Relationship of daily and circatidal activity rhythms of the fiddler crab

Marine Biology (2004) 144: 473–482
DOI 10.1007/s00227-003-1213-6
R ES E AR C H A RT I C L E
J. H. Stillman Æ F. H. Barnwell
Relationship of daily and circatidal activity rhythms of the fiddler crab,
Uca princeps, to the harmonic structure of semidiurnal and mixed tides
Received: 27 March 2003 / Accepted: 26 August 2003 / Published online: 21 October 2003
Springer-Verlag 2003
Abstract Intertidal organisms may employ circatidal
rhythms to track the tidal cycle, but tidal patterns may
vary within a species range and necessitate adaptation
to the local tides. Circatidal rhythms were examined in
populations of the eastern Pacific fiddler crab Uca
princeps (Smith) from four sites with differing tidal
characteristics, La Paz (2410¢N; 11021¢W), San Blas
(2133¢N; 10518¢W) and Manzanillo (196¢N;
10424¢W), Mexico (lower amplitude, mixed semidiurnal
tides) and Mata de Limon, Costa Rica (955¢N;
8443¢W) (high-amplitude, semidiurnal tides). Local
tides were characterized by harmonic constants of M2,
S2, K1, and O1, partial tides that largely determine their
semidiurnal and diurnal features. Rhythmic structure in
continuously recorded locomotor activity of individual
crabs held under laboratory conditions was described by
cosinor and periodogram methods of time-series analysis. Both daily and circatidal rhythms were found in
crabs studied in light–dark cycles set to local conditions
at the time of collection. Crabs at all four sites shared a
tendency toward bimodality, with a mid-morning
activity peak and varying degrees of nocturnal activity.
Circatidal rhythms closely matching the period of the
12.42-h M2 partial tide were consistently present at all
sites except Manzanillo. At Mata de Limon, the circatidal rhythm clearly dominated locomotor activity, but
was strongly modulated by a daily rhythm in a repeating
pattern at a semilunar interval. In contrast, the amplitude of the daily rhythm was higher than that of the
circatidal rhythm in crabs from the three mixed tide sites
Communicated by J.P. Grassle, New Brunswick
J. H. Stillman (&) Æ F. H. Barnwell
Department of Ecology, Evolution and Behavior,
University of Minnesota, St. Paul, MN 55108, USA
E-mail: stillman@hawaii.edu
Fax: +1-808-9569812
Present address: J. H. Stillman
Department of Zoology,
University of Hawaii at Manoa, 152 Edmonson Hall,
2538 McCarthy Mall, Honolulu, HI 96822, USA
on the Mexican coast, where the tidal pattern is dominated by a diurnal inequality arising from the diurnal K1
and O1 partial tides. These results suggest that populations of U. princeps use both daily and circatidal timing
systems to track local forms of the tide generated by
their M2, S2, K1, and O1 geophysical counterparts.
Introduction
The intertidal zone is a dynamic habitat, where the rise
and fall of the tides alternately expose organisms to
conflicting demands of marine and terrestrial biomes
(Newell 1979; Stillman 2002, and references therein). In
response, many intertidal species have evolved mechanisms for timing their activities to predictable elements
of the tidal and solar day–night cycles responsible for
much of the environmental variation (Neumann 1981;
Palmer 1995). In a remarkable parallel with circadian
rhythms, intertidal organisms may possess circatidal
rhythms that allow them to track the local tidal cycle
and program their activities in anticipation of its
changing phases. The presence of circatidal rhythms was
clearly demonstrated in studies of locomotor activity in
three species of fiddler crabs at Woods Hole, Mass.,
USA, where specimens exposed to natural illumination
(roughly 14 h light:10 h dark) under non-tidal laboratory conditions displayed persistent tidal rhythms
approximating the mean 12.42-h period of the local
semidiurnal tides (Barnwell 1966, 1968). Moreover, the
amplitude of the circatidal rhythms was modulated at
specific phases of the 24-h day–night cycle, and these
modulations produced a 2-week rhythm in activity that
matched the 14.8-day semilunar cycle of spring and neap
tides (Barnwell 1966, 1968).
The laboratory findings closely reflected the crabs
dependence upon environmental rhythms in their natural habitat. In local salt marshes fiddler crabs restrict
activity essentially to the period of aerial exposure during the low-water portion of the tidal cycle (Crane 1975);
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they engage in visually oriented daytime courtship displays and nocturnal bouts of acoustic signaling when
low tide occurs at specific phases of the day–night cycle
(Salmon 1965); and all stages of their reproductive
rhythms can be correlated with the semilunar cycle of
spring and neap tides (Kellmeyer and Salmon 2001).
From these and earlier experiments a model was
proposed that all three Uca species in Woods Hole were
adapted to the daily and tidal environmental cycles
through dual timing systems that cued activity to particular phases of each of the two environmental rhythms
(Webb and Brown 1965; Barnwell and Zinnel 1984). One
system generated circatidal rhythms as adjustments to
the 12.42-h cycle of the tide, and the other produced
daily rhythms paralleling the 24.0-h solar cycle. Initially
the daily component was thought to be the output of a
circadian clock, but data from longer recordings of
locomotor activity led to the conclusion that the light–
dark cycle plays a central role in the expression of both
daily and circatidal rhythms (Barnwell 1966, 1968).
