Estuarine ingress timing as revealed by spectral analysis of otolith life history scans

Estuarine ingress timing as revealed by spectralanalysis of otolith life history scans

Reneé R. Hoover, Cynthia M. Jones, and Chester E. Grosch

Abstract: The ability to accurately measure the timing of migration is fundamental in testing hypotheses in marine ecologythat deal with migration and movement of fish populations. Timing and patterns of movement in larval and juvenile fishhave been estimated using life history scans of the chemical signatures encoded in their otoliths. We provide a quantitativeapproach to analyzing life history scan data using spectral analysis, which retrospectively measures the timing of ingress forindividual fish. Saggital otoliths from juvenile Atlantic croaker (Micropogonias undulatus) were sampled using laser abla-tion inductively coupled plasma mass spectrometry (LA-ICP-MS). Spectral analyses on these data estimate the timing of in-gress at 68 days on average using strontium and 85 days using barium. Based on the inflection points of their nonlinearmixing curves, these data reveal entry and subsequent movement up-estuary. Moreover, we use these spectrally derived esti-mates to show that growth rates did not drive ingress timing for our samples. These data thus lend no support to thecritical-size hypothesis in this instance.

Résumé : Pour vérifier des hypothèses en écologie marine touchant à la migration et aux déplacements de populations depoissons, il est essentiel de pouvoir mesurer avec exactitude le moment de la migration. Le moment et les patrons des dépla-cements de poissons larvaires et juvéniles ont été estimés à l’aide de séquences des signatures chimiques enregistrées dansles otolithes de poissons durant leur cycle vital. Nous présentons une approche quantitative d’analyse des données de sé-quence du cycle vital reposant sur l’analyse spectrale, qui permet de mesurer rétrospectivement le moment de l’entrée dansune rivière d’individus donnés. Des otolithes sagittaux de tambours brésiliens (Micropogonias undulatus) juvéniles ont étééchantillonnés par spectrométrie de masse avec plasma à couplage inductif combinée à l’ablation laser (LA-ICP-MS). L’ana-lyse spectrale de ces données permet d’estimer l’âge à l’entrée à 68 jours en moyenne avec le strontium et à 85 jours avecle baryum. À la lumière des points d’inflexion de leurs courbes de mélange non linéaires, ces données révèlent le momentde l’entrée et des déplacements subséquents vers l’amont dans l’estuaire. Nous avons en outre utilisé ces estimations tiréesde l’analyse spectrale pour démontrer que, pour nos échantillons, le moment de l’entrée dans l’estuaire n’est pas contrôlépar le taux de croissance. Aussi, ces données n’appuient pas l’hypothèse de la taille critique dans le cas présent.

[Traduit par la Rédaction]

Introduction

The ability to accurately measure the timing of migrationis fundamental in testing hypotheses in marine ecology thatdeal with migration and movement of fish populations. Forexample, the critical-size hypothesis (Houde 1997), whichlinks an animal’s ability to enter an estuary to its size andage, requires knowledge of both the mean and variance ofthe population’s size or age upon ingress (i.e., the time of es-tuarine entry). Understanding variability in the timing of in-gress is especially essential to evaluate the importance ofnursery habitats in the recruitment of larval or juvenile fishin bays and estuaries. The critical-size hypothesis (see reviewin Sogard 1997) has been supported by results in several spe-cies, but particularly well in salmon (Beamish et al. 2004;Beamish and Mahnken 2001; Farley et al. 2005). While thesestudies have increased our knowledge of complex drivers ofrecruitment dynamics, some of the key elements to testing

the hypothesis itself lack quantifiable estimates, such as thetiming of ingress.Both the timing and patterns of movement in larval and ju-

venile fish are often estimated from scans of the chemicalsignatures encoded in their otoliths (Secor et al. 2001; Thor-rold et al. 1998). The effectiveness of reconstructing theseenvironmental histories from otoliths has been demonstratedconvincingly (Chang et al. 2004; Jones and Campana 2009;Limburg 1995), especially with strontium (see review in Gil-landers 2005). However, while the technical progress inmeasuring otolith chemical concentrations has increased rap-idly, application of appropriate statistical techniques for ana-lyzing such data is still developing.When conducting life history scans on otoliths, one obtains

a series of measurements tracing the chemical compositionfrom the core, when the fish was hatched, to the edge, whichrepresents its date of capture (Campana 2005). Analyses ofthese data have been largely qualitative and graphical or,

Received 19 October 2011. Accepted 11 May 2012. Published at www.nrcresearchpress.com/cjfas on 10 July 2012.J2011-0431

Paper handled by Associate Editor Bronwyn M. Gillanders.

