile
of
the
equivalent
life
1
Papers
from
the
Department
of
Biometry
and
Vital
Statistics,
School
of
Hygiene
and
Public
Health,
Johns
Hopkins
University.
No.
95.
71
72
THE
AMERICAN
NATURALIST
[VoL.
LVIII
span"
base,
except
in
the
case
of
wild
type
males
from
our
original
life tables.
2
The
actual
observations
on
which
the
new
life
tables
of
this
paper
are
based
are
presented
in
Table
I.
It
will
be
seen
that
they
include
a
total
of
2,822
wild
type
flies
of
line
107,
and
980
pure
vestigial
fl
ies.
The
observations
are
recorded
on
a
6
day
base
unit in
the
case
of
wild
type
flies,
and
a
3
day
base
unit
in
the
case
of
vestigials.
We
have
found
these
units
sufficiently
fi
ne
for
purposes
of
tabulation
and
derivative
computation.
The
actual
observations
were
made
daily;
the
data
as
presented
in
Table
I
have
been
subsequently
grouped.
TABLE
I
OBSERVED
DEATHS
(d'
)
)
AND
SURVIVORSHIP
(l'
w
)
IN
WILD
TYPE
LINE
107,
AND
PURE
VESTIGIAL
FLIES
Age
Wild
type,
Line
107
Age
Pure
Vestigial
in
Males
Females
in
Males
Females
days
(P
s
l'
x
d'
x
1',
days
d'
x
l'
x
d'x
l's
1
18
1000
23
1000
1 1
1000
11
1000
7
12
9S7
16
984
4
48
998
43
979
13
26
979
34
972
7
81
893
43
897
19
85
960
86
941
10
86
715
57
815
25
99
900
86
888
13
81
526
55
706
31
132
829
96
827
16
51
349
63
601
37
187
736
159
759
19
33
237
47
481
43
173
603
152
647
22
35
164
51
391
49
206
480
162
539
25
22
88
27
294
55
285
333
275
425
28
5
39
35
242
61
82
131
156
230
31
4
29
30
176
67
62
72
99
120
34
3
20
17
118
73
36
28
64
50
37
3
13
14
86
79
3
3
6
5
40
2
7
14
59
85
1
1 1 1
43
1
2
4
32
46
6
25
49
4
13
52
2
6
55
1
2
Totals
1407
1415
Totals
456
524
In
the
graduation
of
the
material
the
same
plan
was
used
as
in
the
construction
of
the
earlier
life
tables
(loc.
cit.).
The
equations
in
the
present
case
are
as
follows:
Wild
Type,
Liue
107
—Males;
log
l
x
=-_
e
022
"°"x
(2.9999414
—.0674377x
+.000677752x'
—.00000369321x
3
).
Wild
Type,
Line
107
—Females;
log
l
a
,=
e
""""x
(3.0000256
—.0761521x
+.0000854457x
2
—.00000449705x
2
).
Vestigial
—Males;
log
1,=_-
e
0
"
2
'
412.
(2.9961959
—.1959626x
+.00456415x'
—.0000377354x
3
).
Vestigial
—Females;
log
ly=
e•
033
6
7
x(3.00192S3
—.1158025x
+.00165311x
2
—.00000542516e).
2
Cf.
Pearl
(61),
and
Pearl
and
Doering
(63).
No.
654]
STUDIES
ON
THE
DURATION
OF
LIFE
73
The
observations
and
fi
tted
lines
are
shown
in
Fig.
1.
As
a
whole
the
fi
ts
are
reasonable,
if
one
has
as
an
ob-
jective
simply
the
general
sweep
of
the
observations
and
is
not
concerned,
as
the
actuary
is,
to
represent
every
/000
Line
/07
OF
L/ile
/07
/00
Ves
PP
Vest/
ii7/j'c3'
/0
0
7
/3
/9
eS
3/
37
43
49
SS
6/
67
73
7.9
85
9/
/9ge
days
FIGURE
1
Diagram
showing
the
observed
and
graduated
l
x
points
for
(a)
line
107
wild
type,
and
(b)
vestigial
flies.
The
small
circles
are
the
observations
from
Table
I,
and
the
smooth
lines
the
fi
tted
curves
from
the
equations.
fl
uctuation
in
the
curve.
From
this
point
of
view
the
line
107
curves
are
entirely
satisfactory.
The
vestigial
curves
are
close
fi
ts
up
to
31
days
in
the
females
and
49
days
in the
males.
