Modelling the vertical distribution of eggs of anchovy (Engraulis encrasicolus) and sardine (Sardina pilchardus)

Modelling the vertical distribution of eggs of anchovy(Engraulis encrasicolus) and sardine (Sardina pilchardus)

G. BOYRA1,*, L. RUEDA,1 S.H. COOMBS,2

S. SUNDBY,3 B. ADLANDSVIK,3 M. SANTOS1

AND A. URIARTE1

1Fundacion AZTI, Herrera kaia z/g, Portualdea, 20110 Pasaia(Gipuzkoa), Spain 2Marine Biological Association, Citadel Hill,Plymouth PL1 2PB, UK 3Institute of Marine Research, PO Box

1870, Nordnes N-5024 Bergen, Norway

ABSTRACT

Understanding and modelling the vertical distributionof fish eggs in the water column is a major challengefor future use of underway-continuous egg samplers asestimators of the total egg abundance. This studypresents modelling of field data of anchovy (Engraulisencrasicolus) and sardine (Sardina pilchardus) egg ver-tical distribution obtained from LHPR sampling in theBay of Biscay. Starting from Sundby’s model [Deep-SeaRes. 30 (1983) 645], improvements were achievedthrough successive modifications concerning eggbuoyancy and vertical propagation of wind-inducedturbulence. In addition, measurements of egg settlingvelocity and buoyancy by stages were included as in-puts for the model. The best model fitting wasachieved through the adoption of a gradual turbulencevertical decay model (proportional to the inverse ofthe water density profile), a Gaussian variability of eggdensity and adaptability of the egg density to thesurrounding water by means of permeability of thechorion. This led to improvements over the Sundbyoriginal model. The coefficient of determination (R2)of the modelled egg abundance profiles compared withthe observed ones was around 80% for both sardineand anchovy. The model described successfully thevertical distribution of eggs for waters of high surfacesalinity (R2 of almost 90%), but less so for waters oflow surface salinity (R2 of about 70%).

Key words: adaptability, buoyancy, CUFES, DEPM,modelling, terminal velocity, turbulence

INTRODUCTION

Anchovy (Engraulis encrasicolus) and sardine (Sardinapilchardus) are two coastal pelagic fish species thatsupport important fisheries in the Bay of Biscay andIberian Atlantic shores of Europe. Currently, obtain-ing direct estimates of biomass during their spawningseason constitutes the basis for evaluation of theseresources (ICES, 2002).

Several methods have been used to obtain suchestimations. One of these is the Daily Egg ProductionMethod or DEPM (Lasker, 1985), in which adultabundance is estimated from the ratio of fish eggconcentration to the average fecundity of adults.Traditionally, vertical plankton samplers (e.g. theCalVET net; Smith et al., 1985) have been used toestimate egg concentration. This is a reliable samplingmethod but is time consuming.

The introduction of continuous samplers, such asthe CUFES (Continuous Underway Fish Egg Sampler;Checkley, 1997) for egg surveys, has the potential toreduce sampling time (Checkley et al., 2000). A majorlimitation is that continuous samplers collect samplesfrom a fixed depth. The vertical distribution of fisheggs may vary in space according to changes in envi-ronmental conditions (Sundby, 1983, 1991). There-fore, there is no simple relationship between eggconcentration at a fixed depth and total integrated eggabundance, thus potentially introducing an error intotal egg abundance estimates.

One way to cope with this problem is to adjust totalegg concentrations using egg vertical profiles. Thisadjustment factor should be obtained through mathe-matical modelling of the relative egg abundance bydepth layer as a function of hydrographical/environ-mental covariates.

The vertical distribution of epipelagic eggs can beexplained largely by their buoyancy, the density profileof the water column and the spawning depth (Sundby,1991). Buoyancy can be measured using a density gra-dient column (Coombs, 1981; Coombs et al., 1985) orderived from the observed ascent rate of eggs (Coombset al., 1985; Zeldis et al., 1995; Cambalik et al., 1998).Several models have been used to describe the verticaldistributions of fish eggs (Sundby, 1983; Page et al.,

*Correspondence. email: [email protected]

Received 11 November 2002

Revised version accepted 13 June 2003

FISHERIES OCEANOGRAPHY Fish. Oceanogr. 12:4/5, 381–395, 2003

� 2003 Blackwell Publishing Ltd. 381

1989; Westgard, 1989; Cambalik et al., 1998). Valid-ation of models is by comparison against observedvertical distributions obtained from discrete depth layersampling such as the LHPR (Williams et al., 1983).

