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CRYPTIC DENSITY DEPENDENCE: EFFECTS OF COVARIATION BETWEENDENSITY AND SITE QUALITY IN REEF FISH

JEFFREY S. SHIMA1,3 AND CRAIG W. OSENBERG2

1School of Biological Sciences, Kirk Building, Kelburn Parade, P.O. Box 600, Victoria University of Wellington,Wellington, New Zealand

2Department of Zoology, University of Florida, Gainesville, Florida 32611-8525 USA

Abstract. The importance and strength of density dependence continues to engenderdebate because of its central importance to population dynamics and regulation. Here, weshow how confounding effects of site quality can mask strong effects of density dependence.In particular, we explore spatiotemporal variation and covariation among (1) densities ofnewly settled coral reef fish (Thalassoma hardwicke), (2) environmental characteristics,and (3) the strength of density-dependent mortality. Environmental features of patch reefswere spatially and temporally variable and influenced density-dependent survival. Higher-quality sites (i.e., reefs possessing features that yield greater numbers of recruits at anygiven settlement level) received greater settlement, and this relationship masked the op-eration of density dependence when variation in quality among sites (or times) was notdistinguished (a common approach in many observational studies of density dependence).Our work illustrates how spatiotemporal covariation in settlement density and site qualitycan obscure patterns of density dependence at larger scales, contributing to a phenomenonwe call ‘‘cryptic density dependence.’’ Acknowledging patterns and consequences of co-variance may alter the way we study population dynamics, especially of marine organisms,where the link between processes that affect settlement and post-settlement survival remainsrelatively poorly understood.

Key words: density independence; density-dependent survival; environmental variability; post-settlement mortality; recruitment; regulation; settlement; site quality; Thalassoma hardwicke.

INTRODUCTION

The factors that drive spatial and temporal variabilityin population density and structure have long attractedthe attention of ecologists (Nicholson 1933, Andre-wartha and Birch 1954). Much of this focus has cen-tered on the strength and importance of density de-pendence, with some studies leading to the conclusionthat density dependence plays a minor role and otherssuggesting a predominant role. Although these differ-ences may be real, in some cases, the discrepanciesmay result from differences in the approaches used toquantify density dependence (e.g., Murdoch 1994, Tur-chin 1995, Wilson and Osenberg 2002). These issuesare particularly apparent in studies of marine systems,where debate continues over the relative magnitude ofvariation in population dynamics and the processes thatdrive the observed variation (Caley et al. 1996, Schmittet al. 1999).

Most marine reef organisms have a bipartite life his-tory, consisting of a pelagic larval stage followed bya relatively sedentary benthic stage (Sale 1980, Boothand Brosnan 1995). The two life stages are coupledthrough a transition called settlement, in which larvaeare delivered to potential sites through a combinationof currents (e.g., Cowen and Castro 1994) and larval

Manuscript received 14 January 2002; revised 30 July 2001;accepted 31 July 2002. Corresponding Editor: J. R. Bence.

3 E-mail: jeffrey.shima@vuw.ac.nz

behavior (e.g., Stobutzki 1997). Although both settle-ment and post-settlement survival affect the abundanceof benthic populations (e.g., Doherty and Fowler 1994,Forrester 1995, Hixon and Carr 1997, Steele 1997,Schmitt et al. 1999, Shima 2001a, b, Doherty 2002),disproportionate attention has been given to variabilityin settlement as a driver for variation in abundance ofolder life stages, probably because variability in set-tlement is easy to measure and density dependence istypically viewed as homogenizing force. However,many studies have linked variation in a variety of de-mographic rates (e.g., settlement and survival) of ben-thic marine organisms to specific environmental attri-butes, such as substrate composition and densities ofcompetitors and predators (reviewed in Jones 1991).As a result, we expect that spatial variability in settle-ment and environmental characteristics can create amosaic of patches with varying strengths of density-dependent and density-independent processes (e.g.,Shima 1999). Yet our sense of the importance of var-iability in density dependence may be misinformed be-cause most studies fail to estimate variability in thestrength of density dependence or its covariates (Os-enberg et al., in press).