R.R. Hoover and C.M. Jones. Center for Quantitative Fisheries Ecology, 800 West 46th Street, Norfolk, VA 23508, USA.C.E. Grosch. Center for Coastal Physical Oceanography, 4111 Monarch Way, Norfolk, VA 23508, USA.

Corresponding author: Reneé R. Hoover (e-mail: [email protected]).

1266

Can. J. Fish. Aquat. Sci. 69: 1266–1277 (2012) doi:10.1139/F2012-058 Published by NRC Research Press

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when parametric, limited to analysis of variance (ANOVA)(Tsukamoto and Arai 2001; Morris et al. 2003; Ben-Tzvi etal. 2007). Qualitative analyses suffer from being both ad hocand subjective. Moreover, for life history scans, employingcommonly used parametric methods such as ANOVA violatesunderlying assumptions because of the intrinsic autocorrela-tion of scan data. While autocorrelation can be used as atool to find repeating patterns, if unaccounted for, it compro-mises statistical analyses because it violates the fundamentalassumption of independence (Ebisuzaki 1997; Wunsch1999). In contrast, time series analyses account for the inher-ent autocorrelation in data that have a natural order, as withlife history scan data. For example, when using otolith chem-istry to measure movement, the signature found in onegrowth band will be more similar to the preceding band thanto one formed several days earlier. A number of applicationshave been used to analyze time series data, specifically intesting hypotheses that require classification analyses. Fabletet al. (2007) reconstructed fish life histories using unsuper-vised signal processing methods in a Bayesian framework.Later, Daverat et al. (2011) applied this same method in threecatadromous species, revealing colonization tactics. Finally,zoning algorithms were used by Hedger et al. (2008) to clas-sify otolith chemistry sequences.While each of these techniques is an interesting use of life

history scan data, they each have inherent assumptions aboutthe data to achieve classification. Although not rigorously de-fined in the ecological literature, the applied statistics litera-ture clearly defines time series analyses in both the time andfrequency domains. In this paper, we use the statistical defi-nition of time series analysis in the frequency domain. Wechose to concentrate on revealing the timing of ingress usinga time series application that is particularly suited to thequestions that arise in testing life history migration hypothe-ses: spectral analysis.Spectral analysis estimates the spectral density function, or

spectrum, of a given time series (Chatfield 2004). Examiningthe spectrum of a time series allows us to separate statisti-cally significant periodic components exhibited by our datafrom the noise that is intrinsic in most empirical data. Thestrength of this approach is that it simply asks where signifi-cant changes in otolith chemistry occur, without specifying amodel for the movement pattern itself.Spectral analysis is not new to the field of ecology as a

whole; for example, Trancart et al. (2011) applied maximumentropy spectral analysis to the swimming activity of thinlipmullet (Liza remada). We introduce the application of spec-tral analysis to the time series data obtained from life historyscans of otoliths, which, to our knowledge, has not been usedon these data before. We use the ingress of juvenile Atlanticcroaker (Micropogonias undulatus) to estuarine nurseries todemonstrate the ability of this method to distinguish andquantify changes in elemental concentrations in an otolithlife history scan and to test the critical-size hypothesis. Spe-cifically, we relate the peaks in spectral density of multipleelements to measure the timing of ingress. Atlantic croakerspawn offshore in the late fall and juveniles move inshorefrom seawater to brackish water approximately 3 months afterpeak spawning occurs (Warlen and Burke 1990). To estimatethe timing of this movement, our approach makes use of thefull suite of information contained within life history scans,

including the chronology of environmental markers. Perhapsmost importantly, we demonstrate the value of spectral analy-ses in providing a proper statistical tool to test migration hy-potheses. Testing for differences in the distributions ofingress timing for populations from diverse locations, or forthe presence of annual migration through environmental gra-dients, becomes possible with quantifiable estimates formovement.

