A MANUAL ON METHODS FOR THEASSESSMENT OF SECONDARY PRODUCTIVITY

IN FRESH WATERS

A Manual on Methods for theAssessment of Secondary Productivity

in Fresh WatersEDITED BY

JOHN A. DOWNINGDepartement de Sciences Biologique

Universite de Montrealand Biology Department

McGill UniversityMontreal, Quebec, Canada

AND

FRANK H. RIGLERBiology Department

McGill UniversityMontreal, Quebec, Canada

SECOND EDITION

BLACKWELL SCIENTIFIC PUBLICATIONSOXFORD LONDON EDINBURGH

BOSTON MELBOURNE

r 1971, 1984 byBlackwell Scientific PublicationsEditorial offices:Osney Mead, Oxford OX2 OEL8 John Street, London, WC1N 2ES9 Forrest Road, Edinburgh, EH1 2QH

52 Beacon Street, BostonMassachusetts 02108, USA99 Barry Street, Carlton

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All rights reserved. No part of thispublication may be reproduced, storedin a retrieval system, or transmitted, inany form or by any means, electronic,

mechanical, photocopying, recording orotherwise without the prior permissionof the copyright owner

First published 1971Second edition 1984

Printed in Great Britain byGalliard (Printers) Ltd

Great Yarmouth, Norfolk

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British LibraryCataloguing in Publication Data

A Manual on methods for the assessmentof secondary productivity in freshwaters.2nd ed.

1. Freshwater productivity MeasurementI. Downing, John A. II. Rigler.Frank, H.574.5'2632 QH541.5.F7

ISBN 0-632-00616-1

To Frank

The wrong view of science betrays itself in thecraving to be right; for it is not his possession of

knowledge, of irrefutable truth, that makes theman of science, but his persistent and recklesslycritical quest for truth.'

Karl R. PopperThe Logic of Scientific Discovery

Harper & Row, New York

Contents

Contributors, xii

Preface to Second Edition, xiii

Preface to First Edition, xvii

Abbreviations, xix

Assessment of Secondary Production: The First Step, 1John A. Downing

1 Introduction, ]2 Theoretical Justification for Secondary Production Research, 2

2.1 Energy or Material Transfer Within Ecosystems, 22.2 Management of Aquatic Resources, 32.3 Detection of Pollution, 32.4 Formation of General Theories of Biological Production, 43 Factors Affecting Rates of Secondary Production, 4

3.1 Effect of Population Characteristics, 53.2 Effect of Environmental Factors, 83.3 Predation, Competition, and Diversity, 103.4 Lake Morphometry, Lateral Zonation, and Allochthonous Input, 14 Concluding Comments, 11

5 References, 12

The Calculation of Secondary Productivity, 19Frank H. Rigler & John A. Downing

1 Introduction, 192 Four Methods of Calculating Production, 223 The Simplest Case-A Population with Easily Identifiable Cohorts, 244 Populations in a Steady State, 27

4.1 General Comments, 274.2 The Egg-Ratio Method of Calculating Birth Rate, 294.3 Calculation of the Production of Populations in Steady State, 365 Two Apparently Simplified Methods, 42

5.1 Size-Frequency Method ('Average Cohorts'), 425.2 The Use of Production to Biomass Ratios (P/B), 446 Concluding Remarks, 46

viii Contents

Chapter 2 continued7 A Real Example Analyzed by Methods Applicable to Populations with

Recognizable Cohorts, 467.1 Identification of Cohorts. 467.2 Required Data, 477.3 Calculation of Production, 477.4 One Assumption and its Consequences, 498 A Real Example Analyzed by Methods Applicable to Populations in a Steady

