S OF THE E
AN ANAL
JENOUS F
YTHMS
VITY IN AN INTERTIDAL COLLEMBOLID
IN JUMPING ACTI
POPULATION ON THE CENTRAL CALIFORNIA COAST
Michelle Marie MeSpadde
Hopkins Marine Sta
Stanford Univers
Introduction
Biological clocks have been described in a number of insect
orders (Saunders, 1976) and are generally recognized as prominent
in living systems. The literature on biological clocks is exten-
sive, for the large part treating the phenomenon of circadian
oscillators. Other oscillators,b
such as tidal clocks,
are less well documented, and descriptions of how clocks inter-
act in a single system are even fewer. For example, one study
of the coupling of endogenous rhythms is that work done on the
beach amphipod, Orchestroidea corniculata (McGinnis, 1972, Osbeck,
1970); although much has been found in these studies, extensive
data has been difficult to collect, and generalizations about clock
interactions are difficult to make.
In this paper, I describe an investigation conducted at Hop-
kins Marine Station in the Spring of 1978, on the intertidal
collembolid Archisotoma besselsi. Experiments were designed to
document the existence of an endogenous clock, and furthermore,
to quantify the nature of the clock system. This latter work
is still in progress; therefore, many of the questions posed in
this paper will be answered after new data has been analyzed.
Collembolids, more commonly known as springtails, are excel-
lent subjects for the study of biological clocks. They possess
a number of qualities that make the analysis of their oscillator
system reliable, quantifiable and easily reproduced. Collembolids
are, first of all, among the most abundant of insects (Maynard,
1951), and in a single location they number in the millions. That
they are available in enormous numbers allows the investigator
to generate large amounts of data, without fear of depleting his
source of animals. Also, by virtue of their minute size, labora-
tory populations can consist of several thousand individuals; as
sample size increases, so does the resolution of behavioral trends.
Secondly, for the study of temporal patterns in endogenous rhyth-
micity, it is important that there be a discrete activity that
changes dramatically with time and which can be quantified mechani-
cally or electronically to cut observational bias to a minimum;
collembolids show very distinct peaks and lulls in their jumping
pattern, which can be recorded easily and accurately. The beach
collembolid is particularly well suited for such studies because
it spends its entire life cycle in the beach habitat which is
generally predictable, homogenous, and reproducible in the lab
so that populations survive well under laboratory conditions.
Therefore, the investigation of the littoral collembolid as a
model subject for clock studies has generated the extensive data
discussed here.
Materials and Methods
Methods of determining the relative numbers of collembolids
active on the beach at different hours of the day were devised
in conjunction with studies made by DeLapa. (see DeLapa, 1978).
For laboratory investigations, the collembolids were col-
lected from the West beach at Mussel Point in Pacific Grove,
California from May to June 1978. Test populations were esta-
blished in Freezette airtight plastic freezer jars, with a 2-inch
layer of fresh, sifted sand at the bottom. The sand was collected
from a height on the beach approximately 4 feet above mean lower
low water. For each new experiment, a fresh population of col-
lembolids was introduced to each jar by ladling out a monolayer
of insects floating on water of uniform surface area, and esti-
mated to contain from 2000 to 3000 individuals.
Populations exposed to constant darkness were placed in jars
painted on the outside with flat black paint, while those experi-
encing either constant light or a controlled light-dark cycle
had only the bottom and walls of the jar painted with the lid
left as a translucent plastic. In the first experiment, a flour-
escent bulb was used for illumination, whereas small 5 watt bulbs
were employed in the second experiment, one mounted above each
jar. An aluminum foil shell was then fitted over the top and
sides of the containers, so that each could experience its own
light-dark regime but be independent of neighboring jars. Each
