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Comparison and utility of different size-basedmetrics of fish communities for detecting fisheryimpacts1
Daniel E. Duplisea and Martin Castonguay
Abstract: The use of fish community indicators based on size spectra has become popular in the development of anecosystem approach to fisheries. Size spectrum theory arose from basic ecological work on energy flow, predator–preyinteractions, and biomass standing stock and was later applied to fish communities as length–frequency analysis. Amultitude of size spectrum indicators have resulted, but it is not clear if they all present similar information. Here wedevelop a simple framework describing what four size spectra indicators suggest about fish communities, their likelyresponse to fisheries exploitation, their ecological interpretation, and some of their biases. We examined indicators forscientific survey data from six exploited North Atlantic fish communities for the information that they reveal abouteach community. Each indicator revealed different information and had different biases. Combining indicators for themost impacted system (owing to fisheries and environmental change), the eastern Scotian Shelf, revealed a pattern anal-ogous to Holling’s ecological cycle of exploitation, conservation, release, and reorganisation. If this analogy is gener-ally valid, then it suggests that collapsed fish communities are more susceptible to chance events, and recovery is notdirectly reversible and may not be recoverable (to previous known state) at all if the system moves to an alternative cycle.
Résumé : Les indicateurs des communautés de poissons basés sur les spectres de taille servent souvent à donner uneapproche écosystémique aux études halieutiques. La théorie des spectres de taille s’est développée à partir d’étudesécologiques fondamentales sur les flux d’énergie, les interactions prédateurs–proies et la biomasse des stocks et elle aété appliquée subséquemment aux communautés de poissons sous la forme d’analyses de fréquence des longueurs. Ungrand nombre d’indicateurs du spectre de taille ont été proposés, mais il n’est pas clair qu’ils présentent des informa-tions équivalentes. Nous mettons au point un cadre de travail simple pour décrire ce que quatre indicateurs du spectrede taille révèlent au sujet des communautés de poissons et leur réaction probable à l’exploitation par la pêche; nousprésentons aussi l’interprétation écologique et certaines des déformations de ces indicateurs. Nous avons évalué les in-dicateurs à l’aide de données d’inventaire provenant de six peuplements exploités de poissons de l’Atlantique Nord etdéterminé l’information qu’ils dévoilent sur chacun des peuplements. Chaque indicateur révèle des informations diffé-rentes et présente des déformations particulières. La combinaison des indicateurs pour le système le plus affecté (parles pêches et le changement climatique), soit l’est de la plate-forme néo-écossaise, présente un patron analogue aucycle écologique de Holling, d’exploitation, de conservation, de libération et de réorganisation. Si cette analogie est engros valide, elle indique que les peuplements effondrés de poissons sont plus vulnérables aux événements aléatoires,que la récupération n’est pas directement réversible et qu’il peut ne pas y avoir de récupération du tout (retour à l’étatobservé antérieurement) si le système entreprend un cycle de rechange.
[Traduit par la Rédaction] Duplisea and Castonguay 820
Introduction
It is now widely acknowledged that an ecosystem ap-proach will be increasingly used for management ofexploitation of aquatic systems (World Wildlife Fund (WWF)2002), though there is not yet a consensus of what an eco-system approach to fisheries management will entail (e.g.,
Browman and Stergiou 2004). Clearly, to be useful and ac-ceptable, an ecosystem approach to management will meldsocio-economic and ecological considerations (Fisheries Re-search Conservation Council 1998; WWF 2002), fully ac-knowledging that this is difficult to achieve (Degnbol 2002).Socio-economic considerations involve consultation amongstakeholders to reach consensus on individual actions,
Can. J. Fish. Aquat. Sci. 63: 810–820 (2006) doi:10.1139/F05-261 © 2006 NRC Canada
810
Received 1 June 2005. Accepted 20 October 2005. Published on the NRC Research Press Web site at http://cjfas.nrc.ca on1 March 2006.J18720
D.E. Duplisea2 and M. Castonguay. Institut Maurice-Lamontagne, CP 1000, Mont-Joli, QC G5H 3Z4, Canada.
