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The process to estimate mortality and egg production includes 3 steps:
1) estimation of daily cohort abundances by age;
2) mortality estimation considering aggregated data and variables such as temperature and geographical strata;
3) Estimate P0 for each DEPM survey, using the external mortality values obtained from the model selected in step 2.
The mortality curve (Equation 1) is fitted using (a Generalized Linear Model (GLM) assuming a negative binomial distribution. The general model is extended to include temperature and strata (2). The spawning period is considered to occur at 22 hours +/- 2x2 hours (Fig. 4.)
ANCHOVY EGG MORTALITY IN THE GULF OF CADIZ (SW SPAIN) AND ITS APPLICATION TO EGG PRODUCTION
ESTIMATION1Paz Díaz, 1 M. Paz Jiménez, and 2Maria Manuel Angélico
[email protected]; [email protected]; [email protected]
1Instituto Español de Oceanografía (IEO)2Instituto Português do Mar e da Atmosfera (IPMA)
Introduction Material and MethodsFish egg mortality is a relevant parameter for ecological studies and it is also required to estimate egg production by the Daily Egg Production Method (DEPM), with a consequent effect on the Spawning Stock Biomass (SSB) estimation.
Daily egg production (P0) and mortality rates (z) are estimated by fitting an exponential mortality model to the egg abundance by cohorts and corresponding mean age:
E [P] = P0 e -Z age
Several issues relating to surveying and/or to the analytical procedures may affect DEPM applications. A problem common to many species and surveys around the world, and also noticed for the Gulf of Cadiz anchovy (Table 1), are spurious, positive or nearly positive, estimates of egg mortality.
Table 1. Mortality values estimated for anchovy eggs in the Gulf of Cadiz, during the DEPM survey series.
In order to overcome these often unreliable estimates from single surveys a possible solution is to reach mean estimates by aggregating data from various years and/or try to find other variables (e.g. environmental) which may assist in defining a more robust mortality modelling process (Bernal et al 2011).
The present work aims at compiling all available (staged) egg data for the Gulf of Cadiz anchovy and developing alternative mortality models using mean estimation and including external variables (temperature, geographical stratification). The final goal is to regularly achieve consistent egg production and SSB estimates.
Data on abundances by development stage were obtained from the IEO database from several research surveys carried out in waters of the Gulf of Cadiz during 2005-2014 (Table 2 and Fig. 1). A total of 17601 anchovy eggs were classified into the 11 stages described by Moser and Ahlstrom, 1985. For each sample the information on water temperature, sampling depth and location was also recovered.
-7 .4 -7.2 -7 -6.8 -6.6 -6.4 -6.2 -6 -5.8 -5.6
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G uadalquivir R iver
G uadiana R iver
MOROCCO
30 m
100 m
200 m
SPAIN
GOLFO series
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G uada lquivir R iver
S ancti P etri
C ape o f T ra fa lgar
M O R O C C O
S P A IN
STOCA series
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200
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G uada lquivir R iver
G uadiana R iver
M O R O C C O
P O R T U G A L
S ag res
S P A IN
DEPM series
The ProcessThe samples
Daily cohort abundance by age
Stratum Max temp by strata Max age by strata
Algarve 21.9 ºC 37.6 h
Cádiz 23.4 ºC 33.4 h
Figure 5. Egg abundance (egg m-2) distribution by age. Before maximum age selection (left panel) and after maximum age selection (right panel). The dotted line is at 37.6 h (Table 3).
Figure 6. Mortality rate changes according to lower limit (left) and upper limit (right) cut points. The solid line represents the average mortality, while the dotted lines represent the confidence intervals (X-axis is given in hours).
Mortality estimation: Model selection
Model Term Equation AIC Variance explained
1 Temp:age Strata + Temp:age 4032.1 97.3
2 Strata:age Strata + age + Strata:age 4031.7 97.3
3 age Strata + age 4030.0 97.3
Term Estimate Std. ErrorP0 (eggs m-2 day-
1)Z (eggs day-
1) Pr(>|z|)
1
Algarve 5.27653 0.21399 195.7 ------- < 2e-16 ***
Cádiz 5.39972 0.16424 221.3 ------- < 2e-16 ***
Temp:age -0.00089 0.00032 ------- -0.42 (36)** ▲ 0.0062 **
2
Algarve 5.50856 0.35576 246.8 ------- <2e-16 ***
Cádiz 5.40055 0.17632 221.5 ------- <2e-16 ***
Algarve:age -0.03014 0.01638 ------- -0.72 (54). 0.0658 .
