Geostatistics for Estimating Fish Abundance Geostatistics for Estimating Fish Abundance J. Rivoirard,* J. Simmonds,† K.G. Foote,‡ P. Fernandes† and N. Bez* *Centre de Géostatistique de Fontainebleau, Ecole des Mines de Paris, France †FRS Marine Laboratory, Aberdeen, UK ‡Institute of Marine Research, Bergen, Norway Copyright © 2000 Blackwell Science Ltd DISTRIBUTORS Editorial Offices: Marston Book Services Ltd Osney Mead, Oxford OX2 0EL PO Box 269 25 John Street, London WC1N 2BL Abingdon 23 Ainslie Place, Edinburgh EH3 6AJ Oxon OX14 4YN 350 Main Street, Malden (Orders: Tel: 01235 465500 MA 02148 5018, USA Fax: 01235 465555) 54 University Street, Carlton USA Victoria 3053, Australia Blackwell Science, Inc. 10, rue Casimir Delavigne Commerce Place 75006 Paris, France 350 Main Street Malden, MA 02148 5018 Other Editorial Offices: (Orders: Tel: 800 759 6102 Blackwell Wissenschafts-Verlag GmbH 781 388 8250 Kurfürstendamm 57 Fax: 781 388 8255) 10707 Berlin, Germany Canada Login Brothers Book Company Blackwell Science KK 324 Saulteaux Crescent MG Kodenmacho Building Winnipeg, Manitoba R3J 3T2 7–10 Kodenmacho Nihombashi (Orders: Tel: 204 837-2987 Chuo-ku, Tokyo 104, Japan Fax: 204 837-3116) The right of the Authors to be identified Australia as the Authors of this Work has been Blackwell Science Pty Ltd asserted in accordance with the 54 University Street Copyright, Designs and Patents Act 1988. Carlton, Victoria 3053 (Orders: Tel: 03 9347 0300 All rights reserved. No part of Fax: 03 9347 5001) this publication may be reproduced, stored in a retrieval system, or A catalogue record for this title transmitted, in any form or by any is available from the British Library means, electronic, mechanical, ISBN 0-632-05444-1 photocopying, recording or otherwise, except as permitted by the UK Library of Congress Copyright, Designs and Patents Act Cataloging-in-Publication Data 1988, without the prior permission of the publisher. Geostatistics for estimating fish abundance/ by J. Rivoirard … [et al.]. First published 2000 p. cm Includes bibliographical references (p. ). Set in 10/13 Times ISBN 0-632-05444-1 by Sparks Computer Solutions Ltd, Oxford 1. Fish stock assessment. 2. Geology—Statistical Printed and bound in Great Britain by methods. I. Rivoirard, Jacques. MPG Books Ltd, Bodmin, Cornwall II. ICES Statutory Meeting (73rd: 1985: London, England) The Blackwell Science logo is a trade mark of Blackwell Science Ltd, SH329.F56 G46 2000 registered at the United Kingdom 333.95'611—dc21 99-087566 Trade Marks Registry For further information on Blackwell Science, visit our website: www.blackwell-science.com Contents Preface vii 1 Introduction 1 2 Data Collection and Preparation 5 2.1 Survey design 5 2.2 Measurement of fish density 8 2.3 Preparation of data for analysis 10 3 Geostatistical Methods 13 3.1 Introduction: basic hypotheses 13 3.2 Structural analysis 16 3.3 Global abundance, variance and mapping 30 4 Case Studies 41 4.1 Herring in a fjord system: acoustic survey 43 4.2 Young fish surveys 68 4.3 North Sea herring acoustic surveys 82 4.4 North Sea herring acoustic survey trawl data 95 4.5 Cod in the Barents Sea in autumn: trawl survey 104 4.6 Blue whiting on the continental shelf slope in spring: acoustic survey 113 5 Simulation Studies 137 5.1 Robustness of variography 137 5.2 An investigation into the effect of fish movement on abundance, variography and variance derived from surveys 145 5.3 Comparison of some survey designs 164 6 Recommendations and Guidelines 179 6.1 Recommendations for survey design 179 6.2 Scope of geostatistical techniques 182 6.3 Guidelines 184 vi Contents Bibliography 191 Appendix A: Brief Guide to Literature 199 Appendix B: Review of Geostatistical Computer Software 201 Index 205 Preface The application of geostatistics to fisheries data was initially demonstrated at the 73rd Statutory Meeting of the International Council for the Exploration of the Sea (ICES), held in London in 1985. Gohin (1985) contributed a paper on developing geostatistics for estimating biomass, and Conan (1985) presented an analysis of shellfish data. In these papers, a technique that had been developed for mineral resource estimation was applied to marine biological resources. The solution to an outstanding problem in fisheries research was beginning to take shape: how to determine correctly the variance of an abundance estimate, using the pattern of spatial sampling, the observed properties of aggregations, and the extent of the stock. ICES continued to play a central role in the development of geostatistics in fisheries, holding three workshops. Two were held in Brest, first in 1989 to consider shellfish survey data (ICES 1989), then 1 year later to consider acoustic survey data on fish (ICES 1990). A third workshop was held in Reykjavik in September 1991, resulting in an ICES Cooperative Research Report (ICES 1993). It was concluded that the geostatistical estimation variance was an appropriate variance to evaluate the spatial sampling error of abundance estimates from a single survey, and the validity of the technique was accepted. A course was subsequently held in February 1992 at the Centre de Géostatistique in Fontainebleau, France, which provided fisheries scientists with a sound formal basis to apply and develop geostatistics in fisheries research. However, the questions of how reliably these techniques could be employed and how they would perform with typical survey data remained. This was the origin of the tripartite project ‘Geostatistics for fish stock assessment’. The project was proposed for the EU FAIR