While it was controversial at the time to propose that an
organism might possess two separate timing systems, it
is now accepted that circadian organization incorporates
multiple oscillatory components (Page 2001).
The dual rhythm model offers a reasonable explanation for how an organism might adapt to the complex
interplay of daily, tidal, and semilunar cycles in a
semidiurnal tidal habitat like Woods Hole, but the
question has been raised about its utility for regions with
different tidal characteristics (Barnwell 1976). On many
coastlines of the world, particularly in the Pacific and
Indian Oceans, the form of the tide is determined by the
presence of a diurnal inequality that alters the relative
amplitude and interval of the two semidiurnal tidal
peaks. The inequality is produced by the declination of
the moons orbit relative to the earths equator and
achieves its maximum effect every 13.66 days, on average, when the moon reaches the northern or southern
angular limit of the declinational cycle. Tides with a
clear diurnal inequality are referred to as mixed tides,
because they alternate in form at roughly weekly intervals between semidiurnal (equatorial) tides, when the
moon stands over the equator, and more strongly diurnal (tropical) tides, when the moon reaches its declinational maximum near the Tropics of Cancer and
Capricorn (Defant 1961).
Because of regional differences in resonance response
of ocean basins to semidiurnal and diurnal periodicities
of tide-raising forces, prominence of the diurnal
inequality can shift abruptly over a relatively short distance. A good example is seen near Puerto Angel,
Mexico (1540¢N; 9629¢W), where the coastline projects
into the Pacific Ocean at the western end of the Gulf of
Tehuantepec (Fig. 1). The form of tide north of this
point is mixed, with an obvious diurnal inequality and
mean diurnal tidal range of about a meter. Eastward and
south of the point, the diurnal inequality abruptly
diminishes as the tide assumes a semidiurnal form and
increases in amplitude along the coast of Central
America until it reaches a spring tide range of 5 m in the
Bay of Panama (Fig. 1).
We took advantage of the transition in tidal patterns
along the western coast of Mexico to examine the adaptation of locomotor activity rhythms to different forms of
the tide in local populations of the fiddler crab Uca
princeps. This species occurs between the southern Gulf
of California and Peru and is thus a wide-ranging member of the fauna of the tropical eastern Pacific (Crane
1975; Briggs 1995). We studied populations occupying
habitats with mixed tides along the Mexican coast at La
Paz, San Blas, and Manzanillo, and semidiurnal tides at
Mata de Limon near Puntarenas, Costa Rica. The aim of
this study was to characterize the rhythmic nature of the
crabs activity patterns and to determine if they were related to the periodic structure of the local tide. To
accomplish this aim, we visually and statistically analyzed individual crab activity recordings to understand
the complex interactions of daily and circatidal rhythms.
Materials and methods
Study sites and their tidal characteristics
We used predicted values for times and heights of high and low
waters from tidal reference data for each of our sites to represent
tidal patterns (Fig. 1). Values for La Paz are based on corrections
to daily predictions for Guaymas, Mexico (2756¢N; 11054¢W)
(U.S. Department of Commerce, Coast and Geodetic Survey, tide
table for 1979). Those for San Blas are the values for Puerto
Vallarta (2037¢N; 10515¢W)), which, along with those for Manzanillo, were determined as corrections on daily predictions for San
Diego, USA (3243¢N; 11710¢W) (U.S. Department of Commerce,
Coast and Geodetic Survey, tide tables for 1985 and 1988). Values
for Mata de Limon, Costa Rica, are those of daily predictions for
Puntarenas, Costa Rica (958¢N; 8450¢W) (U.S. Department of
Commerce, Coast and Geodetic Survey, tide table for 1966). The
tide curves show that mixed semidiurnal, low-amplitude tides are
present at La Paz, San Blas, and Manzanillo, where the tides shift
between one and two peaks per tidal day in accordance with the
declinational cycle, and that tides at Mata de Limon are strictly
semidiurnal with two high-amplitude peaks per tidal day.
For each location we estimated the mean tidal elevation of the
Uca princeps population, and these elevations are shown as dotted
lines on the tide curves (Fig. 1). Times of tidal immersion were
measured from the line and reconstructed in the form of raster
plots superimposed on the actograms used here for displaying crab
activity patterns.