light was turned off and on by an Intermatic timer set to a
given light cycle. The jars were then placed in a Formatemp con¬
stant temperature bath, which itself was mounted on thick foam
to reduce vibrations from disturbances in the room.
In the first set of experiments, the bath was kept at 17
degrees Centigrade, maintaining an air temperature of 22 degrees
monitored inside one of the plastic jars by a thermister connected
to a Rustrack millameter. In the second set of experiments, a
bath temperature of 13 degrees Centigrade was selected, and the
air temperatures in the jars held a constant 15 degrees when the
overhead light was off, and 18 degrees when it was on. Since
the sand in the container was originally moist, the container
itself was closed, and there was a relatively small volume of air,
the humidity inside was probably very nearly constant. The
entire bath opening was then insulated by a snugly fitting box,
lined with styrofoam.
Analysis of the hopping activity was accomplished by placing
small photorelays (Townsend, 1977) 1/4 inch above the sand where
and individual cèllembolid interrupting the beam of light would
decrease the amount of light impinging on the detector, resulting
in a voltage change which was then amplified to activate a record-
ing pen on an Esterline Angus event recorder. Each photorelay
was wired into a single channel on the event recorder, and cor-
responding to each was a separate channel that counted the peaks
in multiples of ten, to facilitate counting.
The first experiment consisted of exposing two populations
to constant conditions, one experiencing constant light (LL) and
the other constant dark (DD). In the second set of experiments,
five populations were established. One was run in constant light,
two duplicate containers were subjected to a light-dark cycle of
14 hours of light and 10 hours of dark to closely mirror the solar-
day light cycle (LD 14:10 "Normal") and the last two populations
were run as duplicates exposed to a light-dark cycle delayed by
about 8 hours from the natural light cycle (LD 14:10 Delay) with
dawn arriving at 2 in the afternoon.
Results and Discussion
When the two populations of the first experiment are exposed
to constant conditions, one in constant light and one in constant
dark, free-running activity is generated (Figures 1 and 2) where
the populations are uncoupled from other external rhythms such as
the light-dark cycle of the solar day, tidal patterns and temper-
ature periodicities.
The major trend showing in consecutive days (May 9-12) is the
6 a.m. peak of hopping activity in both LL and DD populations,
corresponding with the major period of activity of field popula-
tions. Both laboratory groups also show high counts of events
immediately after the animals were introduced to their separate
containers and again during the late evening. This bimodal peak
on the first day appears in all other runs as well, regardless of
the imposed light conditions. The second peak of this bimodal
pattern always occurs iten hours after the experiment was started.
Beneath the major activity peaks is a star denoting its mean,
calculated by taking a visual estimate of the span of the peak,
and figuring a mean for grouped data on the values of recorded
jumping events. (Table 1). Connecting the stars is a broad line
representing a subjective estimate of the day-to-day trend in
timing of these bursts of activity. A least squares linear re-
gressions test (Box 14.1, Sokal and Rohlf, 1969) was then used
to find the slope of the "best fit" line through these means.
The LL population in the second experiment has an activity
pattern similar to that in the first experiment, as shown by com¬
parison of Figure 1 and 2 with Figure 3. The free-run period in
Figure 3, however, has a discontinuity between May 30 and May 31,
the cause of which is unknown. Any of several exogenous distur-
bances (power failure, disturbing the Formatemp bath, etc.) could
have disrupted the trend in the daily shift; likewise, endogenous
factors might be at work, such as the crossing of two possible
synchronizing agents, high tide and dawn, prior to the phase shift
on May 31.
Analysis of the means for each of the activity peaks in con-
c
stant conditions (see Table 2) shows a daily phase delay in
the first experiment of 27.6 minutes and 29.4 minutes for the
