Variability in fish size/otolith radius relationshipsamong populations of Chinook salmon

Richard W. Zabel & Kerri Haught &Paul M. Chittaro

Received: 1 October 2009 /Accepted: 21 June 2010 /Published online: 13 July 2010# US Government 2010

Abstract Back-calculation of growth trajectoriesfrom otolith microstructure is a valuable tool forunderstanding mechanisms underlying variability ingrowth among fish populations. We analyzed fishlength/otolith radius relationships for Snake Riverspring/summer Chinook and Snake River fall Chi-nook salmon, listed as separate “EvolutionarilySignificant Units” (ESUs) under the US EndangeredSpecies Act, to determine whether these ESUs sharedrelationships. In addition, we analyzed otoliths fromseven separate populations within the Snake Riverspring/summer Chinook ESU to assess the variabilityin relationships among populations, which are muchmore closely related than ESUs. We also examinedseveral potential functional forms for the equations.We found that the separate ESUs had significantlydifferent fish length/otolith radius relationships, butthat variability in otolith growth rate could not explainthe difference. Relationships among populationswithin the spring/summer Chinook ESU did not varynearly as much as those between ESUs. The quadraticmodel and the power model fit the data equally well,and constraining these models to pass through abiological intercept (estimated fish length and otolithradius at hatching) resulted in only a slight decrease in

model fit. To test the ability of the models to back-calculate fish lengths, we predicted the length attagging for 17 PIT-tagged fall Chinook that weremeasured at release and at recapture. The back-calculation demonstrated little bias (<1 mm FL, onaverage) and relatively small standard deviation(∼3.5 mm) for the best model. When we repeatedthe back-calculation with data from both ESUscombined, bias increased substantially (to 15 mmFL), demonstrating the importance of determining theproper taxonomic level at which to combine datawithin a species.

Keywords Otolith . Back-calculation . Growth .

Chinook salmon

Introduction

A rich history exists of relating size of fish to the sizeof their hard parts, particularly scales and otoliths(Lee 1920, Pannella 1971). These types of relation-ships serve many roles, particularly the ability toback-calculate growth trajectories of sampled individ-uals (Francis 1990; Morita and Matsuishi 2001). It isclear that these relationships are species-specific (Fey2006), but it is not clear that the species-specificrelationships apply to all populations that comprise aspecies. An important tool for understanding growthprocesses is to compare how growth varies acrosspopulations under variable physical and environmen-

Environ Biol Fish (2010) 89:267–278DOI 10.1007/s10641-010-9678-x

R. W. Zabel (*) :K. Haught : P. M. ChittaroNorthwest Fisheries Science Center,2725 Montlake Blvd E,Seattle, WA 98112, USAe-mail: rich.zabel@noaa.gov

tal conditions. To apply this tool, we need to knowhow fish size/otolith size relationships vary acrosspopulations, but few studies have examined this issue.Notable exceptions are Radtke et al. (1996), whoobserved different fish size/otolith size relationshipsbetween North American and Asian populations ofDolly Varden (Salvelinus malma), and Strelcheck etal. (2003), who observed differences in relationshipsin populations of gag (Mycteroperca microlepis) inthe Gulf of Mexico. The latter study is particularlyimportant because the authors determined that if theyapplied a species-specific relationship to distinctpopulations, they arrived at misleading conclusionsabout how growth varied among populations. In thisstudy we focus on how relationships between fishlength and otolith radius vary across populations ofChinook salmon in the Columbia River basin in thenorthwestern US.

Fish size, particularly that of juveniles, plays amajor role in the population dynamics of Chinooksalmon. Zabel and Williams (2002) observed strongselection on juvenile length at migration for survivalto adulthood. Furthermore, migration timing is posi-tively related to juvenile length (Zabel and Achord2004; Achord et al. 2007), and migration timinginfluences adult return rate (Scheuerell et al. 2009),with early migrants typically returning at greater rates.Thus understanding juvenile growth processes isfundamental for recovering populations of Chinooksalmon, listed as threatened under the US EndangeredSpecies Act (ESA). However, patterns of growth innatural populations vary in complex ways across timeand space depending on ecological conditions. Forinstance, for Snake River spring/summer Chinook,the relationship between juvenile length and temper-ature shifts from positive to negative, depending ondensity of juveniles (Crozier et al. 2010). The abilityto back-calculate growth trajectories of juvenile fishsampled from a variety of natural populations willprovide a powerful tool to begin understanding thiscomplexity.