The
upper
tails
of
both
vestigial
curves
are
bad
fi
ts,
underestimating
the
observations
in
the
females
and
overestimating
in
the
males.
To
take
74
THE
AMERICAN
NATURALIST
[VoL.
LVIII
care
of
these
end
observations
would
require
additional
constants
in
the
equations.
But
for
all
purposes
to
which
fl
y
life
tables
are
ever
likely
to
be
put
the
present
gradua-
tions
will
probably
be
adequate.
The
complete
life
tables
are
presented
in
Tables
II,
III,
IV
and
V.
From
these
tables
the
following
points
are
to
be
noted:
(1)
As
compared
with
the
genetically
more
heterogen-
eous
earlier
life
tables,
the
purer
strains
of
the
present
tables
exhibit
(a)
a
greater
expectation
of
life
at
emer-
gence
in
both
sexes
of
line
107,
but
a
shorter
total
life
span
than
in
the
general
wild
type
population;
(b)
sub-
stantially
the
same
expectation
of
life
at
emergence
and
total
life
span,
in
male
vestigials
as
in
male
quintuples;
and
(c)
a
distinctly
longer
expectation
of
life
at
emer-
gence
and
longer
total
life
span,
in
female
vestigials
than
in
female
quintuples.
(2)
These
tables
show
the
same
relation
between
sexes
in
respect
of
mortality
that
human
life
tables
do.
The
females
have
lower
cb,
values
(deathrates)
than
do
the
males,
throughout
life.
The
sex
differences
in
mor-
tality
are
much
more
pronounced
in
the
vestigials
than
in
the
wild
type
line
107.
(3)
The
form
of
the
vestigial
life
curve
is
distinctly
different
from
that
of
the
wild
type
fl
ies.
The
vestigial
mortality
is
characterized
by
a
plateau
of
nearly
con-
stant
q
x
values
in
middle
life
(in
the
males
forming
even
a
slight
dip
convex
to
the
base).
This
phenomenon
gives
the
vestigial
l
curves
their
peculiarly
fl
attened
appear-
ance
in
the
middle
portion
of
their
course.
It
is
desirable
to
compare
these
new
Drosophila
life
tables
with
each
other
and
with
the
human
tables
by
put-
ting
the
ages
upon
a
relative
base,
using
as
a
unit
a
centile
(a
hundredth
part)
of
the
equivalent
life
span,
in
the
manner
described
by
Pearl
(61).
The
data
of
Tables
II
to
V
are
transferred
to
a
centile
age
basis
in
Table
VI.
In
Fig.
2
these
centile
distributions
for
Drosophila
are
compared
with
similar
data
from
(a)
human
life
tables
(Glover
(51)),
and
(b)
the
saturniid
moth
Telea
polyphe-
No.
654]
STUDIES
ON
THE
DURATION
OF
LIFE
75
TABLE
II
LIFE
TABLE
FOR
DROSOPHILA
-WILD
TYPE.
Age
in
Age
in
days
Zx
Qx
days
LINE
107
-MALES
ex
1
1000
0.2
45,8
46
551
43.5
12.3
2
1000
0.6
44.8
47
527
46.6
11.8
3
999
1.0
43.8
48
502
49.8
11.3
4
998
1.3
42.9
49
477
53.2
10.9
5
997
1.7
41.9
50
452
56.9
10.4
6
995
2.0
41.0
51
426
60.8
10.0
7
993
A.4
40.1
52
400
65.0
9.6
8
991
2.8
39.2
53
374
69.5
9.2
9
988
3.2
38.3
54
348
74.2
8.8
10
985
3.5
37.4
55
322
79.2
8.4
11
981
3.9
36.5
56
297
84.5
8.0
12
978
4.3
35.7
57
272
90.2
7.7
13
973
4.7
34.8
58
247
96.2
7.4
14
969
5.1
34.0
59
223
102.5
7.0
15
964
5.5
33.2
60
200
109.2
6.7
16
958
6.0
32.3
61
179
116.3
6.4
17
953
6,+.4
31.5
62
158
123.8
6.1
18
947
6.9
30.7
63
138
131.7
5.9
19
940
7.4
29.9
64
120
139.9
5.6
20
933
7.9
29.2
65
103
148.8
5.3
21
926
8.5
28.4
66
88
157.9
5.1
22
918
9.0
27.6
67
74
167.6
4.9
23
910
9.6
26.9
68
62
177.7
4.7
24
901
10.3
26.1
69
51
188.3
4.4
25
892
10.9
25.4
70
41
199.4
4.2
26
882
11.7
24.6
71
33
211.0
4.1
27
872
12.4
23.9
72
26
223.1
3.9
28
861
13.3
23.2
73
20
235.8
3.7
29
849
141.1
22.5
74
15
248.9
3.5
30
837
15.1
21.8
75
12
262.6
3.4
31
825
16.1
21.1
76
9
276.8
3.2
32
811
17.2
20.5
77
6
291.5
3.1
33
798
18.3
19.8
78
4
306.7
2.9
34
783
19.5
19.1
79
3
322.5
2.8
35
768
20.8
18.5
80
2
338.7
2.6
36
752
22,,3
17.9
81
1
355.5
2.4
37
735
23.8
17.3
82
1
372.7
2.2
38
717
25.4
16.7
39
699
27.2
16.1
40
680
29.1
15,.5
41
660
31.1
14.9
42
640
33.3
14.4
43
619
35.5
13.8
44
597
38.0
13.3
45
574
40.7
12.8
76
THE
AMERICAN
NATURALIST
[VoLliVIII
TABLE
III
LIFE
TABLE
FOR
DROSOPHILA
-WILD
TYPE.