We have mathematically characterized the tides at our field sites
by their principal harmonic components, represented as a series of
simple cosine curves referred to as partial or constituent tides
(Defant 1961). Periods of the partial tides are dictated by the
movement of the earth, moon, and sun, while their respective
amplitudes and phase angles are constants that define the features
of the local tides. We used the four major constituents that largely
determine the characteristics of tides in the tropical eastern Pacific
to compare our sites. Two semidiurnal components are the 12.42-h
principal lunar semidiurnal constituent, M2, and the 12.00-h principal solar semidiurnal constituent, S2. The diurnal components,
which are responsible for the diurnal inequality, are the lunisolar
diurnal constituent, K1, with a period of 23.93 h, and the lunar
diurnal constituent, O1, at 25.82 h. The semidiurnal character of
the tide at Mata de Limon is due to the overwhelming amplitude of
the M2 component (Fig. 2). At mixed tide sites, however, the
amplitude of the M2 partial tide was reduced in relation to the
other components, and at Manzanillo its value fell below that of
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Fig. 1 Characterization of tidal patterns in the tropical eastern
Pacific. Left panels: tide curves for dates of activity recordings for
crabs from the four study sites. Data were generated from
published tide tables (U.S. Department of Commerce, Coast and
Geodetic Survey, tide tables for 1966, 1979, 1985 and 1988) using
recommended corrections from tide stations. Horizontal lines
indicate the estimated intertidal elevation for each colony of crabs.
Circles represent phases of the moon (filled new moon; half-filled
half moon; open full moon), and letters denote the declinational
cycle (N northern declinational maximum; E equatorial crossing of
the moon; S southern declinational maximum). Arrows indicate
approximate locations of collection sites. Right panel: map of tidal
form numbers, F=(K1+O1)/(M2+S2), showing variation in
strength of diurnal inequality in the tropical eastern Pacific Ocean.
F values are indicated on the color scale bar, from zero
(semidiurnal) to infinity (diurnal). Data for M2, S2, K1, and O1
were obtained from the NASA Physical Oceanography Distributed
Active Archive Center at the Jet Propulsion Laboratory, California
Institute of Technology (PA Puerto Angel, Mexico)
forms of the tide as semidiurnal (F<0.25), mixed semidiurnal
(0.25<F<1.5), mixed diurnal (1.5<F<3.0), and diurnal (F>3.0).
The semidiurnal tide is indicated for Mata de Limon by an F
number of 0.11, whereas Manzanillo, San Blas, and La Paz have
mixed semidiurnal tides, with F numbers of 0.90, 0.60 and 1.01,
respectively.
Recent advances in satellite monitoring of ocean surface
topography have allowed global-scale analyses of F values. Using
data on the periodic constants K1, O1, M2, and S2 generated from
the satellite data sets, we computed and mapped F numbers for the
tides of the tropical eastern Pacific Ocean (Fig. 1, map). This global
map does not replace the computation of harmonic constants for
coastal localities from tide gauge stations, because the oceanic tide
is modified as it encounters continental shelf depths and irregularities of the coastline. However, the map reveals the steep transition between mixed semidiurnal and semidiurnal forms of the tide
across the range of our study sites.
the S2 partial tide (Fig. 2). The semidiurnality of the tides can be
generally described using the ‘‘formzahl,’’ or form number, F, as
the ratio of the sum of the amplitudes of the primary diurnal
harmonic constituents to that of the primary semidiurnal ones
[F=(K1+O1)/(M2+S2)] (Defant 1961). This ratio defines the
Specimen collection and maintenance
Uca princeps (Smith 1870) is a relatively large fiddler crab assigned
to the subgenus Uca (Rosenberg 2001). Maximum carapace width
is >40 mm (Crane 1975), but our specimens were 16–32 mm. Male
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Santiago, approximately 12 km west of Manzanillo. They were
transported 2 days later to Minneapolis and immediately placed in
actographs containing artificial seawater at 32&, on a 13 h
light:11 h dark schedule set to the twilight times of approximately
30 min before sunrise and after sunset at Manzanillo. Light levels
were the same as for the La Paz experiment, above, and temperature was maintained at 27±1C throughout the experiment.
Mata de Limon, Puntarenas Province, Costa Rica
(ML) (955¢N; 8443¢W)
Five specimens were collected on 28 February 1966 from an open
muddy area on the northwestern edge of the tidal lagoon, transported to San Jose, Costa Rica, and placed in actographs on 1
March with exposure to the natural illumination cycle (roughly
13 h light:11 h dark) through a shaded north-facing window. Air
temperature in the room varied daily from a low of 20.7C to a high
of 26.2C. Crabs were maintained in seawater collected at the study
site.
Data collection and statistical analysis
Fig. 2 Amplitudes of tidal harmonic constants for field sites used in
this study [site abbreviations: LP La Paz, Mexico; SB San Blas,
Mexico; MN Manzanillo, Mexico; ML Mata de Limon, Costa
Rica; tidal constituents: S2 principal solar semidiurnal (12.00 h);
M2 principal lunar semidiurnal (12.42 h); K1 lunisolar diurnal
(23.93 h); O1 lunar diurnal (25.82 h)]. Amplitudes (m) are from
Xtide (D. Flater, http://www.flaterco.com/xtide) for the collection
sites (or the nearest reference station to the site: Puntarenas, C.R.,
for ML and Puerto Vallarta, Mex., for SB)
and female specimens were collected from exposed tidal flats of
each study site on four occasions in February or March 1966, 1979,
1985, and 1988.
