RESEARCH ARTICLE

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 circatidalrhythms to track the tidal cycle, but tidal patterns mayvary within a species� range and necessitate adaptationto the local tides. Circatidal rhythms were examined inpopulations of the eastern Pacific fiddler crab Ucaprinceps (Smith) from four sites with differing tidalcharacteristics, La Paz (24�10¢N; 110�21¢W), San Blas(21�33¢N; 105�18¢W) and Manzanillo (19�6¢N;104�24¢W), Mexico (lower amplitude, mixed semidiurnaltides) and Mata de Limon, Costa Rica (9�55¢N;84�43¢W) (high-amplitude, semidiurnal tides). Localtides were characterized by harmonic constants of M2,S2, K1, and O1, partial tides that largely determine theirsemidiurnal and diurnal features. Rhythmic structure incontinuously recorded locomotor activity of individualcrabs held under laboratory conditions was described bycosinor and periodogram methods of time-series analy-sis. Both daily and circatidal rhythms were found incrabs studied in light–dark cycles set to local conditionsat the time of collection. Crabs at all four sites shared atendency toward bimodality, with a mid-morningactivity peak and varying degrees of nocturnal activity.Circatidal rhythms closely matching the period of the12.42-h M2 partial tide were consistently present at allsites except Manzanillo. At Mata de Limon, the circa-tidal rhythm clearly dominated locomotor activity, butwas strongly modulated by a daily rhythm in a repeatingpattern at a semilunar interval. In contrast, the ampli-tude of the daily rhythm was higher than that of thecircatidal rhythm in crabs from the three mixed tide sites

on the Mexican coast, where the tidal pattern is domi-nated by a diurnal inequality arising from the diurnal K1

and O1 partial tides. These results suggest that popula-tions of U. princeps use both daily and circatidal timingsystems to track local forms of the tide generated bytheir M2, S2, K1, and O1 geophysical counterparts.

Introduction

The intertidal zone is a dynamic habitat, where the riseand fall of the tides alternately expose organisms toconflicting demands of marine and terrestrial biomes(Newell 1979; Stillman 2002, and references therein). Inresponse, many intertidal species have evolved mecha-nisms for timing their activities to predictable elementsof the tidal and solar day–night cycles responsible formuch of the environmental variation (Neumann 1981;Palmer 1995). In a remarkable parallel with circadianrhythms, intertidal organisms may possess circatidalrhythms that allow them to track the local tidal cycleand program their activities in anticipation of itschanging phases. The presence of circatidal rhythms wasclearly demonstrated in studies of locomotor activity inthree 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 labora-tory conditions displayed persistent tidal rhythmsapproximating the mean 12.42-h period of the localsemidiurnal tides (Barnwell 1966, 1968). Moreover, theamplitude of the circatidal rhythms was modulated atspecific phases of the 24-h day–night cycle, and thesemodulations produced a 2-week rhythm in activity thatmatched the 14.8-day semilunar cycle of spring and neaptides (Barnwell 1966, 1968).

The laboratory findings closely reflected the crabs�dependence upon environmental rhythms in their natu-ral habitat. In local salt marshes fiddler crabs restrictactivity essentially to the period of aerial exposure dur-ing the low-water portion of the tidal cycle (Crane 1975);

Marine Biology (2004) 144: 473–482DOI 10.1007/s00227-003-1213-6

Communicated by J.P. Grassle, New Brunswick

J. H. Stillman (&) Æ F. H. BarnwellDepartment of Ecology, Evolution and Behavior,University of Minnesota, St. Paul, MN 55108, USAE-mail: stillman@hawaii.eduFax: +1-808-9569812

Present address: J. H. StillmanDepartment of Zoology,University of Hawaii at Manoa, 152 Edmonson Hall,2538 McCarthy Mall, Honolulu, HI 96822, USA

they engage in visually oriented daytime courtship dis-plays and nocturnal bouts of acoustic signaling whenlow tide occurs at specific phases of the day–night cycle(Salmon 1965); and all stages of their reproductiverhythms can be correlated with the semilunar cycle ofspring and neap tides (Kellmeyer and Salmon 2001).

From these and earlier experiments a model wasproposed that all three Uca species in Woods Hole wereadapted to the daily and tidal environmental cyclesthrough dual timing systems that cued activity to par-ticular phases of each of the two environmental rhythms(Webb and Brown 1965; Barnwell and Zinnel 1984). Onesystem generated circatidal rhythms as adjustments tothe 12.42-h cycle of the tide, and the other produceddaily rhythms paralleling the 24.0-h solar cycle. Initiallythe daily component was thought to be the output of acircadian clock, but data from longer recordings oflocomotor activity led to the conclusion that the light–dark cycle plays a central role in the expression of bothdaily and circatidal rhythms (Barnwell 1966, 1968).While it was controversial at the time to propose that anorganism might possess two separate timing systems, itis now accepted that circadian organization incorporatesmultiple oscillatory components (Page 2001).