Materials and methods

Sample preparation and analysisWe sampled sagittal otoliths of juvenile Atlantic croaker

collected from the Pamlico River in North Carolina (n = 14)after standard length had been measured (57.5 ± 9.4 mm).One otolith from each fish was chosen at random (left orright) and analyzed for trace element chemistry, while thesecond sagittal otolith was used for age and growth rate anal-yses. Otoliths ranged in diameter from 1064 to 1891 µm.Otoliths were prepared for trace element analysis in a class100 clean room using the Center for Quantitative FisheriesEcology standard clean room protocols (Dorval et al. 2005).We cleaned the samples of any attached tissue and rinsedwith ultrapure hydrogen peroxide (H2O2) and ultrapure Milli-Q water. Otoliths were affixed to microscope slides withtrace-element-free silicone adhesive, sectioned through thecore, then polished using 30 and 9 µm lapping paper, ensur-ing a smooth surface for laser ablation. Otoliths were then so-nicated in ultrapure Milli-Q water and allowed to dry.We conducted trace element analysis using the MAT Ele-

ment 2 inductively coupled plasma mass spectrometer (ICP-MS) (Finnigan) at Old Dominion University (Norfolk, Vir-ginia). The ICP-MS was coupled to a 266 mm Nd:YAG la-ser, with spot size of 20 µm, speed of 5 µm·s–1, and powerof 45%, producing a trench depth of 80 µm. Instrument de-tails are given in Jones and Chen (2003). We ablated a linefrom the core of the otolith to the edge, following the meth-ods described by Thorrold et al. (1997). We analyzed otolithcalcium (48Ca), strontium (86Sr), and barium (138Ba) scannedin low-resolution mode. We converted the raw data to ele-ment-to-calcium molar ratios.Transverse thin sections were cut from the otoliths for age-

ing. Sections were mounted and polished to reveal the corefor ageing of daily growth bands. Daily ages were obtainedfollowing the methods for juvenile Atlantic croaker of Nixonand Jones (1997). Daily increment widths, used for growthrate estimation, were obtained using ImagePro Version 5.0.1software (MediaCybernetics Inc., Bethesda, Maryland). Dailyages and increments were measured on the same sample.

Data analysisBecause of the inherently temporal nature of otolith chem-

istry, we related the significant features in the elemental spec-tra to time-specific events in an individual fish’s life history.One issue that arises when interpreting a laser scan is dataspacing. Because the laser samples otoliths at a constantspeed, the resulting data are distributed equally in both laser-space and laser-time. Most fish do not grow at a constantrate, however, as is well demonstrated by many growth mod-els (e.g., Nixon and Jones 1997 and Schaffler et al. 2009a)

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for Atlantic croaker. The number of data points containedwithin each increment, therefore, varies.To convert evenly spaced laser data to nonlinear fish

growth, we translated the distance the laser traveled acrossthe otolith into the amount of growth completed by the indi-vidual fish at each time step. Doing so allowed for a directcalculation of the fish’s age for each otolith chemistry datapoint, which results in assignment of fractional age to eachscan point. To appropriately model the change in incrementwidths over time, we first fit a growth curve to the fish sizedata. The Gompertz growth model (shown below) provided agood fit to the data (Fig. 1):

ð1Þ y ¼ A0 e

eb0

eb1x�1b1

� �" #

where y is the attained growth, A0 is the value of the growthfunction at age 0, b0 is the slope of the logarithm of the rela-tive growth rate at age 0, and b1 is the slope of the logarithmof the relative growth rate (adapted from Song and Kuznet-sova (2003); also in Nixon and Jones (1997) and Gossett etal. (2007)).After fitting individual growth models, we obtained param-

eter estimates for each fish, then back-calculated the frac-tional ages, using the formula below.

ð2Þ x ¼ln

b1lnyA0

� �eb0

þ 1

24

35

b1

where all parameters are as above, and x is the fractional ageat each increment in laser-time (Fig. 1).As a result, the raw data (Fig. 2a) were spaced with re-

spect to the increment width of each day (Fig. 2b). Asidefrom correcting data spacing, the parameters from this modelwere also used in investigating potential relationships be-tween the timing of ingress and the growth rates of individ-ual fish.After we converted laser data into fractional fish ages, the

converted data were nonuniformly spaced (Fig. 2). We there-fore interpolated the data with a cubic spline to a spacing of0.2 days (i.e., Dt = 0.2). Finally, because of the inherentnoise in laser ablation (LA)-ICP-MS data, we applied a low-pass filter to remove the components of the series not addinginformation to our analysis, with the cutoff frequency (f) atfDt = 0.3. The cutoff frequency sets the boundary of the fil-ter, such that the frequencies greater than fDt = 0.3 are notpassed through the filter, hence “low-pass.”