The main objective of this paper is to develop animproved vertical distribution model for eggs ofanchovy and sardine. The model should allow predic-tions of egg vertical distribution profiles in relation tobasic hydrographical parameters (temperature andsalinity) and wind strength (i.e. the vertical mixinginput). The model of Sundby (1983) is used as a start-ing model, which is modified in search of an optimalalternative model. The models are validated againstfield observations of the egg vertical distribution.

MATERIALS AND METHODS

Vertical egg distribution, environmental conditions andbuoyancy measurements

Vertical sampling of eggs was carried out by means ofthe LHPR (Longhurst–Hardy Plankton Recorder;Williams et al., 1983; Pipe et al., 1981) at fixed sta-tions (Fig. 1) along transects in 2000 (32 hauls) and2001 (15 hauls). The LHPR is a towed plankton netsystem with a mounting frame about 2 m in length. Asingle filtering net (generally, 200 lm mesh size,500 lm at a few stations where clogging was a prob-lem) terminates in a mechanical cod end unit fromwhich a series of samples are taken at pre-set timeintervals (30 s, 1 or 2 min in this study) as the sampleris towed on an oblique haul at around 2.5 knots.A self-contained data-recording unit provides data onthe depth range and the volume of water filtered foreach sample (from a flowmeter). Temperature and

salinity profiles are also recorded concurrently, sup-plemented by independent CTD casts at each stationusing a SeaBird SBE-25 system. A typical depthresolution of around 1 m was achieved in the top20 m of the water column.

Samples were preserved in 4% buffered formalde-hyde solution and subsequently sorted for anchovy andsardine eggs.

Eggs were staged to the finest discrimination poss-ible according to Moser and Ahlstrom (1985) foranchovy, and Gamulin and Hure (1955) for sardine,with a separate category for eggs that could be iden-tified to species but were too damaged to be stagedreliably. Some of these damaged eggs could be stagedto a more coarse classification. Therefore, the eggswere grouped in three daily stages that correspond tothe finest ones as follows:• No embryo (NE): stages I–III• Early embryo (EE): stages IV–VI• Late embryo (LE): stages VII–XIFor calculation of the average egg density through-out development, the values for stage XI were excluded.This is because egg density increases markedly in thisshort phase just prior to hatching and would exert anundue bias if used in calculating an overall mean.

The LHPR data were processed into concentrationvalues (eggs per m3), taking into account the samplingdepth and the volume of water filtered. Normalizedprofiles of vertical distribution were prepared for eachhaul. Only those hauls on which 20 or more eggsoccurred for any particular egg stage were analysed.All results are plotted for the top 50 m of the watercolumn, as there were negligible numbers of eggsbelow this depth.

Figure 1. Position of LHPR hauls. Thecrosses are the hauls in 2000 and trian-gles are the hauls in 2001.

382 G. Boyra et al.

� 2003 Blackwell Publishing Ltd, Fish. Oceanogr., 12:4/5, 381–395.

Records of wind speed for each haul (average of theprevious 12 h) were used as inputs for the model tur-bulence estimates.

In addition, experimental measurements of thebuoyancy of the eggs of each species were carriedout in May 2001 using a density gradient column(Coombs, 1981; Coombs et al., 1985).

In order to get a synoptic description of the ver-tical distribution of eggs under different environ-ments, the LHPR stations were grouped into fourenvironmental scenarios according to surface salinityand wind stress. A threshold salinity of 34 was used todistinguish between low and high salinity stations. Forturbulence, a wind speed threshold of 4.5 m s)1 wasselected. As a result, the following four groups wereobtained:• Group 1: low salinity, low turbulence• Group 2: low salinity, high turbulence• Group 3: high salinity, low turbulence• Group 4: high salinity, high turbulenceThe weighted average of the egg vertical distributions,�uuGrðzÞ, for all the stations (st) in each group (Gr) wascalculated as

�uuGrðzÞ ¼P

st2Gr fst � ustðzÞPst2Gr fst

ð1Þ

where, ust(z) is the relative egg abundance at depth zfor each LHPR station and fst is the weighting factorfor the averaging procedure for the same station,obtained as follows:

fst ¼ 1; if Ne � 750

fst ¼ Ne=750; if Ne < 750ð2Þ

Ne being the raw number of eggs at each station.Expressions (1) and (2) were also used for the overallmean profiles.

Averages by the three coarse egg stages of devel-opment were also produced with eqn (1), but withdifferent weighting factors:

fst ¼ 1; if Ne � 250

fst ¼ Ne=250; if Ne < 250ð3Þ

Ne being the number of eggs of no, early or lateembryo.