We focused on Snake River fall Chinook salmonand spring/summer Chinook salmon, which aredistinguished as separate Evolutionarily SignificantUnits (ESUs), the units of conservation in the ESA.This distinction is based on differences in adult runtiming (which is the basis for the designation of fallversus spring/summer), geographical range, genetics,and life history variability. In fact, based on genetic

analyses, Waples et al. (2004) determined that thesetwo ESUs function as separate, but closely relatedspecies, separated for at least 12 000–15 000 years.Within the spring/summer Chinook ESU, 31 separatepopulations have been identified (IC-TRT 2003). Inthis study we address whether fish length/otolithradius relationships vary between the two ESUs andamong populations within the spring/summer Chi-nook ESU. In addition, we evaluate which are themost appropriate models of fish length/otolith radiusrelationships for juvenile Chinook salmon.

Many researchers have emphasized the limitationsof back-calculation methods (Francis 1990). In par-ticular, several studies have demonstrated a decou-pling between somatic and otolith growth, withotolith size related to factors such as growth rate andtemperature in addition to fish size (Mosegaard et al.1988; Secor and Dean 1989). Consequently, we alsoaddressed whether growth rate and temperature areimportant in determining variability about fish length/otolith radius relationships, both within and amongESUs.

Our study was based solely on fish collected fromnatural populations that had experienced ambientconditions, while most other studies examiningvariability in fish length/otolith size relationshipshave been conducted in a laboratory. Specifically,we developed a series of alternative models thatrelated fish length to otolith radius, representingseveral different functional forms, and including orexcluding terms. We used model selection criteria todetermine which models were most appropriate, andin doing so, determined which factors were importantto the relationships. Finally, we performed a validationof back-calculation methods by examining individualsthat were measured, PIT tagged, released, and thenrecaptured and re-measured. Based on several back-calculation equations, we predicted size at taggingbased on size at recapture, otolith size at recapture, andnumber and width of otolith increments.

Methods

Study species, otolith collection and preparation

Snake River Fall Chinook are designated as “ocean-type” fish (Healey 1991), which typically migrates toseawater as subyearlings several months after hatch-

268 Environ Biol Fish (2010) 89:267–278

ing. However, they have recently exhibited increasingpropensity to migrate as yearlings, with the changelikely due to a shift in predominant spawning sitesdue to the construction of impassible dams in HellsCanyon in the 1950s (Williams et al. 2008). Adultsreturn to spawn in the fall after 1–4 years in the oceanand spawn primarily in the lower reaches of the Snakeand Clearwater rivers (Fig. 1a). Snake River spring/summer Chinook are designated as “stream-type” fish(Healey 1991), which spends a full year in freshwaterprior to ocean migration. The adults migrate upstreamduring the spring and summer after 1–4 years in theocean, but typically delay spawning until the fall.Relative to Snake River fall Chinook, they spawn inhigher elevation (approximately 1,200 to 2,200 mcompared to approximately 300 m) and narrowertributaries, typically less than 15 m wide (Fig. 1b).

Fall Chinook were captured at Lower Granite Damon the Snake River in 1993, 1994, 2007, and 2008.The fish were previously PIT tagged upstream fromthe dam in the Snake River, and then diverted using asort-by-code facility at the dam. Fork lengths wererecorded at the time of capture, which occurred fromJune to August. The 1993 and 1994 samples werearchived by the US Geological Survey and stored inresin. A total of 61 fish was included in the fish length/otolith radius relationships, with fish selected to repre-sent the range of fork lengths in the sample. Because wewere restricted to the small set of fish that were captured,we could not select lengths to evenly represent the rangeof lengths as recommended by DeVries and Frie (1996).