LINE
107
-FEMALES
Age
in
days
t
x
qx
ex
Age
in
days
,
6x
qx
ex
1
1000
0.6
48.0
46
619
30.7
14.2
2
999
1.1
47.1
47
600
33.0
13.6
3
998
1.5
46.1
48
580
35.6
13.0
4
997
2.0
45.2
49
560
38.4
12.5
5
995
2.5
44.3
50
538
41.4
1.1.9
6
992
2.9
43.4
51
516
44.7
11.4
7
990
3.3
42.5
52
493
48.3
10.9
8
986
3.7
41.6
53
469
52.3
10.4
9
983
4.2
40.8
54
444
56.5
9.9
10
978
4.5
39.9
55
419
61.1
9.5
11
974
4.9
39.1
56
394
66.1
9.0
12
969
5.3
38.3
57
368
71.4
8.6
13
964
5.7
37.5
58
341
77.3
8.2
14
959
6.0
36.7
59
315
83.4
7.8
15
953
6.4
35.9
60
289
90.2
7.4
16
947
6.7
35.2
61
263
97.3
7.0
17
940
7.1
34.4
62
237
105.0
6.6
18
934
7.4
33.6
63
212
113.2
6.3
19
927
7.7
32.9
64
188
122.0
6.0
20
920
8.0
32.1
65
165
131.3
5.7
21
912
8.4
31.4
66
144
141.3
5.4
22
905
8.7
30.6
67
123
152.0
5.1
23
897
9.1
29.9
68
105
163.2
4.8
24
889
9.4
29.1
69
87
175.1
4.6
25
880
9.8
28.4
70
72
187.7
4.4
26
872
10.2
27.7
71
59
201.0
4.1
27
863
10.6
27.0
72
47
215.0
3.9
28
854
11.0
26.2
73
37
229.7
3.7
29
844
11.5
25.5
74
28
245.2
3.5
30
835
12.0
24.8
75
21
261.3
3.3
31
825
12.5
24.1
76
16
278.3
3.2
32
814
13.1
23.4
77
11
295.9
3.0
33
804
13.7
22.7
78
S
314.4
2.8
34
793
14.4
22.0
79
6
333.4
2.7
35
781
15.2
21.3
80
4
353.2
2.5
36
769
16.0
20.6
81
2
373.6
2.4
37
757
17.0
19.9
82
1
394.7
2.2
38
744
18.0
19.3
83
1
416.6
1.9
39
731
19.1
18.6
40
717
20.3
17.9
41
702
21.7
17.3
42
687
23.1
16.6
43
671
24.8
16.0
44
655
26.6
15.4
45
637
28.5
14.8
No.