1This paper is part of a series derived from the 2003 American Fisheries Society special symposium entitled “Structure and functionof continental shelf ecosystems: then and now”, held in Québec City, Québec (August 2003), and from the DFO Strategic ScienceFund project “Comparative Dynamics of Exploited Ecosystems in the Northwest Atlantic (CDEENA)”.
2Corresponding author (e-mail: [email protected]).
whereas ecological considerations consist of various metricsdescribing fish stocks, ecosystems, or the environment (e.g.,Rice 2000) brought to the table by stakeholders. Science, inthis respect, services stakeholders and policy makers to pro-vide useful metrics of the natural system and potential im-pacts of various actions. Science, therefore, must proposevarious metrics of the natural system that reflect an amal-gam of community characteristics and how a metric respondsto perturbations such as commercial fishing.
Size spectra are a common type of metric used in aquaticecosystems to assess the state of a community (Kerr andDickie 2001). Size spectra are multispecies indicators of theabundance or biomass of organisms plotted as a function oftheir body size. Size spectra data are usually statistically fit-ted with a regression, the parameters of which are used tocharacterise the system under scrutiny. Size spectra havebeen used in fisheries to show that exploitation steepens astraight line slope over time (Pope et al. 1988; Bianchi et al.2000), which indicates a systemic decrease in the abundanceof large fish that are preferentially taken by fisheries. Otherwork corroborates this by showing that fisheries have pro-gressively lowered the trophic level of catches (Pauly et al.1998), which in aquatic ecosystems corresponds with smallerbody size (Jennings et al. 2002). Size spectra are also knownto reflect large changes in management imposed on shelffisheries (Pope et al. 1988; Duplisea and Kerr 1995).
Though size spectra clearly indicate trends in exploitedfish communities, several confusing aspects of size spectraexist, with most confusion arising out of methodological andstatistical treatment of data, as well as the applicability ofcertain theory. We believe that the multitude of treatments ofsize spectra in fisheries, though presently confusing, increasesthe utility of the approach to provide metrics of fish commu-nity state, which could be used in an ecosystem approach tomanaging fisheries. It is our purpose here to outline somecommon treatments of size spectra data, what they representecologically, how they are likely to respond to fishing, andtheir inherent biases. We analysed size spectra data from six
different systems: the northern Gulf of St. Lawrence, theSydney Bight, the eastern Scotian Shelf, the western ScotianShelf, Georges Bank, and the North Sea.
Origins and some common analyses of size spectraThe roots of size spectra can be found in Elton’s trophic
pyramid (Elton 1927), where abundant, low trophic level,and small body size organisms form the base of the pyramidand the apex contains the rare, large-bodied top predators:conceptually, size spectra are merely Eltonian trophic pyra-mids turned on their sides. Sheldon’s work on plankton inthe 1970s examined abundance or biomass in log2 body sizebins and found regularities in vastly different oceanic areas(Sheldon et al. 1972), leading them to propose that the samerelative biomass proportion in adjacent body size bins ex-tends from bacteria to whales. Further work showed that theslope of biomass vs. log body weight was negative (Platt andDenman 1978). When fisheries scientists began examiningmultispecies size distributions, they used length–frequencybased analyses (Pope and Knights 1982), usually fittingstraight lines to them. Almost invariably, fitted straight lineslopes to fish community length–frequency data are negative(Bianchi et al. 2000). Biomass size spectra (log biomass vs.log body weight bins) (Thiebaux and Dickie 1993) havebeen fitted with quadratics quite well, and a theory under-pins such fittings (Dickie et al. 1987).
Size spectra can be constructed using any measurement oforganism size combined with a measure of the prevalence ofthat body size in the system. Additionally, a variety of mod-els can be fitted to size spectra, e.g., straight lines (Pope etal. 1988) and parabolas, to characterise the pattern. No onemethod is universally correct, and the choice will dependentsomewhat on the discipline and the questions being asked ofthe size spectrum metric.