State, 498.1 Required Data, 509 References, 54

3 Methods for the Estimation of Zooplankton Abundance, 59Riccardo de Bernard!

1 Introduction, 592 Descriptions of Sampling Gear, 61

2.1 Sampling Bottles, 612.2 Plankton Traps, 652.3 Pumps and Tubes, 65

2.4 Plankton Nets, 692.5 Towed Plankton Samplers. 743 Sample Manipulation: Killing and Preservation, 784 The Choice of a Sampler, 79

5 Appendix, 816 References, 83

Sampling the Benthos of Standing Waters, 87John A. Downing

1 Introduction, 872 The Benthos of Unconsolidated Substrates, 87

2.1 Data Sources, 882.2 Samplers in Frequent Use, 882.3 The Sampler Must be Suited to the Substrate, 972.4 The Accuracy, Precision, and Efficiency of Sampling Gear, 1002.5 Sieving and Preservation, 1063 Sampling Other Fauna, 110

3.1 Sampling the Benthos of Hard Substrates, 1103.2 Sampling the Benthos Dwelling on Aquatic Macrophytes, 1123.3 Microbenthos. 1194 Conclusions, 120

5 Appendix, 1216 References. 122

5 Sampling the Stream Benthos, 131Barbara L. Peckarsky

1 Introduction, 1312 Review of Traditional Sampling Techniques, 131

Contents ix

Chapter 5 continued3 Experimental Design for Special Problems, 138

3.1 Benthic Density: Production Studies, 1383.2 Life History Studies, 1393.3 Distributional Studies, 1403.4 Dispersal, Colonization Studies, 1413.5 Behavioral Studies, 1453.6 Studies on Biological Interactions, 1474 Choosing the Appropriate Methodology: Summary and Conclusions, 147

5 Appendices, 1486 References, 154

6 Sampling Aquatic Insect Emergence, 161Ian J. Daiies

1 Why Sample Insect Emergence?, 1612 Some General Comments on Emergence Traps, 162

3 Trap Designs, 1633.1 Open Water Traps, 163

3.2 Traps for Shallow Standing Water, 1723.3 Traps for Running Water, 1774 Factors Which Influence the Performance of Emergence Traps, 181

4.1 Transparency, 1824.2 Effect of Trap Size on Catch. 1844.3 Tilting of the Trap, 1864.4 Float Colonization, 1864.5 Trap Depth, 187

4.6 Design of the Sample Chamber, 1884.7 Temperature and Frequency of Emptying, 1894.8 Predation, 1895 Tests of Sampling Efficiency, 190

5.1 Absolute Accuracy, 1905.2 Comparative Efficiency, 1936 Patterns of Emergence, 195

6.1 Larval Migrations Prior to Emergence, 1977 Sampling Strategies and Analytical Techniques, 1978 Predicting Insect Emergence, 2039 Appendices, 205

9.1 Emergence Traps for Open Water Habitats, 2059.2 Emergence Traps for Shallow Water Habitats, 2099.3 Emergence Traps for Running Water, 21510 References, 221

7 The Estimation of the Abundance and Biomass of Zooplankton inSamples, 228

Edward McCauley1 Introduction, 2282 Estimating the Mass of Crustacean Zooplankton, 230

2.1 Predicting Dry Weight from Estimates of Length. 2322.2 Measuring the Length or Dimensions of an Organism. 240

x ContentsChapter 7 continued

2.3 Measuring the Dry Weight of Individuals, 2433 Estimating the Mass of Rotifers, 2464 Determining the Mass of Protozoans, 251

4.1 Estimating Mass from Volume Measurements, 2514.2 Preservation of Protozoans, 2525 Estimating Mass as Carbon Content, 2536 Estimating the Abundance of Zooplankton in a Sample, 2547 Estimating the Biomass of a Population: Decisions, Decisions,

Decisions, 2578 Estimating the Biomass of Groups of Species, 2599 Conclusion, 26110 References, 261