La Paz, Baja Sur Province, Mexico (LP) (2410¢N; 11021¢W)
Twelve specimens were collected on 22 March 1979 from an
open tidal area of soft mud below the highway between La Paz
and Pichilingue on the eastern shore of Bahia de La Paz. Crabs
were transported to Minneapolis, Minn., USA, the next day and
placed in actographs containing artificial seawater at 35& on
the following day, on an illumination cycle of 12.17 h
light:11.83 h dark set to the local time of sunrise and sunset at
La Paz. Fluorescent light levels ranged from 500 to 2000 lux,
depending on the position of the actograph. Temperature of the
room was maintained at 25±1C throughout the experiment.
Crabs were not fed, as was the case with all recordings in this
study.
San Blas, Nayarit Province, Mexico (SB) (2133¢N; 10518¢W)
Fifteen specimens were collected on 29 March 1985 from a shallow
muddy-sand tidal flat along the eastern margin of Estero el Pozo.
They were flown to Minneapolis on 31 March and immediately
placed in actographs containing artificial seawater at 35&, on a
13.67 h light:10.33 h dark schedule set to encompass twilight times
of 40 min before sunrise and after sunset at San Blas. Light levels
and temperature were the same as for the La Paz experiment,
above.
Manzanillo, Colima Province, Mexico (MN) (196¢N; 10424¢W)
Eleven specimens were collected on 25 March 1988 from a muddysand tidal flat just within the mouth of Laguna Juluapan on Bahia
Two types of actographs were employed for the detection of
locomotor activity. Round plastic cups as illustrated in Brown
(1970) were used in San Jose, Costa Rica, and plastic boxes fitted
with a false floor as shown in Thurman (1998) in Minnesota. A
single crab was placed with seawater in either device where its
locomotor activity rocked the cup or false floor and triggered a
movement-sensitive contact switch. The signal from the switch
caused a pen deflection on an Esterline–Angus strip chart recorder,
giving a continuous trace of activity for the duration of the
experiment. Pen tracings on strip charts were quantified for each
10-min interval on a scale of from 0 to 3 (0=no activity, 1=one or
two traces, 2=up to one-half of the interval filled in by traces, and
3=more than one-half of the interval filled by traces). The data
were hand-entered in computer spreadsheet files, and data analyses
were performed with cosinor and periodogram procedures.
Cosinor analysis uses a least squares method to identify the best
fit of a cosine curve to periodicities in the data and to provide
estimates of period length, amplitude, and phase angle of the fitted
curve, along with a statistical test of significance for each estimate
(Halberg et al. 1977, 1987). We utilized the non-linear method that
reanalyzes the statistically significant peaks initially identified by
linear analysis. While the cosine curve may not resemble the biological waveform, it serves as a useful mathematical model for
characterizing important parameters of rhythm components
(Dowse and Ringo 1991).
Periodogram analysis (Enright 1965) with TAU software (MiniMitter, Sunriver, Ore.) cuts a time series into segments of a specified period length, adds the segments to determine their average
waveform, and computes the standard deviation. The procedure is
repeated across a specified range of periods (e.g. at 0.01-h intervals
from 10 to 30 h) to produce a spectrum (periodogram) of standard
deviations plotted against period length. High standard deviations
generally indicate period lengths with strong repetitive patterns as
well as submultiples and supermultiples of the fundamental frequencies (Enright 1965; Sokolove and Bushell 1978).
We compared the power of periodogram and cosinor analysis
methods to resolve the presence of multiple periodicities in LP tides
and one crab specimen from LP (Fig. 3). The tide data for periodogram analysis were obtained by reading hourly values from the
saw-tooth graph of the times and heights of high- and low-water
predictions of a 40-day series (Fig. 1). Cosinor analysis does not
require equidistant data, so we used only the values for daily highand low-water predictions along with midpoint values for the lines
connecting these points in a 60-day series. Cosinor and periodogram analyses produced similar outcomes in data sets longer than
14 days, but, because cosinor analysis returns both period lengths
and error estimates, we have only reported estimates of crab
rhythm parameters using this method.
477
Fig. 3A–D Uca princeps. Comparison of cosinor and periodogram time-series analysis methods for tide and crab locomotor
activity data. Results of: A cosinor and B periodogram analysis of
40- and 60-day series of tidal prediction data for La Paz, Mexico (*
statistically significant components for four principal harmonic
constituents of the tide). Inset in B shows the entire periodogram
for values from 10 to 30 h. Results of: C cosinor and
D periodogram analysis applied to 54 days of activity data for
crab LP10 from La Paz [* statistically significant periods (cosinor
linear least-squares test, P<0.01)]. Vertical lines mark the expected
harmonic component period lengths for the tides (A, B) (S2:
12.00 h, M2: 12.42 h, K1: 23.93 h, O1: 25.82 h) and for locomotor
activity (C, D) (12.0 h, 12.42 h, 24.0 h). Lines are also drawn for
supermultiples of S2 and M2 periods for periodogram analyses (B,
D). See ‘‘Materials and methods’’ for details
Double-plotted activity histograms (actograms) and mean
daily and circatidal waveforms for all specimens from each site
were generated with TAU graphics and examined visually to
confirm the presence of components identified by cosinor analysis.