LL and DD regimes respectively. In Figure 3, best fit lines and
estimates of phase shifts were determined for the two periods
May 25-28 and May 29-Junel separately as indicated by the clear
shift in the peak mean at May 29; in each case there was a phase ad-
vance, the first by 5.7 minutes and the second by 13.2 minutes
per day. Whether these phase shifts are significantly dif-
ferent from each other can be determined by the F-test for the
difference between two regression coefficients (Box 14.8, Sokal
and Rohlf, 1969). This test showed that (1) the discontinous
phase delays in the second experiment were very similar, (2) the
phase shifts in LL and DD conditions (in the first experiment)
are remarkably alike and (3) among all four groups, the phase
shifts are significantly different from those in the second ex-
periment. Since the only obvious difference between the first
and second experiments was the temperature at which they were
run, this suggests that perhaps the oscillator in question is
temperature labile.
Nevertheless, that activity corresponds with dawn, an
obvious reference point in the daily cycle, and that the aver-
age natural free-run period calculated from the LL regime in the
second experiment is 23.8 hours, indicate that the oscillator
in question is a circadian one.
It is well to note here that in comparing the activity
pattern of the populations run in LL against DD, the absolute am-
plitudes of the peaks are greater in LL, indicating a higher num-
ber of animals active per hour, and having no apparent effect on
the pattern of rhythmic behavior. There are several possible ex-
planations for this: (1) a possible greater number of animals in
LL; (2) the greater activity found in LL is a function of the
slightly higher temperature associated with the light; or (3) the
animals could simply be more active in the light. Comparing the
LL populations in the two experiments with each other, the average
peak amplitudes are also different, the probable cause once again
being a different sample size, or the variable temperatures in
each experiment (air temperatures were 18 degrees Centigrade and
22 degrees Centigrade).
Imposing different light regimes on a circadian rhythm causes
it to become phase labile (resettable) and entrainable, so that
the persistent rhythm obtains the same period as the light dark
or entraining cycle (Palmer 1974). This means that if it can
be entrained to a light-dark cycle, then there is an underlying
phase response to light (Palmer 1976). In Figure 4, a "normal
light-dark cycle is imposed, and the circadian peaks again are
initially centered at 6 a.m. but are phase advanced on consecutive
days by 15.0 minutes per day. That they are not immediately en¬
trained by this light regime is expected if one keeps in mind
that this "normal" cycle does not mimic the actual external perio¬
dicity in light cycles. Not only is the first light of actual
dawn occuring earlier that 6 a.m., but it is not known what aspect
of this light cycle is actually the entraining agent, i.e., whe¬
ther it is light intensity or the temperature cycle associated
with the light-dark regime that actually synchronize the internal
periodicity. Furthermore, if light intensity is the cue, then
it still remains a question as to whether it is the steady state
that is synchronizing the clock, or the transition from one state
to the other, or even at what light intensity the cue is effective
It may also be possible that if a second clock is operating in the
system, then a second Zeitgeber is at work and only together will
the two give the entire system its exact periodicity.
Similarly, the delayed light-dark cycle (LD 14:10 Delay) shows
circadian peaks that phase delay from 6 a.m. by 27,9 minutes per
day (Figure 5). The persistent circadian rhythm should again
adopt the same period as the entraining light-dark cycle. While
the exact Zeitgeber for the LD cycle may be in question, that
the delayed light regime populations show a phase delay (as
opposed to a phase advance in LD 14:10 "Normal") is significant.
The two systems are compensating independently according to the
differential effect of their corresponding light regimes. As the
one advances and the other delays, they will diverge towards a
point that holds a common period relation to their respective "dawns".
Therefore, by extrapolating along these lines and computing