8 Some Statistical Methods for the Design of Experiments and Analysis ofSamples, 266Ellie E. Prepas

1 Introduction, 2661.1 Descriptive Statistics, 2661.2 Distribution of the Data, 2682 Sampling Design, 270

2.1 Random Sampling, 2702.2 Stratified Random Sampling, 2752.3 Systematic Sampling, 2772.4 Ratio and Regression Estimates, 2782.5 Gradients in Space, 2782.6 Composite Samples, 2783 Preparation of Samples for Statistical Analysis, 279

3.1 Enumeration of Samples, 2793.2 Estimation of Population Numbers, 280

3.3 Smoothing Data, 2813.4 Determining the Distribution of the Data, 2833.5 The *2-Test, 2873.6 Transformations, 2894 Comparison of Means and Related Topics, 292

4.1 Calculation of an Average Variance and Tests for Homogeneity ofSample Variance, 2924.2 t-Test for Comparison of a Sample Mean with the Population Mean, 2964.3 Comparison of Two Independent Means, 2974.4 Paired Comparisons, 3014.5 Multiple Comparisons Among a Set of Means, 3034.6 Notes on Analysis of Variance, 3084.7 Combining Probabilities from Independent Tests of Significance, 3125 Regression and Correlation, 314

5.1 Standard Linear Regression, 3145.2 Alternatives to Standard Linear Regression, 3255.3 Correlation, 3275.4 Some Other Regression Models, 3306 Summary, 332

7 References. 333

Contents xi

9 Methods for the Study of Feeding, Filtering and Assimilation byZooplankton, 336

Robert H. Peters1 Introduction, 3362 Basic Concepts, 337

2.1 Definition of Terms, 3372.2 Feeding and Grazing, 3372.3 The Feeding Process, 3382.4 Assimilation, 3423 Techniques for Measurement of Feeding and Grazing Rates, 342

3.1 Morphology and Microscopy, 3423.2 Behavioral Studies, 345

3.3 Laboratory Determinations of Feeding and Grazing Rate, 3493.4 Field Estimates of Feeding and Grazing, 3703.5 Feeding Rates of Other Organisms, 3743.6 Factors Influencing Grazing and Feeding Rates, 3763.7 Average Experimental Conditions, 3813.8 Comparison of Methods, 3823.9 Calculated Grazing and Feeding Rates, 387

3.10 The Expression of Selectivity, 3884 Assimilation, 390

4.1 Estimates Based on Defecation Rates, 3904.2 Estimates Based on Fecal Analysis, 3914.3 Direct Measurement of Assimilation, 3925 Conclusions, 3956 References, 395

10 The Measurement of Respiration, 413Winfried Lampert

1 Introduction, 4132 Measures of Metabolism, 415

2.1 Choice of the Principle Method, 4152.2 Direct Calorimetry, 4162.3 Oxygen Consumption, 4172.4 Excretion of Carbon Dioxide, 4392.5 ETS Activity, 4442.6 Conversions, 4453 Factors Affecting the Respiratory Rate, 445

3.1 Endogenous Factors, 4453.2 Exogenous Factors, 4484 In situ Studies, 456

5 Similarities and Dissimilarities, 4576 References, 460

Author Index, 469

Taxonomic Index, 481

Subject Index, 485

Contributors

I. J. DA VIES Freshwater Institute, 501 University Crescent, Winnipeg,Manitoba, Canada R3T 2N6R. DE BERNARD! lstituto lialiano di Jdrobiologia, Consiglio Nazionale

delie Ricerche, 28048 Pallanza, ItalyJ. A. DOWNING Universite de Montreal, Departement de Sciences

Biologiques, C.P. 6128, Succursale L/T, Montreal, Quebec, CanadaH3C 3J7; and McGill University, Department of BiologyW. LAM PERT Max-Planck-lnstitut fur Limnologie, Postfach 165, D-2320

PIon, West GermanyE. McCAULEY Department ofBiological Sciences, University of California,

Santa Barbara, California 93106, USAB. L. PECKARSKY Cornell University, Department of Entomology,

Comstock Hall Ithaca, New York 14853, USAR. H. PETERS McGill University, Department of Biology. 1205 Avenue

Docteur Penfield, Montreal, Quebec, Canada H3A IBIE. E. PREPAS The University of Alberta, Department of Zoology,

Biological Sciences Centre, Edmonton, Alberta, Canada T6G 2E9F. H. RIGLER McGill University, Department of Biology, 1205 Avenue

Docteur Penfield, Montreal, Quebec, Canada H3A IBI.