In order to average the water density profiles, thesame weighting procedure was applied in each case.This procedure was applied separately for each species.

The model of Sundby (1983)

The model of vertical distribution of eggs is basedupon the model by Sundby (1983), modified to im-prove its efficiency.

The Sundby model was based on the assumptionthat fish eggs are impermeable spheres with a givendensity, submersed in a viscous fluid, subject to theeffect of the wind-induced turbulence. Under theseconditions, we obtain wt the terminal velocity, withwhich the eggs move to their neutral position, as afunction of egg buoyancy and diameter, and the vis-cosity of the surrounding water.

Basically, the process commences with reading therelevant density and turbulence profiles. The programthen simulates the introduction of a number of eggsunder these conditions by solving numerically theStokes’ equations and the vertical transport equationfor the stationary state. The density of the eggs wasconsidered equal to the average density obtained fromexperiments with the density gradient column. In thisway, the model simulates the final vertical distributionof the eggs.

The modifications considered in this paper to im-prove the basic Sundby model are related to thevariability of egg densities, their adaptability to themedium, a non-spherical shape correction for anchovyeggs and the model of turbulence decay.

Egg-density variability

The improved model allowed a normal distribution ofegg densities centred on the mean obtained from thedensity gradient, with the width dependent on thestandard deviation of measurements for eggs of all stages(excluding the last stage, stage XI). The standard devi-ation was obtained by multiplying the standard errors ofthe egg densities measured in the gradient column bythe square root of the average number of eggs used in theexperiments for each species (

ffiffiffi�nn

p� 5 for anchovy and

3.5 for sardine). The probability function was:

PðqÞ ¼ 1ffiffiffip

p� r exp ðq q0Þ2

2r2

( )ð4Þ

where q0 is the average egg density in the experiment,r is the standard deviation, and q are 50 equidistantpossible egg density values covering the range:

q0 2:6r < q < q0 þ 2:6r ð5Þ

Permeability and adaptation of egg buoyancy

The external membrane (or chorion) of eggs of tele-osts is freely permeable to water (Holliday, 1971), andsardine eggs are known to change their density becauseof altered salinity of the external medium (Coombset al., 1985). In general, the permeability of themembrane permits some adaptation of egg density tothe density of the environment. This effect is likely to

Vertical distribution model of anchovy and sardine eggs 383


be more marked for sardine eggs, which have a largeperivitelline space, than for anchovy eggs, which havea much smaller perivitelline volume.

An improved model was explored to account forthis effect; the adaptation of the egg to the density ofthe external medium because of the permeability ofthe chorion being simulated by the following formula:

qe ¼ 1 Vpv

Ve

� �q0

w þ Vpv

Veqw ð6Þ

Here, qe is the density of the egg, q0w, the density

obtained experimentally with the density gradient andqw is, for each station, the density from the CTDprofile that is closest to q0

w. Vpv/Ve is the ratio of thevolume of the perivitelline space to the total eggvolume for eggs of each species (about 0.05 foranchovy and 0.9 for sardine).

Non-spherical correction for anchovy eggs

A further improvement was the correction for non-spherical eggs. Stokes law applies to spherical objects,but anchovy eggs are prolate ellipsoids. This may affectthe sinking or ascent velocities of the eggs.

Two different approaches were developed. First, thefrictional force of an egg moving through a viscousmedium was considered as inversely proportional to itscross sectional area in the direction of propagation.Under this postulate, the terminal velocity variesproportionally to the ratio of the cross-sectional areaof an equivalent sphere (i.e. a sphere of the samevolume) and the actual cross-sectional area of the egg:

wellip ¼ Asphere

Aellip� wsphere ð7Þ

Anchovy eggs are prolate ellipsoids with a minorradius of about 0.3 mm, and major radius of0.7 mm. Under these conditions, the radius of theequivalent sphere would be 0.4 mm and the rangeof possible values for the corrected settling velocityranges from about 0.8 to 1.5 times the velocity ofthe equivalent sphere, depending on the orientationof the egg.

The second approach was taken from McNown andMalaika (1950) and corrected the range from 0.25 to 1times the velocity of the equivalent sphere, alsodepending on orientation. In the model, the overallrange provided by both approaches was assayed:

wellipsoidt � CNS � wsphere

t ð8Þwhere the corrected factor CN ) S was between 0.25and 1.5.

The final corrected value was obtained by optimi-zing to the observed LHPR data.

Turbulence profile

In order to produce vertical propagation models forturbulence, the water column was separated into dif-ferent layers. The pycnocline was defined as the depthlayer starting at Zp), defined as the depth at which a5% or larger density increment in 1 m was recorded.The bottom of the pycnocline (Zp+) was considered asthe depth at which the change in density in 1 m wasless than 10%. These reference depths separate thewater column into three depth layers: the mixed layer,the pycnocline layer and the deep layer (Fig. 2a).