for the time T until the two activity trends maintain a constant
relationship to their respective dawns, it is found that by June
6, the normal cycle should arise and maintain its periodicity
at 3:33 a.m., 2 hours and 27 minutes (2.45 hours) before its dawn
and the peak of activity in the delayed cycle population should
arrive 2 hours and 36 minutes (2.60 hours) prior to the delayed
sunrise (2 p.m.) at 11:24 a.m. (See Table 3). Analysis by the
F-test for difference between two regression coefficients can
again be calculated to determine if the activity peaks after June
6 are actually entrained to a 24-hour period (Box 14.8, Sokal and
Rohlf, 1969). This test shows that the slope and the period for
the days June 6-Junelo is significantly different from the slope
for the previous days May 26-June 2, and yet not significantly
different from the perpendicular, which would be the equivalent
of a 24-hour periodicity, and therefore, the entrained state.
It is also interesting to note the difference between the
timings of these activity peaks in the lab and under field con-
ditions. In the field, the peak activity lasts an hour or less
(DeLapa, 1978), with virtually no jumping outside of this time
span, whereas the laboratory populations show activity periods
of several hours, even during the initial days of the experiment.
Here, the width of the peak holds constant, suggesting that the
clock mechanism is a precise one and is not appreciably altered
by laboratory conditions. The synchrony among field populations
might be controlled not only by exogenous agents (Zeitgeber) but
also absolute limits for the activity periods may be delineated
by overriding environmental cues. That there are additional li-
miting factors that lock the rhythms onto such discrete times
in the field, is also suggested by the condensed distribution of
animal activity in the laboratory. The activity distribution in
the lab follows a leptokurtic distribution (g, from Box 6.2, S.E.
of go from Box 7.1agø significant at p«.05 withT-test of Box 7.4,
Sokal and Rohlf, 1969), meaningthat the jumping of individuals
is clumped around the mean, more so than would be expected in a
random distribution. This again indicates a high degree of pre-
cision in the clock mechanism; individuals may mutually entrain
one another, or else their clocks are all very highly synchronized
onto the same periodicity.
Furthermore, that the persistent period is so close to 24 hours,
reinforces the notion that the oscillator in question is very strictly
defined. Even though the internal periodicity is more difficult
to entrain if it is very close to 24 hours, collembolids would
gain the advantage of excellent timing of their activity, sug
gested in the field to be am important survival benefit.
Both of these light cycle regimes show a second activity
peak (hereinafter referred to as the B peak as opposed to the
circadian A peak) arising close to 1800 on the second and third
days (May 26 and 27) of these experiments, progressively increas¬
ing in amplitude and phase delaying through the day. These peaks
have been shown to be statistically distinct from the daytime peaks
by the Student's T-test for grouped data (Sokal and Rohlf, 1969).
When the amount of daily phase shift for the A and B peaks
is compared for the two light regimes LD 14:10 "Normal" and LD 14:10
Delay, it can be seen that a constant difference between the period
of the A and B oscillations is maintained, independent of the im¬
posed light-dark cycles. Thus, in the normal LD cycle, the A
peaks occur 15.0 minutes earlier each day and the B peaks, 26.4
minutes later, so that the two peaks are converging at the rate
of the sum of these two values, or 39.40 minutes per day. Simi¬
larly, in the delayed LD cycle, when the B peak delays 67.2 minutes
per day, the A peak follows it with a delay of 27.9 minutes. The
difference between the two phase shifts is 39.30 minutes, indi¬
cating that the interval between the two peaks is decreasing at
a nearly identical rate to that found in the "normal" light cycle.
If the circadian (A) peaks lock onto an exact 24-hour perio¬
dicity, such as they would when entrained to the given light-dark
cycle, the B peaks will have an average period of 24 hours and
39.35 minutes, a period quite close to the tidal period of 24