Spring/summer Chinook otoliths were collectedfrom age 0 parr collected in their rearing areas in theSalmon River basin in central Idaho, USA. We reliedon fish that were collected for other studies (e.g.,Achord et al. 2007). Fish were collected over threeyears (2004–2006) in July, August and September.Fish were sampled from seven separate populations: 5populations in the Middle Fork Salmon subbasin(Bear Valley Creek, lower Big Creek, Elk Creek,Marsh Creek), two populations in the South ForkSalmon River subbasin (South Fork Salmon Riverand Lake Creek), and one population from a tributaryto the main fork of the Salmon River Valley. A totalof 296 fish was collected, and fork lengths wererecorded at capture, with fish sampled during July,August, or September. We did not have control of thedistribution of fish lengths sampled, so we could notproduce an even distribution of lengths across the

range. For each spring Chinook population, we alsorecorded daily average stream temperatures in theirrearing areas using a Tidbit in-stream data logger thatrecords °C at five-minute intervals. We removedsagittal otoliths from each individual, removed adher-ing tissue, and stored dry. Left sagittal otoliths weremounted to a microscope slide with Crystal Bond©(http://www.crystalbond.com/). Each otolith was pol-ished on both sides in a sagittal plane, using slurries(grit sizes of 1 and 5 alumina micropolish) and agrinding wheel with Buehler© 1500 and micro-polishing pads. Polishing ceased when the core ofthe otolith was exposed and daily increments werevisible under a light microscope.

We photographed polished otoliths using a digitalcamera (Cybernetics©) mounted on a compoundmicroscope (Zeiss©; set at 20× magnification). UsingImage Pro software (MediaCybernetics©), we firstmeasured total otolith radius (i.e, distance from theotolith core to its margin) along a transect perpendic-ular to the longitudinal axis on the ventral side of theleft otolith. This transect was selected for its reliableclarity. When possible, we also identified eachotolith’s hatch check, which was identified by a darkband and a secondary primordium (Zhang et al. 1995)and correspond to the transition in the fish’s life fromembryo to fry. We measured the distance from theprimordium to the hatch checks along a transectperpendicular to the longest axis, as above.

For the growth rate analysis (see below), we measuredotolith increments over a variable period prior tocollection (28 to 84 d) for a subsample of fall Chinookwith discernable daily increments collected in 1993, 1994and 2007 (n=38). For spring Chinook, we measureddaily otolith increments over the 40 days prior tocollection for the subsample of fish collected duringSeptember in 2005 and 2006 (n=86). We measuredthese increments along a transect perpendicular to thelongest axis on the ventral side, as above.

Analyses

Our approach was to develop relationships, bothlinear and nonlinear, between fish length and otolithradius. By comparing alternative models usingAkaike’s Information Criterion (AIC; Burnham andAnderson 2002), we could determine which factorsexplained the greatest amount of variability in theserelationships. The model with the lowest AIC value

Environ Biol Fish (2010) 89:267–278 269

Salmon River

Salmon River

Sout

hFo

rkSa

lmon

Riv

er

Mid

dle

For

kS

alm

onR

iver

Elk

Lake

Marsh

Valley

Lower Big

South Fork

Bear Valley

0 5025 Km

a

b

Fig. 1 Maps of spawningareas for Snake River fallChinook (a) and SnakeRiver spring/summer Chi-nook (b). The current extentof spawning by fall Chinookin the Snake River is shaded(a). Specific spawning sitesof spring/summer used inthis study are indicated byfish symbols (b)

270 Environ Biol Fish (2010) 89:267–278

had the best fit. Differences between models of lessthan 2 indicated that models performed similarly,whereas differences of greater than 10 were strongsupport for the model with the lower AIC (Burnhamand Anderson 2002).

We first examined whether difference existedbetween ESUs, using models of the form

Li ¼ aþ b � Oi þ c � O2i þ c � ESUi

þ d � ESU � Oi þ e � ESUi � O2i þ "i

ð1Þ

where Li is the fork length, and Oi is the otolith radiusfor the ith individual. ESUi is a dummy variablerepresenting whether a fish was from the fall Chinookor spring/summer Chinook ESU. In addition, εi is theerror term, which was assumed normally distributedwith mean 0 and variance σ2. The lower case letters arecoefficients. We included interactions between O andESU to represent separate slopes for the separate ESUs.Eq. 1 can be abbreviated as L ¼ I þ ESU»ðOþ O2Þ,indicating that the model contains an intercept term (I)and an interaction between ESU and O and O2. The “*”term indicates that the model includes both interactionsand all main effects. By constructing simpler modelsnested within Eq. 1, we tested for the importance ofmodel terms, particularly that of ESU. Note thatalthough we used a quadratic equation for this part ofthe analysis, we tested other forms.