Individual actograms having rhythm parameters similar to those
of the population means were selected to show the interactions of
daily and circatidal rhythm components in relation to the lunar
phase and declinational cycle. Mean waveforms were computed
for each crab beginning with midnight on the first day of
recording; thus, phase relationships of the mean circatidal waveforms to the local tidal cycle were those that existed on the first
day of the experiment. Daily and circatidal waveforms for all
individuals at each study site were then pooled to obtain mean
waveforms for each population.
Results
Comparison of cosinor and periodogram
time-series analysis methods
Cosinor analysis performed better than periodogram
analysis at clearly resolving the principal harmonic
constituents in LP tide data. M2, S2, K1, and O1 constituents were identified, with period estimates accurate
to 0.01 h (Fig. 3A). Periodogram analysis identified M2,
S2, and O1 constituents at a similar level of resolution,
but also produced supermultiples of S2 and M2 periods,
resulting in peaks at 24.0 and 24.8 h (although the 24.0 h
peak was essentially superimposed on that of K1 to form
a composite peak with its high value at 23.96 h)
(Fig. 3B). The La Paz tidal periodogram closely resembled others computed for mixed semidiurnal tides at Los
Angeles, Calif., USA (Enright 1965), and San Francisco,
Calif., USA (Evans 1976). Both cosinor and periodogram analyses of the 54-day activity record of crab LP10
identified a 12.4-h circatidal component and a daily
rhythm at 24 h, and its bimodal components at 11.9–
12.0 h (Fig. 3C, D).
Description of activity patterns of a representative
crab from each site
The 54-day actogram for crab LP10 shows the daily
patterns that produced statistically significant cosinor
peaks at 11.99, 12.44, and 24.01 h in Fig. 3, and it
demonstrates their day-to-day relationship to the
changing schedule of tidal immersion (Fig. 4). The daily
activity pattern is bimodal, with a strong peak centered
shortly after the beginning of the light period and a
second peak that is initially strong in the early evening,
but weakens during the course of the experiment. The
bimodality is described by the cosinor peak at 11.99 h,
but the mean difference in amplitude between the
morning and evening peaks also results in a daily component at 24.01 h (Table 1). Timing of the evening peak
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Fig. 4 Uca princeps. Doubleplotted actograms for a
representative crab specimen
from each study site. For each
actogram, tidal immersion
patterns, determined from
Fig. 1, are shown as a stippled
overlay. The bar at the top of the
actogram indicates the light–
dark regime. Letters denote
stage of the declinational cycle
as in Fig. 1 for the right panels
of LP, SB, and MN actograms,
and symbols denote lunar phase
for ML. Early evening clusters
of activity indicative of
circatidal modulation are
encircled. A double plot of the
mean daily waveform is
represented in the first panel
below each actogram as a curve
consisting of mean values for
the 20-min bins of activity from
the actogram directly above.
Amplitudes are given in activity
units from 0 to 3. The second
panel below each actogram
shows the mean circatidal
waveform drawn in the period
detected by non-linear, leastsquares cosinor analysis and
aligned according to the phase
on the first day of recording; the
waveforms were scaled to the
20-min bin with the maximum
amplitude so that waveform
patterns could be more clearly
visualized even when the
amplitude of the periodic
component was small
Table 1 Uca princeps. Results
of cosinor analysis for period
lengths and amplitudes of
statistically significant activity
components of representative
crabs in Fig. 4. Reported data
for periods are the highest
amplitudes (±95% confidence
intervals) (ND no significant
periodic component was
detected)
Periodic component
12-h period
Period (h)
Amplitude
12.4-h period
Period (h)
Amplitude
24-h period
Period (h)
Amplitude
Crab specimen
LP10
SB14
MN05
ML14
11.986±0.015
0.23±0.055
11.986±0.015
0.36±0.05
12.160±0.07
0.38±0.10
11.910±0.07
0.36±0.13
12.439±0.020
0.19±0.05
12.440±0.07
0.16±0.05
ND
12.400±0.03
0.81±0.13
24.005±0.065
0.18±0.05
23.781±0.10
0.16±0.05
24.103±0.11
0.97±0.10
23.87±0.26
0.30±0.13
coincides with the immersion of the crabs habitat by the
23.93-h K1 diurnal component of the LP tide. Both
peaks of the daily activity pattern are strongly expressed
during the semidiurnal equatorial tides occurring during
the first week of the recording period. However, as the
moon approaches its northern declinational extreme on
3 April and the tropical tide develops (Figs. 1, 4), the
evening onset of activity undergoes a series of delaying
phase shifts that track the progression of the tropical
tide across the dark phase of the light–dark cycle (Fig. 4,
encircled activity). The tracking pattern is repeated, with
the tropical tides centered on 18 and 30 April. These
modulations of the daily rhythm contribute to the statistically significant circatidal peak at 12.44 h, but the
daily rhythm still dominates the overall activity pattern
just as the diurnal K1 constituent of the tidal immersion
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mid-morning and evening bouts of activity in the mean
daily waveform are absent from the actogram until 7
March, when their emergence can be explained by the
changing phase relationship between the daily and circatidal rhythms. On the first day of the experiment (1
March), the mid-morning and evening maxima of the
daily rhythm were cancelled by the minima of the circatidal component as the daily and circatidal components were in antiphase (Fig. 4, middle and lower panel).