Given the multitude of methods for size spectra construc-tion and different kinds of statistical model fits that exist inthe literature, size spectra work can be confusing, thoughsome work has been done to relate and clarify the methods
© 2006 NRC Canada
Duplisea and Castonguay 811
Fig. 1. Map of the different systems studied with statistical management areas demarcated: (a) 4RS, northern Gulf of St. Lawrence;(b) 4Vn, Sydney Bight; (c) 4VsW, eastern Scotian Shelf; (d) 4X, western Scotian Shelf; (e) 5Z, Georges Bank; (f) IVabc, North Sea.Surveys represent continental shelf and shelf slope areas, which are roughly shown as the hatched areas inside the larger statistical areas.
(Han and Straškraba 1998). No single method is correct andwe propose that analysing the same data set in several wayscan reveal complementary information about the system be-ing studied. It is important to realise which analyses mightbe useful for particular questions or under which conditionsrelated to data bias.
Materials and methods
Six different regions (Fig. 1) were studied by examiningdata from four separate sources: (1) Atlantic Canadiangroundfish summer survey for the Scotian Shelf, (2) the Ca-nadian winter trawl survey on Georges Bank, (3) northernGulf of St. Lawrence groundfish and shrimp summer survey,and (4) the English groundfish summer survey for the NorthSea. From survey 1, we obtained data for the Sydney Bight(4Vn) and the eastern (4VsW) and western (4X) ScotianShelf. From survey 2, we obtained data for Georges Bank(5Z), and from surveys 3 and 4, we obtained data for thenorthern Gulf of St. Lawrence (4RS) and the North Sea(IVabc), respectively. Each of these survey types has differ-ent protocols for fishing and gear and different modes ofdata storage; hence they were treated separately and are notdirectly comparable in all respects. The Canadian surveysare represented here under the statistical areas of the North-west Atlantic Fisheries Organization (NAFO; www.nafo.ca).The English survey is represented under the statistical areasof the International Council for the Exploration of the Sea(ICES; www.ices.dk).
The Canadian surveys utilise a stratified random samplingdesign (Doubleday 1981) with a standard tow using a ben-thic otter trawl. For each tow, all the fish were weighed anda subsample (200 individuals per species) was taken forcomputing length–frequency distributions. These length–frequency distributions were the basis of the data used here.Weights of individuals were used directly if available orwere calculated from species-specific length–weight regres-sions.
The English groundfish survey of the North Sea is con-ducted by performing standard tows of 0.5 to 1 h duration atfixed stations each year. Tow time and gear changes oc-curred in the early 1990s. All data were standardised to a 1-h tow.
Our analyses include vertebrates and Loligo and Illexsquids. The vertebrates consisted mostly of teleosts, but alarge elasmobranch component is also represented in all thesystems. Squids usually constituted only a small portion ofbiomass in any tow. A complete listing of species includedin analyses of each system is available (Supplementarydata).3 This list represents the total potential species pool asnot all species were caught in all tows or even in all years.Only seven species had a consistent length–frequency recordeach year of the northern Gulf survey, but we used all spe-cies if they were measured, even though the protocol changedover the survey. We compared analyses (not presented here)conducted on all measured species vs. only the seven corespecies: the core species usually constituted 80% of the totalbiomass and changes in the trend in the size spectrum slope
did not vary considerably, both showing a shallowing slopefrom 1990. The all-species slope steepened slightly after1996, whereas the core-species slope continued shallowing.Because of the noise in the northern Gulf survey and our in-ability to characterise trends in this system (with all speciesor just core species), we did not pursue this comparativeanalysis further.
For each system, we constructed two types of multispeciesbody size abundance distributions, and four size spectrumindicators were derived from these fits: from a length–frequency distribution, where 5 cm body length categorieswere used and abundance (number·haul–1) within each 5 cmlength bin was summed and logged (log2), the size spectrummetric of a straight line slope was taken from this fitting(Fig. 2a). From log2 biomass (g·haul–1) at log2 body weight(g) distributions, commonly known as biomass spectra
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812 Can. J. Fish. Aquat. Sci. Vol. 63, 2006
Fig. 2. Demonstration plots of (a) a straight line slope fitted tolog number vs. length size spectra and (b) a quadratic curve fittedto log biomass vs. log body weight size spectra. Least square fit-ted size spectra parameters (linear slope, quadratic curvature,X vertex, Y vertex, and r2) analysed in this study are shown on theplots. Data shown are for Georges Bank survey data from 1987.