DetrendingTo conduct spectral analyses on the interpolated data, we

applied the general time series techniques of detrending andnormalizing before calculating our spectral estimates (Brock-well and Davis 2002). These techniques are best describedthrough a statistical example. Suppose our data set{X(jDt) ≡ Xj} for j = 1, 2, …, N, with a mean X and var-iance s2

x , represents the time series of Ba:Ca measurementsthrough time. The spectrum S(f) is an estimate of the distri-bution of the signal “energy”, with f as the frequency. Here f

lies in the range 0 < f < fNy � 12Dt

, the Nyquist frequency(fNy). Because the spectrum is symmetric about f = 0:

ð3Þ 2

Z fNy

0

Sðf Þ df ¼ s2X

If Xj contains a trend, a large fraction (in some cases most)of the spectral energy will reside at low frequencies (i.e., ator in the vicinity of f = 0). This large energy density at lowfrequencies will obscure the variation of S(f) at higher fre-quencies. For example, in our case we sought to determinewhether or not there are any significant spectral “peaks” indi-cating a significant periodic component in our data. Presenceof the low frequency peak caused by the trend (Fig. 3) madeit difficult to separate these higher frequency peaks frombackground noise. We plotted the scan data to observe itsmain features, and trends were apparent, reflecting the well-studied transit from offshore to inshore. Uncovering the trendthat is both obvious in the data and well-known to the lifehistory of this fish, however, does not advance our knowl-edge of its ingress timing.Therefore, the trend was modeled by fitting either a linear

Xj ¼ A1 þ B1tj

or quadratic function

ð4Þ Xj ¼ A2 þ B2tj þ C2t2j

to the data. The coefficients of the fit were found by the leastsquares method. The fitted trend curve was then subtractedfrom the original data. The criterion for determining if thetrend was significant was computation of the variance beforeand after the fit and use of an F test to determine if the var-iances were significantly different for each individual. Of the28 trend fits this entailed calculating, 17 were quadratictrends (p values ranging from <0.0001 to 0.0119) and 11were linear trends (p values ranging from <0.0005 to 0.025).Only those trends that were significant at the a = 0.05 levelwere removed. We caution that detrending must be done

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 20 40 60 80 100 120

Age (days)

Pro

port

ional oto

lith r

adiu

s

Fig. 1. Example plot of the fitted retrospective otolith radius data(sample j). The solid line shows the predicted cumulative otolith ra-dius, and the cross-hatch (×) line shows the observed otolith radius

data, using the Gompertz model (eq. 1): y ¼ A0 e

eb0

eb1x�1b1

� �" #.

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carefully, and with knowledge of the species life history, toensure no loss of valuable information occurs.

NormalizationSuppose we now have more than one time series (i.e., Ba:

Ca measurements for sample 1 = X and Ba:Ca concentrationsfor sample 2 = Y). We standardized the data to have meansof zero and variances s2

X ¼ s2Y ¼ 1 and

ð5ÞZ fNy

0

SXðf Þ df ¼Z fNy

0

SYðf Þ df ¼ 1

2

With normalization, the relative magnitudes of significantpeaks in the respective normalized spectra, SX(f) and SY(f),are an accurate measure of the relative fraction of the total

energy in each of the peaks. Therefore, the relative magni-tude of peaks in the SY spectrum can be compared with thosein the SX spectrum, solving the problems of differing spectralvariability.

Spectral estimateFourier methods are the basis of nearly all spectral estima-

tion methods. A fundamental limitation of all such methodsis that the frequency of resolution is fixed (i.e., spectral esti-mates are obtained for a set of N frequencies):

ð6Þ fk

fNy¼ k

N; k ¼ 0; 1; 2; . . . ;N � 1

The maximum entropy method (MEM) (Press et al. 1994;

Fig. 2. (a) Sr:Ca versus distance. (b) Sr:Ca versus age of the fish.

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Priestley 1982; Ulrych and Bishop 1975) is a technique thatallows spectral estimation for any arbitrary set of frequenciesbetween zero frequency and the Nyquist frequency.The MEM is particularly good, as compared with Fourier

methods, at resolving spectral peaks at relatively low frequen-cies. The MEM is based on fitting the N data values, the{Xj}, with an autoregressive model of order M(AR(M)) proc-ess, M < N. An autoregressive process is said to be of orderM if

ð7Þ Xt ¼ a1Xt�1 þ � � � þ apXt�M þ Zt

where ai are coefficients and Zt are random variates, withmean of zero and standard deviation of one. Here, Xt is re-gressed on past values of Xt rather than independent vari-ables; hence, the model is autoregressive. The MEM spectralestimator is a function of the continuously varying frequencyf with ð0 � f � fNyÞ and is found using the formula for thespectrum of the AR(M) process as a function of f.The spectra presented here were computed using the algo-

rithm for MEM given in Press et al. (1994). The spectral es-timates were obtained for 5000 values of f in (0, fNy) andequivalently for fDt in (0, ½). A test of the numerical accu-racy of the calculation is to numerically integrate the spec-trum and compare the results with ½. In all cases, the errorwas ≤0.5%.