The dual rhythm model offers a reasonable explana-tion for how an organism might adapt to the complexinterplay of daily, tidal, and semilunar cycles in asemidiurnal tidal habitat like Woods Hole, but thequestion has been raised about its utility for regions withdifferent tidal characteristics (Barnwell 1976). On manycoastlines of the world, particularly in the Pacific andIndian Oceans, the form of the tide is determined by thepresence of a diurnal inequality that alters the relativeamplitude and interval of the two semidiurnal tidalpeaks. The inequality is produced by the declination ofthe moon�s orbit relative to the earth�s equator andachieves its maximum effect every 13.66 days, on aver-age, when the moon reaches the northern or southernangular limit of the declinational cycle. Tides with aclear diurnal inequality are referred to as mixed tides,because they alternate in form at roughly weekly inter-vals between semidiurnal (equatorial) tides, when themoon stands over the equator, and more strongly diur-nal (tropical) tides, when the moon reaches its declina-tional maximum near the Tropics of Cancer andCapricorn (Defant 1961).

Because of regional differences in resonance responseof ocean basins to semidiurnal and diurnal periodicitiesof tide-raising forces, prominence of the diurnalinequality can shift abruptly over a relatively short dis-tance. A good example is seen near Puerto Angel,Mexico (15�40¢N; 96�29¢W), where the coastline projectsinto the Pacific Ocean at the western end of the Gulf ofTehuantepec (Fig. 1). The form of tide north of thispoint is mixed, with an obvious diurnal inequality andmean diurnal tidal range of about a meter. Eastward andsouth of the point, the diurnal inequality abruptlydiminishes as the tide assumes a semidiurnal form andincreases in amplitude along the coast of Central

America until it reaches a spring tide range of 5 m in theBay of Panama (Fig. 1).

We took advantage of the transition in tidal patternsalong the western coast of Mexico to examine the adap-tation of locomotor activity rhythms to different forms ofthe tide in local populations of the fiddler crab Ucaprinceps. This species occurs between the southern Gulfof California and Peru and is thus a wide-ranging mem-ber of the fauna of the tropical eastern Pacific (Crane1975; Briggs 1995). We studied populations occupyinghabitats with mixed tides along the Mexican coast at LaPaz, San Blas, and Manzanillo, and semidiurnal tides atMata de Limon near Puntarenas, Costa Rica. The aim ofthis study was to characterize the rhythmic nature of thecrabs� activity patterns and to determine if they were re-lated to the periodic structure of the local tide. Toaccomplish this aim, we visually and statistically ana-lyzed individual crab activity recordings to understandthe 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 lowwaters from tidal reference data for each of our sites to representtidal patterns (Fig. 1). Values for La Paz are based on correctionsto daily predictions for Guaymas, Mexico (27�56¢N; 110�54¢W)(U.S. Department of Commerce, Coast and Geodetic Survey, tidetable for 1979). Those for San Blas are the values for PuertoVallarta (20�37¢N; 105�15¢W)), which, along with those for Man-zanillo, were determined as corrections on daily predictions for SanDiego, USA (32�43¢N; 117�10¢W) (U.S. Department of Commerce,Coast and Geodetic Survey, tide tables for 1985 and 1988). Valuesfor Mata de Limon, Costa Rica, are those of daily predictions forPuntarenas, Costa Rica (9�58¢N; 84�50¢W) (U.S. Department ofCommerce, Coast and Geodetic Survey, tide table for 1966). Thetide curves show that mixed semidiurnal, low-amplitude tides arepresent at La Paz, San Blas, and Manzanillo, where the tides shiftbetween one and two peaks per tidal day in accordance with thedeclinational cycle, and that tides at Mata de Limon are strictlysemidiurnal with two high-amplitude peaks per tidal day.

For each location we estimated the mean tidal elevation of theUca princeps population, and these elevations are shown as dottedlines on the tide curves (Fig. 1). Times of tidal immersion weremeasured from the line and reconstructed in the form of rasterplots superimposed on the actograms used here for displaying crabactivity patterns.

We have mathematically characterized the tides at our field sitesby their principal harmonic components, represented as a series ofsimple cosine curves referred to as partial or constituent tides(Defant 1961). Periods of the partial tides are dictated by themovement of the earth, moon, and sun, while their respectiveamplitudes and phase angles are constants that define the featuresof the local tides. We used the four major constituents that largelydetermine the characteristics of tides in the tropical eastern Pacificto compare our sites. Two semidiurnal components are the 12.42-hprincipal lunar semidiurnal constituent, M2, and the 12.00-h prin-cipal solar semidiurnal constituent, S2. The diurnal components,which are responsible for the diurnal inequality, are the lunisolardiurnal constituent, K1, with a period of 23.93 h, and the lunardiurnal constituent, O1, at 25.82 h. The semidiurnal character ofthe tide at Mata de Limon is due to the overwhelming amplitude ofthe M2 component (Fig. 2). At mixed tide sites, however, theamplitude of the M2 partial tide was reduced in relation to theother components, and at Manzanillo its value fell below that of

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the S2 partial tide (Fig. 2). The semidiurnality of the tides can begenerally described using the ‘‘formzahl,’’ or form number, F, asthe ratio of the sum of the amplitudes of the primary diurnalharmonic constituents to that of the primary semidiurnal ones[F=(K1+O1)/(M2+S2)] (Defant 1961). This ratio defines the

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 Fnumber of 0.11, whereas Manzanillo, San Blas, and La Paz havemixed semidiurnal tides, with F numbers of 0.90, 0.60 and 1.01,respectively.