654]
STUDIES
ON
THE
DURATION
OF
LIFE
77
TABLE
IV
LIFE
TABLE
FOR
DROSOPHILA
-VESTIGIAL
--MALES
Age
in
days
i
fc
1000
0.0
ex
14.1
Age
in
d
ays
26
1
x
72
qz
162.7
ex
1
5.8
2
1000
9.0
13.1
27
61
162.5
5.7
3
991
18.1
12.2
28
51
162.0
5.6
4
973
27.4
11.7
29
43
161.1
5.5
5
946
36.7
10.7
30
36
160.8
5.4
6
912
45.8
10.1
31
30
160.7
5.3
7
870
55.4
9.6
32
25
161.5
5.1
8
821
64.7
9.1
33
21
163.6
4.9
9
768
73.8
8.6
34
18
167.7
4.6
10
712
82.8
8.2
35
15
174.5
4.4
11
653
91.5
7.9
36
12
184.8
4.1
12
593
100.0
7.6
37
10
198.5
3.8
13
534
108.1
7.3
38
8
219.6
3.4
14
476
115.9
7.0
39
6
246.0
3.1
15
421
123.1
6.8
40
5
279.6
2.8
16
369
129.9
6.7
41
3
320.9
2.5
17
32]
136.2
6.5
42
2
370.4
2.3
18
277
141.8
6.4
43
1
427.7
2.0
19
238
146.8
6.3
44
1
491.9
1.7
20
203
151.2
6.2
21
172
154.8
6.1
22
146
157.8
6.0
23
123
160.0
6.0
24
103
161.5
5.9
25
86
162.4
5.9
mus,
on
the
basis
of
our
calculations
of
an
ungraduated
life
table
from
data
as
to
the
duration
of
life
of
this
form
in
the
adult
stage
given.
by
the
Bans
(64).
From
these
data
it
appears
that
:
(1)
The
distribution
of
mortality
in
the
different
parts
of
the
biologically
equivalent
life
span
is
substantially
identical
quantitatively
in
an
inbred
strain
of
Drosophila
(line
107)
an.d
in
human
beings
of
the
present
time.
That
is
to
say,
if
we
take
as
our
base
line
biological
age,
mor-
tality
is
distributed
along
that
base
line
in
quantitatively
the
same
manner
in
man
and
a
particular
inbred
strain
of
wild.
type
Drosophila.
This
does
not,
of
course,
in
the
least
warrant
the
assertion
that
the
forces
determining
rates
of
mortality
in
the
two
cases
are
identical.
In
de-
tail
they
obviously
are
not.
So
far
as
is
known,
for
ex-
ample,
the
tubercle
bacillus
is
not
pathogenic
to
Droso-
78
THE
AMERICAN
NATURALIST
[VoL.
LVIII
TABLE
V
Age
in
days
LIFE
TABLE
lro
qz
FOR
DROSOPHILA
-VESTIGIAL
---FEMALES
Age
in
ez
days
l
x
qx
ez
1
1000
7.7
19.8
36
88
124.9
7.1
2
992
11.0
19.0
37
77
127.6
6.9
3
981
14.3
18.2
38
67
130.3
6.8
4
967
17.7
17.4
39
58
133.1
6.7
5
950
21.2
16.7
40
50
135.8
6.5
6
930
24.7
16.1
41
44
138.6
6.4
7
907
28.2
15.5
42
38
141.4
6.3
8
882
31.7
14.9
43
32
144.3
6.1
9
854
35.3
14.3
44
28
147.3
6.0
10
824
38.8
13.3
45
24
150.4
5.9
11
792
42.4
13.3
46
20
153.6
5.7
12
758
46.0
12.9
47
17
157.0
5.6
13
723
49.6
12.5
48
14
160.7
5.4
14
687
53.2
12.1
49
12
164.7
5.3
15
651
56.8
11.7
50
10
169.0
5.1
16
614
60.4
11.3
51
8
173.6
5.0
17
577
64.0
11.0
52
7
178.7
4.8
18
540
67.6
10.7
53
6
184.3
4.7
19
503
71.1
10.4
54
5
190.5
4.5
20
467
74.7
10.1
55
4
197.3
4.3
21
432
78.1
9.8
56
3
2.04.9
4.1
22
399
81.6
9.6
57
2
213.3
3.9
23
366
85.0
9.3
58
2
222.6
3.7
24
335
88.4
9.1
59
1
232.9
3.5
25
305
91.7
3.9
60
1
244.3
3.2
26
277
95.0
8.7
61
1
256.8
2.9
27
251
98.2
8.5
28
226
101.4
8.3
29
203
104.5
8.1
30
182
107.5
8.0
31
163
110.5
7.8
32
145
113.5
7.6
33
123
116.4
7.5
34
113
120.1
7.3
35
100
122.2
7.2
phila.
The
facts
only
mean
that
different
in
their
quali-
tative
details
as
are
the
lethal
forces
which
attack
the
two
organisms,
man
and
a
certain
kind
of
Drosophila,
they
are
alike
in
their
quantitative
relations
to
biological
age.