Confidence limitsThe confidence limits of the spectral estimates depend on

two factors, the null hypothesis as to the form of the assumednoise spectrum, and the number of degrees of freedom (df)of the spectral estimate. The null hypothesis often involvesthe assumption that the {Xj} are white noise. For the calcu-lated spectra, we observed that all of the spectral peaks foundwere at relatively low frequencies, so we used a stronger nullhypothesis; the {Xj} was red noise as generated by an AR(1)process. If {Xj} was generated by an AR(1) process, then itfollows that the constant a = r(1), the autocorrelation coeffi-cient of the {Xj} at lag 1, and the normalized spectrum ofthis AR(1) process, SAR(1), are

ð8Þ SARð1Þðf Þ ¼ 1� a2

1� 2a cos ðqÞ þ a2

where q = 2pfDt, with 0 ≤ fDt ≤ ½.

We computed the value of r(1) of the detrended and nor-malized time series of each data set and the basic red noisespectrum as above. The 0.95 and 0.99 confidence limits forthis spectrum were assumed to be those of the c2 distributionwith the df of the computed MEM spectrum. In all cases, Mwas chosen to be N/2, so the process was an AR(N/2) proc-ess with

ð9Þ df ¼ N

M¼ 2

for these spectra. Thus the confidence limits for the calcu-lated MEM spectrum are those of the c2 0.99 limits, withdf = 2, for the SAR(1) spectrum. Peaks that are significant re-present changes in elemental composition that reflected lifehistory, environment, or habitat change. The highest peak inthe spectral density plot represented the most significant per-iodic component of the series.We chose to analyze these data in a univariate setting be-

cause each element offers different information pertaining tothe timing of movement up-estuary. While both barium andstrontium are obtained from the same scan, we analyzedeach element to obtain univariate elemental signals, eachcontaining its own unique information.To test the critical-size hypothesis, we selected the highest

peak in spectral density for each individual, and regressed thetime (in days) of that peak against the growth rate of each indi-vidual. Were the critical-size hypothesis to be supported by ourdata, we would expect the fastest-growing individuals to havethe earliest timing of ingress relative to slower-growing fish.

Results

We analyzed 14 juvenile Atlantic croaker ranging in agefrom 78 to 145 days old (mean = 121.5 days, 1 standard de-viation (SD) = 18.62 days) and standard length ranged from41 to 70 mm (mean = 56.6 mm, 1 SD = 8.61 mm).The mean growth rate was 0.0115 mm·day–1 (1 SD =

0.004 mm·day–1). Growth curves showed consistently goodfits to the observed data (e.g., Fig. 1). The mean parameterestimates were A0 = 0.0279, b0 = –2.939, and b1 = –0.0111,with average proportional standard errors being 4.996%,1.049%, and 6.195%, respectively.Mean Sr:Ca (Fig. 4a) and Ba:Ca (Fig. 4b) plots demon-

strate the overall trends in the raw data. The barium signal

Fig. 3. Example spectrum of raw data for strontium over all fDt from zero to fNy.



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shows the expected pattern of low to high concentrations asthe fish move from a higher to lower salinity environment.Conversely, strontium decreases over time. A representativeplot of the raw Ba:Ca data illustrates the change in both theslope of the curve and the variability of the signal at approx-imately 85 days (Fig. 5).We calculated the spectral density and confidence limits

(a = 0.01) of strontium (Fig. 6) for each fish. The most sig-

nificant (highest) peaks in strontium spectral density werefairly uniform in their frequency distribution across ages(Fig. 7a), with a range of 29 to 111 days for all samples.The spectral density and confidence limits (a = 0.01) for

barium (Fig. 8) showed a slightly negatively skewed fre-quency distribution of peaks (Fig. 7b). The range in most sig-nificant peaks for barium was 26 to 95 days, with 43%occurring near 85 days.

Fig. 4. (a) Mean Sr:Ca versus laser scan time (seconds). (b) Mean Ba:Ca versus laser scan time (seconds).