Based on the results of the ESU analysis, wetreated the ESUs separately when we tested differentmodel forms. We considered the following abbreviat-ed equations:

Linear : L ¼ I þ O ð2Þ

Log=Exponential : L ¼ expðI þ OÞ ð3Þ

Quadratic : L ¼ I þ Oþ O2 ð4Þ

Power : L ¼ I þ Oc ð5ÞSimilar to Eq. 1, each of these models contains a

normally distributed error term. Note that weexpressed the log model in the exponential form sothat it would have the same response variable anderror structure as the other models, allowing forpossible model comparisons.

We also constrained the four models in Eqs. 2–5such that they passed through a biological intercept.We defined this intercept to represent otolith radiusand fish length at the time of hatching. We estimatedseparate intercepts for each ESU by first estimatingotolith radius at the hatch check marks for the subsetof individuals where a hatch check mark was readilyidentifiable, and then taking means across ESUs(mean = 110.4 microns, cv=0.164, n=57 for fallChinook, and mean = 95.8 microns, cv=0.180, n=162 for spring/summer Chinook). These means werehighly significantly different (t test, P<0.001), justi-fying a separate value for each ESU. We estimatedfish length at hatching using mean egg mass forstream- and ocean-type Chinook (Healey 2001)applied to published hatch length/egg mass relation-ships (Beacham and Murray 1990) (mean = 22.4 mmfor fall Chinook and 21.6 for spring/summer Chi-nook). To constrain the models to pass through theseintercepts, we first subtracted the intercept from eachindividual’s fork length and otolith radius, designatingthese terms as LB and OB. We then constructedmodels that did not contain intercept terms. Forinstance, a quadratic model constrained to passthrough the biological intercept is designated asLB ¼ OB þ O2

B.To test whether individual populations within the

Snake River spring/summer Chinook ESU havedistinct fish length/otolith radius relationships, weexamined a series of models with and withoutpopulation effects. The fullest model had the form

L ¼ I þ O»POP þ O2 ð6Þwhere POP is a factor with levels represented by eachof the seven populations, meaning each population had aseparate intercept and slope coefficient. We did notconsider an interaction between POP and O2 becausethis model would have required too many parameters.In addition, when we considered models constrained topass through the biological intercept, we also had todrop the POP main effects because these would haveproduced curves that did not pass through the biologicalintercept. We designated the quadratic form of thismodel as LB ¼ OB þ POP : OB þ O2

B, where the “:”term designates an interaction without the main effect.

Finally, we tested for the effects of growth rate andtemperature. We measured daily otolith incrementsfor a subsample of the individuals analyzed. We thencalculated mean increment width per individual to

Environ Biol Fish (2010) 89:267–278 271

represent otolith growth rate. We used two approachesto test whether a “decoupling” existed betweensomatic growth rate and otolith growth rate. First,we examined the performance of models thatcontained interactions between otolith growth rateand otolith radius, reasoning that the growth rateeffect would be expressed as differences in slopebetween fish length and otolith radius. We did notexamine models that contained otolith growth rate asa main effect because although we expected a positiverelationship between fish size and otolith growth rate,we were really testing for an effect of growth rate thatchanged the slope of relationship. To further test forthis effect, similar to Fey (2006) and Wilson et al.(2009), we related residuals frommodels that containedO and O2 to growth rate. If the growth-rate effectexisted, we would expect to see residuals above thepredicted relationship to have greater growth rates thanthose below. We tested these models both within andbetween ESUs to determine if differences in growthrate could explain observed differences between ESUs.We had rearing temperature data for spring/summerChinook populations, which were sampled in theirrespective rearing areas, but not for the fall Chinookbecause they migrated through river segments withdifferent temperature regimes. Temperature was mea-sured as the mean stream temperature over the 40 daysprior to collection.

Temperature was introduced to the models additivelyand as an interaction with otolith radius. Models thatincluded temperature and otolith growth rate were notconstrained to pass through the biological interceptbecause wewere initially concernedwith the contributionof these effects to the more general model.

Back calculations and validations

We used 17 fall Chinook juveniles with discernableincrements from 2007 that were PIT tagged at a knownFL, released, and then recaptured approximately1 month later to perform a validation of back-calculations based on the equations described above.Wemeasured daily increments so that we could estimateotolith size at the time the fish were initially PIT tagged.We used the linear and quadratic equations, withunconstrained and biological intercepts. For modelswith unconstrained intercepts, we used the “regressionapproach” (Campana 1990), where the back-calculatedtrajectory is parallel to the regression-based relation-

ship. For the models with biological intercepts, weused the “biological intercept approach” (Campana1990), where back-calculated trajectories were con-strained to pass through the biological intercept.

