Implementing an external mortality model to estimate egg mortality and egg production for anchovy in the

Gulf of Cadiz (2005-2014)

ICES Working Group on Atlantic Fish Larvae and Eggs Surveys. Pasaia (Spain), 1 - 5 December 2014

1Paz Díaz, 1Paz Jiménez, and 2MM Angélico

1Instituto Español de Oceanografía (IEO)2Instituto Português do Mar e da Atmosfera (IPMA)

Vigo - Cádiz - Lisboa

Estimate Std.error t value Pr(>[t]) CV (%)2005 -0.03941 0.03137 -1.256 0.213 79.62008 -0.05752 0.01735 -3.315 0.00139** 30.22011 -0.01227 0.01397 -0.878 0.382 113.82014 -0.01389 0.01309 -1.061 0.291 94.2

E [P] = P0 e -Z age

E[P] : density of eggs per ageP0 :rate of egg production (eggs/day/area) Z : rate of mortality

BOCADEVA series

External Mortality Model

(Bernal et al., 2011)

Anchovy DEPM surveys 2005-2014

Data set

Data come from several research surveys, that included plankton sampling, carried out in waters of the Gulf of Cadiz, between 2005 to July 2014.

-7.4 -7.2 -7 -6.8 -6.6 -6.4 -6.2 -6 -5.8 -5.6

35.8

36

36.2

36.4

36.6

36.8

37

37.2

37.4

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HUELVA

CADIZ

Río G uadalqu ivir

R ío G uadiana

Tarifa

M ARRUECOS

Barbate

M azagón

Is la C ristina

Sanlúcar de Barram eda

30 m

100 m

200 m

-7.4 -7.2 -7 -6.8 -6.6 -6.4 -6.2 -6 -5.8 -5.6

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36

36.2

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37

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GD -01GD -02

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SP -01

SP -02

SP -03SP -04

SP -05

SP -06 TF -01

TF -02

TF -03

TF -04

R ío G uadalquivir

Sancti Petri

C abo de Trafa lgar

GOLFO series(Feb. 2006 – Sep. 2007

(Monthly)

STOCA series(Jul. 2009 – Nov. 2011

(Quarterly)

BOCADEVA series(summer 2005,2008,2011 and 2014

(Trienal)

Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec2005 X2006 X X X X X X X X X X X2007 X X X X X X X X X 2008 X X 2009 X X 2010 X X X 2011 X X X X 2014 X

[1] Survey : Factor w/ 33 levels "","BOCADEVA 0714 [2] Sampler : Factor w/ 3 levels "","Bongo-40",..: [3] Station : Factor w/ 166 levels "","10","100", [4] Lat : num 36.6 36.6 37 36.4 36.4 ... [5] Long : num -6.59 -6.65 -7.38 -6.42 -6.51 ... [6] Date : int 20060222 20060223 20060223 [7] Time : num 15.65 14.82 15.42 8.38 9.4 ... [8] Depth : num 29 43 73 15 48 33 58 4 14 22 ... [9] Bottom : int 43 73 94 22 76 44 74 12 18 30 ... [10] Vol..m3. : num 55.1 79.7 106.3 49.4 35.9 ... [11] Efarea : num NA NA NA NA NA NA NA [12] SST : num 14.9 15 14.8 14.5 14.5 14.7 [13] I : num 0 0 0 0 0 1 0 0 0 0 ... [14] II : num 0 4 17 2 1 74 1 1 4 1 ... [15] III : num 0 0 0 1 1 0 0 0 0 0 ... [16] IV : num 0 0 0 0 0 0 8 0 0 0 ... [17] V : num 2 2 0 0 0 9 18 0 0 6 ... [18] VI : num 0 0 0 0 3 10 10 0 3 8 ... [19] VII : num 2 0 0 0 0 6 0 0 0 0 ... [20] VIII : num 0 0 0 1 0 0 6 0 1 0 ... [21] IX : num 0 0 0 0 0 1 11 0 1 0 ... [22] X : num 1 0 0 0 0 2 0 0 0 0 ... [23] XI : num 0 0 0 0 0 0 2 0 0 0 ... [24] Dis. : num 1 0 0 0 1 4 0 0 0 0 ... [25] Total staged eggs: int 6 6 17 4 6 107 56 1 9 15 ...

Surveys within the area limits for which data on egg abundance by stage and temperature are available will used to estimate mortality

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s i n g l e c e l l

S t a g e I I

s t a r t c e l l d i v i s i o n

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Moser and Ahlstrom (1985)

Egg stageing key

Data set

A total 31119 Anchovy eggs classified into the different development stages

I II III IV V VI VII VIII IX X XI

Series1 376 6077 4242 1394 3311 5605 2208 2245 2928 2470 263

0

1000

2000

3000

4000

5000

6000

7000

Num

ber

Anchovy GoC. Num. eggs by stageI

1%

II20%

III14%

IV4%V

11%

VI18%

VII7%

VIII7%

IX9%

X8%

XI1%

Summary Data set

Step 3

Getting p0 estimates with external mortality

Step 2Mortality estimation

Step 1

Estimation of age Cohort abundance

Egg age & mortality(All data available)

Egg production(Data from DEPM)

Process to estimate mortality and egg production

Bernal et al., 2011

Multinomial model of anchovy egg development (Duarte et al., 2007, Bernal et al., 2011) will used to relate egg stage and age for the sampled temperatures

Assumed peak spawning time will used to define the daily cohorts, cohorts abundance and mean cohort age for all stations

what.control <- depm.control(spawn.mu = 22, spawn.sig = 2, how.complete=0.95)

New data with observed abundance-by-cohort used to fit the mortality curve

1. Estimation of age and cohort abundance

Bernal et al., 2011

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

E[Na] = g−1(offset(log(Efarea)) + log(D0) − ma) (1)

Equation (1) for the dataset is then formulated as (2) to allow both egg production and mortality to vary between spatial strata and temperature

E[Na] = g−1(offset(log(Efarea)) + Sstrata + Temp + Sstrata :Temp + age + Sstrata :age + Temp: age) (2)

“age” involved: mortality terms

Equation (1) will fitted to the entire database using the statistical language R.

2. Mortality estimation

Bernal et al., 2011

Stepwise backward model selection will carried out from this model. At each

step, the term with least significance (<5%) will dropped, and this procedure

repeated until dropping terms led to no improvement.

A comparison with Akaike information criterion (AIC) profiles of the model

selection procedure will also performed.

To avoid bias in the mortality model caused for the extremes of the data: lower

limit and upper limits will set on the tails of the mortality curve

2. Mortality estimation

Bernal et al., 2011

glm.nb(formula = cohort ~ offset(log(Efarea) - death * age) - 1 + Sstrata, data, weights = Rel.area)

3. Egg production estimates

Bernal et al., 2011

1 2

Strait of Gibraltar

Cape San Vicente

In 2005 it was necessary poststratification In 2008 it was necessary poststratification

weights = Rel.area used to account for increased sampling in areas of expected high egg densities

P0 (eggs/m2/day) Z (day-1) 2005 51(1) - 225(2) -0.942008 184(1) - 348(2) -1.432011 276 -0.292014 313.5 -0.33

Egg production and mortality rate comparison with data from literature (Z values in day-1 )

DEPM BOCADEVAGulf of Cádiz

(1) Stratum 1(2) Stratum 2

Carvajalino, J.F, 2011

A special thanks to Miguel Bernal, for the useful help and comments about the daily egg production estimation methods and external mortality model.

Thank you

Acknowledgements