By 7 March the 24.80-h circatidal rhythm shifted 4.8 h
(0.80 h day)1·6 days) to bring its peaks into phase
alignment with the daily peaks, thereby augmenting
them and producing the prominent mid-morning and
early evening peaks of the mean daily waveform.
pattern is more prominent than the semidiurnal M2
partial tide.
Crab SB14 resembles LP10 in possessing a conspicuous bimodal daily component, with a clear midmorning peak and another in the early evening. The two
peaks are closer in amplitude than those in LP10,
resulting in a strong cosinor component at 11.99 h and a
weaker one at 23.78 h (Table 1). The strength of the
evening peak waxes and wanes in synchrony with the
tropical and equatorial tidal cycle and undergoes phase
shifts resembling those in LP10, although the influence
of the K1 diurnal constituent is not as pronounced at SB
as at LP (Fig. 4, encircled areas). As in crab LP10, the
tide-related character of these modulations is confirmed
by the low-amplitude but statistically significant circatidal component at 12.44 h (Table 1). A surprising feature of the actogram is the apparent leftward drift of the
times of mid-morning onset, roughly paralleling the
progression of the 23.93-h diurnal K1 tidal constituent
across the solar day (Fig. 4, drift indicated by sloping
line in right panel). The drift would appear to explain
why the period of the daily component was significantly
<24.0 h.
Crab MN05 is the most intensely nocturnal of all
crabs studied, but its activity was nevertheless suppressed in the early evening between 1 and 5 April, when
the home beach was immersed by tropical tides (Fig. 4).
This suppression is insufficient to produce a detectable
circatidal rhythm in the face of the dominant 24.1-h
daily component, although it may have contributed to
the lengthening of the weak bimodal daily component to
12.2 h (Table 1). Recall that the S2 semidiurnal tidal
component is dominant over the M2 component at this
site (Fig. 2).
Crab ML14 demonstrates strong interplay between a
daily rhythm and a circatidal rhythm of more than twice
its cosinor amplitude (Fig. 4; Table 1). The mean daily
waveform is sharply defined by a brief suppression of
activity at dawn, strong mid-morning peak, afternoon
decline, and extended nocturnal activity. The prominent
Daily and circatidal rhythms were consistently observed
in all crabs from all populations, except MN, where only
4 of 9 crabs showed evidence of circatidal rhythms, and
these were low in amplitude and variable in waveform
(Table 2). Waveforms of the mean daily rhythms for the
four populations were similar in their tendency toward
bimodality, but differed in relative amplitudes of
morning and evening peaks (Fig. 5, left panels). In
general, crabs exhibited a low level of activity prior to
sunrise or lights-on and then a small spike at sunrise,
followed by a rapid increase to a mid-morning high.
Activity level declined across the afternoon, but was
elevated at sunset and then dropped through the night,
except at MN where nocturnal activity levels remained
high. The mid-morning peak tended to occur earlier in
crabs from ML and LP than those at SB, and crabs from
MN had the lowest daytime activity peak in relation to
nocturnal activity levels (Fig. 4).
Persistent circatidal rhythms had mean period lengths
that were consistently within a standard deviation of the
12.42-h period of the M2 partial tide (Table 2). The
amplitude of the circatidal rhythms varied among study
Table 2 Uca princeps. Results of cosinor analysis for all crabs at
each study site, with a statistical analysis of difference in tidal
periodic behavior among sites; each period value is a mean (±SD).
%Tidal
was
calculated
as
follows:
%Tidal=[12.4 h/
(12 h+12.4 h+24 h)]·100. Capital letters denote significant differences in percent activity in a tidal periodicity (%Tidal) between
ML and other sites (ANOVA, Tukeys honestly significant differences, P<0.05 for significance)
Periodic
component
12-h period
Period (h)
Amplitude
12.4-h period
Period (h)
Amplitude
24-h period
Period (h)
Amplitude
%Tidal
a
Population summaries for each site
Site
LP (n=12)
SB (n=15)
MN (n=9)
ML (n=5)
12.00±0.05
0.22±0.07
11.98±0.04
0.21±0.10
12.01±0.10
0.14±0.11
11.92±0.04
0.22±0.09
12.44±0.12
0.14±0.07
12.40±0.08
0.11±0.05
12.40±0.05a
0.07±0.04
12.41±0.02
0.43±0.23
24.1±0.62
0.17±0.07
25.72±9.04B
23.76±0.52
0.13±0.09
24.67±7.70B
24.37±0.67
0.20±0.29
12.92±16.11Bb
23.94±0.09
0.19±0.09
55.08±8.28A
n=4 individuals with significant periods of 12.4 h
Values of 0 were input for the five individuals that had no significant period of 12.4 h in the calculation of %Tidal
b
480
significant rhythms identified by cosinor analysis (%Tidal; Table 2). The %Tidal was significantly greater for
the collection from ML than for any of the other data
sets, but none of the other collections were found to be
statistically different from one another (Table 2; ANOVA, P<.05).