hours and 51 minutes. These two values are within 1.61% of each
other indicating that the suggestion that the B component is actu-
ally an expression of a tidal clock is a reasonable one.
The B component also maintains a constant position in the
tidal cycle. In both the "normal" and delayed light regime ex¬
periments, these activity highs correspond to a tidal height of
3.5 to 5.0 feet, suggesting that these bursts of activity may
be the expression of a tidal rhythm. In the field, this tidal
range would correspond to the condition wherh station 18, the
collection site of these particular animals, would be just unco¬
vered by the tide.
Furthermore, that the A and B peaks maintain a constant dif-
ference between their respective phase shifts regardless of the
light-dark cycle suggests that the B peak has its own oscillation
and the two oscillations (daily and tidal) are mutually entrained.
It remains, however, that the B periodicity is in fact being greatly
affected by the A system, without being entrainable by light cycles.
If this is indeed a separate tidal periodicity, light independent,
but phase-locked to the A peaks, it would follow that in the ab-
sence of external Zeitgeber, such as we find in persistent rhythms,
the B peaks would free-run, except for being phase-shifted rela-
tive to A. Then, if an appropriate tide-related cue were given,
they would shift into a new phase relationship with A, so that
the two oscillators would again be mutually entrained and their
activity peaks more precisely timed. In this regard, it is inter-
esting to note that the leptokurtic distribution discussed earlier
may very well be a result of the coupling and mutual entrainment
of the two clocks, thus increasing the temporal precision of jumping
activity.
The investigations considered above suggest a number of con¬
timuing and additional studies. First, asking whether it is light
intensity or the change in temperature associated with light cycles
that cues the clock onto the external periodicity, control studies
should be conducted, isolating each of these variables. Then the
effect of different temperatures on free-running clocks should be
investigated, to see if there is a range of temperature sensitivities
of the clock mechanism. Also, another constant condition popula¬
tion should be established not only as a control, but to get better
resolution of the LL patterns in the present study. If the B peaks
in the LD cycles eventually cross below the circadian peaks and
maintain a constant phase relationship, their independence from
solar-day rhythms will be confirmed and when this particular pat-
tern of light and tidal cyclese is again encountered in the external
world, it will be interesting to resolve how it affects the ampli-
tude of these supposed tidal peaks, and whether the relative po-
sition of the A and B peaks affects the trend in increasing the
size of the peaks. Also, as well as simulating tides to investi-
gate the tidal Zeitgeber, when a high tide again coincides with
dawn, speculations as to its shifting effect in constant light
conditions might be checked. Lastly, numerous studies may be made
to determine the exact mechanism of how the clock-driven rhythm
is adjusted to the LD cycle, by determining a phase-response curve
and evaluating the magnitude of the phase shifts produced by a
given stimulus.
Summary
Investigations of the rhythmic jumping activity of the
intertidal collembolid A. besselsi has resulted in the following
findings:
(1) A circadian rhythmicity is present which indicates a
sensitivity to the light-dark cycle of the solar day.
(2) The free-running period for this rhythm is approximately
23.8 hours.
(3) Different light regimes cause the rhythmic pattern to
phase advance and delay in different ways, showing that the
systems compensate independently addording to the particular
imposed light cycles.
(4) The circadian clock is entrained to a light-dark cycle
at a point in the cycle approximately 2 hours and 30 minutes before
dawn.
(5) Phase shifts in persistent rhythms seemed to vary as
a function of temperature.
(6) The circadian activity peaks and a set of smaller peaks
maintian a constant difference between their two periods, indi-
cating that the two rhythms are caused by separate endogenous
oscillators.
(7) A tidal clock may be the driving oscillator for this