Recent advances in satellite monitoring of ocean surfacetopography have allowed global-scale analyses of F values. Usingdata on the periodic constants K1, O1, M2, and S2 generated fromthe satellite data sets, we computed and mapped F numbers for thetides of the tropical eastern Pacific Ocean (Fig. 1, map). This globalmap does not replace the computation of harmonic constants forcoastal localities from tide gauge stations, because the oceanic tideis modified as it encounters continental shelf depths and irregu-larities of the coastline. However, the map reveals the steep tran-sition between mixed semidiurnal and semidiurnal forms of the tideacross the range of our study sites.

Specimen collection and maintenance

Uca princeps (Smith 1870) is a relatively large fiddler crab assignedto the subgenus Uca (Rosenberg 2001). Maximum carapace widthis >40 mm (Crane 1975), but our specimens were 16–32 mm. Male

Fig. 1 Characterization of tidal patterns in the tropical easternPacific. Left panels: tide curves for dates of activity recordings forcrabs from the four study sites. Data were generated frompublished tide tables (U.S. Department of Commerce, Coast andGeodetic Survey, tide tables for 1966, 1979, 1985 and 1988) usingrecommended corrections from tide stations. Horizontal linesindicate the estimated intertidal elevation for each colony of crabs.Circles represent phases of the moon (filled new moon; half-filledhalf moon; open full moon), and letters denote the declinationalcycle (N northern declinational maximum; E equatorial crossing ofthe moon; S southern declinational maximum). Arrows indicateapproximate locations of collection sites. Right panel: map of tidalform numbers, F=(K1+O1)/(M2+S2), showing variation instrength 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 DistributedActive Archive Center at the Jet Propulsion Laboratory, CaliforniaInstitute of Technology (PA Puerto Angel, Mexico)

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and female specimens were collected from exposed tidal flats ofeach study site on four occasions in February or March 1966, 1979,1985, and 1988.

La Paz, Baja Sur Province, Mexico (LP) (24�10¢N; 110�21¢W)

Twelve specimens were collected on 22 March 1979 from anopen tidal area of soft mud below the highway between La Pazand Pichilingue on the eastern shore of Bahia de La Paz. Crabswere transported to Minneapolis, Minn., USA, the next day andplaced in actographs containing artificial seawater at 35& onthe following day, on an illumination cycle of 12.17 hlight:11.83 h dark set to the local time of sunrise and sunset atLa Paz. Fluorescent light levels ranged from 500 to 2000 lux,depending on the position of the actograph. Temperature of theroom was maintained at 25±1�C throughout the experiment.Crabs were not fed, as was the case with all recordings in thisstudy.

San Blas, Nayarit Province, Mexico (SB) (21�33¢N; 105�18¢W)

Fifteen specimens were collected on 29 March 1985 from a shallowmuddy-sand tidal flat along the eastern margin of Estero el Pozo.They were flown to Minneapolis on 31 March and immediatelyplaced in actographs containing artificial seawater at 35&, on a13.67 h light:10.33 h dark schedule set to encompass twilight timesof 40 min before sunrise and after sunset at San Blas. Light levelsand temperature were the same as for the La Paz experiment,above.

Manzanillo, Colima Province, Mexico (MN) (19�6¢N; 104�24¢W)

Eleven specimens were collected on 25 March 1988 from a muddy-sand tidal flat just within the mouth of Laguna Juluapan on Bahia

Santiago, approximately 12 km west of Manzanillo. They weretransported 2 days later to Minneapolis and immediately placed inactographs containing artificial seawater at 32&, on a 13 hlight:11 h dark schedule set to the twilight times of approximately30 min before sunrise and after sunset at Manzanillo. Light levelswere the same as for the La Paz experiment, above, and tempera-ture was maintained at 27±1�C throughout the experiment.

Mata de Limon, Puntarenas Province, Costa Rica(ML) (9�55¢N; 84�43¢W)

Five specimens were collected on 28 February 1966 from an openmuddy area on the northwestern edge of the tidal lagoon, trans-ported to San Jose, Costa Rica, and placed in actographs on 1March with exposure to the natural illumination cycle (roughly13 h light:11 h dark) through a shaded north-facing window. Airtemperature in the room varied daily from a low of 20.7�C to a highof 26.2�C. Crabs were maintained in seawater collected at the studysite.

Data collection and statistical analysis

Two types of actographs were employed for the detection oflocomotor activity. Round plastic cups as illustrated in Brown(1970) were used in San Jose, Costa Rica, and plastic boxes fittedwith a false floor as shown in Thurman (1998) in Minnesota. Asingle crab was placed with seawater in either device where itslocomotor activity rocked the cup or false floor and triggered amovement-sensitive contact switch. The signal from the switchcaused a pen deflection on an Esterline–Angus strip chart recorder,giving a continuous trace of activity for the duration of theexperiment. Pen tracings on strip charts were quantified for each10-min interval on a scale of from 0 to 3 (0=no activity, 1=one ortwo traces, 2=up to one-half of the interval filled in by traces, and3=more than one-half of the interval filled by traces). The datawere hand-entered in computer spreadsheet files, and data analyseswere performed with cosinor and periodogram procedures.

Cosinor analysis uses a least squares method to identify the bestfit of a cosine curve to periodicities in the data and to provideestimates of period length, amplitude, and phase angle of the fittedcurve, along with a statistical test of significance for each estimate(Halberg et al. 1977, 1987). We utilized the non-linear method thatreanalyzes the statistically significant peaks initially identified bylinear analysis. While the cosine curve may not resemble the bio-logical waveform, it serves as a useful mathematical model forcharacterizing important parameters of rhythm components(Dowse and Ringo 1991).