By emphasizing spatial variation in the strengths ofpost-settlement processes within a context of variablesettlement, we are forced to conceptually link, and ex-plicitly study patterns of covariance between these two

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sources of variation for older life stages. Patterns ofcovariance are particularly informative because theycan mask the importance of processes that determinepatterns of abundance (e.g., Beukers and Jones 1997,Shima 2001a, b, Wilson and Osenberg 2002), and per-haps more importantly, because they can give rise todiverse dynamics that alter the way we conceptualizethe functioning of marine systems (e.g., Chesson 1998),in particular the role and importance of density depen-dence.

Here we developed an approach to explore the effectof spatial variation in environmental factors on sitequality and the strength of density dependence, andinvestigated some of the consequences of spatial co-variation in site quality and settlement intensity. Spe-cifically, we tested the conceptual model proposed byWilson and Osenberg (2002) to explain the dramaticdifferences in effects of density that they detected inan experimental study compared to an observationalstudy. Wilson and Osenberg argued that their obser-vational study underestimated the effect of density de-pendence because of the confounding effects of sitequality and the underlying association between settle-ment intensity and site quality: sites that naturally re-ceived more settlers were better able to support thosefish, thus obscuring the true effects of density on sur-vival. We term this phenomenon ‘‘cryptic density de-pendence.’’ Their experimental study, which relied onrandom assignment of treatments to sites, decoupledthis confounding influence and therefore revealedstrong effects of density. There were, however, severalalternative explanations for the disparity between theexperimental and observational results discussed byWilson and Osenberg, including the possibility thathandling led to the stronger density dependence in theexperimental study. Our approach, based entirely onobservational data, avoids this potential confoundinginfluence and therefore provides a strong test of theirmodel. Furthermore, our results underscore the need toconsider spatiotemporal variation in quality whenquantifying density dependence.

METHODS

A framework to evaluate site quality and the strengthof density dependence

We model the relationship between the per capitasurvival of recently settled fish and the density of thecohort as

dN/Ndt 5 2a 2 bN (1)

where N is the density of fish in the cohort, b is thedensity-dependent mortality rate (measured per con-specific), and a is the density-independent mortalityrate. Both a and b take on values .0 (unless mortalitydecreases with density, in which case b , 0). Eq. 1can be integrated to yield the Beverton–Holt recruit-ment function (Beverton and Holt 1957):

2ate N0N 5 (2)t 2atb(1 2 e )N01 1a

which describes the relationship between the numberof surviving juveniles (Nt) and the initial number ofsettlers (N0). Eq. 2 results by assuming that density-dependent mortality changes instantaneously as densitychanges. If, in contrast, the intensity of density depen-dence is set by initial density and does not change asnumbers in the cohort decline, the result is a Rickerrecruitment function (Ricker 1954):

2bN t0N 5 N aet 0 (3)

where a 5 e2at.In principal, a and/or b in these expressions may be

constant in space and time, or they may vary as func-tions of environmental characteristics. If they vary,some sites will have characteristics associated withlower mortality rates (via a or b), and hence will beof higher ‘‘quality.’’ For example, if the variation infactors that influence b is large among sites (relativeto those that affect a), then overall variation in sitequality may be produced primarily by variation in b.The ‘‘best’’ sites, by definition, will harbor individualsthat experience weaker per capita effects of conspe-cifics, and will yield the greatest numbers of individualsat time t for any particular level of settlement. Weapplied this approach to (1) describe spatial and tem-poral variability in environmental characteristics, (2)quantify how variation in a and b, and hence site qual-ity, correlates with the environmental variation, (3)quantify the covariation between site quality and set-tlement intensity, and (4) examine how this covariationaffects the detection of density dependence.

Study system and data collection

Fieldwork was conducted in the lagoons surroundingthe island of Moorea, French Polynesia (178309 S,1498509 W) and focused on the six bar wrasse (Thal-assoma hardwicke; see Plate 1). Six bar wrasse larvaedevelop in the pelagic environment for ;47 d (Victor1986) before settling to reef habitat. Because settlementoccurs during discrete lunar periods, and because set-tlers have different morphology and behavior than old-er fishes, accurate estimates of daily settlement andcohort survival are easily obtained (for details see Shi-ma 1999, 2001a, b). In addition, settlers and juvenilesutilize a broad range of habitats (Shima 2001b), albeitwith unknown demographic consequences.