(2)
In
another
kind
of
Drosophila,
differing
so
far
as
is
known
from
the
kind
mentioned
in
the
previous
para-
graph
only
in
respect
of
one
single
second
chromosome
gene
(and
its
somatic
expression),
the
distribution
of
mortality
in
respect
to
biological
age
is
widely
different
No.
654]
STUDIES
ON
THE
DURATION
OF
LIFE
79
TABLE
VI
SURVIVORSHIP
DISTRIBUTIONS
OF
DROSOPHILA
BY
CENTILES
OF
LIFE
SPAN
Centiles
of
Line
107
Equivalent
Life
Span
a
9
Vestigial
a
9
Line
Centiles
of
Equivalent
Life
Span
8
-
107
9
Vestigial
8
9
0
1000 1000
1000 1000
50
654
689
137
168
1
1000 1000 1000
996
51
637
676
127
157
2
999 999
1000
991
52
620
662
11S
146
3
999
99S
998
984
53
602
64S
110
136
4
99S
996
994
976
54
583
634
102
127
5
997
994
989
968
55
564
619
94
118
6
996
992
982
958
56
545
604
87
110
7
994
990
973
947
57
526
588
S1
102
S
992
988
963
935
5S
506
571
75
94
9
990
985
951
922
59
486
554
70
87
10
988
982
938
909
60
466
537
65
80
11
985
979
923
894
61
446
51S
60
74
12
982
975
907
S78
62
426
499 56
68
13
979
971
889
861
63
405
480
52
63
14
976
967
S70
844
64
384
460
48
5S
15
973
963
851
826
65
363
440
44
53
16
969
958
S30
S07
66
342
419
41
49
17
965
953
SOS
788
67
321
398
3S
45
18
961
948
785
768
6S
300
377
35
41
19
957
943
762
74S
69
278
356
32
37
20
952
938
738
727
70
258
334
30
34
21
947
933
713
706
71
240
312
28
31
22
942
927
688
685
72
221
290
26
2S
23
936
921
663 663
73
202
269
24
26
24
930
915
63S
641
74
184
248
23
24
25
924
909
613
619
75
167
227
21
22
26
918
903
587
597
76
150
207
19
20
27
911
896
561
575
77
135
188
18
18
2S
904
889
536
553
78
120
169
17
16
29
897
882
511
530
79
106
151
15
14
30
890
875
486
508
80
94
134
14
13
31
882
S68
462
487
81
82
118
13
12
32
874
861
439
466
82
72
103
12
11
33
S65
854
416
445
83
62
89
11
9.4
34
856 846
393
425
84
53
76
10
S.4
35
847
838
371
405
85
45
64
9.2
7.6
36
837
830
350
386
86
38
54
8.4
6.8
37
827
S22
330
367
87
31
45
7.6
6.0
3S
816
S14
311
348
88
26
37
6.9
5.4
39
805
805
292
330
S9
21
30
6.2
4.8
90
17
24
5.5
4.2
40
794
796
274
312
91
14
19
4.8
3.7
41
782
787
257
295
92
11
15
4.2
3.2
42
769
777
240
278
93
8.3
11
3.7
2.8
43
756
767
225
263
94
6.4
8.3
3.2
2.4
44
743
757
210
248
95
4.8
6.1
2.7
2.1
45
730
747
196
233
96
3.6
4.5
2.3
1.8
46
716 736
182
219
97
2.6
3.2
1.9
1.6
47
701
725
170
206
98
2.0
2.2
1.6
1.4
48
686
713
159
193
99
1.4
1.4
1.3
1.2
49
670
701
148
180
100
1.0 1.0
1.0 1.0
80
THE
AMERICAN
NATURALIST
[VoL.
LVIII
/009
/V
/0
...,
,
......
Human
1
i'
---
Oroso
/
ohdo
Line
/07
ea
...
,,
,-,
--,
a-osoph,A,
1
.
4,e
/07.81
,...
'
A
..,
Huttron
deS
s
\
\
z t
e
-
c
' ' '
s
'N
,..,
s
0
,
"
1\
1
-\
\
\
,
0 1
8
/2
/6
eo
2.9
28
32
36
40
14
48
52
.56
60
64
68
78
76
60
84
88
92
96
/0d
Centi/es
of
Fe.,iva/ent
FIGURE
2
Comparing
the
survivorship
distributions
of
(a)
Drosophila
line
107
males;
(b)
Drosophila
line
107
females;
(c)
Drosophila
vestigial
males;
(d)
Drosophila
females;
(e)
human
males;
(f)
human
females;
(g)
Telea
polyphemas,
both
sexes
together,
over
the
equivalent
life
spans.
quantitatively
from
that
found
either
in
man
or
in
wild
type
Drosophila,
even
in
spite
of
the
fact
that
both
kinds
of
Drosophila
spent
their
entire
lives
in
statistically
iden-
tical
environments,
so
far
at
least
as
concerns
tempera-
ture,
optimum
population
density
and
housing,
food,
sea-
son
and
climate.