The eddy diffusivity coefficient provides a value forwind-induced turbulence at the sea surface (Sundby,1983) and is calculated from wind speed values w:

K0 ¼ 76:1 � 104 þ 2:26 � 104w2 ð9ÞIn general, turbulence is highest near the surface anddecays with depth. Two turbulence models wereinvestigated, both decaying from a turbulence valueequal to K0 at the surface to one per cent of this valueat z ¼ 50 m depth. In Sunby’s model, a step functioncentred at Zpyc ¼ (Zp+ + Zp))/2 was used as the tur-bulence profile (Fig. 2b). The alternative was a moregradually decaying model in which the turbulence wasset to follow the inverse of the water density profile(Fig. 2c). Other possible approaches were consideredfor obtaining a gradual turbulence profile but, finally,the inverse of the density model was adopted as thesimplest and the most robust one.

Stratification effect

When studying the relationship between the verticaldistribution of eggs found by the LHPR and the densityprofiles, it was often observed that, at stations with lowsurface salinity, sub-surface peaks appeared at all windconditions. This seems to indicate the existence of anunexpected decrease in turbulence at stations with lowsurface salinity. This effect was ascribed to high strati-fication in low surface salinity areas associated with theplumes of the Gironde and Adour rivers. The stratifi-cation confers high stability to the water column, with asupposition that the wind-induced turbulence is dissi-pated at the surface or the very first few metres and thuswith little effect on the remainder of the water column.

This stratification effect was simulated in the modelby reducing the value for rate of change of turbulencewith depth by a ratio dependent on the surface salinity,

KredðzÞ ¼ KðzÞ=a ð10Þwhere a is defined as a sigmoid function of the salinity:

aðq0Þ ¼ 1 þ 99

1 þ exp 6ðq0 þ 23:65Þf g ð11Þ

384 G. Boyra et al.


that is, a ¼ 1 for surface densities higher than23.65 kg m)3, and tends asymptotically to 100 fordensities lower than this value.

Model application and checking

The program was run separately for each stage usingthe appropriate average density. Thus, a vertical dis-tribution profile was obtained for each stage; theconcentration profile for all eggs was obtained byaveraging these profiles by stages, weighted by theactual abundance of each stage at that station:

uuðzÞ ¼P

stg ustgTot � uu

stg% ðzÞP

stg ustgTot

ð12Þ

where uuðzÞ is the predicted concentration in depth(eggs per m3), ustg

Tot the total observed abundance ofeach stage (egg per m2) at that station and uustg

% ðzÞ isthe predicted vertical distribution profile (in per cent)for each stage of development. As the vertical depthresolution is 1 m, the egg abundance for the entirewater column (in eggs per m2) is obtained by summingthe abundances for every metre in the water column.For a group of stations (as with the environmentalgroups) the profiles by stages were averaged using thesame weighting values ustg

Tot ¼ 250 for all stages.The model outputs were validated against the

LHPR egg abundance profiles both visually (by graphs)and statistically. The statistical comparison was madeby calculation of the coefficient of determination (R2

values) of the modelled profiles (for eggs of all stagestogether), using the following expression:

R2 ¼ 100 � 1 PZplus

z¼1 ðuz uuzÞ2PZplusz¼1 ðuz �uuÞ2

!ð13Þ

where uz is the observed relative egg concentration atdepth z, �uu is the mean relative concentration of eggsacross depths of the observed data and uuz is the modelpredicted relative egg concentration at depth z. Thus,the coefficient of determination provides the goodnessof the fit of the model to the observed data, referencedto the mean value in the water column. This com-parison was not extended to the entire vertical profile,but only to the first part of it, from z ¼ 1m to z ¼ Zplus,where Zplus is the depth at which the model-expectedor the LHPR observed absolute egg densities becomeless than three eggs. The abundances at Zplus arecalculated as the sum of the remaining relative abun-dances from z ¼ Zplus to z ¼ 45 m. The abundances ofthe last 5 m of the water column (from 45 to 50 m) werediscarded to avoid boundary effects in the model.

As the model has not been adjusted by the sum ofleast squares, sometimes the model values were (onaverage) farther from the data than the mean values.In these cases the R2 values were negative. For sim-plicity, we converted these negative values to zero inthe tables of results (meaning that in those cases themodel was performing worse than the simple mean ofrelative concentrations across depths).