Contributors to First Edition

The following scientists contributed principal parts of the text, were chairmenof working groups, or both.

Blazka P. Kajak Z. Patalas K.Brinkhurst R. Klekowski R. Pieczyhska E.Cassie R.M. Kofinek V. Richman S.Cooper W.E. Ladle M. Rigler F.H.

Edmondson W.T. Lawton J. Ruttner-Kolisko A.Fischer Z. Lellak J. Sladeckova A.Hall DJ. Loffler H. Straskraba M.HrbacekJ. Mann K.H. Teal J.M.

Hynes H.B.N. Morgan N.C. Winberg G.G.Ilkowska A. Mundie J.H. Wright J.C.

Preface to Second Edition

The second edition of this handbook has resulted from a very different processto the first. In the following few paragraphs I will discuss the history of thisbook, its organization, and its strengths and weaknesses. In this way I will

show the manner in which this edition differs from the original yet how itattempts to fulfill the same purpose. Finally I will give thanks to the many

scientists and colleagues that have helped make this new edition possible.First of all, it is obvious that few authors contributing to this book wereinvolved in the first edition. To understand the reason for this, one must knowsomething of the history of this handbook. In 1978, Frank Rigler agreed toedit a new edition of IBP Handbook No. 17. He felt that one could decrease

the massive editorial effort and increase the continuity in the second edition bydecreasing the number of authors. He also felt that one should continue toview science from new perspectives as well as learning from past experiences.

For this reason he wanted to assemble a group of young scientists to write therequisite chapters. Most of the authors contributing to this manual are insome ways products of IBP, not original contributors to it. Because of this onecan see in this edition the manner in which the often brilliant work of the

authors in the original edition has been translated into scientific progress andeducation. We have the chance to view the problem of the assessment ofsecondary productivity in freshwaters from fresh perspectives.

My involvement as an editor of this manual was less philosophical andmore practical. In early 1980, FHR decided that he would not have the time tofulfill all the editorial duties himself, and asked me to be a co-editor. I felthonoured to accept a chance to help organize this important manual. As astudent 1 learned much from the original edition and have continued to use it

in my research. I hope that this effort will be as useful to others as the originalwas to me.

The organization of the chapters in this edition has been an impossiblechoice and will appear haphazard to some. The conclusions of each of thechapters suggested that the book should start with an introduction to the

general justification for and the hypotheses under examination by productionecology. Starting from this chapter, I have tried to organize chapterscorresponding to the chronology of a research problem. After choice of the

problem should come a comprehension of the calculation of production so

xiv Preface to Second Editionthat one can decide which variables must be estimated (Chapter 2). Thesampling routine must be planned next and Chapters 3, 4, 5, and 6 explorethese techniques. Once samples are taken they must be processed (Chapter 7)and the data analyzed (Chapter 8). Finally, one might re-examine thecomponents of the variables under consideration (Chapters 9 and 10). Onecould convincingly argue, however, that Chapter 8 (Statistics and Experi

mental Design) should be Chapter 2, or that other chapters should berearranged. All such choices would seem equally arbitrary. The reason for thisis that research does not always advance linearly, unlike the chapters in a bookor the words in a sentence, but moves as an advancing front like a wavewashing a beach. It may be necessary, therefore, for readers to turn fromchapter to chapter seeking the information they desire. To facilitate this, the

authors and the editors of this manual have put considerable effort into bothauthor and subject indices.