3 Supplementary data for this article are available on the our Web site (http://cjfas.nrc.ca) or may be purchased from the Depository of Un-published Data, Document Delivery, CISTI, National Research Council Canada, Building M-55, 1200 Montreal Road, Ottawa, ON K1A0R6, Canada. DUD 4078. For more information on obtaining material refer to http://cisti-icist.nrc-cnrc.gc.ca/irm/unpub_e.shtml.
(Fig. 2b), three indicators were derived: curvature of the fit-ted parabola, body size at the parabola vertex, and biomassat the parabola vertex. The vertex coordinates of the parab-ola can be determined by fitting the quadratic in the form
f x a x h k( ) ( )= − +2
where the vertex coordinates are (h, k).All data were prefiltered to include individuals of lengths
between 15 cm and 150 cm, primarily to avoid problemswith low catchability of fish smaller than 15 cm. Time seriesof the various size spectrum indicators are presented foreach system. Additionally, we fitted linear models of indica-tor vs. time to show the general trends and to aid compari-son between systems. If these models had a significant 1st-order residual autocorrelation error (5 of 24 models), thenthe linear model was refitted with an AR1 correlation struc-ture. Fittings were conducted in S-PLUS 6.1 using the GLS(generalized least squares) function (Insightful Corporation2002).
Total annual fisheries catch for each of these systems is pre-sented, as this provides some indication of the level of fishingpressure, which is a prime driver in all these systems. We didnot attempt to standardise catches as community exploitation ormake direct year-to-year comparison with various metricsowing to nonlinear and (or) lagged community response andnumerous other assumptions that could result in a misleading
analysis. Total catch data are freely available as Fishstat data-bases (FAO; www.fao.org) or from NAFO (www.nafo.ca;spreadsheet format available as well for demersal fish only) forthe western Atlantic and from ICES (www.ices.dk; Fishstatdatabase only) for the North Sea (IVabc).
We created a qualitative framework for comparing thefour size spectrum metrics analysed, their expected responseto exploitation, the ecological interpretation of this, and theirbiases (Table 1). With more empirical and simulation work,it might be possible to come up with definitions of commu-nity status (e.g., sustainably fished or overfished) based onsuch indicators, though that is beyond the scope of this study.The scheme in Table 1 is to show how we expect indicators tochange in response to fishing and ecologically why this is so.
Results
Northern Gulf of St. LawrenceVarious metrics were inconsistent in this system (Table 2;
Fig. 3). That is, according to the scheme outlined in Table 1and the ecological interpretation of these metrics, it is un-clear what occurred in the northern Gulf system based on the1990–2002 Needler summer survey. Slopes of indicator vs.time showed small increases for all but biomass at the parab-ola vertex. These results, especially the increase in body size(slope and vertex body size) from 1990 to 1995, are incon-
© 2006 NRC Canada
Duplisea and Castonguay 813
IndicatorExpected responseto exploitation Ecological interpretation Biases
Linear slope Decrease (steepens) Relative abundance of large fish and lossof largest fish owing to size-selectivefishery; potentially creates cultivationeffect where small fish increase in num-ber owing to release from predation byreduction in numbers of large fish
Reflects catchability of gear at larg-est and smallest sizes.Morphologies of fish (e.g., lengthof eel vs. lumpfish) are not alwayscomparable size indicators. Be-cause of equal length bins, sam-pling power is quite differentbetween bins.
Parabola curvature Equivocal Predator–prey body size ratio and specificproduction: limbs of quadratic canchange in same directions because ofloss of large fish and increase in smallfish leading to a less sensitive and (or)interpretable indicator of fishing.
Regression residuals are less likely toreflect changes in size range end-point gear catchability.
Body size at parabolavertex
Decrease Biomass where the bulk of the communitybiomass is located (like a biomassmode), consequently changes willreflect important ecological alterations:decreases reflect fisheries deriving largeyields from the sizes around the vertex
As with curvature.
Biomass at parabolavertex
Increase thendecrease
Closely follows total community biomass:may increase in early years of exploita-tion as midsizes obtain more resourceowing to competitive release from larg-est fish removed by new fisheries; withcontinued exploitation of the system,fisheries will more specifically targetmiddle size classes leading to reduc-tions in biomass.