Figure 2. Different turbulence decaymodels: (a) the density profile with thelocation of the reference depths; (b) thestep to Zpyc (i.e. as used in the basicSundby, 1983, model) and (c) the grad-ual turbulence model.



In addition to the comparison of the relative ver-tical profiles of egg concentrations, the predicted andobserved abundances at 3 m (the depth of CUFESsampling) were also compared for both the groups ofstations and the individual stations. The relative errorswere calculated for the different environmental sce-narios as

RE ¼ 100 � uð3Þ uuð3Þuuð3Þ ð14Þ

RESULTS

Egg profiles by environmental scenario

The series of plots in Fig. 3 summarize the verticaldistribution of eggs of both species under differentenvironmental scenarios. In general terms, the distri-bution in high salinity areas showed an exponentialincrease towards the surface, this distribution beingmore superficial for low than for high turbulenceconditions. In low salinity areas, the vertical distri-butions tended to form sub-surface peaks of abundanceunder both low and high turbulence conditions.

Egg density measurements

Table 1 shows the average values of egg density byspecies for the three coarse stages of egg developmentfrom measurements obtained from the density gradientexperiments.

Modelling the anchovy egg distributions

Table 2 shows the change of R2 values for anchovyeggs obtained with the successive modification ofSundby’s original (1983) model with the incorporationof additional modifiers considered for its optimization.

The model proposed here as the optimum includesthe combination of the following features: graduallydecaying turbulence (inverse to the water densityprofile), egg density variability and adaptability of eggbuoyancy. The adoption of gradual turbulence pro-duced the greatest improvement over the initialmodel. On the other hand, neither the non-sphericalcorrection for anchovy eggs nor the stratification effectled to any noticeable improvement of the final fitting.

Table 2 shows that the optimum model had an R2

ranging between 70 and 90%; thus providing animprovement of about 20% over Sundby’s model forall the environmental scenarios. Remarkably betterperformance for both models is noted for high salinityareas compared with those of low salinity.

Egg densities profiles of both Sundby and theoptimum model fitted are plotted against the averageof all LHPR hauls combined in Fig. 4. The gradual

turbulence decay used in the optimized modelobtained smoother profiles, closer to the observedones. The fittings of the optimum model for the dif-ferent environmental scenarios are shown in Fig. 5. Aswas observed statistically, the figures show the lowerperformance of the model in low salinity scenarios,due to sub-surface peaks of egg abundance that themodel was not able to predict effectively.

The results obtained by the optimum model forindividual stations, are presented in Fig. 6. This showsthe plots of the R2 values for all the individual stationsagainst the number of eggs at each station. Results arepoorer than those obtained for the groups of stations ofthe environmental scenarios, with an average R2 of27.42%. The figure shows both the relatively betterperformance of the stations with high surface salinityand, in case of high salinity stations, the increase of R2

values with the number of eggs per station.Table 3 shows the relative errors of the abundances

predicted by the improved model against the observedabundances at 3 m depth for the different groups ofstations. Again, the errors were higher for low salinitystations.

Predicted versus observed relative frequencies at 3 mdepth for the individual stations are presented in Fig. 7,showing a statistically significant relationship betweenthe variables but with a very low R2 value. This rela-tionship is particularly evident for the high salinitystations. Besides, when forcing the regression to passthrough the origin for all the points, the slope was equalto 1.1, being not significantly different from unity.

Modelling the sardine egg distributions

Table 4 presents the contribution of the most relevantfeatures incorporated in the basic model in terms of R2

The model proposed as the optimum presents thecombination of the following features: graduallydecaying turbulence, egg density variability andadaptability of egg buoyancy.

Similarly to the anchovy case, the stratificationeffect made no statistical improvement. On the otherhand, in this case, the most important improvementwas achieved by the inclusion of density variabilityplus adaptability of the eggs.

The optimum model presents R2 ranging between60 and 90% depending upon the different environ-mental scenarios (Table 4), showing on average animprovement of about 10% in R2 over Sundby’smodel. Remarkably better performance of both modelsis noted for high salinity areas compared with those oflow salinity.

Figure 8 compares the fitted profiles of both modelsfor the overall mean of all LHPR hauls. The plots for

386 G. Boyra et al.


Figure 3. Vertical distribution of sardine and anchovy eggs observed for the different environmental scenarios. The bars showthe standard deviations of the distribution, and the dashed lines show the density profiles. N is the number of LHPR stationsaveraged for each scenario and n is the number of eggs sampled.



this species show slight improvements using the opti-mized model, likely related to the use of a gradualturbulence profile.