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Secondary peaks were present, however, and we noted thata significant peak occurring at some point between 50 and95 days was present in 57% of the strontium spectra and93% of the barium spectra. Additionally, none of the sam-ples’ peak densities occurred at an age of less than 26 days.We plotted the highest peak in spectral density against the

absolute value of the fish growth rates (Fig. 9a) and found nolinear relationship for either strontium (R2 = 0.1564, p =0.1617) or barium (R2 = 0.1251, p = 0.2147). However, plot-ting the highest peak in spectral density against fish age(Fig. 9b) did reveal a relationship with barium (R2 = 0.8523,p < 0.001) but not strontium (R2 = 0.0368, p = 0.5111). We

Fig. 5. Raw Ba:Ca versus age, demonstrating the clear midpoint change in otolith chemistry at 90 days (sample j).

Fig. 6. Spectral density plots for strontium (n = 14). The x axis is the periodicity of the signal in days; the y axis is the strength of the signal(as measured by energy density). The solid lines indicate the spectral density, and the dotted lines represent the 99% confidence band. Thosepeaks exceeding the confidence band are significant periodic components, and the magnitude of each peak is related to its level of signifi-cance (i.e., the highest peaks are the most significant components).



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report these results only as an example of the types of teststhat could be conducted using these data.

Discussion

Our results produced a quantitative point estimate for thetiming of migration for each individual fish. We account forthe inherent autocorrelation of scan data, while at the sametime fully employing the spatial and temporal informationcontained in each time series. The point estimates we gener-ate are unique in that they measure the point in time with thehighest probability of transition from one habitat to the next.Qualitative assessments might estimate the inception point ofthe change, the midpoint, or even the end of the change be-fore a new elemental equilibrium is reached. Our methodconsistently provides a quantitative measure of both whenthe change had the highest probability of occurring andwhether that change was statistically significant. These re-sults have important implications for understanding migratorypatterns and environmental histories of fish species. We cannow use this method to accurately determine the timing offish movement across environmental gradients.Non-integration of elemental concentrations in the field

could be a source of bias for certain questions, but in thiscase, we seek to determine the relative changes in elemental

concentrations, not their absolute values. Walther and Thor-rold (2006) showed 83% and 98% of the strontium and ba-rium, respectively, deposited in otoliths are derived from theambient water chemistry for marine species. Additionally,Bath et al. (2000) sampled laboratory-reared sciaenids andshowed barium to be an excellent marker of the physico-chemical properties of an individual’s environment, with nobiological overprint. They also showed strontium to be agood recorder of salinity, but cautioned the need for consid-ering temperature effects in tandem with strontium whencrossing latitudinal gradients. To better contextualize oursamples’ otolith chemistry with the water chemistry in oursystem, however, we looked to previous work conducted inthe same drainage basin by Dorval et al. (2007) and Hanni-gan et al. (2010).Considering the mixing curves and the well-documented

life history of this species (Hoskin 2002; Schaffler et al.2009a), we were able to draw meaningful conclusions fromthe significant peaks produced by our spectral estimation.Significant peaks in spectral density can occur in two ways.The first is when a significant change in the original seriesoccurs, as is the case with croaker ingress. This change inthe original series can be conceptualized as a step function,with a single large shift in the signal. Because we are usingMEM, a sufficiently large oscillation emerges in the calcu-lated spectrum, which in turn appears as a peak in the spec-tral density. When the change is significant, there will be apeak in the spectral density even if it only occurred once inthe record. Consequently, if a croaker had lived to 500 daysand ingressed only once, we would still be able to discernthat a significant change in the otolith chemistry had oc-curred at 85 days.The second way significant peaks in the spectral density

occur is when consistent changes take place on a periodic ba-sis, such as a fish moving onshore and offshore over annualtime scales. The periodic nature of such a change would ap-pear as a peak in the spectral density at a certain period, in-dicating the most important periodic component of the data.The height of the peak indicates the significance of that peri-odic component, which is why we chose the highest peak asthe strongest indicator of the transition from one state to an-other. The width of the peak, however, indicates the uncer-tainty about a given periodic component. The peak’s shapetells us how consistent a given periodic component was; thatis, if the peak was broad, there may be variability around thatannual time signal; if it were narrow, the annual movement islikely to have been very consistent through years. Much thesame as a probability density, the more narrow a peak, thegreater the certainty about the estimate.Additionally, secondary peaks occur. The secondary peak,

which occurs at one-half of the period of the highest peak, isactually a harmonic of the signal. This secondary peak ap-pears in the spectral density as a fundamental in the Fourierexpansion of the signal. Because we evaluated the spectraldensity over 5000 frequencies, far more spurious peaks ap-pear than would be present at coarser frequency scales. Thesesecondary peaks are not biologically relevant, and we hence-forth refer to the most significant peaks for our estimates ofingress timing.A potential use for these ingress timing estimates is as pre-

dictors for the timing of movement, against which we can

Fig. 7. Frequency distribution of the most significant spectral den-sity peaks for (a) strontium and (b) barium.