The first step was to use the radius of the otolithmeasured at recapture, along with a parameterizedequation to predict fish length at recapture. We thencalculated the deviation of observed fish length atrecapture from the predicted length. In cases where theintercept was unconstrained, we maintained this devia-tion through the entire back-calculated trajectory. If theequation was constrained to pass through an intercept,we linearly decreased the deviation with respect tootolith radius such that the deviation was zero at thebiological intercept. We knew the dates of recapture andtagging, so we counted otolith increments to estimatethe otolith increment corresponding to the date oftagging. Based on the estimated size of the otolith atthe time of tagging, we estimated fish length at time oftagging by applying the regression equation predictivelyand then applying the appropriate deviation from thepredicted line. Finally, we compared our predictedlength at tagging to the observed length at tagging andcalculated this deviation.

Results

We measured fish lengths and otolith radii for 296spring/summer Chinook distributed across years andpopulations (Table 1) and 61 fall Chinook distributed

Table 1 Sample sizes by year for the fish length/otolith radiusregressions

Year BVA ELK LAK LBG MAR SFS VAL

Snake River spring/summer Chinook salmon populations

2004 10 8 13 10 11 14 16

2005 13 15 20 18 16 15 21

2006 20 15 20 – 15 15 13

Snake River fall Chinook salmon

1993 25

1994 10

2007 18

2008 8

BVA Bear Valley Creek; ELK Elk Creek; LAK Lake Creek; LBGlower Big Creek; MAR Marsh Creek; SFS South Fork SalmonRiver; VAL Valley Creek

272 Environ Biol Fish (2010) 89:267–278

across years (Table 1). The spring/summer Chinookranged from 34 to 93 mm, and the fall Chinookranged from 53 to 168 mm. The two ESUs demon-strated clear differences in their fish length/otolithradius relationships (Fig. 2, Table 2). Using AICvalues as an index of model performance, models thatcontained the ESU term (Table 2, models 3–5)performed better than those that did not (Table 2,models 1–2): inclusion of the ESU term conferred adecrease in AIC of over 200. The best model was onethat contained an interaction between ESU and O(Table 2, model 4). The more complex model (Table 2,model 5), which also had an interaction between ESUand O2, had a comparable AIC, but the interactionterm was not significantly different from 0 (P=0.160).

Based on R2, all models fit the data similarly well(within an ESU) when an intercept term was included(Fig. 3, Table 3, odd numbered models). However,when models were constrained to pass through thebiological intercept, the logarithmic model (Table 3,models 6 and 8; Fig. 3c and d) fit the data poorly. Inthese cases, constraining the models produced suchpoor fits that the R2 values were <0.0. Overall, thelinear model (Table 3, models 2 and 4; Fig. 3a and b)did not perform as well as the quadratic or powermodels (Table 3, models 10, 12, 14, and 16). In fact,the fits of quadratic (Table 3, models 9–12; Fig. 4eand f) and power models (Table 3, models 13–16;Fig. 4g and h) were similar in all cases, and both ofthese models fit the biological intercept withoutmuch drop off in performance compared to thecorresponding unconstrained models. Both the quadraticand power models had the best overall performance, and

despite the power model being more prevalent in theliterature, we adopted the quadratic model because it islinear and thus easier to apply to the hypothesis testingexercises that follow.

The best fitting model (based on AIC) in thepopulation analysis was the one that contained anunconstrained intercept and an interaction betweenpopulation and otolith radius (Table 4, model 2;Fig. 4a). However, we do not recommend this modelbecause the predicted relationships were inconsistentin the region of the biological intercept (Fig. 4a).When the model was constrained to pass through thebiological intercept, the best model still contained aninteraction between population and otolith radius(Table 4, model 4; Fig. 4b). However, this modelcontains several non-significant terms (P>0.05), andwe therefore preferred the simplicity of the model thatassumes no effect of population without sufferingmuch of a loss in performance (Table 4, model 3;Fig. 4c). We selected the quadratic model constrainedto pass through the biological intercept because theunconstrained model exhibited unrealistic curvaturenear the biological intercept (see Fig. 3f), and thelinear model did not fit as well (see Fig. 3b) andexhibited biased residuals.