The vertical distributions given by the optimizedmodel are compared to the sardine field data forthe different environmental scenarios in Fig. 9.Consistent with the anchovy case, the low salinityareas showed a poorer performance than highsalinity ones. In addition, the individual plots pre-sented for the different stages show that none of thestages achieved any particular better accordancewith the observed profiles when compared againsteach other.

For the individual stations, the results obtainedfrom the optimum model, were worse than for theenvironmental groupings (Fig. 10), with an average R2

of only 9%. As for anchovy, the best average per-formance was for the stations with high surface salinity.

Table 3 shows the relative errors of the egg abun-dances predicted by the improved model against theobserved abundances at 3 m depth for the differentgroups of stations. Again, the errors appeared higherfor low salinity stations.

Finally, Fig. 11 plots predicted against observedrelative frequencies at 3 m depth for the individualstations for sardine. There was no statistically signifi-cant relationship between the variables (P ¼ 0.5) andthe R2 value was very low. When forcing the regres-sion to pass through the origin, the slope was 0.85, notsignificantly different from unity. Besides this, thepoints corresponding to high salinity stations have apositive significant tendency, although this is not thecase for the low salinity stations.

DISCUSSION

Egg vertical distributions

Anchovy and sardine egg vertical distributions byenvironmental scenario (LHPR averages, Fig. 3) wererather similar for both species. In high salinity areas,

Table 2. R2 values obtained for anchovy eggs using Sundby’s (1983) model, the successive incorporation of additional modi-fications and, finally, the proposed optimum model (see text). The results are presented for all hauls (Total) and for the differentenvironmental scenarios.

Total

Highsalinity–highturbulence

Highsalinity–lowturbulence


Lowsalinity–lowturbulence

Step turbulence (Sundby) 66.76 80.73 71.67 40.29 56.78Gradual turbulence 90.48 86.29 90.09 69.58 70.89Gradual turbulence + variability 98.21 66.46 98.34 81.84 44.79Gradual turbulence + variability + adaptability 89.79 89.73 88.67 68.55 74.44Gradual turbulence + variability + non-sphericity, Cn-s

1.3 95.78 56.97 95.57 75.68 54.021 98.21 66.46 98.34 81.84 44.790.8 84.57 94.29 83.07 64.87 80.90.5 69.13 85.66 63.88 51.62 81.17

Gradual turbulence + variability +stratification effect

92.5 90.3 90.28 0 0

Gradual turbulence + variability + adaptability + non-sphericity, Cn-s1.3 95.17 66.37 95.07 75.09 56.581 89.79 89.73 88.67 68.55 74.440.8 83.36 94.44 81.62 64.27 81.280.5 67.85 84.14 62.27 51.07 80.77

Optimum model 89.79 89.73 88.67 68.55 74.44

Table 1. Average densities and standard deviations of an-chovy and sardine eggs obtained in the density gradientexperiments (excluding values for the last stage, stage XI, ofdevelopment).

Totalaverage

Noembryo

Earlyembryo

Lateembryo

AnchovyDensity (sigma-t) 23.264 22.963 23.536 23.138Std. dev. 0.629 0.158 0.587 0.647

SardineDensity (sigma-t) 23.488 22.771 23.438 23.516Std. dev. 0.445 0.088 0.338 0.505

388 G. Boyra et al.


the egg concentration increased towards the surface.This can be explained by the higher density of thewater, and thus egg buoyancy. In low salinity areas, afraction of the eggs are negatively buoyant in the firstfew metres of the water column, resulting in sub-surface peaks or dome shaped profiles of egg abun-dance.

Under high turbulence conditions, in high salinityareas, egg abundance increased towards the surface.

But this increase was not as sharp as in calm situations.This was because of the turbulence, which tends tohomogenize the egg distribution by mixing throughthe first few metres of the water column. These resultsare in good agreement with Sundby’s model (1983).

However, at low salinity stations, high turbulenceconditions did not eliminate the sub-surface peak ofabundance, contrary to expectations. This is a conse-quence of the stratification effect mentioned above

Figure 4. Predicted (continuous line)against observed (dotted line) verticaldistributions of anchovy eggs for the2000–01 average of all hauls (Total),using the Sundby (1983) model (a), andthe optimized model (b). N is the num-ber of LHPR stations averaged and n isthe number of eggs found.



and indicates a decrease of the vertical propagation ofthe turbulence in low salinity areas. This can berelated to the sampling area of the Bay of Biscay

having low salinity areas occurring as outflow plumesof rivers flowing out of the French continental shelf,such as the Gironde and the Adour; these waters have

Figure 5. Predicted (continuous line) against observed (dotted line) vertical distributions of anchovy eggs for the differentenvironmental scenarios using the optimized model.