As with curvature.
Table 1. Framework describing four size spectrum indicators examined here, including their potential response to exploitation and theecological interpretation of the indicator and response to fishing and biases.
sistent with our knowledge of the fishery collapse leading toa moratorium on cod fishing in 1994. Although the modelfits were generally good (Fig. 3, R2 values as points in thefigures), the interannual variability was quite large, suggest-ing that individual year effects are very strong for this sur-vey and (or) fish community and this makes it difficult todetermine temporal trends in the data. Catch (primarily cod,Gadus morhua, and redfish, Sebastes spp.) in this system de-clined approaching the 1994 moratorium and there were mi-nor increases in catch, mostly cod after 1996 and turbot,Reinhardtius hippoglossoides, thereafter.
Sydney BightBody size (as linear slope and quadratic vertex) showed a
continual decrease over time and a rapid decline in biomassat the vertex of the fitted quadratic after the mid-1980s(Fig. 4). Quadratic curvature showed a slight but noisy de-cline over the time period, suggesting a weak trend towardsa reduced range of fish sizes in the system. The decrease inall indicators with time was greatest for vertex body size(Table 2). Demersal catch followed the biomass at the vertexin this system as in most other systems.
Eastern Scotian ShelfTrends in this system were very similar to those of the
Sydney Bight but more pronounced (Fig. 5). Body sizesharply declined in the largest sizes (linear slope), as well asbody size at the quadratic vertex representing the single sizecontaining the most biomass, the latter showing the largestdecrease over time (Table 2). The biomass at the vertex in-creased to peak in the mid-1980s and declined thereafter.This is a collapsed fishery production system as only smallcatches were recorded after 1992 consisting mostly of silverhake (Merluccius bilinearis).
Western Scotian ShelfBody size, as both the linear size spectrum slope and body
size at the vertex of the parabola, decreased in this commu-nity (Fig. 6; Table 2). Biomass at the vertex of the parabolawas level until about 1980 and showed a noisy increase (re-sulting in an overall slight increase; Table 2) thereafter, sug-gesting that ecological processes buffered changes in totalbiomass resulting from fisheries. According to the scheme inTable 1, indicators suggest that this system is relativelyhealthy (or similar to early years in the series) from a com-munity body size perspective. Demersal fish catch from thiscommunity was fairly constant until about the mid-1980sand declined thereafter to about 25%–50% of the mean pre-1985 catch level.
Georges BankBody size showed a decreasing though variable trend over
time (Fig. 7; Table 2), measured as both size spectrum slopeand vertex body size. Biomass at the quadratic vertex wasvariable and showed only a slightly decreasing trend overthe time series, suggesting, according to the Table 1 scheme,that fisheries and other disturbances have not much affectedthe amount of biomass in the middle sizes even if speciescomposition did change. After about 1991, interannual vari-ability in both linear slope and quadratic curvature (depar-ture about smoother Fig. 7) increased.
© 2006 NRC Canada
814 Can. J. Fish. Aquat. Sci. Vol. 63, 2006
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North SeaBody size for the North Sea fish community decreased by
both measures, whereas biomass at the quadratic vertexshowed a small increase over time (Fig. 8; Table 2). This is asituation similar to that of Georges Bank. Body size at thevertex in 1995 was very small because of the appearance ofa large abundance of blue whiting, Micromesistius poutassou,and the fitted quadratic curvature increased (widened) to ac-commodate the presence of these relatively small fish. Thisindicator can therefore be quite sensitive to strong recruit-ment events in the North Sea. The slope of the linear modelfitted to curvature vs. time was negative when 1st-order re-sidual autocorrelation was accounted for in the model, even
though the trend appears to be increasing. This suggests a flip-flop behaviour for this indicator in the North Sea demersalfishes. Most metrics showed more interannual variability afterabout 1990 (r2 values in Fig. 8). This may be a result ofchanges in the English Groundfish Survey design in the early1990s, which may have changed catchability properties. Totalfisheries catch in the North Sea since the mid-1980s has re-mained at a level near 2 × 106 tonnes·year–1.