Periodogram analysis (Enright 1965) with TAU software (Mini-Mitter, Sunriver, Ore.) cuts a time series into segments of a speci-fied period length, adds the segments to determine their averagewaveform, and computes the standard deviation. The procedure isrepeated across a specified range of periods (e.g. at 0.01-h intervalsfrom 10 to 30 h) to produce a spectrum (periodogram) of standarddeviations plotted against period length. High standard deviationsgenerally indicate period lengths with strong repetitive patterns aswell as submultiples and supermultiples of the fundamental fre-quencies (Enright 1965; Sokolove and Bushell 1978).

We compared the power of periodogram and cosinor analysismethods to resolve the presence of multiple periodicities in LP tidesand one crab specimen from LP (Fig. 3). The tide data for peri-odogram analysis were obtained by reading hourly values from thesaw-tooth graph of the times and heights of high- and low-waterpredictions of a 40-day series (Fig. 1). Cosinor analysis does notrequire equidistant data, so we used only the values for daily high-and low-water predictions along with midpoint values for the linesconnecting these points in a 60-day series. Cosinor and periodo-gram analyses produced similar outcomes in data sets longer than14 days, but, because cosinor analysis returns both period lengthsand error estimates, we have only reported estimates of crabrhythm parameters using this method.

Fig. 2 Amplitudes of tidal harmonic constants for field sites used inthis study [site abbreviations: LP La Paz, Mexico; SB San Blas,Mexico; MN Manzanillo, Mexico; ML Mata de Limon, CostaRica; 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 fromXtide (D. Flater, http://www.flaterco.com/xtide) for the collectionsites (or the nearest reference station to the site: Puntarenas, C.R.,for ML and Puerto Vallarta, Mex., for SB)

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Double-plotted activity histograms (actograms) and meandaily and circatidal waveforms for all specimens from each sitewere generated with TAU graphics and examined visually toconfirm the presence of components identified by cosinor analysis.Individual actograms having rhythm parameters similar to thoseof the population means were selected to show the interactions ofdaily and circatidal rhythm components in relation to the lunarphase and declinational cycle. Mean waveforms were computedfor each crab beginning with midnight on the first day ofrecording; thus, phase relationships of the mean circatidal wave-forms to the local tidal cycle were those that existed on the firstday of the experiment. Daily and circatidal waveforms for allindividuals at each study site were then pooled to obtain meanwaveforms for each population.

Results

Comparison of cosinor and periodogramtime-series analysis methods

Cosinor analysis performed better than periodogramanalysis at clearly resolving the principal harmonic

constituents in LP tide data. M2, S2, K1, and O1 con-stituents were identified, with period estimates accurateto 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 hpeak was essentially superimposed on that of K1 to forma composite peak with its high value at 23.96 h)(Fig. 3B). The La Paz tidal periodogram closely resem-bled others computed for mixed semidiurnal tides at LosAngeles, Calif., USA (Enright 1965), and San Francisco,Calif., USA (Evans 1976). Both cosinor and periodo-gram analyses of the 54-day activity record of crab LP10identified a 12.4-h circatidal component and a dailyrhythm at 24 h, and its bimodal components at 11.9–12.0 h (Fig. 3C, D).

Description of activity patterns of a representativecrab from each site

The 54-day actogram for crab LP10 shows the dailypatterns that produced statistically significant cosinorpeaks at 11.99, 12.44, and 24.01 h in Fig. 3, and itdemonstrates their day-to-day relationship to thechanging schedule of tidal immersion (Fig. 4). The dailyactivity pattern is bimodal, with a strong peak centeredshortly after the beginning of the light period and asecond peak that is initially strong in the early evening,but weakens during the course of the experiment. Thebimodality is described by the cosinor peak at 11.99 h,but the mean difference in amplitude between themorning and evening peaks also results in a daily com-ponent at 24.01 h (Table 1). Timing of the evening peak

Fig. 3A–D Uca princeps. Comparison of cosinor and periodo-gram time-series analysis methods for tide and crab locomotoractivity data. Results of: A cosinor and B periodogram analysis of40- and 60-day series of tidal prediction data for La Paz, Mexico (*statistically significant components for four principal harmonicconstituents of the tide). Inset in B shows the entire periodogramfor values from 10 to 30 h. Results of: C cosinor andD periodogram analysis applied to 54 days of activity data forcrab LP10 from La Paz [* statistically significant periods (cosinorlinear least-squares test, P<0.01)]. Vertical lines mark the expectedharmonic 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 locomotoractivity (C, D) (12.0 h, 12.42 h, 24.0 h). Lines are also drawn forsupermultiples of S2 and M2 periods for periodogram analyses (B,D). See ‘‘Materials and methods’’ for details