Figure 6. Representation of R2 valuesobtained using the optimum model forindividual stations against the number ofeggs at each station for anchovy. Thecircles represent high salinity stationsand the diamond symbols the low salin-ity ones.

390 G. Boyra et al.


a highly stratified structure and are consequently verystable with the wind-induced turbulence being dissi-pated in the top few metres.

Models and goodness of fit to the egg density profiles

The best model fitting was achieved through theadoption of a gradual turbulence vertical decay model(compared with the single step model), by allowing a

Gaussian variability in egg density and adaptabilityof egg density to the environmental water densitythrough the permeability model. This led to improve-ments over the base Sundby (1983) model.

In the Results section, we stressed not so muchthe coefficient of determination (R2) for the combi-nation of all LHPR hauls as for the different envi-ronmental scenarios, trying to obtain optimum fits forall together. This balanced coefficient of determin-ation was similar for sardine and anchovy at around80% (geometric mean of the R2 values of the fourenvironmental scenarios), despite the better sardinethan anchovy R2 for all LHPR hauls combined. Inhigh salinity environments, R2 values of almost 90%were achieved, whereas in the low salinity scenarios,R2 values of about 70% were obtained. The lowsalinity regions have not been sufficiently welldescribed by the former model adopted above.According to Figs 5 and 9 this seems to be a con-sequence of the sub-surface peaks of egg abundanceseen in the LHPR results.

Non-spherical correction

The introduction of the non-spherical correctionfor the terminal velocity was tested for different valuesof the correction coefficient. However, the optimumvalues for this coefficient were close to unity, thushaving a negligible effect. One explanation for thiscould be that, because of the orientation dependence

Table 3. Relative errors (in percentage) at 3 m depth of the optimized model for anchovy and sardine eggs. The results arepresented for all hauls combined (Total) and for the different environmental scenarios.

TotalHigh salinity–highturbulence

High salinity–lowturbulence

Low salinity–highturbulence

Low salinity–lowturbulence

Anchovy 18.49 )9.25 21.42 31.39 )29.13Sardine 10.28 13.90 8.34 28.46 )27.61

Figure 7. Observed against predicted abundances at 3 mdepth for individual 2000 and 2001 stations for anchovyeggs. High salinity stations are represented by circles and thelow salinity ones by diamonds.

Table 4. R2 values obtained for sardine eggs using Sundby’s (1983) model, the successive incorporation of additional modifiersand, finally, the proposed optimum model (see text). The results are presented for all hauls (Total) and for the differentenvironmental scenarios.

Total


Highsalinity–lowturbulence

Lowsalinity–highturbulence

Lowsalinity–lowturbulence

Step turbulence (Sundby) 94.96 63.39 82.76 54.14 67.44Gradual turbulence 83.28 46.04 82.84 72.02 21.37Gradual turbulence + variability 94.35 72.89 93.96 65.6 70.73Gradual turbulence + variability + adaptability 94.78 89.62 85.01 61.55 82.48Gradual turbulence + variability + stratification effect 86.07 54.07 85.82 0 0Optimum model 94.78 89.62 85.01 61.55 82.48



of the velocity and the range of orientations adoptedby the eggs, the correction may have an individualeffect but not on average.

Low salinity regions

The model was least capable of providing good pre-dictions for stations with low surface salinity, possiblybecause of the effect of the stronger near-surfacestratification. This was characterized by the presenceof sub-surface peaks of egg abundance where turbu-

lence might otherwise have mixed them more fullythrough the water column (e.g. see Fig. 12).

In order to simulate this effect in the model, areduction factor was tested for the turbulence profiledependent on surface salinity. Using this factor, themodel was more successful in predicting some of theobserved sub-surface peaks of egg abundance in the lowsalinity areas. Nevertheless, new problems were associ-ated with this method, because of the high variability ofthe distributions in the first few metres of the water

Figure 8. Predicted (continuous line)against observed (dotted line) verticaldistributions of sardine eggs for the2000–01 average of all hauls (Total),using the Sundby (1983) model (a), andthe optimized model (b). N is the num-ber of LHPR stations averaged and n isthe number of eggs found.

392 G. Boyra et al.


column. Thus, even when the program predicted a peakof egg abundance, it failed to match precisely the ob-served distribution in the few metres above the peak(Fig. 12c), that is, the statistical fit was poor. In othercases, the sub-surface peaks of abundance were notcorrectly located in depth or not predicted at all.