Discussion
Various size spectrum measures provide complementaryinformation on the state of systems. For example, the linearsize spectrum slope is indicative primarily of the decline in
© 2006 NRC Canada
Duplisea and Castonguay 815
Fig. 3. Temporal trend in four size spectrum indicators for thenorthern Gulf of St. Lawrence trawlable fish community andfishery yield: (a) length–frequency spectrum slope; (b) biomassspectrum quadratic curvature; (c) log2 body size at parabola ver-tex; (d) log2 biomass at parabola vertex; (e) total reported fisher-ies catch (tonnes, from NAFO). Points appearing as numbers arethe r2 values of the regression fitting. Lines are spline smoothsto show trends.
Fig. 4. Temporal trend in four size spectrum indicators for theSydney Bight trawlable fish community and fishery yield:(a) length–frequency spectrum slope; (b) biomass spectrum qua-dratic curvature; (c) log2 body size at parabola vertex; (d) log2
biomass at parabola vertex; (e) total reported fisheries catch(tonnes, from NAFO). Points appearing as numbers are the r2
values of the regression fitting. Lines are spline smooths to showtrends.
abundance of the larger fish in a system (Pope et al. 1988),which has declined in all of the studied systems. The bodyweight at the vertex of a quadratic fitted to biomass spectra,however, not only reflects the abundance of large fish in thesystem, but also the body size of fish where the communitybiomass peaks; hence, vertex body weight is a biomass-weighted mode. These are different pieces of informationwith different sensitivities to perturbation and biases. Thelinear slope is quite sensitive to abundance of large andsmall fish, rather than to body size where the bulk of theecologically active biomass is located. Consequently, linearslope is likely more sensitive to gear and vessel changesthan is body size at the parabola vertex. This is because sur-vey changes are more likely to affect the catchability of fishat the endpoints of the sampled size range (e.g., Trenkel et
al. 2004; ICES 2005), whereas the midrange body size ismore likely to be well sampled by most gears.
Biomass at the parabola vertex is a reflection of the bio-mass at the most common (as measured by biomass) bodysize in the community. Though not shown here, the vertexbiomass value is very closely correlated with total surveybiomass as a large proportion of the surveyed biomass co-mes from these intermediate body sizes. The parabola vertexis akin to total biomass or numbers in a similar manner tothe linear size spectrum intercept (Sprules and Munawar1986). The intercept often shows an increase with fishingand as slope decreases (Bianchi et al. 2000, which has some-times been attributed to a cultivation effect (Walters andKitchell 2001) where decreased abundance of large preda-tors leads to increases in abundance of small prey fish. There
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816 Can. J. Fish. Aquat. Sci. Vol. 63, 2006
Fig. 5. Temporal trend in four size spectrum indicators for theeastern Scotian Shelf trawlable fish community and fishery yield:(a) length–frequency spectrum slope; (b) biomass spectrum qua-dratic curvature; (c) log2 body size at parabola vertex; (d) log2
biomass at parabola vertex; (e) total reported fisheries catch(tonnes, from NAFO). Points appearing as numbers are the r2
values of the regression fitting. Lines are spline smooths to showtrends.
Fig. 6. Temporal trend in four size spectrum indicators for thewestern Scotian Shelf trawlable fish community and fisheryyield: (a) length–frequency spectrum slope; (b) biomass spectrumquadratic curvature; (c) log2 body size at parabola vertex;(d) log2 biomass at parabola vertex; (e) total reported fisheriescatch (tonnes, from NAFO). Points appearing as numbers are ther2 values of the regression fitting. Lines are spline smooths toshow trends.
may be a cultivation effect in the North Sea (Daan et al.2005), but in most other systems, adequate analyses havenot be conducted to verify the effect. Because the linear sizespectrum intercept is usually strongly correlated with theslope, an apparent cultivation effect may be a statistical arte-fact of fitting the straight line. Unless the intercept is centred(referred to as “height”; Daan et al. 2005), it is difficult todetermine if a cultivation effect has occurred. The biomassat the parabola vertex, however, is like the height of thestraight line fitted to length–frequency spectra and may morereadily reveal release in competition or predation owing todeclines in large fish abundance.
