A MANUAL ON METHODS FOR THE
ASSESSMENT OF SECONDARY PRODUCTIVITY
IN FRESH WATERS
A Manual on Methods for the
Assessment of Secondary Productivity
in Fresh Waters
EDITED
BY
JOHN A. DOWNING
Departement de Sciences Biologique
Universite de Montreal
and Biology Department
McGill University
Montreal, Quebec, Canada
AND
FRANK H. RIGLER
Biology Department
McGill University
Montreal, Quebec, Canada
SECOND
EDITION
BLACKWELL SCIENTIFIC PUBLICATIONS
OXFORD
LONDON
BOSTON
EDINBURGH
MELBOURNE
r
1971, 1984 by
Blackwell Scientific Publications
Editorial offices:
Osney Mead, Oxford OX2 OEL
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publication may be reproduced, stored
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mechanical, photocopying, recording or
otherwise without the prior permission
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British Library
Cataloguing in Publication Data
A Manual on methods for the assessment
of secondary productivity in fresh
First published 1971
Second edition 1984
waters.—2nd ed.
1. Freshwater productivity —
Measurement
I. Downing, John A.
Printed in Great Britain by
Galliard (Printers) Ltd
Great Yarmouth, Norfolk
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 the
craving to be right; for it is not his possession of
knowledge, of irrefutable truth, that makes the
man of science, but his persistent and recklessly
critical quest for truth.'
Karl R. Popper
The 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, 1
John A. Downing
1
Introduction, ]
2 Theoretical Justification for Secondary Production Research, 2
2.1 Energy or Material Transfer Within Ecosystems, 2
2.2 Management of Aquatic Resources, 3
2.3 Detection of Pollution, 3
2.4 Formation of General Theories of Biological Production, 4
3 Factors Affecting Rates of Secondary Production, 4
3.1 Effect of Population Characteristics, 5
3.2 Effect of Environmental Factors, 8
3.3 Predation, Competition, and Diversity, 10
3.4 Lake Morphometry, Lateral Zonation, and Allochthonous Input, 1
4 Concluding Comments, 11
5 References, 12
The Calculation of Secondary Productivity, 19
Frank H. Rigler & John A. Downing
1 Introduction, 19
2 Four Methods of Calculating Production, 22
3 The Simplest Case-A Population with Easily Identifiable Cohorts, 24
4 Populations in a Steady State, 27
4.1 General Comments, 27
4.2 The Egg-Ratio Method of Calculating Birth Rate, 29
4.3 Calculation of the Production of Populations in Steady State, 36
5 Two Apparently Simplified Methods, 42
5.1 Size-Frequency Method ('Average Cohorts'), 42
5.2 The Use of Production to Biomass Ratios (P/B), 44
6 Concluding Remarks, 46
viii
Contents
Chapter 2 continued
7 A Real Example Analyzed by Methods Applicable to Populations with
Recognizable Cohorts, 46
7.1 Identification of Cohorts. 46
7.2 Required Data, 47
7.3 Calculation of Production, 47
7.4 One Assumption and its Consequences, 49
8 A Real Example Analyzed by Methods Applicable to Populations in a Steady
State, 49
8.1 Required Data, 50
9 References, 54
3
Methods for the Estimation of Zooplankton Abundance, 59
Riccardo de Bernard!