The strengths of this handbook lie in its summarization of currentliterature and the synthesis of our technical progress. The authors have eachtried to present an even-handed review of the existing knowledge of relevant

techniques, and they have tried to make clear recommendations whereverpossible. This task is difficult because different recommendations are

appropriate to different studies. Whether or not our coverage has beensufficient can only bejudged by the scientific community. I have no doubt thatwe have missed important topics or references. Similarly, I have little doubt

that this handbook improves our situation because 70 % ofthe 1300 referencescited have been published since the first edition went to press. Because most of

the authors are new to this sort of publication, I cannot help but agree withFHR that many of them have supplied a fresh look at the topics at hand.

It is easier to point out the weaknesses of a book than to list its strengths;one can simply look for topics that are not covered. There are some relevant

topics that are not covered in depth here, including subsampling andtreatment of benthos samples, feeding and assimilation in the benthos,prediction of sampling variance for zooplankton samples, etc. We felt thatcomplete coverage of all subjects for each sort of taxonomic category was not

feasible within the size constraints of this book. Where specific information isnot included, one can consult chapters on the same topic for different taxa.

For example, researchers interested in subsampling benthos samples shouldconsult Chapters 7 and 8, those interested in feeding and assimilation inbenthos should consult Chapter 9, and those interested in optimizing zoo-

plankton sampling programs can draw general guidance from Chapters 4and 8. Regardless of the length of the book, some information could always

be found lacking. I only hope that few serious omissions have been made, thatwe have covered the most important subjects thoroughly and accurately, and

that readers are sympathetic to the enormity of this task.

Preface to Second Edition xvFinally I would like to thank those people who have contributed to thequality of this handbook, although the final responsibility for errors rests with

FHR and me. First, we thank the institutions that have made this handbookpossible, most notably the Natural Sciences and Engineering ResearchCouncil of Canada, the Quebec Minister of Education (FCAC), the McGill

University Centre for Northern Studies, Environment Canada, AtomicEnergy Canada Ltd., Indian and Northern Affairs Canada, The CanadianNational Sportsman's Fund, the faculty of graduate studies and research of

McGill University, and the McGill University Department of Biology. Iwould especially like to acknowledge the indulgence of the Universite de

Montreal Departement de Sciences Biologiques. All individuals who havehelped are too numerous to mention. En masse we would like to thank theecologists at McGill, the Limnological Research Group (i.e. Memphremagogand Schefferville projects) also at McGill, and the Groupe d'Ecologie des

Eaux douces at TUniversite de Montreal. Most valuable assistance has comefrom R.H.Peters, E.McCauley, P.Harper, B.Leggett, J.Kalff, L.Legendre,

P.Legendre, A.Morin, P.Andre, and M.Pace. Many other scientists,colleagues, and friends have contributed, among them are J.H.Mundie,

S.C.Mozley, A.C.Benke, K.Patalas, J.T.Lehman, R.J.Conover, R.Epp,J.J.Peterka, R.H.Green, B.Marcotte, N.C.Morgan, V.H.Resh, G.Milbrink,W.T.Edmondson, W.L.Downing, E.L.Schmidt, C.Hudon, D.Bird, L.Rath,

D.Rosenberg, M.Downing, R.Anderson, J.-G.Pilon, H.Evans, D.Skraba,A.Marnik, and E.Gnaiger. We also thank Robert Campbell, John Robsonand Blackwell Scientific Publications for being patient and helpful. Last,

FHR and I thank our families for understanding the extra time a work suchas this requires.

Montreal 1982 John Ashley Downing

Author's Acknowledgments

Some of the authors have asked to include acknowledgments of their own.These are assembled below.