Cádiz:age -0.01943 0.00763 ------- -0.47 (39)* 0.0109 *
3
Algarve 5.34800 0.21881 210.2 ------- < 2e-16 ***
Cádiz 5.44161 0.16337 230.8 ------- < 2e-16 ***
age -0.02142 0.00692 ------- -0.51 (32)** 0.00197 **
About the eggs
About the strata
Table 2. Overall information about the sampling by survey series.
Figure 1. Surveyed area and sampling design by survey series.
Table 4. Model selection after backward stepwise discard from the full model indicated in Equation (3)
Table 5. Summary of the selected model. Terms with age are associated with mortality, while the others are associated with egg production.(▲estimation using temp 19.5ºC)
Results and Discussion
Table 6. Summary of Engraulis encrasicolus egg mortality rates (z) and daily egg production (P0) from different studies.
Year Z (eggs hour-1) Z (eggs day-1) Pr(>| t| ) CV (%)2005 -0.00164 -0.03941 0.213 79.62008 -0.05752 -1.38048 0.00139** 30.22011 -0.01227 -0.29448 0.382 113.82014 -0.01389 -0.33336 0.291 94.2
Survey Series Period Sampler Haul type Mesh size (µ)N.
samplesN. staged
eggs
GOLFOJ une 2005, 2006, 2007
J uly 2006, 2007Bongo-40 double oblique 200 89 9536
STOCA J uly 2009, 2010 Bongo-40 double oblique 200 15 1351
DEPMJ une 2005, 2008 J uly 2011, 2014
PairoVET vertical 150 258 6714
17601
Two spatial strata were defined on the basis of the regional oceanography and anchovy population structure.
Figure 2. Proportion of anchovy eggs in samples by development stage by Moser and Ahlstrom (1985) .
Ni,t ~ Mult ( N , pi,t )
pi,t = f (Edad, Temp.)
Figure 3. Probability of occurence and duration of each egg stages during a dedicated incubation experiment (Bernal et al. 2012) The numbers (1–11) represent the observed frequencies of the different stages (stage 1 to stage 11) at each sampling time.
The most abundant development stages in the samples were II and VI (Fig. 2). These stages have a longer duration compared with other stages, as indicated by the width of the fitted curves , according to the multinomial approach by Bernal et al., 2012 (Fig. 3). Stages I and XI are quick and their spatial distribution very patchy therefore scarce in the samples (1% in both cases). The frequently low abundances of these stages have implication during mortality curve fitting.
Figure 4. Frequency of occurrence of stage I egg in the samples along the day.
Stage I was most abundant in the period 20-2 hours with a peak centred at 22 hours.
E [Na] = expected number of eggs in a cohort of mean age aD0 = the rate of egg production m = the mortality rate g1 = the inverse of the link function that relates the linear predictor and the response, Na
Aggregated data Multinomial model for egg ageing (Fig. 3) Peak spawning time used to define the daily cohorts (Fig. 4) Estimate cohorts abundance and mean cohort age for all stations Define lower and upper cut points for the distribution
STEP 1: Estimation of age and cohort abundance
STEP 2: Mortality estimation
E[Na] = g−1(offset(log(Efarea)) + log(D0) − ma)(1)
E[Na] = g−1(offset(log(Efarea)) + Sstrata + Temp + Sstrata :Temp + age + Sstrata :age + Temp: age)
(2)
STEP 3: Getting p0 estimates by DEPM years using the external model
Stepwise backward model selection, using the likelihood ratio test Finding optimal model: Akaike information criterion (AIC)
Table 3. Maximum temperature and maximum age by strata
A frequent source of bias during mortality curve fitting arises from the observations at the tails of the abundance distribution and therefore lower and upper cut points are regularly defined. Fig. 6 shows potential changes in mortality estimation due to variation in lower and upper cut points. Here the upper age cutting limit is determined using a maximum age (dependent on the temperature) for the strata considered (Table 3 and Fig. 5). The cut at the lower tail is defined as the limit where eggs were not fully spawned between (0 and 3 hrs).11
From the general full model three equally coherent models were selected (Tables 4 ). The aggregation of data proved to be useful for the consistency of the estimations allowing statistically significant and biologically plausible mortality rates. Temperature and geographical stratification may improve model construction.
The daily mortality estimates obtained using the three models (Table 5) ranged from -0.42 to -0.72 within the limits found in the literature for the species (Table 6).