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coincides with the immersion of the crab�s habitat by the23.93-h K1 diurnal component of the LP tide. Bothpeaks of the daily activity pattern are strongly expressedduring the semidiurnal equatorial tides occurring duringthe first week of the recording period. However, as themoon approaches its northern declinational extreme on3 April and the tropical tide develops (Figs. 1, 4), theevening onset of activity undergoes a series of delaying

phase shifts that track the progression of the tropicaltide across the dark phase of the light–dark cycle (Fig. 4,encircled activity). The tracking pattern is repeated, withthe tropical tides centered on 18 and 30 April. Thesemodulations of the daily rhythm contribute to the sta-tistically significant circatidal peak at 12.44 h, but thedaily rhythm still dominates the overall activity patternjust as the diurnal K1 constituent of the tidal immersion

Fig. 4 Uca princeps. Double-plotted actograms for arepresentative crab specimenfrom each study site. For eachactogram, tidal immersionpatterns, determined fromFig. 1, are shown as a stippledoverlay. The bar at the top of theactogram indicates the light–dark regime. Letters denotestage of the declinational cycleas in Fig. 1 for the right panelsof LP, SB, and MN actograms,and symbols denote lunar phasefor ML. Early evening clustersof activity indicative ofcircatidal modulation areencircled. A double plot of themean daily waveform isrepresented in the first panelbelow each actogram as a curveconsisting of mean values forthe 20-min bins of activity fromthe actogram directly above.Amplitudes are given in activityunits from 0 to 3. The secondpanel below each actogramshows the mean circatidalwaveform drawn in the perioddetected by non-linear, least-squares cosinor analysis andaligned according to the phaseon the first day of recording; thewaveforms were scaled to the20-min bin with the maximumamplitude so that waveformpatterns could be more clearlyvisualized even when theamplitude of the periodiccomponent was small

Table 1 Uca princeps. Resultsof cosinor analysis for periodlengths and amplitudes ofstatistically significant activitycomponents of representativecrabs in Fig. 4. Reported datafor periods are the highestamplitudes (±95% confidenceintervals) (ND no significantperiodic component wasdetected)

Periodic component Crab specimen

LP10 SB14 MN05 ML14

�12-h periodPeriod (h) 11.986±0.015 11.986±0.015 12.160±0.07 11.910±0.07Amplitude 0.23±0.055 0.36±0.05 0.38±0.10 0.36±0.13

�12.4-h periodPeriod (h) 12.439±0.020 12.440±0.07 ND 12.400±0.03Amplitude 0.19±0.05 0.16±0.05 0.81±0.13

�24-h periodPeriod (h) 24.005±0.065 23.781±0.10 24.103±0.11 23.87±0.26Amplitude 0.18±0.05 0.16±0.05 0.97±0.10 0.30±0.13

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pattern is more prominent than the semidiurnal M2

partial tide.Crab SB14 resembles LP10 in possessing a conspic-

uous bimodal daily component, with a clear mid-morning peak and another in the early evening. The twopeaks are closer in amplitude than those in LP10,resulting in a strong cosinor component at 11.99 h and aweaker one at 23.78 h (Table 1). The strength of theevening peak waxes and wanes in synchrony with thetropical and equatorial tidal cycle and undergoes phaseshifts resembling those in LP10, although the influenceof the K1 diurnal constituent is not as pronounced at SBas at LP (Fig. 4, encircled areas). As in crab LP10, thetide-related character of these modulations is confirmedby the low-amplitude but statistically significant circa-tidal component at 12.44 h (Table 1). A surprising fea-ture of the actogram is the apparent leftward drift of thetimes of mid-morning onset, roughly paralleling theprogression of the 23.93-h diurnal K1 tidal constituentacross the solar day (Fig. 4, drift indicated by slopingline in right panel). The drift would appear to explainwhy the period of the daily component was significantly<24.0 h.

Crab MN05 is the most intensely nocturnal of allcrabs studied, but its activity was nevertheless sup-pressed in the early evening between 1 and 5 April, whenthe home beach was immersed by tropical tides (Fig. 4).This suppression is insufficient to produce a detectablecircatidal rhythm in the face of the dominant 24.1-hdaily component, although it may have contributed tothe lengthening of the weak bimodal daily component to12.2 h (Table 1). Recall that the S2 semidiurnal tidalcomponent is dominant over the M2 component at thissite (Fig. 2).

Crab ML14 demonstrates strong interplay between adaily rhythm and a circatidal rhythm of more than twiceits cosinor amplitude (Fig. 4; Table 1). The mean dailywaveform is sharply defined by a brief suppression ofactivity at dawn, strong mid-morning peak, afternoondecline, and extended nocturnal activity. The prominent

mid-morning and evening bouts of activity in the meandaily waveform are absent from the actogram until 7March, when their emergence can be explained by thechanging phase relationship between the daily and cir-catidal rhythms. On the first day of the experiment (1March), the mid-morning and evening maxima of thedaily rhythm were cancelled by the minima of the cir-catidal component as the daily and circatidal compo-nents 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 phasealignment with the daily peaks, thereby augmentingthem and producing the prominent mid-morning andearly evening peaks of the mean daily waveform.

Population summaries for each site

Daily and circatidal rhythms were consistently observedin all crabs from all populations, except MN, where only4 of 9 crabs showed evidence of circatidal rhythms, andthese were low in amplitude and variable in waveform(Table 2). Waveforms of the mean daily rhythms for thefour populations were similar in their tendency towardbimodality, but differed in relative amplitudes ofmorning and evening peaks (Fig. 5, left panels). Ingeneral, crabs exhibited a low level of activity prior tosunrise 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 waselevated at sunset and then dropped through the night,except at MN where nocturnal activity levels remainedhigh. The mid-morning peak tended to occur earlier incrabs from ML and LP than those at SB, and crabs fromMN had the lowest daytime activity peak in relation tonocturnal activity levels (Fig. 4).