We made 480 observations of settlement events (i.e.,pulses of settlement to individual sites) and monitoredsurvivorship of six bar wrasse cohorts formed by theseevents. These were made during and after three periodsof heavy settlement in May 1996, May 1997, and June1997, using 192 patch reefs. Patch reefs were originallyselected in two categories: (1) those with damselfish

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PLATE 1. Adult six bar wrasse (Thalassomahardwicke) on Moorea, French Polynesia.Shown are a group of adults preying upon theeggs of a territorial damselfish, Stegastes ni-gricans. These adult wrasse represent the prod-uct of recruitment. (Photo credit: J. Shima.)

(Stegastes nigricans) territories composed primarily ofalgal turf (n 5 96 reefs, surveyed during all three set-tlement periods), or (2) those lacking damselfish ter-ritories and composed primarily of living coral (Poriteslobata; n 5 96 reefs, surveyed during May and Juneof 1997 only). Other than this difference, all reefs wereselected to be relatively similar in size, rugosity, anddistance from nearest neighbors (described in Shima2001b). Reefs were censused daily during periods ofheavy settlement, and every third day during othertimes for densities of (1) settlers (and these cohortswere then followed through time), (2) older conspe-cifics, (3) heterospecific labrids and scarids, and (4)resident piscivores. Censuses were continued for a pe-riod of 90 d following each settlement event. At theend of the study in each year, we recorded the densitiesand sizes (aerial coverage) of fine-branching corals(Pocillopora spp.) on each reef.

Environmental variability among sites andheterogeneity in a and b

We used a principal components analysis (PRIN-COMP procedure in SAS version 8.02; SAS 1999) tosummarize the observed environmental variationamong reefs, and subsequently used the results of theprincipal components analysis (PCA) to model hetero-geneity in a and b.

PCA.—The environmental variables used in the PCAwere the time-averaged (over the 90-d post-settlementperiod specific to each focal cohort) density of potentialcompetitors (older conspecifics, heterospecific labridsand scarids), and density of potential predators (resi-dent piscivores), as well as refuge availability (i.e.,Pocillopora coverage), and substrate type (algal turf orliving coral). Each of these factors might influence, orotherwise be indicative of, site quality for newly settledwrasses. Densities and refuge availability were trans-formed using log10(x 1 0.1). Substrate type was coded

as a categorical variable: 1 for sites without damselfishterritories (i.e., primarily Porites), and 2 for sites withdamselfish territories (i.e., primarily algal turf). Thefirst principal component accounted for 56.5% of theoverall variance in the data set, and exhibited positiveloadings for all variables, which were approximatelyequal in magnitude (all were between 0.65 and 0.82).We therefore used the first principal component as adescription of the environment (and we give this thesymbol E).

Estimation of a and b.—We examined whether themajor source of environmental variability (i.e., E) wasrelated to site quality, by contrasting a series of statis-tical models that described alternative relationships be-tween the environment (i.e., E) and site quality (i.e.,a and b). These models were constructed in a crossedfashion based upon (1) the form of the recruitmentfunction (Beverton–Holt, Eq. 2 vs. Ricker, Eq. 3), (2)the relationship between b and E (independent: b 5 0or b 5 b0; linearly related: b 5 b0 1 bEE; or nonlinearlyrelated: b 5 b0 /(1 1 bEE), and (3) the relationshipbetween a and E (same possible forms as for b). Thisyielded a total of 32 (2 3 4 3 4) possible models,although four were redundant, so we evaluated 28 mod-els. Parameters for each model were estimated usingnonlinear regression (SAS NLIN procedure, method 5Marquardt, constrained by the condition that a # 0;SAS 1999). We then evaluated alternative models usingAkaike’s Information Criterion (AIC, Akaike 1992);the best model was the one with the smallest AIC.