Neither otolith growth rate, which ranged from1.64 to 3.92 microns per day, nor daily averagetemperature, which ranged from 10.97 to 16.15°C,improved the model fits for spring/summer Chinook(Table 5, models 1–5). In addition, the residuals froma model without growth rate were not related tootolith growth rate (R2=0.0125, P=0.302). For fallChinook, the addition of otolith growth rate, whichranged from 4.20 to 6.18 microns per day, conferred aslight advantage in model fit (AIC decreased slightlyin models 8 and 9 compared to models 6 and 7).

Fig. 2 Relationship between fish length and otolith radius forSnake River fall Chinook (triangles) and Snake River spring/summer Chinook salmon (circles). The dashed lines are 95%prediction intervals

Table 2 Model results for regressions between fish length andotolith radius that also included the factor ESU, which refers toEvolutionarily Significant Unit. NP refers to the number ofparameters in each model; L refers to fish length; O refers tootolith length; ESU refers to evolutionarily significant unit

Model NP R2 AIC

1. L=O 2 0.766 2783.8

2. L ¼ Oþ O2 3 0.839 2651.7

3. L ¼ Oþ O2 þ ESU 4 0.927 2372.1

4. L ¼ O»ESU þ O2 5 0.934 2334.5

5. L ¼ ðOþ O2Þ»ESU 6 0.935 2334.5

Environ Biol Fish (2010) 89:267–278 273

Similarly, the regression between the residuals andotolith growth rate was marginally significant (R2=0.103, P=0.0495). When we combined the two ESUs,models that contained growth rate (Table 5, models12, 13, 16 and 17) fit the data substantially better thanthose that did not (Table 5, models 10, 11, 14, and15). However, models that contained only ESU as afactor (Table 5, models 14 and 15) explained morevariability than those without ESU but with otolithgrowth rate (Table 5, models 12 and 13). In addition,when added to models with ESU, the otolith growthrate term did not improve model fit (comparing model16 to 14 and 17 to 15) and the associated coefficientswere not significantly different from zero.

For the 17 fall Chinook included in the validationstudy, the mean number of days between tagging andrecapture was 26.3 (s.d. = 9.7 days), and mean growthduring this interval was 30.5 mm FL (s.d. = 11.6 mm).The linear models and the quadratic model using thebiological intercept were reasonably unbiased whenback-calculating fish length at PIT tagging, with meandeviations from observed lengths close to 1 mm FL orless (Fig. 5a, b, and d). However, the quadratic modelwith unconstrained intercept performed poorly(Fig. 5c), with a bias of nearly −6.5 mm FL. Inaddition, the unconstrained linear model (Fig. 5a) had arelatively large standard deviation in spite of havingthe smallest mean deviation. Thus, back-calculation

Fig. 3 Relationshipbetween fish length andotolith radius for popula-tions within the Snake Riverspring/summer ChinookESU. In a, each populationhad a separate quadraticrelationship, but the indi-vidual relationships werenot constrained at the bio-logical intercept. In b, eachpopulation had a separaterelationship, but all rela-tionships were constrainedto pass through the biologi-cal intercept. In the c, allpopulations shared a com-mon relationship that wasconstrained to pass throughthe biological intercept. Inthis plot, the dashed linesrepresent the 95% predic-tion interval. Abbreviations:BVA Bear Valley Creek;ELK Elk Creek; LAK LakeCreek; LBC Lower BigCreek; MAR Marsh Creek;SF South Fork SalmonRiver; VAL = Valley Creek

274 Environ Biol Fish (2010) 89:267–278

methods that constrained the growth trajectory to passthrough the biological intercept performed best, withthe quadratic model performing slightly better than thelinear model due to its slightly lower standarddeviation and its more symmetric distribution ofdeviations (Fig. 5c and d).

Discussion

In this study we investigated fish length/otolith radiusrelationships of Chinook salmon from the ColumbiaRiver Basin to determine whether this relationshipvaried between two Evolutionarily Significant Units

Table 3 Model results for regressions between fish length and otolith radius using four different equations. Int. refers to intercept, andU means the intercept was unconstrained at the biological intercept, and B means the equation was constrained to pass through thebiological intercept. L refers to fish length, and LB refers to fish length minus the biological intercept. O refers to otolith radius, and OB

refers to otolith radius minus the biological intercept

Model Int. Fall Chinook Spring/Summer Chinook

AIC R2 Equation AIC R2 Equation

Linear U 454.5 0.857 1. L ¼ �26:54þ 0:23 � L 1851.7 0.817 3. L ¼ 5:06þ 0:13 � LB 465.8 0.822 2. LB ¼ 0:19 � OB 1860.9 0.810 4. LB ¼ 0:12 � OB