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test hypotheses of observed movement and migration pat-terns. Based on barium, we show that peaks are occurring atapproximately 85 days in fish that have a mean age of121.5 days. As a result, this periodic component can occuronly once over the organism’s entire life span. A second os-cillation would occur only at 180 days or more, and none ofthe fish collected were over 145 days old. Therefore, thesepeaks in spectral density suggest that the most significant pe-riodic component was in fact a single change in otolith chem-istry. Studies showing a 2- to 3-month ingress time for thesespecies (Warlen and Burke 1990; Hettler 1998; Hoskin 2002)suggest this major change in otolith chemistry is a direct re-sult of ingress to the estuary.We see this clearly in the plots of the raw element-to-

calcium ratios of barium life history scans. Knowing that thepeak in spectral density lies near 85 days, we plainly observea change in both the slope of the curve and the variability ofthe signal at that point. Even if this large change only occursonce, it will appear as an oscillation after detrending. We seethe corresponding peak in spectral densities plot near85 days. Assessing these features visually would be not onlysubjective, but also likely inaccurate. Additionally, changes inelemental concentrations seldom show such unambiguouschanges through time; estimating timing of ingress loses ob-jectivity in the qualitative setting. Using spectral analysis al-lows us to obtain an objective measure of the timing ofingress events through life history scans.The advantage of our approach is that we obtain objective

measures for inherently noisy data, according to an unbiasedcriterion. In a subjective approach (e.g., visually estimatingtiming of ingress from a life history scan), the results aresubject to reinterpretation from one researcher to another.This lack of objectivity allows for the introduction of un-known, and unknowable, bias. Conversely, the spectral ap-proach offers complete repeatability and a means to estimateits bias.The power of examining our estimates for all fish samples

together is that we create a single frequency distribution. Inessence, the frequency distributions that we see in our dataproduce a probability distribution of the timing of ingress forthe population. We can refine this distribution with increasedsample size. By modeling such a distribution, however, weinfer the timing of a population’s movement across an envi-ronmental gradient from an objective basis, while under-standing the potential for bias. Given a distribution function,we would obtain many measures about the population’s be-havior, including the mean time of ingress, the variability ofingress timing across individuals, and the overall shape of thedistribution.We gain powerful insight once the underlying distribution

of our sample data is revealed. If the distribution is uniform,as we see for strontium, the data suggest that time of ingressis not dependent on size (i.e., competency to settle). To fur-ther illustrate the value of these statistically derived estimates,we plotted the strontium and barium spectral peaks againstfish growth rates and age, thus testing the critical-size hy-

Fig. 8. Spectral density plots for barium (n = 14). The x axis is the periodicity of the signal in days; the y axis is the strength of the signal (asmeasured by energy density). The solid lines indicate the spectral density, and the dotted lines represent the 99% confidence band. Thosepeaks exceeding the confidence band are significant periodic components, and the magnitude of each peak is related to its level of signifi-cance (i.e., the highest peaks are the most significant components). Note the consistent highly significant peak at approximately 50–90 days.



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pothesis (as shown in Beamish and Mahnken 2001; Cowanand James 1988; Heintz and Vollenweider 2010). Based onthe expected relationship, we would hypothesize that thefastest-growing fish ingress at an earlier age. The absence ofany relationship between age at time of ingress and growthrate implies these two theoretically related metrics may infact be independent. These data, although limited, suggestAtlantic croaker ingress likely occurs on a time scale of 2 to3 months after spawning. That this timing occurs regardlessof growth rate points to physical processes, such as wind pat-terns and currents, as determining ingress patterns for thisspecies and does not support the critical-size hypothesis inthis case. To accurately test such a hypothesis on the popula-tion level, however, a sample size on the order of severalhundred fish would be necessary.The distribution of peaks for barium was slightly nega-