Effects on the detection of density dependence

We compared system-wide estimates of density de-pendence using three approaches. First, we averagedthe estimates of b from each settlement event obtainedfrom the best model (see Estimation of a and b) to geta system-wide estimate of density dependence. We callthis the ‘‘heterogeneous case,’’ because local sites dif-

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FIG. 1. Cryptic density-dependent survival of Thalasso-ma hardwicke. For presentation, 480 survivor settler eventshave been aggregated into 24 groups of 20 events, based onsimilarities in environmental characters. The figure presentsfitted relationships (based on mean b within each group: seeEq. 4) between predicted density of survivors and initial den-sity of settlers for patch reefs with similar environmentalcharacters. Departure of the relationships from a linear re-lationship passing through the origin arises from the effectof density dependence. The curves that lie above others arecharacterized by weaker density dependence. Average settle-ment (and predicted recruitment) for each group is super-imposed on each relationship (solid circles). Note that failureto discriminate variation in site quality would lead to a re-cruitment function that was approximately linear (i.e., leadingto the erroneous inference that survival was density inde-pendent), despite underlying effects of density (i.e., a rela-tionship fit to the points would be much more linear than theplotted relationships).

fered in b. We contrasted this result with two ‘‘ho-mogeneous’’ cases, each of which assumed that a andb were invariant in space and time. The homogeneouscases are more typical of what is usually done in es-timating patterns of density dependence using obser-vational data. In the first of these homogeneous cases,we simply fit a single Beverton–Holt recruitment func-tion to the 480 events. As demonstrated in the results,Beverton–Holt models generally outperformed Rickermodels. In the second case, we aggregated the data,which is often done in field studies by sampling overlarger spatial scales to reduce noise in the data set. Wesimulated this by combining data based on environ-mental traits, in part, because environmental features(and, hence, site quality) appear to have a spatial com-ponent when evaluated at a large scale (Shima 1999).We ranked sites by E, sorted the 480 events into 24groups (each consisting of 20 observations), summedthe settlement and recruitment within these groups, andthen fit a Beverton–Holt recruitment function these 24estimates of Nt and N0.

RESULTS

Demographic variation among reefs ofdiffering quality

There was considerable variation in the performanceof the statistical models describing the relationship be-tween the environment and site quality. The Beverton–Holt function consistently outperformed the Rickerfunction. For example, in comparing each Beverton–Holt and Ricker pair (each with the same functionalform for a and b), the Beverton–Holt model fit betterin 11out of 12 comparisons (mean AICRicker 2AICBev-Holt 5 25.6). All Beverton–Holt models with anunderlying relationship between b and the environment(E), performed better than the model with a and bconstant (the minimum difference in AIC was 37).Overall, the best model (based on the smallest AIC)was the one in which the relationship between Nt andN0 was described by a Beverton–Holt recruitment func-tion, with a 5 0 and b a nonlinear function of E:

N0N 5 (4)tb01 1 N t01 2(1 1 b E )E

where b0 and bE define the relationship between b andE, with b0 5 0.0341 (95% CI, 6 0.0035) and bE 50.3148 (60.0602). Eq. 4 explained 45.5% of the var-iation in Nt across all 480 settlement events. However,because our 480 observations of settlement events in-cluded 132 observations of zero settlement (and, hence,zero recruitment), these observations were not infor-mative in distinguishing among competing models.Therefore, we reevaluated the fit of the best modelexcluding these observations: r2 decreased to 0.28, andconfidence intervals for b0 and bE increased slightly

(to 60.0042 and 60.0709, respectively), due to thereduction in degrees of freedom.

We used a random effects ANOVA to partition var-iation in quality (i.e., b) to spatial (patch reef), temporal(settlement pulse), and spatiotemporal (error) variation(using the VARCOMP procedure in SAS 1999). Only16% of the variation in b was attributable to maineffects of patch reef or time. The remaining 84% ofthe variation was unexplained, suggesting that varia-tion in quality is highly dynamic and can be interpretedas primarily spatiotemporal, with no consistent varia-tion among patch reefs or settlement pulses. Overall,these results provide convincing evidence that there isspatiotemporal variation in the strength of density de-pendence, and, hence, what we call site quality.

Importantly, settlement was positively correlatedwith site quality (i.e., settlement intensity and b werenegatively correlated: P , 0.0001, n 5 480, r 5 0.39),indicating that settlement was greatest to sites wheredensity dependence was weakest (see Fig. 1). Althoughit is unclear what mechanisms produced this result(e.g., active habitat selection by larvae or physicaltransport processes: see Wilson and Osenberg 2002),