smaller activity peak.
c
Acknowledgements
I would like to express my thanks to the faculty, staff
and students of Hopkins Marine Station for their support,
guidance and enthusiasm at all hours of the day and night;
to Luigi, who had me on the other end of the aspirator sucking
up collembolids; and to Ellen, a knowing smile. To Dr. Robin
Burnett goes my very deepest appreciation and heartfelt thanks
for his advice, patience and faith in me and the collembolids.
iterature Cited
DeLapa
M. 1978. Jumping rhythmicity in a collembolid popu-
lation on a Central California beach and the effect
of temoerature on jumping activity. Unpublished,
Biology 175H, Hopkins Marine Station, Stanford Uni-
versity. 17 pp.
Maynard
Elliott A. 1951. A Monograph of the Collembola
or springtail insects of New fork State. New York:
comstock Publishing Co., Inc.
McGinnis, J.W. 1972. A Tidal Rhythm in the Sand Beach
Amphipod Orchestoidea corniculata. Unpublished,
Biology 175H, Hopkins Marine Station, Stanford Uni-
3pp.
versity.
B.L. 1970 Circadian and Tidal Rhythms in the
Osbeck
San Beach Amphipod Genus Orchestoidea (Talitridae)
Unpublished M.A. thesis, University of California,
Santa Barbara. 47 pp.
Palmer
J.D. 1974. Biological Clocks in Marine Organisms:
The Control of Physiological and Behavioral Tidal
Rhythms. New fork: John Wiley and Sons.
Palmer,
J.D. 1976. An Introduction to Biological Rhythms.
New York: Academic Press, inc.
Saunders.
D.S. 1976. Insect Clocks. New York: Pergamon
Press.
Sokal, R.R. and F. James Rohlf. 1969. Biometry. San
Francisco: W.H. Freeman and Co.
Townsend,
H. 1977. Effects of Light Intensity, Temperature
and Salinity upon Water Column Distribution of Tigriopus
californicus. Unpublished, Biology 175H, Hopkins
Marine Station, Stanford University. 9 pp.
Figure and Table Legend
Figure 1-
A bar histogram showing the pattern of activity in a
collembolid population in the laboratory in LL at 22° c.
(Note: In Figure 1 and 2, the values for the counts/hour
are derived from the sum of the events recorded in
three different photorelays placed at various heights
in the collembolid jar.)
Figure 2-
A bar histogram showing the pattern of activity in a
collembolid population in the laboratory in DD at 22° C.
Figure 3-
A bar higtogram showing the pattern of activity in
LL at 18 C. Consecutive days read down the ordinate;
paired days read across the absissa. For example,
May 26-27 shows as one time span, May 27-28, May 28-29,
and so on, are shown vertically below it so that the
activity pattern is shown continuously through the
night.
(Note: In Figures 3, 4 and 5 the values for the number
of counts/hour are those recorded from a single photo-
relay.)
Figure 4-
A bar histogram showing the pattern of activity in a
population exposed to a "normal light-dark cycle of
14 hours of light and 10 hours dark (LD 14:10 "Normal)
such that dawn occurs at 6 a.m.
Figure 5-
A bar histogram showing the pattern of activity in a
population exposed to a delayed light-dark cycle of
14 hours light and 10 hours dark (LD 14:10 Delay)
such that dawn occurs at 2 p.m.
Table of the means (x) calculated for the A and B acti¬
Table 1-
vity peaks, the slope of the best fit line through those
means (a,), and the coefficient of distribution (r2) for
goodness of fit.
LL-1 £ population in LL, experiment (see Figure
DD-1 = population in DD, experiment (see Figure 2
LL-2 = population in LL, experiment (see Figure
LD-Normal = population in LD 14:10 "Normal cycle,
experiment 2 (see Figure 4)
LD-Delay - population in LD 14:10 Dealy cycle, experi
ment 2 (see Figure 5)
Table 2-
Table showing values derived from the F-test for the
difference between two regression coefficients, calcu-
lated to compare whether the amount of phase shift
was significantly different from each other in the
two LL runs in experiment 1 and 2, and in the DD run
as compared to the LL runs.
(Symbols are the same as those used in Table 1; LL-2a
and LL-2b refer to the phase shifts for the first four
days and the second four days respectively of the
LL run in experiment 2.)
Table 3.
Table showing the derivation of the times when the
a peaks in the normal and delay cycles will both
maintain a constant relationship with their respective
dawns, i.e., the times of expected entrainment of the
a peaks.
1500
May
1000-
500
1000 10
500
1000
May 11
500
1000
May 12
500
L