Sampling variability

Considering the discrepancy between model outputand the observed LHPR egg distributions, some ofthis may be because of limitations of the LHPRsampling. The LHPR is not a perfect sampler,especially in the top few (0–3) metres of the watercolumn, where flow measurements (and hencecomputed egg concentrations) can be biased by thesampler intake being only partly immersed at times.The sampler was also being used at the extreme

limit of its depth resolution (1 m). Another sourceof error is the natural spatial variability of the eggdistributions because of the contagious distributionof eggs in space and the limited number of LHPRhauls for each environmental scenario. Support forthis is provided by the better fits of the model tothe observed data for groupings, which containedhigher numbers of eggs, suggesting a lack of preci-sion, and reliability of the LHPR hauls with low eggnumbers. This problem becomes more significantwhen dealing with comparisons of model output forindividual station results. These sources of variabil-ity of sampling associated to LHPR are partlyreflected in the error bars of the egg vertical profilesof Fig. 4, which are at their maximum in the topfew metres of the water column or around sub-sur-face peaks.

Figure 9. Predicted (continuous line) against observed (dotted line) vertical distributions of sardine eggs for the differentenvironmental scenarios using the optimized model.



Applicability of the model

The long-term application of the model is to convertCUFES inferred egg concentrations sampled at 3 mdepth to total egg abundance for the entire watercolumn, e.g. for egg production estimates in DEPMapplications. Proper testing of this potential use wasoutside the scope of this study and would need to becarried out through broad comparisons of CUFES eggabundance estimates against CalVET (Smith et al.,1985) estimates with known hydrographical profilesand wind conditions.

As a preliminary test of the applicability of theoptimized model, Table 3 shows the relative errorswhen predicting egg concentrations at 3 m depthunder the four environmental scenarios. For lowsalinity stations, relative errors of about 30% arecommon for both species, although in high salinity

areas the errors were smaller. Nevertheless, bothnegative and positive values are obtained for the er-rors, thus showing that no systematic bias was foundon this 3 m depth prediction.

However, making similar comparisons for theindividual LHPR stations (Fig. 7 for anchovy andFig. 11 for sardine) gives rather poor relationships(R2 about 15–20% for both species). When fitting aregression forced trough to the origin, slopes werenot different from 1 and hence no clear bias ap-peared, but the precision was low, with wide errorsof the predicted percentage of eggs at 3 m depth.Figures 7 and 11 also show a poorer relationshipbetween expected and observed egg abundance at3 m depth for the low surface salinity stations than

Figure 12. Example of the stratification effect at a particularlow salinity station. The figure shows: (a) the density profile,(b) the predicted (continuous line) against observed (dottedline) vertical distribution profiles, and (c) the predictedagainst observed (as in (b)) but applying a reduction of theturbulence to simulate the stratification effect.

Figure 10. Representation of R2 valuesobtained using the optimum model forindividual stations against the number ofeggs at each station for sardine. Thecircles represent high salinity stationsand the diamond symbols, the lowsalinity ones.

Figure 11. Observed against predicted abundances at 3 mdepth for individual 2000 and 2001 stations for sardine eggs.High salinity stations are represented by circles and the lowsalinity ones by diamonds.

394 G. Boyra et al.


for the high salinity ones. Certainly, the individualhaul results are worse than for the averages used inthe environmental scenarios: hence, the potentialapplication cannot be yet properly assessed in thisway, but requires a broad checking with field pairedCUFES and CalVET sampling. As much as theprocedure followed of testing the performanceagainst the egg vertical distribution in averageenvironmental scenarios is correct, the applicabilityof the model may be better than what the checkingwith the individual LHPR hauls suggest.

In this study, the additional variables added tothe original Sundby (1983) model have given im-proved performance in modelling the egg verticaldistributions. However, problems associated with themodelling of low salinity areas require furtherattention. In addition, the optimum model proposedhere (with the inclusion of gradual turbulence, eggdensities variability and adaptability of egg densityto the hydrographical environment) has helped to acertain extent in the search for the ultimate optimalmodel. Features such as including a better turbu-lence model and a non-stationary approach mayneed further consideration.

ACKNOWLEDGEMENTS

This work was partially funded by the EuropeanCommission (PELASSES, Study Project 99/010) andthe Gobierno Vasco, Departamento de Agricultura yPesca. We are grateful to Mr Nick Halliday andDr Dave Conway for their support with the LHPRsampling. We also want to thank the skipper and thecrew of the R/V Investigador and, finally, Dr PaulaAlvarez and the technicians of AZTI for their work onthe samples.

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Modelling the vertical distribution of eggs of anchovy (Engraulis encrasicolus) and sardine (Sardina pilchardus)