Persistent circatidal rhythms had mean period lengthsthat were consistently within a standard deviation of the12.42-h period of the M2 partial tide (Table 2). Theamplitude of the circatidal rhythms varied among study

Table 2 Uca princeps. Results of cosinor analysis for all crabs ateach study site, with a statistical analysis of difference in tidalperiodic 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 dif-ferences in percent activity in a tidal periodicity (%Tidal) betweenML and other sites (ANOVA, Tukey�s honestly significant differ-ences, P<0.05 for significance)

Periodiccomponent

Site

LP (n=12) SB (n=15) MN (n=9) ML (n=5)

�12-h periodPeriod (h) 12.00±0.05 11.98±0.04 12.01±0.10 11.92±0.04Amplitude 0.22±0.07 0.21±0.10 0.14±0.11 0.22±0.09�12.4-h periodPeriod (h) 12.44±0.12 12.40±0.08 12.40±0.05a 12.41±0.02Amplitude 0.14±0.07 0.11±0.05 0.07±0.04 0.43±0.23�24-h periodPeriod (h) 24.1±0.62 23.76±0.52 24.37±0.67 23.94±0.09Amplitude 0.17±0.07 0.13±0.09 0.20±0.29 0.19±0.09

%Tidal 25.72±9.04B 24.67±7.70B 12.92±16.11Bb 55.08±8.28A

an=4 individuals with significant periods of �12.4 hbValues of 0 were input for the five individuals that had no significant period of �12.4 h in the calculation of %Tidal

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sites and was lowest in crabs from MN and highest forML (Table 2; Fig. 5, right panels). Circatidal activity atML was initiated near the times of high tide and peakedon the ebbing tide, whereas peaks in mean circatidalwaveforms at mixed tide sites appeared to more nearlyparallel those of the local M2 constituents (Fig. 5, rightpanels and blue tide traces). To compare locomotorpatterns from the four locations, we calculated the per-centage of activity in the circatidal period out of thetotal amplitude contributed by each of the statistically

significant rhythms identified by cosinor analysis (%Ti-dal; Table 2). The %Tidal was significantly greater forthe collection from ML than for any of the other datasets, but none of the other collections were found to bestatistically different from one another (Table 2; ANO-VA, P<.05).

Discussion

Intertidal organisms whose behavior is determined bytiming daily and tidal cycles must be able to adjust theirbiological rhythms to local variation in the form of thetide. Our results indicate that different populations ofUca princeps can regulate the interplay of daily andcircatidal rhythms to produce activity patterns thatconform to semidiurnal and mixed types of tide. Strongmean daily rhythms were present in all four study pop-ulations, and statistically significant circatidal rhythms,in three. These findings suggest that the dual daily and

Fig. 5 Uca princeps. Mean waveforms (solid lines) ±SE (dottedlines) for all crabs from each study site for 24-h periods (left) andcircatidal periods (right). Blue curves superimposed on thecircatidal waveforms of LP, SB, and MN are the mean 24.84-hperiodic components of the tidal data from a 28-day series of tidalprediction values from Xtide (D. Flater, http://www.flaterco.com/xtide), generated using periodogram analysis. The blue curvesuperimposed on the circatidal waveform for ML is the tidal curveon the first day of data collection (see Fig. 1), as the M2 componentat this site is so strong that it is coincident with the mean 24.84-hperiodic component from this site

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circatidal timing model proposed to account foradjustment to semidiurnal tides at Woods Hole can beextended to U. princeps from both semidiurnal andmixed tide habitats.

The expression of daily rhythms is presumably con-trolled by the provision of a light–dark cycle, just as itwas for crabs at Woods Hole (Barnwell 1966). Underthe light–dark cycle, laboratory recordings of activity inU. princeps conformed to the general daily pattern offield behavior in tropical fiddler crabs (Crane 1975).Greatest activity took place on mid-morning low tidesand decreased as the tide shifted into the afternoon.When nocturnal activity was present, it tended to occuron the low tides before midnight. Our finding of noc-turnal activity was consistent with reports that otherspecies of fiddler crabs often engage in nocturnal for-aging and acoustical communication (Crane 1975) andthat female fiddler crabs release their freshly hatchedlarvae on high amplitude tides under cover of darkness(Morgan 1995). We did not establish a linkage betweenreproduction and activity patterns, since we did notdetermine the reproductive status of the females, and,although three females showed strong nocturnalbehavior in the representative actograms, so did males inother recordings.