I. J. Da vies. I would like to thank L.A.Davies, who illustrated this chapterand gave me immeasurable help and encouragement during its preparation. Ialso thank L.Wilson for typing the manuscript and P.Campbell,J.A.Downing, J.F.Flannagan, J.H.Mundie, D.J.Ramsey, D.W.Schindler,and H.E.Welch who reviewed various drafts of the work and offered many

helpful criticisms. Special thanks go to D.M.Rosenberg and K.E.Marshall fortheir suggestions and additional assistance.

xvi Preface to Second EditionE.McCauley. I wish to thank M.Pace, R.Peters, J.Downing, andD.Laflamme for constructive criticism and assistance. R.Anderson, A.Vezina,and D.Currie made numerous suggestions and checked calculations.

E.Bentzen generously helped to assemble the manuscript. Finally, I wish tothank J.Downing and F.H.Rigler, for inviting me to contribute to thishandbook.

B.L.Peckarsky. I would like to acknowledge Stan Dodson's unfailingsupport and inspiration, and ability to devise simple yet elegant techniques toanswer difficult questions. Dick Ganje constructed all cages and observation

boxes, and was very instrumental in their design. I thank Steve Horn andCheryl Hughes for drafting the illustrations, and Beth French and Susan Pohlfor editing this manuscript. Reviews by Peter Harper, and the editors of thismanual (Downing and Rigler) considerably improved an earlier draft of thischapter.

R.H.Peters. Conversations with many scientists added immeasurably tothis review. I particularly thank J.A.Downing, B.M.Marcotte, F.H.Rigler,and P.Starkweather.

E.E.Prepas. I thank G.Hutchinson and J.Vickery for their assistance withdata analysis and manuscript preparation, J.O.Murie, P.A.Murtaugh,T.Reynoldson, and C.J.Strobeck for reviewing the manuscript, J.A.Downingand F.H.Rigler for their patience and encouragement, D.O.Trew,

E.McCauley, and P.A.Murtaugh for providing unpublished data, K.Baert,P.Miller, and J.Scheinas for typing the manuscript, and the National Scienceand Engineering Research Council ofCanada for financial support in the form

of an operating grant.

Preface to First Edition

This book took form at a working meeting held at Liblice, Czechoslovakia,3-8 April 1967 under joint chairmanship of W.T.Edmondson andG.G.Winberg. The meeting had been preceded by much correspondence, andpreliminary drafts of most of the book were written i n advance. At the meeting

the participants worked in groups to examine the material, and maderecommendations of changes and additions. After the meeting, most of themanuscripts were revised in accordance with the recommendations of theworking groups. Some material was requested from people who did not attend

the working meeting. Inevitably, some duplication occurred, and some topicswere not given adequate attention. It has been the task of the editor to put

together all these pieces into what is hoped to be a useful whole. Because ofoverlap and decisions about scope and emphasis that had to be made after the

initial work, no manuscript is printed here exactly as it was written, and somehave been greatly changed to fit them to the purpose of the book as the editorssee it. An attempt has been made to indicate the primary authorship of thevarious sections, but some of them have been put together from contributions

by so many people that it is impracticable to give a very exact authorship. Theeditor regrets any errors or omissions of attribution that may have been made.

It should be understood that this book has a somewhat transitory andephemeral character. During the process of production, a steady stream of

pertinent contributions has appeared in the scientific literature, and as thebook goes to press, papers are about to appear that will make some sections ofthis book obsolete. Further, there is disagreement about the merits of certainmethods and apparatus. Readers are encouraged to use the book as a guide to

the literature and to look out for new papers appearing in the journals cited.More important, some of the basic concepts and theories are imperfectlydeveloped.

Many people are owed thanks for making this volume possible. Primarily,we express our gratitude to the authors who worked so hard to prepare

manuscripts, and who have cheerfully agreed to having them extensivelyrevised for the special purposes of the book. For the very effective meeting at

Liblice, thanks are due the organizer, Dr Jaroslav Hrbacek. The persons whoagreed to chair sessions of the working groups made a valuable contribution.