1 Introduction, 59
2 Descriptions of Sampling Gear, 61
2.1 Sampling Bottles, 61
2.2 Plankton Traps, 65
2.3 Pumps and Tubes, 65
2.4 Plankton Nets, 69
2.5 Towed Plankton Samplers. 74
3 Sample Manipulation: Killing and Preservation, 78
4 The Choice of a Sampler, 79
5 Appendix, 81
6 References, 83
Sampling the Benthos of Standing Waters, 87
John A. Downing
1 Introduction, 87
2 The Benthos of Unconsolidated Substrates, 87
2.1 Data Sources, 88
2.2 Samplers in Frequent Use, 88
2.3 The Sampler Must be Suited to the Substrate, 97
2.4 The Accuracy, Precision, and Efficiency of Sampling Gear, 100
2.5 Sieving and Preservation, 106
3 Sampling Other Fauna, 110
3.1 Sampling the Benthos of Hard Substrates, 110
3.2 Sampling the Benthos Dwelling on Aquatic Macrophytes, 112
3.3 Microbenthos. 119
4 Conclusions, 120
5 Appendix, 121
6 References. 122
5
Sampling the Stream Benthos, 131
Barbara L. Peckarsky
1 Introduction, 131
2 Review of Traditional Sampling Techniques, 131
Contents
ix
Chapter 5 continued
3 Experimental Design for Special Problems, 138
3.1 Benthic Density: Production Studies, 138
3.2 Life History Studies, 139
3.3 Distributional Studies, 140
3.4 Dispersal, Colonization Studies, 141
3.5 Behavioral Studies, 145
3.6 Studies on Biological Interactions, 147
4 Choosing the Appropriate Methodology: Summary and Conclusions, 147
5 Appendices, 148
6 References, 154
6
Sampling Aquatic Insect Emergence, 161
Ian J. Daiies
1 Why Sample Insect Emergence?, 161
2 Some General Comments on Emergence Traps, 162
3 Trap Designs, 163
3.1 Open Water Traps, 163
3.2 Traps for Shallow Standing Water, 172
3.3 Traps for Running Water, 177
4 Factors Which Influence the Performance of Emergence Traps, 181
4.1 Transparency, 182
4.2 Effect of Trap Size on Catch. 184
4.3 Tilting of the Trap, 186
4.4 Float Colonization, 186
4.5 Trap Depth, 187
4.6 Design of the Sample Chamber, 188
4.7 Temperature and Frequency of Emptying, 189
4.8 Predation, 189
5 Tests of Sampling Efficiency, 190
5.1 Absolute Accuracy, 190
5.2 Comparative Efficiency, 193
6 Patterns of Emergence, 195
6.1 Larval Migrations Prior to Emergence, 197
7 Sampling Strategies and Analytical Techniques, 197
8 Predicting Insect Emergence, 203
9 Appendices, 205
9.1 Emergence Traps for Open Water Habitats, 205
9.2 Emergence Traps for Shallow Water Habitats, 209
9.3 Emergence Traps for Running Water, 215
10 References, 221
7
The Estimation of the Abundance and Biomass of Zooplankton in
Samples, 228
Edward McCauley
1
Introduction, 228
2 Estimating the Mass of Crustacean Zooplankton, 230
2.1 Predicting Dry Weight from Estimates of Length. 232
2.2 Measuring the Length or Dimensions of an Organism. 240
x
Contents
Chapter 7 continued
2.3 Measuring the Dry Weight of Individuals, 243
3 Estimating the Mass of Rotifers, 246
4 Determining the Mass of Protozoans, 251
4.1 Estimating Mass from Volume Measurements, 251
4.2 Preservation of Protozoans, 252
5 Estimating Mass as Carbon Content, 253
6 Estimating the Abundance of Zooplankton in a Sample, 254
7 Estimating the Biomass of a
Population:
Decisions,
Decisions,
Decisions, 257
8 Estimating the Biomass of Groups of Species, 259
9 Conclusion, 261
10 References, 261
8
Some Statistical Methods for the Design of Experiments and Analysis of
Samples, 266
Ellie E. Prepas
1
Introduction, 266
1.1 Descriptive Statistics, 266
1.2 Distribution of the Data, 268
2 Sampling Design, 270
2.1 Random Sampling, 270
2.2 Stratified Random Sampling, 275
2.3 Systematic Sampling, 277
2.4 Ratio and Regression Estimates, 278
2.5 Gradients in Space, 278
2.6 Composite Samples, 278
3 Preparation of Samples for Statistical Analysis, 279
3.1 Enumeration of Samples, 279
3.2 Estimation of Population Numbers, 280
3.3 Smoothing Data, 281
3.4 Determining the Distribution of the Data, 283
3.5 The *2-Test, 287
3.6 Transformations, 289
4 Comparison of Means and Related Topics, 292
4.1 Calculation of an Average Variance and Tests for Homogeneity of
Sample Variance, 292
4.2 t-Test for Comparison of a Sample Mean with the Population Mean, 296
4.3 Comparison of Two Independent Means, 297
4.4 Paired Comparisons, 301
4.5 Multiple Comparisons Among a Set of Means, 303