Circatidal rhythms were a consistent component ofactivity patterns for all study sites except MN. Periodsof the rhythms showed a remarkably accurate match tothe 12.42-h period of the oceanographic M2 partial tide.This agrees with findings of similar accuracy for circa-tidal rhythms studied under natural light–dark cycles atWoods Hole (Barnwell 1966, 1968). Also in agreementwith results from Woods Hole was the tendency ofcircatidal activity at ML to be initiated during high tideand to peak in advance of low water (Webb and Brown1965, Barnwell 1966, 1968, Palmer 1988). This rela-tionship has been considered enigmatic, because fiddlercrabs are typically regarded as being active at ‘‘low’’tide (Palmer 1988). The laboratory results may beindicative of the importance to crabs of emergingquickly from their burrows on the ebbing tide so as tomaximize surface time for establishing territories, feed-ing, and finding mates and, in the case of ovigerousfemales, to hatch their larvae for dispersal as close aspossible to the onset of the ebbing spring tide (Morgan1995). At mixed tide sites, circatidal activity corre-sponded rather consistently with high tides. This agreedwith the actogram patterns of LP10 and SB14, forwhich circatidal bands of activity overlapped the stip-pled areas, indicating periods of tidal immersion(Fig. 4). Further analysis of the complex interactionsbetween weak circatidal rhythms and strong daily onesmay increase our understanding of the phase relation-ship of circatidal rhythms and the tide.

Although similar in period length, circatidal rhythmsfrom the study sites reflected major differences betweenamplitudes of the local M2 partial tides. This was shownby the significantly greater prominence of the circatidalcomponent in the overall activity of crabs from the

strong semidiurnal tidal location at ML as compared toLP, SB, and MN, where M2 amplitudes were muchlower (Table 2). The greater strength of the circatidalrhythm compared to the daily rhythm was yet anotherfeature shared by U. princeps at ML with crabs from thesemidiurnal tidal coast at Woods Hole (Barnwell 1966,1968). Moreover, at both sites, circatidal rhythmsinteracted with daily rhythms to produce elevated boutsof activity at semilunar intervals correlated to the springtide cycle. In this regard, and because of its bimodality,the daily component in U. princeps acted as the biolog-ical counterpart to the 12.00-h S2 partial tide, whichproduces the spring tide cycle by phase synchronizationof its peaks with those of the M2 partial tide at semilunarintervals.

At mixed tide sites the dominance of the crabs� cir-catidal and daily rhythms was reversed, and dailyrhythms were more strongly and consistently expressedon a day-to-day basis than at ML. A circatidal com-ponent was still present in crabs from LP and SB, but asa lower amplitude modulation of the daily rhythm. Themodulated changes in activity pattern mirrored the shiftin amplitude between semidiurnal and diurnal tidalcomponents, resulting from the diurnal inequality at themixed tide sites. During the diurnal inequality one of thetwo semidiurnal M2 peaks in the tidal day is suppressedand the other is amplified, resulting in a band ofimmersion by tropical tides occurring for several suc-cessive days as the moon passes through a declinationalmaximum. At the time of year that our recordings weremade, onsets of this band of immersion occurred duringthe early evening and into the daylight hours of lateafternoon, as was indicated most prominently by theimmersion stippling on the actograms of representativecrabs from LP and SB (Fig. 4). It was during thesetropical tides that the evening peak of activity showedthe strongest evidence of circatidal modulation in thetiming of its onsets.

The match between daily (24.0 h) activity rhythms ofthe crabs and the mixed tide pattern was imperfect,however, because the tidal diurnal inequality is driven bythe 23.93-h sidereal period of the K1 tide (Barnwell1976). Because of its shorter period, the K1 componentwill occur progressively earlier in relation to the dailycycle at a rate of 2 h month)1 and will scan it entirely inthe course of a year. In order to maintain a consistentphase relationship to the K1 flood tide, the daily rhythmwould require constant rephasing at the sidereal rate.Because the recordings of our study were obtained onlybetween late March and early May, we do not have apicture of how the daily rhythm responds at other timesof year. We observed some evidence that crabs from LPand 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 thisbehavior to determine if it represented a distinct form ofrhythmic adjustment to the K1 tide or was simply acoincidental phase drift or transformation in the wave-form of the daily rhythm.

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Attempts to replicate the results of activity studies ofthree species of Uca from Woods Hole have been com-plicated by large differences in the strength and clarity inthe expression of rhythms in different populations andspecies of Uca (Neumann 1981). As an example, studiesof a population of U. crenulata from the mixed tide coastof southern California yielded poorly defined activitypatterns (Honegger 1973a, 1973b). Only about half ofthe crabs showed evidence of circadian or circatidalrhythms, and these were often present for no more than3–4 days. Of the rhythmic crabs, about half had tidalrhythms, and, interestingly, some of these appeared toreflect the degree of diurnal inequality on the day ofcollection. U. crenulata inhabits the upper intertidalzone and experiences a complex pattern of tidalimmersion on the mixed tide shores of its habitat (Ho-negger 1973a) and, thus, may rely upon a flexiblestrategy of more direct response to local tidal changes(Neumann 1981). On the other hand, results fromU. princeps at ML in the present study and from otherspecies at Woods Hole (Barnwell 1966) suggest thatfiddler crabs most favorable for the investigation ofclock-timed circatidal rhythms may be those that expe-rience regular flooding by tides with a strong M2 con-stituent.

In conclusion, this study indicates that the fiddler crabU. princeps possesses a circatidal rhythm, tuned in bothperiod and amplitude to the 12.4-h M2 constituent of thelocal tide. A second component of the crabs� timing sys-tem is a daily rhythm that primarily serves as an adap-tation to the solar day–night cycle, but also plays animportant role in tidal adjustment. In semidiurnal tidalhabitats, the daily rhythm functions as the counterpart ofthe 12.0-h S2 tidal constituent through its modulation ofthe circatidal rhythm to produce semilunar rhythmstracking the spring tide cycle. In mixed tide habitats thedaily rhythm increases in prominence, with the result thatbehavior more closely approximates the diurnal tidalpattern produced by the 23.93-h K1 tidal constituent.