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FIG. 2. Sensitivity of parameter estimation to variation insite quality. The figure presents parameter estimates (and up-per bounds of symmetric 95% confidence intervals) for (a)density-dependent effects (per capita effects of conspecifics,b; D-D effect) and (b) density-independent effects (D-I mor-tality rate, a). Results for the heterogeneous case are basedon the best model (evaluated using AIC) describing a rela-tionship between environmental characters and the strengthof density dependence (see Eq. 4). Results for the homoge-neous cases (i.e., assuming a single fixed a and b) were ob-tained by fitting Eq. 2 to all 480 survivor settler events (smallscale) or to 24 groupings of data based on aggregations of20 observations (large scale). Units for b are square metersper fish per day (m2·[fish]21·d21); those for a are per day (d21).

the correlation has important implications for the de-tection of density dependence. Specifically, this com-bination of variation in site quality and the correlationbetween settlement and site quality gives rise to whatwe call cryptic density dependence, which we illustrateby comparing the above results with more standardanalyses that ignore underlying variation in site quality(Fig. 1).

If the observed settlement events are used to estimatea single recruitment function, as is commonly done inthe literature (e.g., Jones 1990, 1991, Doherty 1991,Doherty and Fowler 1994, Shima 2001a), the observedrelationship between Nt and N0 indicates much less se-vere density dependence than that found using the het-erogeneous model (Fig. 2). Indeed, the average percapita effect of conspecifics assessed using our hetero-geneous model (b 5 0.0562) was almost four-foldgreater than estimated with the homogeneous model at

the smallest scale (b 5 0.0142), and nearly 30-foldgreater than obtained at a larger scale based on aggre-gated data (b 5 0.00193, a value statistically indistin-guishable from 0; Fig. 2a). Thus, the effect of densitydependence was hidden by the underlying variation insite quality and the correlated patterns of settlement(see Fig. 1). Interestingly, the estimated effects of den-sity-independent mortality (a) varied inversely with es-timates of density-dependent mortality (b) obtainedfrom these different approaches (Fig. 2b).

DISCUSSION

Our results show how environmental attributes oflocal sites can affect the strength of density dependenceto create a mosaic of patches of variable quality. Pat-terns of settlement in our system positively covariedwith b (the main component of site quality), and thisproduced an approximately linear relationship betweensurvivors and settlers, despite the presence of strong,albeit spatially variable, effects of density. Linear re-lationships between densities of initial (N0) and sub-sequent (Nt) life stages are typically interpreted as ev-idence for the absence of density dependence (reviewedin Doherty 1991). Thus, failure to distinguish vari-ability in site quality may inhibit our ability to detect,and accurately quantify, density dependence, especiallyin systems where interactions occur on small spatialscales or within local neighborhoods.

We found the magnitude of cryptic density depen-dence in our data set to be particularly striking giventhat the reefs used in this study were selected a priorito minimize potential variation in quality (i.e., patchreefs were of similar size, rugosity, isolation, and lim-ited to two substrate types). Our analyses suggest thatfailing to account for the observed heterogeneity inquality among sites underestimated the strength of den-sity dependence by nearly 75% relative to the hetero-geneous case. Aggregation of the data to simulate thesampling of our system over a larger spatial scale un-derestimated b by ;97%. Estimates of density inde-pendence varied in the opposite direction among thethree approaches. Thus, the correlation between settle-ment and site quality could have led to the misassign-ment of effects of density into the density-independentterm: e.g., based on the aggregated data set, the likely,but erroneous, conclusion would be that fish incurreda density-independent mortality rate of over 1% perday and that density had no effect on this rate. Thisraises the possibility that debate about the relativestrength of density-dependent vs. density-independentprocesses might be attributable to variation in the ap-proach (experiment vs. observational: Wilson and Os-enberg 2002) or the similarity of the sites used in ob-servational studies (and thus the strength of crypticdensity dependence), and not the actual strength of den-sity-dependent and density-independent processes. Inaddition, such large differences in parameter estimatesalso could have profound effects on predicted respons-

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es of a population to environmental change or man-agement strategies.

A principal components analysis allowed us to char-acterize variation in environmental attributes, facili-tating estimates of a and b as functions of environ-mental characteristics. Our analyses revealed that‘‘good’’ sites were those with more Pocillopora (a fine-branching coral), but less Porites (a mounding coral),and containing damselfish territories (and thus morealgal turf). Branching corals and algae are used as shel-ter by young six bar wrasse, and thus might representrefuge from predators. The presence of territorial dam-selfish might also deter predators. Oddly, however,‘‘good’’ sites also had high densities of potential com-petitors and predators. We speculate that a generic fea-ture of site quality (e.g., shelter availability or currentregimes) may increase general fish abundance, result-ing in sites of high quality that simply support morefish. Additional manipulations of habitat attributes arebe required to disentangle determinants of site quality.