This
fact
seems
to
us
quite
as
signifi-
cant
as
the
identity
established
in
the
preceding
para-
graph.
It
shows
that
a
unit
change
in
the
genetic
consti-
tution
of
an
organism
may
not
only
be
associated
with
a
marked
alteration
of
the
absolute
length
of
the
life
span,
but
also
with
a
profound
alteration
of
the
form
of
the
life
curve.
No.
654]
STUDIES
ON
THE
DURATION
OF
LIFE
81
(3)
Wild
type
Drosophila
and
vestigial
are
plainly
approximating
two
quite
distinct
theoretically
possible
forms
of
life
curves.
One
of
these
types,
which
may
be
called
the
rectangular,
would
in
the
limit
show
all
the
individuals
starting
at
birth
together
living
to
the
same
age
and
then
all
dying
together
at
the
same
time.
q,,
would
equal
zero
up
to
this
"day
of
judgment,"
and
then
would
on
that
day
take
the
extreme
value
of
1,000
(on
a
per
-thousand
base).
The
closest
approximation
yet
seen
in
living
nature
to
the
theoretical
limit
is
Proales,
as
set
forth
by
Pearl
and
Doering
(63)
;
the
next
closest
ap-
proximation
yet
described
is
that
of
Drosophila
line
107
and
present
day
human
beings,
as
shown
in
Fig.
2
above.
The
other
theoretical
type
of
life
curve
which
concerns
the
present
discussion
may
be
called
the
diagonal.
This,
in
the
limit,
would
be
a
case
where
the
instantaneous
death
rate
q,
would
be
constant
at
all
ages
from
the
start
at
birth
to
the
demise
of
the
last
survivor.
Plotted
-
on.
arithlog
paper
the
l„
line
would
be
a
straight
diagonal
line.
The
closest
approach
yet
found
in
living
nature
to
this
theoretical
type
of
life
curve
is
that
given
by
vesti-
gial
Drosophila,
as
shown
in
Fig.
2.
All
other
life
curves
yet
known
fall
between
the
rectangular
and
diagonal
types.
There
is
a
third
type
theoretically
possible,
but
not
actually
realized
in
experience
as
yet.
This
is
the
case
in
which
q„,
has
very
large
values
in
early
ages,
and
there-
after
nearly
constant
values
until
the
last
survivor
is
reached.
This
would
mean
an
line
which
dropped
sharply
to
a
low
level
in
the
earliest
ages
and
then
ran.
along
a
nearly
horizontal
course
to
the
end
of
the
life
span
of
the
last
survivor.
This
would
be
the
life
curve
of
a
very
heavy
selective
mortality
of
early
life.
It
is
diffi-
cult
to
see
how
it
could
occur
in
a
population
genetically
homogeneous
in
respect
of
factors
influencing
duration
of
life.
But
it
could
readily
occur
in
a
population
genetic-
ally
mixed
relative
to
these
factors.
6
82
THE
AMERICAN
NATURALIST
[VoL.
LVIII
LITERATURE
CITED
(The
plan
of
numbering
citations
is
explained
in
the
second
of
these
Studies,
AMER.
Nat.,
Vol.
56,
p.
174.)
62.
Gonzalez,
B.
M.
Experimental
Studies
on
the
Duration
of
Life.
VIII.
The
Influence
upon
Duration
of
Life
of
Certain
Mutant
Genes
of
Drosophila
melamogaster.
AMER.
NAT.,
Vol.
57,
pp.
289-328.
1923.
63.
Pearl,
R.,
and
Doering,
C.
R.
A
Comparison
of
the
Mortality
of
Cer-
tain
Lower
Organisms
with
that
of
Man.
Science,
Vol.
57,
pp.
209-
212,
1923.
64.
Rau,
P.,
and
Rau,
N.
Longevity
in
Saturniid
Moths
and
its
Relation
to
the
Function
of
Reproduction.
Trans.
Acad.
Sci.
St.
Louis,
Vol.
23,
pp.
1-78,
pl.
I
—V,
1914.