Log U 458.9 0.846 5. L ¼ expð3:44þ 0:0021 � OÞ 1833.3 0.828 7. L ¼ expð3:17þ 0:0021 � OÞB 623.5 −1.364 6. LB ¼ expð0:0081 � OBÞ 2555.6 −0.969 8. LB ¼ expð0:0088 � OBÞ

Quad U 456.4 0.857 9. L ¼ �17:4þ 0:20 � Oþ 0:000029 � O2 1833.7 0.829 11. L ¼ 27:9þ 0:017 � Oþ 0:00013 � O2

B 455.2 0.855 10. LB ¼ 0:133 � OB þ 0:00011 � OB2 1839.8 0.824 12. LB ¼ 0:096 � OB þ 0:000053 � OB

2

Power U 456.5 0.857 13. L ¼ �13:55þ 0:104 � O1:11 1833.5 0.829 15. L ¼ 29:15þ 0:00044 � O1:84

B 454.8 0.856 14. LB ¼ 0:0328 � OB1:28 1843.5 0.822 16. LB ¼ 0:0458 � OB

1:16

Table 3 Model results for regressions between fish length andotolith radius using four different equations. Int. refers tointercept, and U means the intercept was unconstrained at thebiological intercept, and B means the equation was constrained

to pass through the biological intercept. L refers to fish length,and LB refers to fish length minus the biological intercept. Orefers to otolith radius, and OB refers to otolith radius minus thebiological intercept

Fig. 4 Model fits fordifferent forms of the fishlength/otolith radius rela-tionships. Data from SnakeRiver fall Chinook are in theleft column and data forSnake River spring/summerChinook are in the rightcolumn

Environ Biol Fish (2010) 89:267–278 275

(ESUs) and among populations within the spring/summer Chinook ESU. Our analyses demonstratedclear differences in fish length/otolith radius relation-ships between ESUs of Chinook salmon, but much finerdifference among populations that were more closelyrelated to each other than were fish from the two ESUs.These results demonstrate the need to determine the

proper taxonomic level at which to combine fish datawhen developing fish length/otolith radius relationships.Otherwise, as demonstrated by Strelcheck et al. (2003),studies using back-calculations derived from distinctpopulations lumped together can produce unrealisticconclusions regarding the variability in growth amongpopulations. Below we conduct a sensitivity analysisthat demonstrates the same potential for error withChinook. Researchers will need to develop the abilityto detect these differences in their sampling designs.

The differences in fish length/otolith radius relation-ships among ESUs were consistent with predictionsfrom the growth rate hypothesis (Secor and Dean 1989)that fall Chinook has greater growth rate and is largerthan spring/summer Chinook with the same otolithradius (Fig. 2). Although models that contained vari-ability in otolith growth rate could explain some of thedifference between ESUs, using only an ESU factorresulted in much stronger fits to the data. Further, weobserved very little effect of otolith growth rate on thefish length/otolith radius relationship within ESUs,lending support to the conclusion that the differenceswe observed between ESUs were not solely the result ofvariability in growth rates. In addition, we do not believethe differences exhibited between were due to samplesbeing collected in different years (spring Chinook:2004–2006; fall Chinook 1993, 1994, 2007, and 2008).First the differences in fish growth rates we observedwere consistent with the expectation that fall Chinookgrow faster the spring/summer Chinook, which rear inhigher elevation streams and require an extra year toreach the smolt stage. Further, when we included yeareffects in models within ESUs, it did not improve modelfits, indicating no year-to-year variability in fish length/otolith radius relationships within ESUs.

It is therefore unclear why these two ESUsdemonstrated differences in the fish length/otolithradius relationship. Because these populations havebeen separated for thousands of years, and becausethe fish length/otolith size relationships have a geneticbasis (Fey 2006), it is quite possible that the differ-ences we observed in fish length/otolith radiusrelationships also have a genetic basis (as a result ofselection or drift). Differences in these relationshipsmay also be due to factors, environmental orotherwise, that were not measured in this study. Oneway to approach this issue would be to conductinvestigations whereby fish from the two ESUs areraised in common environments.

