SCRS/2016/024 Collect. Vol. Sci. Pap. ICCAT, 73(4): 1328-1338 (2017)

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AN OBSERVATION ERROR MODEL FOR NORTH ATLANTIC ALBACORE

Laurence Kell1, Haritz Arrizabalaga2, and Paul De Bruyn1,

Gorka Merino2, Iago Mosqueira3, Rishi Sharma4 and Jose-Maria Ortiz de Urbina5

SUMMARY

In this paper we describe the development of an Observation Error for North Atlantic albacore.

When conducting Management Strategy Evaluation an Operating Model is used to simulate

resource dynamics in simulation trials in order to evaluate the performance of a Management

Procedure, where the Management Procedure is the combination of pre-defined data, together

with an algorithm to which such data are input to provide a value for a management control

measure. To link the Operating Model and the Management Procedure it is necessary to

develop an Observation Error Model to generate fishery-dependent or fishery-independent

resource monitoring data. The Observation Error reflects the uncertainties between the actual

dynamics of the resource and the perceptions arising from observations and assumptions by

modelling the differences between the measured value of a resource index and the actual value

in the Operating Model. We show how an analysis of catch per unit effort data and hypotheses

about fisher behaviour can be used to parameterise an Observation Error Model.

RÉSUMÉ

Le développement d’une erreur d'observation concernant le germon de l’Atlantique Nord est

décrit dans le présent document. Pour réaliser une évaluation de la stratégie de gestion, un

modèle opérationnel est utilisé pour simuler les dynamiques de la ressource au moyen d'essais

de simulation visant à évaluer la performance d’une procédure de gestion, dans le cadre duquel

la procédure de gestion est une combinaison de données prédéfinies et d’un algorithme dans

lequel ces données sont saisies afin d’obtenir une valeur d’une mesure de contrôle de la

gestion. Pour relier le modèle opérationnel et la procédure de gestion, il est nécessaire

d’élaborer un modèle d’erreur d’observation afin de générer des données de suivi de la

ressource dépendantes ou indépendantes des pêcheries. L'erreur d'observation reflète

l’incertitude existant entre les dynamiques réelles de la ressource et les perceptions découlant

des observations et des postulats en modélisant les différences entre la valeur mesurée d’un

indice de la ressource et la valeur réelle dans le modèle opérationnel. Le présent document

montre la façon dont une analyse des données de prise par unité d'effort et les postulats sur le

comportement des pêcheurs peuvent être utilisés pour paramétriser un modèle d’erreur

d'observation.

RESUMEN

En este documento se describe el desarrollo de un error de observación para el atún blanco del

Atlántico norte. Al realizar la evaluación de estrategias de ordenación se utiliza un modelo

operativo para simular la dinámica del recurso en ensayos de simulación para evaluar el

rendimiento del procedimiento de ordenación, donde el procedimiento de ordenación es una

combinación de datos predefinidos, junto con un algoritmo en el que se introducen dichos datos

para proporcionar un valor para una medida de control de ordenación. Para vincular el

1 ICCAT Secretariat, C/Corazón de María, 8. 28002 Madrid, Spain; Laurie.Kell@iccat.int; Phone: +34 914 165 600; Fax: +34 914 152 612. 2 AZTI -Tecnalia, Herrera Kaia Portualdea, 20110, Pasaia, Spain 3 European Commission Joint Research Centre (JRC), Institute for the Protection and Security of the Citizen (IPSC), Maritime Affairs

Unit, Via E. Fermi 2749, 21027, Ispra, VA, Italy 4 U.S. National Marine Fisheries Service, Southeast Fisheries Center, Sustainable Fisheries Division, 75 Virginia Beach Drive, Miami, FL,

33149-1099, USA 5 Instituto Español de Oceanografía (IEO- CO Málaga).

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modelo operativo y el procedimiento de ordenación es necesario desarrollar un modelo de

error de observación con miras a generar datos de seguimiento del recurso dependientes o

independientes de la pesquería. El error de observación refleja las incertidumbres entre la

dinámica real del recurso y la percepción procedente de las observaciones y supuestos

mediante la modelación de las diferencias entre el valor medido de un índice de recurso y el

valor real en el modelo operativo. Se muestra cómo pueden utilizarse un análisis de datos de

captura por unidad de esfuerzo y las hipótesis sobre la conducta de los pescadores para

parametrizar un modelo de error de observación.

KEYWORDS

Albacore, Observation Error Model, Operating Model,

Management Strategy Evaluation, Measurement Error, Uncertainty

Introduction

In Management Strategy Evaluation (MSE) an Operating Model (OM) is used to simulate resource dynamics in

simulation trials in order to evaluate the performance of a Management Procedure (MP). Where the MP is the

combination of pre-defined data, together with an algorithm to which such data are input to provide a value for a

management control measure. To link the OM and the MP it is necessary to develop an Observation Error Model

(OEM) to generate fishery-dependent or fishery-independent resource monitoring data. The OEM reflects the

uncertainties, between the actual dynamics of the resource and perceptions arising from observations and

assumptions by modelling the differences between the measured value of a resource index and the actual value in

the OM. In this paper we describe the development of an OEM for North Atlantic albacore for use in MSE.