4.6 Notes on Analysis of Variance, 308
4.7 Combining Probabilities from Independent Tests of Significance, 312
5 Regression and Correlation, 314
5.1 Standard Linear Regression, 314
5.2 Alternatives to Standard Linear Regression, 325
5.3 Correlation, 327
5.4 Some Other Regression Models, 330
6 Summary, 332
7 References. 333
Contents
9
Methods for the Study of Feeding, Filtering and Assimilation by
Zooplankton, 336
Robert H. Peters
1 Introduction, 336
2 Basic Concepts, 337
2.1 Definition of Terms, 337
2.2 Feeding and Grazing, 337
2.3 The Feeding Process, 338
2.4 Assimilation, 342
3 Techniques for Measurement of Feeding and Grazing Rates, 342
3.1
3.2
Morphology and Microscopy, 342
Behavioral Studies, 345
3.3 Laboratory Determinations of Feeding and Grazing Rate, 349
3.4 Field Estimates of Feeding and Grazing, 370
3.5 Feeding Rates of Other Organisms, 374
3.6 Factors Influencing Grazing and Feeding Rates, 376
3.7 Average Experimental Conditions, 381
3.8 Comparison of Methods, 382
3.9 Calculated Grazing and Feeding Rates, 387
3.10 The Expression of Selectivity, 388
4 Assimilation, 390
4.1 Estimates Based on Defecation Rates, 390
4.2 Estimates Based on Fecal Analysis, 391
4.3 Direct Measurement of Assimilation, 392
5 Conclusions, 395
6 References, 395
10
xi
The Measurement of Respiration, 413
Winfried Lampert
1 Introduction, 413
2 Measures of Metabolism, 415
2.1 Choice of the Principle Method, 415
2.2 Direct Calorimetry, 416
2.3 Oxygen Consumption, 417
2.4 Excretion of Carbon Dioxide, 439
2.5 ETS Activity, 444
2.6 Conversions, 445
3 Factors Affecting the Respiratory Rate, 445
3.1 Endogenous Factors, 445
3.2 Exogenous Factors, 448
4 In situ Studies, 456
5 Similarities and Dissimilarities, 457
6 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 2N6
R. DE BERNARD! lstituto lialiano di Jdrobiologia, Consiglio Nazionale
delie Ricerche, 28048 Pallanza, Italy
J. A. DOWNING Universite
Biologiques,
C.P.
de
Montreal,
6128, Succursale L/T,
Departement
Montreal,
de
Sciences
Quebec,
Canada
H3C 3J7; and McGill University, Department of Biology
W. LAM PERT Max-Planck-lnstitut fur Limnologie, Postfach 165, D-2320
PIon, West Germany
E. McCAULEY Department of Biological Sciences, University of California,
Santa Barbara, California 93106, USA
B. L. PECKARSKY Cornell
University,
Department
of Entomology,
Comstock Hall Ithaca, New York 14853, USA
R. H. PETERS McGill University, Department of Biology. 1205 Avenue
Docteur Penfield, Montreal, Quebec, Canada H3A IBI
E. E. PREPAS The
University
of Alberta,
Department
of Zoology,
Biological Sciences Centre, Edmonton, Alberta, Canada T6G 2E9
F. 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 chairmen
of working groups, or both.
Blazka P.
Kajak Z.
Brinkhurst R.
Klekowski R.
Patalas K.
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 process
to the first. In the following few paragraphs I will discuss the history of this
book, 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 it
attempts 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 were
involved in the first edition. To understand the reason for this, one must know
something of the history of this handbook. In 1978, Frank Rigler agreed to
edit 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 by
decreasing the number of authors. He also felt that one should continue to
view 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 the
requisite chapters. Most of the authors contributing to this manual are in
some ways products of IBP, not original contributors to it. Because of this one
can 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 and
education. We have the chance to view the problem of the assessment of
secondary productivity in freshwaters from fresh perspectives.
My involvement as an editor of this manual was less philosophical and
more practical. In early 1980, FHR decided that he would not have the time to
fulfill all the editorial duties himself, and asked me to be a co-editor. I felt
honoured to accept a chance to help organize this important manual. As a
student 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 original
was to me.