It is not clear ecologically what quadratic curvature re-flects in these systems. Theoretical work suggests that cur-vature reflects a combined effect of changed predator–prey
size ratio and production–biomass ratio (Thiebaux and Dickie1993), though it is difficult to disentangle those two parame-ters to make ecological inferences without fixing one of theparameters (Duplisea and Kerr 1995). Certainly, decreasesin curvature reflect a parabola fit over a smaller range ofbody size, but one could describe situations where body sizerange decreases or increases for a variety of reasons thatmay be unrelated to fishing, e.g., recruitment events orgrowth of fish to a large size owing to low exploitation inunfished systems combined with poor recruitment. The lattercould be a partial explanation for the increase in curvaturevalue in the northern Gulf of St. Lawrence after the fisheriesmoratorium imposed in 1994. Long-term sustained changesin curvature may reflect changes in the system resulting
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Fig. 7. Temporal trend in four size spectrum indicators for theGeorges Bank trawlable fish community and fishery yield:(a) length–frequency spectrum slope; (b) biomass spectrum qua-dratic curvature; (c) log2 body size at parabola vertex; (d) log2
biomass at parabola vertex; (e) total reported fisheries catch(tonnes, from NAFO), catch data from the USA after 1993 is notincluded. Points appearing as numbers are the r2 values of theregression fitting. Lines are spline smooths to show trends.
Fig. 8. Temporal trend in four size spectrum indicators for theNorth Sea trawlable fish community and fishery yield:(a) length–frequency spectrum slope; (b) biomass spectrum qua-dratic curvature; (c) log2 body size at parabola vertex; (d) log2
biomass at parabola vertex; (e) total reported fisheries catch(tonnes, from ICES). Points appearing as numbers are the r2 val-ues of the regression fitting. Lines are spline smooths to showtrends.
from increased or decreased abundance of species with verylarge or very small adult body size.
Body size at the parabola vertex will be sensitive to datathat move the fitted parabola vertex outside the sampledbody size range. This can occur if large recruitment eventsarise in a system over several size classes, which is probablywhat is represented by the low vertex body size in 1995 inthe North Sea where abundance of fish <130 g was quitehigh compared with that in other years. The concomitant in-crease in curvature in 1995 reflects not only the shift in theparabola position, but also its widening to accommodate thelarge abundance of small fish. The original steady state the-ory for fitting parabolas (Thiebaux and Dickie 1993) andempirical fits (Sprules and Goyke 1994) have suggested thatonly horizontal and vertical shifts in parabola vertices,though not changes in curvature, should occur across broadgroups such as phytoplankton, zooplankton, and fish. Thiswork for communities far from steady state shows that con-comitant shifts and changes in curvature are likely indicativeof nonequilibrium events such as large recruitment events inthe system. Therefore, although quadratic curvature is diffi-cult to interpret, large interannual changes in its value cansuggest the occurrence of an event beyond what steady statetheory predicts, and this is useful to interpret why largechanges in the body size at the vertex may occur.
Different size spectrum indicators usually reflect differentaspects of the community response to exploitation; therefore,by combining indicators we are likely to develop a morecomplete indication of community state. For example, thebiomass at the vertex of a fitted parabola concomitant with adecrease in body size at the vertex suggests that a fisherymay be taking more than the community surplus yield, i.e.,exploitation that leads to decrease not only in communitybody size, but also in biomass. Vertex biomass is likely toincrease in early stages of exploitation owing to competitiverelease of resources as fisheries target the largest fish in thesystem; however, continuing fisheries usually begin to targetsmaller individuals and the biomass will begin to decline inintermediate sizes if yield exceeds surplus production. Whenboth the body size and biomass positions of the vertex aredecreasing, essentially there is a situation in which the com-munity is overfished, i.e., surplus production is surpassedand fisheries begin to target ever smaller sizes to maintainyields. This is a different casting of the concept of “fishingdown food webs” (Pauly et al. 1998). If we are to eventuallydefine community or ecosystem sustainability and over-fishing (Link and Brodziak 2003), it will most likely comeabout through combining various indicators of the fish com-munity.