programme in 1992 and accepted for funding in 1993. This book is the direct result of that project, which was carried out with the financial support from the Commission of the European Communities, AIR specific RTD programme, CT 94-1007, ‘Geostatistics for fish stock assessment’. The authors have been extensively involved in the development of geostatistics for fisheries over the last 5 years. They wish to acknowledge the contributions of a number of colleagues. Philippe Guiblin participated significantly at an early stage of the project. Marek Ostrowski contributed to data analysis and especially visualisation including many of the figures published here. Rob Fryer provided advice and help, particularly with the work on optimum survey strategies. A number of discussions have taken place at various stages with prominent fisheries scientists, which have provided a broader view of the practice. In establishing a set of guidelines for the use of geostatistics in estimating fish viii Preface abundance, a number of other people should be acknowledged: Gérard Conan, Pierre Petitgas and Yvan Simard provided a broader perspective on the subject at a workshop in Fontainebleau in 1998. Earlier, Pierre Petitgas and Neal Williamson organised a workshop in 1996 in Montpellier, France, on time variability and space–time interaction in fisheries acoustic surveys. This workshop provided an excellent basis for studies of the influence of temporal variability in geostatistics. Chapter 1 Introduction The questions asked by fisheries managers can be deceptively simple: what is the abun- dance of a particular stock? How is it distributed? What is its size structure? To help answer such questions, a number of tools have been developed by resource engineers and scientists. Examples are the trawl survey and acoustic survey, performed especially on demersal and pelagic fishes, respectively (Gunderson 1993; Foote 1996); these are briefly described in Chapter 2. These and other survey tools remain objects of critical examina- tion, always ripe for further development or extension, for their application provides valu- able information about fish stocks that cannot be acquired in any other way. Another apparently simple question that is asked by fisheries managers – in fact, in- variably the next one – is: how good is the estimate of abundance? In more technical terms the question is: what is the variance of the abundance estimate? The answer to this ques- tion involves two parts. One depends on the measurement error in the determination of fish density at sampling points or stations. The other depends on the sampling error, or statistical representativity of the samples of the fish distribution over the geographical area to be surveyed. It is the random component of the measurement error and the sam- pling error together that are quantified by the so-called geostatistical estimation variance. This estimation variance describes the variability of an individual survey abundance estimation for a single survey arising from, among other things, spatial sampling. It is to be distinguished from the variance of a series of survey abundance estimates over time. The two variances, the geostatistical estimation variance for a single survey and the variance of a survey time series, may be illustrated by two contrasting cases. (1) A very precise survey with a poor time series may be indicative of variability that is not caused by spatial sampling. (2) Where a survey may be characterised by a geostatistical estimation variance that is numerically similar to the variance of the time series, the spatial sampling can ex- plain much or all of the variability of the time series. In either case, and in the general case too, knowledge of the individual survey variance may be crucial to understanding how a time-series estimate may be improved. The importance of the variance question is illustrated by some of the extreme measures that have been taken to address it. In some cases, because fish are certainly not distributed at random, statisticians have advised fish stock biologists to change their surveying strat- 2 Geostatistics for Estimating Fish Abundance egy. Specifically, they have recommended incorporation of large elements of randomness into the survey design; namely, in the placement of trawl stations or line transects (Jolly & Hampton 1990). The bald purpose of this tactic is to enable statisticians to estimate vari- ance according to conventional notions, without having to consider the spatial structure of the stock. However, for fish stocks, randomness in sampling design degrades the precision of the estimate of abundance (Gohin 1985; Simmonds & Fryer 1996). This has been ac- cepted (or in many cases ignored) because the perception has been that only random sur- veys can give the correct estimate of variance. Fortunately, there is a viable alternative statistical approach to the problem of variance estimation that avoids degrading the estimate of abundance: that of geostatistics. Far from using a specific design to avoid dealing with the pattern of spatial aggregation, geostatistics exploits this through a so-called structural tool; for example, the covariance or variogram. The variance explicitly accounts for the degree of coverage and placement of the sampling stations in relation to the area to be covered and the properties of aggregation. This discus- sion is continued in Chapter 3, where mathematical expressions for the variance are given. Here, the larger subject is introduced. Geostatistics is a relatively young field, whose theoretical