While it is difficult to single out individuals for special mention from among so

xviii Preface to First Editionmany who helped, the work of Dr K.H.Mann and Dr F.H.Rigler at themeeting and later was especially useful to the editorial work. The indefatigable

Dr Julian Rzoska has contributed more to the production of this book thanmeets the eye or can ever be defined and expressed.

Finally, a special word ofthanks goes to the late Professor Vittorio Tonolliwho, as former Convenor of Section PF of the IBP, initiated the process that

has resulted in this book. His last piece of scientific writing, the section onzooplankton sampling in the book, was written when the end of his life was insight.

W.T.Edmondson, EditorG.G.Winberg, Co-editor

Abbreviations

Abbreviations are listed by chapter. Where a single abbreviation is used formore than one term, the meaning of the abbreviation is described in text.

Chapter 1a, b, c: fitted constants.

B: mean biomass.M: body-size (mass).N: average population density.

P, Ps: secondary production.Pp: primary production.

Chapter 2

A: area under curve of number plotted against time.b: instantaneous birth rate./?: finite birth rate.

B: biomass of population, size class, or development stage.Cl, C2, C3...etc.: first, second, third copepodite stage.d: instantaneous death rate.

D: time that it takes to grow through a size class. Also referred to as durationof embryonic development, or development time,g: instantaneous growth rate.

*m: mmax-mmin-m{: mean body mass of an individual.mraax: mmaxi-mmajti: upper size limit of stage i.mmin: mminimmini: lower size limit of stage i.

Nl, N2, N3 ... etc.: first, second and third naupliar stage.NCM: number of eggs in the population.Nmi: number of individuals in a size class with mean body mass of m.

N,: number of animals at time /.Ntl,Nl2: number of individuals in population at times tt and t2.

xx AbbreriaiionsP: secondary production.P;: production in size class or developmental stage Tr: instantaneous rate of change of population size.TN, TB: turnover time of numbers and biomass.

Chapter 3

d: distance through which a plankton net is towed,r: radius of a plankton net.s: standard deviation.

Chapter 4

A: area of a sampling device.CV: coefficient of variation.

L: largest length of a stone.M: mean density of benthic organisms.n: number of replicate samples.

P: ratio of standard error to mean density, and the largest perimeter of astone.s2: variance,x: mean of replicate samples.

Chapter 5

x: mean density of benthic organisms.

Chapter 6

A: area covered by an emergence trap; or number of adults retained by anemergence trap.Aji area of the jth sample stratum.

B: lake average dry biomass.B95: the depth above which 95% of biomass emerges.BZ1: average integral biomass of emerging insects.CV: coefficient of variation,d: total number of sampling days in a season.

E: number of exuviae found in an emergence trap.E: lake average number of emergent insects.

E}: mean seasonal emergence per unit in the jth sample stratum.ELA: Experimental Lakes Area (Ontario, Canada).E95: the depth above which 95 % of numbers emerge.

Abbreviations xxiEzi: average integral number of emerging insects.h: height of an emergence trap.N: average number of insects emerging per gC of PPzi.

PP: lake average phytoplankton production.PP2I: average integral phytoplankton production in the ith depth interval.R': radius of the base of an emergence trap.R.I.: refractive index.S.G.: specific gravity.T,: mid-point time of the ith sampling period.

W: mean dry weight of an individual insect.X: mean emergence (m~2 year"1).

Xj: emergence per unit area per day on the ith sampling day.Zc: mean depth of 1 % surface irradiance.

t. pitch or angle of a cone.0: angle of a pie shaped cut out of a cone.

Chapter 7B: biomass.C: biomass of crustacean zooplankton determined by counting and weighing,

or biomass as carbon content.C.L.: 95% confidence limits.CV: coefficient of variation.

DM: dry weight determined by direct measurement.DW: biomass as dry weight.

F: biomass ofcrustacean zooplankton determined using a filtering technique,or ratio of explained to residual variance.FW: biomass as fresh weight.In L: geometric mean length of individuals.