tively skewed, with a large number of individuals migratinginto brackish water at older ages and very few moving atages less than 60 days. Again, most individuals exhibited apeak in spectral density on the order of 2 to 3 months ofage. That the peaks in both strontium and barium occur at50 to 90 days is no coincidence. Atlantic croaker begin

spawning near Cape Hatteras in early September, withspawning activity peaking in October and declining by lateDecember (Morse 1980). Both Warlen and Burke (1990) andHettler (1998) show larval croaker ingress on the time scaleof approximately 3 months in North Carolina estuaries. Addi-tionally, Hoskin (2002) demonstrates similar results forcroaker in her work specifically in Pamlico Sound. Our re-sults strongly support these studies. However, the strength ofour approach lies in our ability to retrospectively examinesurvivors of the ingress process and quantitatively link envi-ronmental forcing effects with the ingress process, such asthe mixing curves of the elements with respect to salinityand temperature.When interpreting the results of both strontium and barium

together, we must consider the mixing curves of the watermasses through which the fish traverse. Although both stron-tium and barium have been shown to be incorporated propor-tionally to ambient water chemistry (Bath et al. 2000;Walther and Thorrold 2006), the inflection of the concentra-tion of each of these elements occurs at different salinities, asshown by Dorval (2004) and Dorval et al. (2007) for thisdrainage basin. We see this pattern in the lag in timing of ba-rium as compared with strontium. We surmise that strontiumpeaks reflect ingress into the estuarine environment, whilebarium peaks reflect movement timing up-estuary. Further,our results call for the investigation of barium as a potentialmarker in addition to the more commonly used strontium. Incertain chemical environments, one element may prove morevaluable than the other. Although we advocate the univariateanalysis of elements for that case of estimating ingress tim-ing, we are also aware that there is great value of multivariateretrospective classification, such as the approach of Fablet etal. (2007).Because the most significant peak for all samples fell

above 26 days, these data support a natural threshold for tim-ing of ingress, as was also seen in Nixon and Jones (1997).Being able to discern these changes proves quite useful incharacterizing the movement of the local population. Giveninformation from other areas, we could then use strong statis-tical tools such as the Kruskal–Wallis one-way ANOVA totest whether distributions between locations were equal. Byperforming this test, we would see whether a mean differencein the timing of ingress was present without assuming oursample came from a normal distribution.Considering our limited sample size, we proceed with cau-

tion in applying these interpretations, as any population-scaleconclusions necessitate broader sampling, and the purpose ofthis work was to demonstrate the method and its value intesting hypotheses. Additionally, we emphasize that thismethod could reflect changes in chemical environment thatare either linked to salinity or other environmental gradients.Differing otolith chemistry signatures might result from be-havioral changes as well, such as switching from a pelagicto a benthic or demersal life history (Hare et al. 2005). Anadvantage of this technique is that it discriminates not onlywhich events are more distinct in the environmental past, butalso uncovers potentially important components of the lifehistory not previously revealed. While we have shown thepower of this technique in detecting such changes, we alsocaution that life history must always be considered to under-stand the causes for the patterns revealed. In our case, the

Fig. 9. (a) Peak in spectral density (estimated time of ingress) versusthe fish growth rate (eq. 1). (b) Peak in spectral density (estimatedtime of ingress) versus the fish age (eq. 2) for both strontium (dia-monds) and barium (cross-hatches).

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general trend showed a well-documented ingress from saltwater to the estuarine environment, however, and becausewe had a well-studied life history pattern, we were able toevaluate the more nuanced dynamics of timing. The advant-age here is we are able to calculate these estimates retrospec-tively, eliminating the need for intensive in situ sampling asdone for this species by Hare and colleagues (Hare et al.2005).The unique signatures associated with various water

masses are reflected in croaker otolith chemistries (Schaffleret al. 2009b). With our new application of spectral analysis,we now anticipate applying these techniques to fish from var-ious locations to compare not only timing, but also overallpatterns of ingress in both juvenile and adult samples.

AcknowledgementsThe authors thank Norou Diawara, Jason J. Schaffler,

Stacy K. Beharry, Serena Turner, and the entire faculty andstaff at the Center for Quantitative Fisheries Ecology for sci-entific discussions and technical help. The specimens werecollected by the National Marine Fisheries Service BeaufortLaboratory. Funding for this work was provided by the Na-tional Science Foundation (OCE-0961421).

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Estuarine ingress timing as revealed by spectral analysis of otolith life history scans