Furthermore, we can only speculate on the mecha-nisms that may drive cryptic density dependence in oursystem, but we expect that (1) local hydrodynamicsunderlying both patterns of settlement and site qualityand/or (2) active choices by settling larvae among sitesof variable quality (e.g., achieving an ‘‘ideal free dis-tribution’’, sensu Fretwell and Lucas 1970) contributeto this pattern (see also Wilson and Osenberg 2002).Previous observations and experiments suggest thelikelihood of both processes driving cryptic densitydependence for T. hardwicke (Shima 2001b).

Cryptic density dependence results from the positivecorrelation between settlement and site quality (Fig. 1).Although our data, and the likely mechanisms, involvepositive correlations between settlement and site qual-ity, other patterns are possible. For example, a negativecorrelation would lead to overestimates of density de-pendence. Furthermore, the strength of density depen-dence may never be unambiguously estimated usingobservational data. Here, we have shown how it canbe underestimated with homogeneous models, but it isnot clear to what extent the PCA captures all relevantenvironmental features that influence site quality; ifnot, then our heterogeneous model will yield under-estimates of the strength of density dependence. Ex-perimental manipulations remain the best approach toresolve this problem, although they are not feasible inall (or even most) systems. Interestingly, Shima(2001a) conducted experimental manipulations of den-sity in this same system. The b estimated from thosedata was 0.12 m2·fish·d (approximately two-fold greaterthan estimated here, although the 95% condifence in-tervals are large: 20.09 to 0.34; Osenberg et al. 2002).Thus, it is unclear whether the estimates based on theobservational data that incorporate environmental sitevariation capture most of the relevant variation in sitequality.

The extent to which cryptic density dependence is acommon feature of systems is currently unknown, ow-ing to a lack of studies that quantify within-systemvariability in the strength of density dependence andits covariates. However, at least one other study (Wil-son and Osenberg 2002) suggests similar patterns ofcovariance for small reef fishes (Gobiosoma spp.) inSt. Croix, U.S. Virgin Islands. Wilson and Osenberg(2002) hypothesized that a mismatch in the strengthsof density dependence estimated from experiments(with random assignment of treatments) and observa-tional studies (lacking randomization) could be ex-plained by confounding effects of site quality and anunderlying association between settlement intensityand site quality in the latter. Our work from Mooreacompliments the hypotheses posed by Wilson and Os-enberg (2002). For example, Shima’s (2001) experi-mental data yielded estimates of b that were ;10-foldgreater than the observation data based on a homo-geneous model. This 10-fold difference between ex-perimental and observational data is similar to thatfound by Wilson and Osenberg (2002). Together, thesestudies emphasize the need to consider multiple de-mographic rates (e.g., settlement and post-settlementsurvival), and particularly how they covary with oneanother, to better understand sources of spatial varia-tion that drive population dynamics, especially in open,marine systems.

ACKNOWLEDGMENTS

We thank A. Ammann, S. Kleinschmidt, and C. Shumanfor their valuable assistance in the field; J. Bence, J. Byers,N. Phillips, H. Lenihan, R. Schmitt, and two anonymous re-viewers for improving the quality of this manuscript; and B.Bolker, B. Gaylord, C. St.Mary, and especially J. Wilson forinsightful discussion. Logistical support was provided by F.Murphy, S. Strand, T. You-Sing, and J. You-Sing of the UCBerkeley Gump Biological Station, and by M. Arnold, K.Seydel, and B. Williamson at UCSB. Funding was providedby a Research Training Grant and Graduate Research TraineeProgram in Spatial Ecology (NSF BIR94-13141 and NSFGER93-54870, both to W. Murdoch), The Lerner-Gray Fundfor Marine Research (American Museum of Natural History),Sigma Xi, The Raney Award (American Society of Ichthy-ologists and Herpetologists), the Partnership for the Inter-disciplinary Study of Coastal Oceans (PISCO, Supported bythe Packard Foundation), and the Florida and National SeaGrant Programs. This paper is contribution No. 93 of theGump South Pacific Biological Station, and contribution No.85 of PISCO.

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