The large decline in both body size and biomass of thebiomass spectrum vertex along with low recent fisheries yieldfor the eastern Scotian Shelf suggest that it is a “collapsed”fish production system. Relatively large fish catches weretaken in the mid-1980s at a time when biomass spectrumvertex biomass was maximised and body size was still rela-tively large. Such a situation might be considered an opti-mum community configuration for maximising use of thefish production system. Unfortunately, this pattern does notappear to be universal; however, no other system studied hascollapsed so clearly as the eastern Scotian Shelf (Frank et al.2005), where cod biomass is practically undetectable in re-
cent years (Canadian Science Advisory Secretariat 2003),predatory grey seal (Halichoerus grypus) abundance is veryhigh, and water cooled in the 1990s (Fu et al. 2001; Choi etal. 2004).
The pattern for the eastern Scotian Shelf is reminiscent ofthe four stage pattern of (i) exploitation, (ii) conservation,(iii) release, and (iv) reorganisation in ecosystems describedby Holling (1992), subsequently termed the “lazy-8” as thepattern resembles the figure “8” turned on its side. That is,we can view a modified lazy-8 (reflected on a horizontalaxis) in biomass spectrum vertex space (vertex body size vs.vertex biomass), though not completely horizontal (lazy)(Fig. 9). This speculative casting of the lazy-8 for size spec-tra suggests that fisheries and other disturbances will reducethe abundance of large fish, subsequently leading to a de-cline in competition such that smaller (yet still commerciallyexploitable) fish increase in biomass. Ultimately the commu-nity decline in biomass and body size is defined as a col-lapsed state. The community may then rebuild to theprevious state following a sequence that is not merely a re-versal of the decline, or it may switch to an alternate state.The numbered stages in Fig. 9 correspond to Holling’s num-bered stages such that Fig. 9 stages 1, 2, 3, and 4 correspond
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818 Can. J. Fish. Aquat. Sci. Vol. 63, 2006
Fig. 9. The “lazy-8” from Holling (1992) modified to representthe situation for an exploited temperate/boreal marine fish com-munity as depicted by size spectrum parameters. The closenessof the arrows represents the rate of change in state; the solid ar-rows represent the states that have been observed (eastern Sco-tian Shelf), and the shaded arrows are hypothetical and have notbeen observed. The width of the path in stages 3 and 4 repre-sents the large variability of the size structure then and the po-tential to occupy a much larger range of possibilities in statethan at stages 1 and 2. The eastern Scotian Shelf, the mostchanged or collapsed system, would be in the lower left part ofthe diagram.
to Holling’s stages 2, 3, 4, and 1, respectively. If a fish com-munity does respond in a similar manner to the process out-lined, which may be true for at least the eastern ScotianShelf demersal fish community (presently in lower left areaof the diagram), then there are several caveats of which weshould be aware relating to management and recovery ofexploited fish communities. (i) Exploitation is a disturbanceto which a fish community is resilient to a point but can andwill collapse if pushed too far (Duplisea and Blanchard 2005).Though this is obvious, it takes on a greater meaning in thecontext of Holling’s lazy-8. (ii) Community biomass can beoptimally exploited at the intersection of maximum biomassand modal body size. (iii) Fish community recovery aftercollapse may not be directly reversible, but there arehysteretic (hysteresis) effects that may be both counter-intuitive and undesirable. (iv) This suggests that all areas inmulti- and single-species biomass space may not be able tobe occupied in both directions (nonreversibility), contrary tocurrent assumptions of stock management approaches. (v) Acollapsed fish community is more susceptible to random in-fluence such that it may switch to alternative communityconfigurations and therefore never recover to a previous stateregardless of the management action. (vi) Given the two pre-vious points, risk management of fisheries with referencepoints should be highly risk averse in relation to limit refer-ence points, as we are not sure that all the space betweencurrent stock state and the limit reference point can be occu-pied, i.e., single-species reference points may not be ap-proachable continuously.
Acknowledgements
The Virtual Data Centre (a Fisheries and Oceans Canadadata-gathering initiative) was instrumental in obtaining dataand analysing results in the present study. CEFAS kindly al-lowed us the use of their English groundfish survey data forconstruction of size spectra. We thank the anonymous refer-ees for valuable comments on the manuscript.
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