Time of day in hours
Figure 1
2
5
5
200
May 9
150
100
50
LI
L
100 M7 10
50
ME
100 M27 11
50
R LL
10
May 12
50

18.
Time of day in hours
Figure 2
FIGURE 3.
L






100 27
L
U


L


10 20


2




100 1

100 | 1 2


I
100 1
50


N18M6N88 M
TIME OF DAY IN HOURS

5
FIGURE 4.
LD 14:10 "NORMAL









M





—





— 273

.»

L






6 N 18 M
TINE OF DAY IN HOURS
FIGURE 5.
LD 14:10 DELAY
27u. 23





a


ke



.
s
L







A

A
N 18 M
6 N 18
TIME OF DAY IN HOURS
5
Table 1.
BIMODAL PEAKS (2nd mode)
51-1
DATE
19.87
5/9
XIL-2
20.04
"A" PEAKS
(Circadian peaks)
LL-1
DATE
5/10
4.38
a,=.46
4.66
5/11
=27.6 min.
5.29
5/12
delay
r =.93
LL-2
5.53
First four
5/26
5/27
values
5.09
5.19
5/28
a,--.095
5.18
=5.7 min.
.65
.46
advance
5/31
.47
6/1
r =.58
-.07
6/2
Second four
values
6/
6/4
a,--.215
6/5
3.2 min.
6/6
advance
6/7
r22.797
6/9
6/10
"B" PEAKS
DATE
5/26
3/28
5/29
5/3.
(Time of the peak; experiment begins at
at 10.00.)
5pp-1
19.41
LD-Normal
3D-Delay
20.98
20.02
0-1
5.71
a=.49
5.74
=29.4 min.
6.68
delay
r22.77
LD-Normal
XID-Delay
6.35
.95
6.62
5.76
a,=-.25
7.14
a,-.465
5.84
8.04
=15.0 min.
=27.9 min.
5.81
8.04
advance
delay
5.46
8.50
4.60
r =.84
8.88
r°-.99
4.41
9.52
4.21
4.47
a,=-.02
4.17
4.30
=1.2 min.
4.11
advance
4.45
r22.13
4.12
4.10
LD-Normal
LD-Delay
17.19
a,=.44
18.00
18.00
a,=1.12
19.03
20.57
=26.4 min.
=67.2 min.
20.98
18.50
delay
delay
19.19
21.97
19.98
r2-.87
23.40
r?=.95
19.88
24.97
0
Table 2.
Phase shift
slope of best fit line
Light Regime
(see Tabl
(see Table 1
LL-1 (220
.46
27.6 min. advance
DD-1 1220
.49
2914 min. advance
LL-2a (189
09
5.7 min. delay
first four values
LL-2b (18
13.2 min. delay
-.215
second four values
F-test for difference between two reg
gression coefficients
degrees
Light Regimes
freedom
LL-1, vs. LL-2a
(.O5
3.86
1.94
LL-1
vs. LL-2b
p«.02
LL-1 vs. DD-1
.11
p».92
LL-2a vs. LL-2b
p2.2
LL-2a vs. DD-1
2.66
.08
LL-2b vs. DD-1
3.27
p(.O5
Table 3.
T-time after day 5 when Normal and Delay cycle
Find:
A peaks are at the same point relative to their
respective dawns.
LD-Normal Cycle:
a,=-. 263
Day 5 (5/29): A peak occurs at 5.64 a.m.- 0.36 hours
before dawn (6 a.m.) (predicted value;
observed value = 5.84)
LD-Delay Cycle:
a15.478
Day 5 (5/29): A peak occurs at 7.57 a.m.= 6.43 hours
before dawn (2 p.m.) (predicted value;
observed value = 7.66)
Tx (rate at which - (time of = Tx (rate at which - (time of
Delay "A
"A pea
"peak
Normal "A"
peaks delay)
on day 5)
peaks advance) on day 5
TX (.478) - 6.43
Tx (-.263) - (.36)
Tx (-.263 -.478)
6.43 - .36
T =
8.19 day
or, the Normal and Delay cycle peaks will have the
same time relative to their dawns on the 13th day,
or June 6.
From the rate at which the peaks phase shift through
the day, the time of the peak on June 6 can be found:
Time of - [(time of peak
(rate of phase x 8 days)
dawn
(predicted) on
shift
Day 5)
LD-Normal: A peak will arise 2.45 hours before its dawn
at 3:33 a.m.
LD-Delay: A peak will arise 2.60 hours before its dawn
at 11:24 a.m.