Fig. 5 Uca princeps. Mean waveforms (solid lines) ±SE (dotted
lines) for all crabs from each study site for 24-h periods (left) and
circatidal periods (right). Blue curves superimposed on the
circatidal waveforms of LP, SB, and MN are the mean 24.84-h
periodic components of the tidal data from a 28-day series of tidal
prediction values from Xtide (D. Flater, http://www.flaterco.com/
xtide), generated using periodogram analysis. The blue curve
superimposed on the circatidal waveform for ML is the tidal curve
on the first day of data collection (see Fig. 1), as the M2 component
at this site is so strong that it is coincident with the mean 24.84-h
periodic component from this site
Discussion
sites and was lowest in crabs from MN and highest for
ML (Table 2; Fig. 5, right panels). Circatidal activity at
ML was initiated near the times of high tide and peaked
on the ebbing tide, whereas peaks in mean circatidal
waveforms at mixed tide sites appeared to more nearly
parallel those of the local M2 constituents (Fig. 5, right
panels and blue tide traces). To compare locomotor
patterns from the four locations, we calculated the percentage of activity in the circatidal period out of the
total amplitude contributed by each of the statistically
Intertidal organisms whose behavior is determined by
timing daily and tidal cycles must be able to adjust their
biological rhythms to local variation in the form of the
tide. Our results indicate that different populations of
Uca princeps can regulate the interplay of daily and
circatidal rhythms to produce activity patterns that
conform to semidiurnal and mixed types of tide. Strong
mean daily rhythms were present in all four study populations, and statistically significant circatidal rhythms,
in three. These findings suggest that the dual daily and
481
circatidal timing model proposed to account for
adjustment to semidiurnal tides at Woods Hole can be
extended to U. princeps from both semidiurnal and
mixed tide habitats.
The expression of daily rhythms is presumably controlled by the provision of a light–dark cycle, just as it
was for crabs at Woods Hole (Barnwell 1966). Under
the light–dark cycle, laboratory recordings of activity in
U. princeps conformed to the general daily pattern of
field behavior in tropical fiddler crabs (Crane 1975).
Greatest activity took place on mid-morning low tides
and decreased as the tide shifted into the afternoon.
When nocturnal activity was present, it tended to occur
on the low tides before midnight. Our finding of nocturnal activity was consistent with reports that other
species of fiddler crabs often engage in nocturnal foraging and acoustical communication (Crane 1975) and
that female fiddler crabs release their freshly hatched
larvae on high amplitude tides under cover of darkness
(Morgan 1995). We did not establish a linkage between
reproduction and activity patterns, since we did not
determine the reproductive status of the females, and,
although three females showed strong nocturnal
behavior in the representative actograms, so did males in
other recordings.
Circatidal rhythms were a consistent component of
activity patterns for all study sites except MN. Periods
of the rhythms showed a remarkably accurate match to
the 12.42-h period of the oceanographic M2 partial tide.
This agrees with findings of similar accuracy for circatidal rhythms studied under natural light–dark cycles at
Woods Hole (Barnwell 1966, 1968). Also in agreement
with results from Woods Hole was the tendency of
circatidal activity at ML to be initiated during high tide
and to peak in advance of low water (Webb and Brown
1965, Barnwell 1966, 1968, Palmer 1988). This relationship has been considered enigmatic, because fiddler
crabs are typically regarded as being active at ‘‘low’’
tide (Palmer 1988). The laboratory results may be
indicative of the importance to crabs of emerging
quickly from their burrows on the ebbing tide so as to
maximize surface time for establishing territories, feeding, and finding mates and, in the case of ovigerous
females, to hatch their larvae for dispersal as close as
possible to the onset of the ebbing spring tide (Morgan
1995). At mixed tide sites, circatidal activity corresponded rather consistently with high tides. This agreed
with the actogram patterns of LP10 and SB14, for
which circatidal bands of activity overlapped the stippled areas, indicating periods of tidal immersion
(Fig. 4). Further analysis of the complex interactions
between weak circatidal rhythms and strong daily ones
may increase our understanding of the phase relationship of circatidal rhythms and the tide.