foundations were established initially by G. Matheron (Matheron 1965, 1967). A relevant and still contemporary expo- sition of the subject is available in Matheron (1971). Selected recent expositions in the form of textbooks are given in David (1977, 1988), Journel & Huijbregts (1978), Isaaks & Srivastava (1989), Cressie (1991), Armstrong (1998), and Chilès & Delfiner (1999). Some notable recent reviews are found in Rossi et al. (1992) and Petitgas (1993a, 1996). Admittedly, the mining application of geostatistics dominates many of these works, but the generality of the subject and diversity of applications are apparent in Cressie (1991). Not only is geostatistics applied to such subterranean resources as diamonds, gold, coal, oil, gas, and water, but also to terrestrial problems in hydrology (Bardossy 1992) and forestry, for example, and to marine problems in bathymetry (David et al. 1986), hydrography (Kielland & Dagbert 1992), mapping sea surface temperature (Gohin 1989), and the estimation of various marine biological resources. Included in this latter class are shellfish (Conan 1985; Gohin 1985; Nicolajsen & Conan 1987; Conan et al. 1988a; Armstrong et al. 1989), crustacea (Conan et al. 1989; Simard et al. 1992; Gonzalez- Gurriaranet al. 1993; Maynou et al. 1996) and Chironomidae (Smit et al. 1992), in addi- tion to fish eggs (Bez et al. 1996, 1997), plankton, and the present subject, fish. An immediate question to be asked is how a methodology devised for physically sta- tionary resources can be applied to such conspicuously mobile resources as migrating fish, drifting fish eggs, and plankton. The answer is that spatial information on such resources can often be gathered over time periods that are rather short compared with those of large- or even intermediate-scale movements of the stock being surveyed. In addition, as in the case of ore reserve estimation for commercial exploitation, synoptic surveys of fish stocks may be performed only during a single, limited period of time. It is not generally possible to collect additional samples after the survey is completed; it may be impossible for rea- sons of movement in the case of fish, and infeasible for economic reasons in the case of ore reserves. The number of applications of geostatistics to fish up until about 1990 was very mod- est. Some individual works – for example, Conan et al. (1988b), Petitgas & Poulard (1989), Introduction 3 and Guillard et al. (1990) – suggested the potential of the technique. This was further acknowledged at workshops held in 1990 and 1991 (ICES 1990, 1993), which were organ- ised by the International Council for the Exploration of the Sea (ICES). At the same time the need for improved information from surveys to assist methods of management was becoming apparent, as evidenced by the development of the precaution- ary approach. This approach is being increasingly adopted by management authorities, as recommended and defined by the FAO (1995). Accordingly, management advice reflects the quality of information on the fish stock. It requires specific consideration of uncertain- ties in estimates of abundance [FAO, 1995: paragraph 67 (a)]. Implementation of a sys- tematic survey can give a more precise estimate of abundance, and geostatistics provides the measure of uncertainty associated with the sampling process. Geostatistics can also be used to map the spatial distribution of the stock. Application of its structural tools, related to the spatial correlation, may enable changes in stock abundance to be detected at an early stage. An example is provided by the Canadian northern cod stock, where a trend was observed from a population with strong spatial structure in the middle of the 1980s, to one with little or no structure in 1992, coincident with the collapse of the stock (Warren 1997). In order to explore the application of geostatistics in fish stock assessment and to make forthcoming results available to those involved in fish stock assessment, as well as to the larger research community, a proposal was submitted to the European Community Spe- cific Programme for Research, Technological Development and Demonstration in The Field of Agriculture and Agro-Industry, Including Fisheries in autumn 1992. The pro- posed shared-cost project ‘Geostatistics for fish stock assessment’ was eventually approved, and work commenced formally in July 1994. The specific objective of the project was to develop geostatistics to estimate fish abun- dance and associated variance, from: (1) acoustic measurements of fish density along line transects; and (2) trawl measurements of density at finite stations. The project was conducted within the framework of five tasks: (1) data selection; (2) application of geostatistical techniques; (3) preliminary publication; (4) establishing guidelines for applying geostatistics; and (5) publication of a comprehensive document. It is this fifth and final task that is being addressed here. Central to this book is a series of case studies and simulations. Presentation of these is preceded by chapters on data collection and preparation, and geostatistical methods. The chapter on data collection and preparation considers elementary survey methodology, the measurement of fish density, basic statistics, geographical referencing, and dimensionality. The chapter on geostatistical methods gives an overview of fundamentals, emphasising methods that are used in the case studies, especially structural analysis, global estimation of abundance and variance, and mapping. A total of six case studies are described in some