Source Year P0 (eggs m-2 day-1) Z (eggs day-1) Area
Present study 2005-2014
208.5 -0.42
Gulf of Cadiz234.2 -0.72/-0.47
220.5 -0.51
Carvajalino 2011 1983-2008
93.9 -0.36North area of NW
Mediterranean
67.4 -0.62South area of NW
Mediterranean
Santos et al., 2008, 2011, 2013
2008 53.27 -0.32
Bay of Biscay2011 126.68 -0.3
2013 91.51 -0.21
Palomera et al., 2009
2008
55.67 -0.23North area of NW
Mediterranean
24.53 -0.31South area of NW
Mediterranean
Somarakis et al., 2004
1993 64.3 -1.09 NW Mediterranean1994 61.53 -0.47
The present results are the first attempt to develop a mortality modeling approach for the Gulf of Cadiz anchovy based on compiled data which will allow yearly estimation in a more robust manner. From here non coherent mortality rates may be avoided and consequently bias and imprecision in SSB estimation may be reduced.
Future work includes re-analyses of the DEPM survey data using the external models developed in order to obtain egg production and mortality per survey and stratum.
▲ estimation using temp 19.5ºC
Bernal, M., Y. Stratoudakis, S. Wood, L. Ibaibarriaga, A. Uriarte, L. Valdés and D. Borchers 2011 . A revision of daily egg production estimation methods, with application to Atlanto-Iberian sardine. 1. Daily spawning synchronicity and estimates of egg mortality. ICES Journal of Marine Science, 68: 519–527.
Bernal, M., M.P. Jiménez y J. Duarte, 2012. Anchovy egg development in the Gulf of Cádiz and its comparison with development rates in the Bay of Biscay. Fisheries Research, 117: 112-120.
Carvajalino, 2011. Egg production and mortality of the European anchovy Engraulis encrasicolus in Northwestern Mediterranean. Tesis de Máster. Uni. Barcelona (Spain)
Moser and Ahlstrom, 1985. Staging anchovy eggs In: An Egg Production Method for Estimating Spawning Biomass of Pelagic Fish: Application to the Northern Anchovy (Engraulis mordax), pp. 37–41. Ed. by R. Lasker. NOAA Technical report, NMFS 36. 105pp
Palomera, I.; Olivar, M.P.; Salat, J.; Sabatés, A.; Coll, M.; García, A. and Morales-Nin, B. 2007. Small pelagic fish in the NW Mediterranean Sea: An ecological review. Progress in Oceanography, Vol.74: 377 - 396pp.
Santos, M, A. Uriarte and L. Ibaibarriaga, 2008. Spawning Stock Biomass estimates of the Bay of Biscay anchovy(Engraulis encrasicolus, L.) in 2008 applying the DEPM. WD ICES WGACEGG, 24 - 28 November 2008 at Nantes (France)
Santos, M, A. Uriarte and L. Ibaibarriaga, 2011. Spawning Stock Biomass estimates of the Bay of Biscay anchovy (Engraulis encrasicolus, L.) in 2011 applying the DEPM. WD ICES WGACEGG, 21 - 25 November 2011 at Barcelona (Spain)
Santos, M. L. Ibaibarriaga, G. Boyra and A. Uriarte, 2013. Anchovy DEPM in Bay of Biscay 2013 & Sardine egg abundance. ICES WGACEGG, Lisbon 25-29 Nov 2013.
Somarakis, S.; Palomera, I.; García, A.; Quintanilla, L.; Koustsikopoulos, C.; Uriarte, A. and Motos , L. 2004. Daily egg
production of anchovy in European waters. Journal of Marine Science,Vol.61: 944 – 958pp.
References
-9 -8 .8 -8 .6 -8 .4 -8 .2 -8 -7 .8 -7 .6 -7 .4 -7 .2 -7 -6 .8 -6 .6 -6 .4 -6 .2 -6 -5 .8 -5 .635 .5
36 .5
37 .5
200
500
Stratum 1 (Algarve)
N. items = 60N. Staged eggs = 1361Temperature (ºC)max. 22.9min. 15.9Mean 19.9
Stratum 2 (Cádiz)
N. items = 302N. Staged eggs = 16240Temperature (ºC):max. 25.5min. 17.0Mean 21.4
Acknowledgements
A special thanks is due to Miguel Bernal for his work in this subject and support to make the present study possible.
glm.nb(formula = cohort ~ offset(log(Efarea) - death * age) - 1 + Sstrata, data, weights = Rel.area)