Although similar in period length, circatidal rhythms
from the study sites reflected major differences between
amplitudes of the local M2 partial tides. This was shown
by the significantly greater prominence of the circatidal
component in the overall activity of crabs from the
strong semidiurnal tidal location at ML as compared to
LP, SB, and MN, where M2 amplitudes were much
lower (Table 2). The greater strength of the circatidal
rhythm compared to the daily rhythm was yet another
feature shared by U. princeps at ML with crabs from the
semidiurnal tidal coast at Woods Hole (Barnwell 1966,
1968). Moreover, at both sites, circatidal rhythms
interacted with daily rhythms to produce elevated bouts
of activity at semilunar intervals correlated to the spring
tide cycle. In this regard, and because of its bimodality,
the daily component in U. princeps acted as the biological counterpart to the 12.00-h S2 partial tide, which
produces the spring tide cycle by phase synchronization
of its peaks with those of the M2 partial tide at semilunar
intervals.
At mixed tide sites the dominance of the crabs circatidal and daily rhythms was reversed, and daily
rhythms were more strongly and consistently expressed
on a day-to-day basis than at ML. A circatidal component was still present in crabs from LP and SB, but as
a lower amplitude modulation of the daily rhythm. The
modulated changes in activity pattern mirrored the shift
in amplitude between semidiurnal and diurnal tidal
components, resulting from the diurnal inequality at the
mixed tide sites. During the diurnal inequality one of the
two semidiurnal M2 peaks in the tidal day is suppressed
and the other is amplified, resulting in a band of
immersion by tropical tides occurring for several successive days as the moon passes through a declinational
maximum. At the time of year that our recordings were
made, onsets of this band of immersion occurred during
the early evening and into the daylight hours of late
afternoon, as was indicated most prominently by the
immersion stippling on the actograms of representative
crabs from LP and SB (Fig. 4). It was during these
tropical tides that the evening peak of activity showed
the strongest evidence of circatidal modulation in the
timing of its onsets.
The match between daily (24.0 h) activity rhythms of
the crabs and the mixed tide pattern was imperfect,
however, because the tidal diurnal inequality is driven by
the 23.93-h sidereal period of the K1 tide (Barnwell
1976). Because of its shorter period, the K1 component
will occur progressively earlier in relation to the daily
cycle at a rate of 2 h month)1 and will scan it entirely in
the course of a year. In order to maintain a consistent
phase relationship to the K1 flood tide, the daily rhythm
would require constant rephasing at the sidereal rate.
Because the recordings of our study were obtained only
between late March and early May, we do not have a
picture of how the daily rhythm responds at other times
of year. We observed some evidence that crabs from LP
and SB advanced the phase of the mid-morning peak,
mirroring the shift of the K1 partial tide (Fig. 4, SB14).
It will be necessary to search for other examples of this
behavior to determine if it represented a distinct form of
rhythmic adjustment to the K1 tide or was simply a
coincidental phase drift or transformation in the waveform of the daily rhythm.
482
Attempts to replicate the results of activity studies of
three species of Uca from Woods Hole have been complicated by large differences in the strength and clarity in
the expression of rhythms in different populations and
species of Uca (Neumann 1981). As an example, studies
of a population of U. crenulata from the mixed tide coast
of southern California yielded poorly defined activity
patterns (Honegger 1973a, 1973b). Only about half of
the crabs showed evidence of circadian or circatidal
rhythms, and these were often present for no more than
3–4 days. Of the rhythmic crabs, about half had tidal
rhythms, and, interestingly, some of these appeared to
reflect the degree of diurnal inequality on the day of
collection. U. crenulata inhabits the upper intertidal
zone and experiences a complex pattern of tidal
immersion on the mixed tide shores of its habitat (Honegger 1973a) and, thus, may rely upon a flexible
strategy of more direct response to local tidal changes
(Neumann 1981). On the other hand, results from
U. princeps at ML in the present study and from other
species at Woods Hole (Barnwell 1966) suggest that
fiddler crabs most favorable for the investigation of
clock-timed circatidal rhythms may be those that experience regular flooding by tides with a strong M2 constituent.
In conclusion, this study indicates that the fiddler crab
U. princeps possesses a circatidal rhythm, tuned in both
period and amplitude to the 12.4-h M2 constituent of the
local tide. A second component of the crabs timing system is a daily rhythm that primarily serves as an adaptation to the solar day–night cycle, but also plays an
important role in tidal adjustment. In semidiurnal tidal
habitats, the daily rhythm functions as the counterpart of
the 12.0-h S2 tidal constituent through its modulation of
the circatidal rhythm to produce semilunar rhythms
tracking the spring tide cycle. In mixed tide habitats the
daily rhythm increases in prominence, with the result that
behavior more closely approximates the diurnal tidal
pattern produced by the 23.93-h K1 tidal constituent.
Acknowledgements F. Halberg and the staff at the Chronobiology
Laboratories, University of Minnesota Medical School, provided
access to the cosinor analysis program. R. Ray, Goddard Space
Flight Center, Greenbelt, Md., guided us to NASA/JPL TOPEX/
POSEIDON global ocean sea surface height data, and J. Ganong,
Stanford University, helped us to plot the data. The Organization
for Tropical Studies facilitated research in Costa Rica.
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