Table 5 Model results for regressions between fish length andotolith radius that also included mean otolith growth rate (GO)and mean temperature (T, degrees C). NP refers to the numberof parameters in each model; L refers to fish length; O refers tootolith length; ESU refers to evolutionarily significant unit

Model NP R2 AIC

Spring/Summer Chinook

1. L=O 2 0.634 565.7

2. L ¼ Oþ O2 3 0.637 567.1

3. L ¼ Oþ O : GO 3 0.635 567.4

4. L ¼ Oþ T 3 0.636 567.3

5. L ¼ O»T 4 0.643 567.6

Fall Chinook

6. L=O 2 0.768 287.8

7. L ¼ Oþ O2 3 0.795 285.1

8. L ¼ Oþ O : GO 3 0.797 284.7

9. L ¼ Oþ O : GO þ O2 4 0.810 284.3

Combined

10. L=O 2 0.672 1029.8

11. L ¼ Oþ O2 3 0.720 1012.1

12. L ¼ Oþ O : GO 3 0.856 928.6

13. L ¼ Oþ O : GO þ O2 4 0.862 925.2

14. L ¼ Oþ ESU 3 0.891 894.1

15. L ¼ Oþ O2 þ ESU 4 0.915 865.4

16. L ¼ Oþ O : GO þ ESU 4 0.893 893.8

17. L ¼ Oþ O2 þ O : GO þ ESU 5 0.915 866.4

Table 4 Model results for regressions between fish length andotolith radius that also included the factor POP, which refers toPopulation. NP refers to the number of parameters in eachmodel. L refers to fish length, and LB refers to fish length minusthe biological intercept. O refers to otolith radius, and OB refersto otolith radius minus the biological intercept

Model NP R2 AIC

1. L ¼ Oþ O2 3 0.829 1833.7

2. L ¼ O»POP þ O2 15 0.858 1803.3

3. LB ¼ OB þ OB2 2 0.824 1839.8

4. LB ¼ OB : POP þ OB2 8 0.840 1824.4

276 Environ Biol Fish (2010) 89:267–278

Our simple back-calculation methodology performedwell when comparing our predictions of fish length to theobserved lengths of fish tagged 26 days earlier (onaverage). Although our validation method was not ideal,given that we needed to estimate the otolith incrementcorresponding to the day of tagging by counting incre-ments, the results were informative and encouraging.The validation exercise was clearly able to distinguishamong alternative methods and confirmed the advantageof using methods that constrain back-calculated growthtrajectories to pass through a meaningful biologicalintercept.

As a demonstration of how important it is to treat thesalmon ESUs separately, we repeated the validationexercise, but instead of using model parameters specificto fall Chinook salmon, we used parameters obtainedfrom fitting both ESUs together. When we thenpredicted size of fish at tagging using the constrained

quadratic model (with the biological intercept set to themean of both ESUs), the bias increased from absolutevalue less than 1.0 mm FL (Fig. 5d) to almost 15 mmFL. Clearly this magnitude of bias would severelyhinder the utility of these back-calculations.

Several other studies have examined fish length/otolith size relationships in Chinook salmon (Neilsonand Geen 1982; Zhang et al. 1995; Titus et al. 2004).Although each study uses slightly different approaches,our method is comparable to the Titus et al. (2004)study. Comparing our linear model to theirs, it appearsthat our slopes are approximately twice as large astheirs, further reinforcing the need to treat populations ofChinook separately when developing fish size/otolithsize relationships.

We note that our study was conducted on fish rearedin natural conditions, which created some logisticalchallenges, such as not having complete control over

Fig. 5 Histograms of deviations between observed and predicted (from back-calculations) fish lengths for four methods of back-calculation

Environ Biol Fish (2010) 89:267–278 277

sample sizes and distributions of fish sizes. Most studiesof this type have been performed in controlled laboratoryconditions that allow for clear resolution of the effects ofvarious factors. However, the value of methods used inthis study is to understand the population dynamics ofnatural populations, particularly those at risk, such as theChinook salmon populations in this study. Thus,understanding the response of otolith growth to fishgrowth under a variety of natural conditions and acrossclosely related taxa will be an important tool for themanagement of at-risk fish populations.

Acknowledgements This paper was a contribution to the 4thInternational Otolith Symposium, Monterey CA, August 2009.We thank B. Sanderson, S. Achord, K. Tiffan, and W. Connor forcollecting fish samples. We thank Lisa Crozier for providing themap of Salmon River basin populations. John Williams and twoanonymous reviewers provided valuable comments that greatlyimproved an earlier draft.

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