LW: dry weight determined by length-weight regression.M: average mass of a size class, cohort, or species,n: number of paired observations used to determine regression.

N: number of individuals in a size class, cohort, or species.P: phytoplankton biomass.R: correlation coefficient.

RMS: residual mean square,s.d.: standard deviation.s2: variance.t: constant from the Student's t distribution,w: dry weight.

W: dry weight of a group of organisms,x: mean of a group of measurements.

xxii AbbreviationsChapter 8A: area under a normal curve.

C: correction factor for Bartlett's test.CV: coefficient of variation.

D: ratio of standard error to mean,df: degrees of freedom.D(: difference between the ith pair of observations.

F: ratio of two variances.j\: observed frequency.

F,: expected frequency.L: allowable error in the sample mean, or linear combination of means.loge: natural logarithm.log10: logarithm to the base 10.M: test statistic for Bartlett's test.n: number of observations.

N: size of the total population.p: proportion of a population containing a particular attribute.

P: probability.q\ 1-p.

Q\ studentized range.r. correlation coefficient.r2: coefficient of determination.s: standard deviation.SE: standard error of the mean.s^. standard error of the mean.s2: variance of a set of samples.

/: student's t value.W{. size of a stratum to be weighted.X: arithmetic mean.Xt: the ith observation.

X\: transformed observation.Z: standard deviation unit,ju: true population mean.

a2: population variance.X2: chi-square statistic./,-: fixed numbers.

Chapter 9

A: the amount of food assimilated or assimilation rate.Aa: radioactivity of animals.Aap: concentration of 32P in animals.

Abbreviations xxiiiAal: concentration of 3H in animals.A.E.: assimilation efficiency.As: radioactivity of suspension.Asp: concentration of 32P in suspension.Asl: concentration of 3H in suspension.A2, A3: radioactivity of animal at times 2 and 3.

b: growth rate constant.B: number of beads in an animal's gut.C: average food concentration.Cc: cell carbon.COO, CCt: initial and final food concentration in control containers.Co: initial cell concentration.

Q: final cell concentration.f: feeding rate.F.R.: forage ratio.G: grazing rate.Gp: gut passage time.

H: volume of water per animal in container.I: amount of food ingested.L: volume of container.

M: wet weight of food cells, or duration of feeding experiment.N: number of animals in container.Np.: amount of food type i in the environment.Nr.: amount of food type i eaten.pi*, the proportion of food type i in the environment.q: constant of proportionality.

r: instantaneous rate of increase.R: electrical resistance of a suspension of food cells.rc: resistivity of electrolyte.r;: proportion of food type i eaten.rp: resistivity of particle.S: concentration of particles in suspension.

t: length of time animals are allowed to feed.T: temperature.

U: proportion of unassimilable material in diet.U': proportion of unassimilable material in feces.V: volume of container.V;: volume of individual cells.

Chapter 10C: carbon content of animals.

xxiv AbbreviationsCp Ca, Cc: oxygen concentration of the initials, bottles with animals, andcontrols.

DPMa: radioactivity of animals.DPMW: radioactivity of CO2 per ml water.

ETS: electron transport system.J: system flushing characteristic time.

Lc: carbon loss.LSC: liquid scintillation counter.AP: change of equilibrium pressure.

Pa: barometric pressure.pCO2: partial pressure of CO2.

Po: normal pressure.pO2: partial pressure of oxygen.

QI0: ratio of rates resulting from a temperature increase of 10C.r: gas constant.R: respiratory rate.RQ: respiratory quotient.S: solubility of oxygen at a given temperature.

STP: standard temperature and pressure.T: water temperature.

At: time interval between readings.ta, lc: incubation periods of bottles.

U: velocity of water flow.V: volume of container or respiration bottles.Vg: diver constant.VO2; rate of oxygen consumption.w: chamber volume.

W: body weight./