The OM is based upon the Multifan-CL assessment conducted during the 2013 ICCAT North Atlantic Albacore

stock assessment (Kell et al. in press a). We first summarise the characteristics of the CPUE series to allow

CPUEs with different properties to me simulated then provide example simulations under a variety of

assumptions.

Operating Model

Ten scenarios were considered when fitting Multifan-CL, the scenarios are described and the results summarised

in Kell et al. (in press a).

When fitting the albacore stock assessments commercial catch per unit effort (CPUE) is used as a proxy for

relative abundance. The CPUE series (per fleets) used in the Multifan-CL assessment are summarised in Table

1.

It has long been recognised, however, that time series of CPUE may not accurately reflect trends in population

abundance (e.g. Beverton and Holt, 1993; Maunder et al., 2006; McKechnie et al., 2013; Polacheck, 2006).

Particularly since changes can occur in in the spatial distribution of populations and the allocation of effort in

response to management. In the latter case economic drivers can affect catch and effort independent of stock

abundance (e.g. Paloheimo and Dickie, 1964; Tidd et al., 2011). Furthermore Interactions between changes in

oceanographic conditions and exploitation can drive spatial and temporal dynamics (Fromentin et al., 2013). In

addition, technological developments can produce bias on the relation between stock abundance and fleet’s

CPUE. Therefore CPUE may not be proportional to stock abundance (Hilborn et al., 1992). For example CPUE

may be hyperstable where catches remain high as a population declines (Erisman et al., 2011) or hyperdepletion

may occur where catches decline faster than the population.

CPUE Series

First the selection patterns of the fleets and the error structure of the CPUEs are explored. Then, simulations are

conducted to evaluate the bias and uncertainties for different assumptions. The selection patterns for the 10

CPUE series are plotted in Figures 1 and 2. The residuals are plotted to check the error model and to look for

systematic patterns that may suggest that some assumptions are violated. In Figure 3 the residuals are plotted

(on the log scale) against year to check for systematic patterns over time. The residuals are then plotted against

the fitted values to check the variance function (Figure 4). Figure 5 plots residuals with 1 year lag to check for

auto-correlation, and quantile-quantile plots to check for error assumptions are provided in Figure 6.

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Simulations

Eight simulations were conducted corresponding to different assumptions about the potential error structure and

biases in the CPUE series, the index was based on biomass in all but one case, a lognormal error with a CV of

30%. The index is simulated using the Multifan-CL Base Case estimates of numbers-at-age (ICCAT, in press).

The simulations were i) unbiased, ii) hyperstability, iii) trend in catchability, iv) auto-correlation, v) a decrease in

variance with time, vi) an index based on juvenile age-classes, vii) index based on mature age-classes, and viii)

index based on numbers. The simulated CPUE series are shown in Figure 7, the ribbons show the 50th and 80th

percentiles. Two individual simulations are also shown (red and cyan), the blue line an unbiased index and the

black line the median of the simulated series. The unbiased index captures the stock trends although individual

CPUE series show a wide variation. The same random deviates were used for all simulated series and therefore

in all cases, but for auto-correlation, the peaks of the indices coincide. For a trend in catchability and

hyperstability the trend in the index underestimates the true decline. For a decrease in variance no bias was seen.

The scenario based on a juvenile index showed more variability, due to the effect of year class strength, using an

index based on the mature biomass alone or numbers provided results similar to the unbiased index with slightly

more variation.

Summary

The residual patterns in the fits of the CPUE series could be used to simulate alternative hypotheses about

processes that could affect catch and effort. The properties of the indices, e.g. ages selected, catchability,

availability or vulnerability could also be used simulated hypotheses about the processes to be implemented as

scenarios in an MSE. The impact of using alternative simulated CPUE series to plug into a Management

Procedure need to be evaluated through Management Strategy Evaluation (see paper Kell et al. in press b).

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References

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Canadian Journal of Statistics, 34(1):5–27.jack-knife,

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of plenty: hyperstability masks collapses in two recreational fisheries that target fish spawning aggregations.

Canadian Journal of Fisheries and Aquatic Sciences, 68(10):1705–1716, 2011.

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Committee on Statistics meeting. 15 pp. Document SCRS/2016/013.

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Atlantic Albacore. Document SCRS/2016/023: 32 p.

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Table 1. Catch per unit effort series used in the 2013 assessment.

Figure 1. A comparison of fleet selection patterns.

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Figure 2. Selection patterns by fleet.

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Figure 3. Plots of residuals against year to check for systematic patterns.

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Figure 4. Plots of residuals against fitted values to check variance function.

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Figure 5. Plots of residuals with 1 year lag to check for auto-correlation.

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Figure 6. Quantile-quantile plots to check for normal error.

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Figure 7. Simulated CPUE series.