Acknowledgements F. Halberg and the staff at the ChronobiologyLaboratories, University of Minnesota Medical School, providedaccess to the cosinor analysis program. R. Ray, Goddard SpaceFlight 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 Organizationfor Tropical Studies facilitated research in Costa Rica.

References

Barnwell FH (1966) Daily and tidal patterns of activity in indi-vidual fiddler crabs (genus Uca) from the Woods Hole region.Biol Bull (Woods Hole) 130:1–17

Barnwell FH (1968) The role of rhythmic systems in the adaptationof fiddler crabs to the intertidal zone. Am Zool 8:569–583

Barnwell FH (1976) Variation in the form of the tide and someproblems it poses for biological timing systems. In: DeCourseyPJ (ed) Biological rhythms in the marine environment. Uni-versity of South Carolina Press, Columbia, pp 161–187

Barnwell FH, Zinnel KC (1984) The fiddler crab: a model for thestudy of the internal desynchronization of circadian rhythms.In: Haus E, Kabat HF (eds) Chronobiology 1982–83. Karger,New York, pp 250–256

Briggs JC (1995) Global biogeography. Elsevier, AmsterdamBrown FA Jr (1970) Hypothesis of environmental timing of the

clock. In: Brown FA Jr, Hastings JW, Palmer JD (eds) Thebiological clock. Two views. Academic, New York, pp 13–59

Crane J (1975) Fiddler crabs of the world (Ocypodidae: genus Uca).Princeton University Press, Princeton

Defant A (1961) Physical oceanography, vol II. Pergamon, NewYork

Dowse HB, Ringo JM (1991) Comparisons between ‘‘periodo-grams’’ and spectral analysis: apples are apples after all. J TheorBiol 148:139–144

Enright JT (1965) The search for rhythmicity in biological timeseries. J Theor Biol 8:426–468

Evans WG (1976) Circadian and circatidal locomotory rhythms inthe intertidal beetle Thalassotrechus barbarae (Horn): Carabi-dae. J Exp Mar Biol Ecol 22:79–90

Halberg F, Carandenta F, Cornelissen G, Katinas GS (1977)Glossary of chronobiology. Chronobiologia 4:1–189

Halberg F, Shankaraiah K, Giese AC (1987) The chronobiology ofmarine invertebrates: methods of analysis. In: Giese AC, PearseJS, Pearse VB (eds) Reproduction of marine invertebrates,vol IX. General aspects: seeking unity in diversity. Blackwell,Palo Alto, and Boxwood, Pacific Grove, pp 331–384

Honegger H-W (1973a) Rhythmic motor activity responses of theCalifornia fiddler crab Uca crenulata to artificial light condi-tions. Mar Biol 18:19–31

Honegger H-W (1973b) Rhythmic activity responses of the fiddlercrab Uca crenulata to artificial tides and artificial light. MarBiol 21:196–202

Kellmeyer K, Salmon M (2001) Hatching rhythms of Uca thayeriRathbun: timing in semidiurnal and mixed tidal regimes. J ExpMar Biol Ecol 260:169–183

Morgan SG (1995) The timing of larval release. In: McEdward L(ed) Ecology of marine invertebrate larvae. CRC Press, BocaRaton, Fla., pp 157–191

Neumann D (1981) Tidal and lunar rhythms. In: Aschoff J (ed)Handbook of behavioral neurobiology, vol 4. Biologicalrhythms. Plenum, New York, pp 351–380

Newell RC (1979) Biology of intertidal animals. Marine EcologicalSurveys, Kent

Page T (2001) Circadian systems of invertebrates. In: Takahashi JS,Turek FW, Moore RY (eds) Handbook of behavioral neuro-biology, vol 12. Circadian clocks. Plenum, New York, pp 79–110

Palmer JD (1988) Comparative studies of tidal rhythms. VI. Sev-eral clocks govern the activity of two species of fiddler crabs.Mar Behav Physiol 13:201–219

Palmer JD (1995) The biological rhythms and clocks of intertidalanimals. Oxford University Press, New York

Rosenberg MS (2001) The systematics and taxonomy of fiddlercrabs: a phylogeny of the genus Uca. J Crustac Biol 21:839–869

Salmon M (1965) Waving display and sound production in Ucapugilator Bosc, with comparisons to U. minax and U. pugnax.Zoologica (NY) 50:123–150

Smith SI (1870) Notes on American Crustacea, no. 1. Ocypodoi-dea. Trans Conn Acad Arts Sci 2:113–176

Sokolove PG, Bushell WN (1978) The chi square periodogram: itsutility for analysis of circadian rhythms. J Theor Biol 72:131–160

Stillman JH (2002) Causes and consequences of thermal tolerancelimits in rocky intertidal porcelain crab species, genus Petro-listhes. Int Comp Biol 42:790–796

Thurman CL (1998) Locomotor rhythms in the fiddler crab, Ucasubcylindrica. Biol Rhythm Res 29:179–196

Webb HM, Brown FA Jr (1965) Interactions of diurnal and tidalrhythms in the fiddler crab Uca pugnax. Biol Bull (Woods Hole)129:582–591

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