The organization of the chapters in this edition has been an impossible
choice and will appear haphazard to some. The conclusions of each of the
chapters suggested that the book should start with an introduction to the
general justification for and the hypotheses under examination by production
ecology. Starting from this chapter, I have tried to organize chapters
corresponding 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 Edition
that one can decide which variables must be estimated (Chapter 2). The
sampling routine must be planned next and Chapters 3, 4, 5, and 6 explore
these techniques. Once samples are taken they must be processed (Chapter 7)
and the data analyzed (Chapter 8). Finally, one might re-examine the
components of the variables under consideration (Chapters 9 and 10). One
could convincingly argue, however, that Chapter 8 (Statistics and Experi
mental Design) should be Chapter 2, or that other chapters should be
rearranged. All such choices would seem equally arbitrary. The reason for this
is that research does not always advance linearly, unlike the chapters in a book
or the words in a sentence, but moves as an advancing front like a wave
washing a beach. It may be necessary, therefore, for readers to turn from
chapter to chapter seeking the information they desire. To facilitate this, the
authors and the editors of this manual have put considerable effort into both
author and subject indices.
The strengths of this handbook lie in its summarization of current
literature and the synthesis of our technical progress. The authors have each
tried to present an even-handed review of the existing knowledge of relevant
techniques, and they have tried to make clear recommendations wherever
possible. This task is difficult because different recommendations are
appropriate to different studies. Whether or not our coverage has been
sufficient can only be judged by the scientific community. I have no doubt that
we have missed important topics or references. Similarly, I have little doubt
that this handbook improves our situation because 70 % of the 1300 references
cited 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 with
FHR 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 and
treatment of benthos samples, feeding and assimilation in the benthos,
prediction of sampling variance for zooplankton samples, etc. We felt that
complete coverage of all subjects for each sort of taxonomic category was not
feasible within the size constraints of this book. Where specific information is
not included, one can consult chapters on the same topic for different taxa.
For example, researchers interested in subsampling benthos samples should
consult Chapters 7 and 8, those interested in feeding and assimilation in
benthos should consult Chapter 9, and those interested in optimizing zooplankton sampling programs can draw general guidance from Chapters 4
and 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, that
we have covered the most important subjects thoroughly and accurately, and
that readers are sympathetic to the enormity of this task.
Preface to Second Edition
xv
Finally I would like to thank those people who have contributed to the
quality of this handbook, although the final responsibility for errors rests with
FHR and me. First, we thank the institutions that have made this handbook
possible, most notably the Natural Sciences and Engineering Research
Council of Canada, the Quebec Minister of Education (FCAC), the McGill
University Centre for Northern Studies, Environment Canada, Atomic
Energy Canada Ltd., Indian and Northern Affairs Canada, The Canadian
National Sportsman's Fund, the faculty of graduate studies and research of
McGill University, and the McGill University Department of Biology. I
would especially like to acknowledge the indulgence of the Universite de
Montreal Departement de Sciences Biologiques. All individuals who have
helped are too numerous to mention. En masse we would like to thank the
ecologists at McGill, the Limnological Research Group (i.e. Memphremagog
and Schefferville projects) also at McGill, and the Groupe d'Ecologie des
Eaux douces at TUniversite de Montreal. Most valuable assistance has come
from 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 Robson
and Blackwell Scientific Publications for being patient and helpful. Last,
FHR and I thank our families for understanding the extra time a work such
as 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 chapter
and gave me immeasurable help and encouragement during its preparation. I
also 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 for
their suggestions and additional assistance.
xvi
Preface to Second Edition
E.McCauley.
I
wish
to
thank
M.Pace,
R.Peters, J.Downing, and
D.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 to
thank J.Downing and F.H.Rigler, for inviting me to contribute to this
handbook.
B.L.Peckarsky. I would like to acknowledge Stan Dodson's unfailing
support and inspiration, and ability to devise simple yet elegant techniques to
answer difficult questions. Dick Ganje constructed all cages and observation
boxes, and was very instrumental in their design. I thank Steve Horn and
Cheryl Hughes for drafting the illustrations, and Beth French and Susan Pohl
for editing this manuscript. Reviews by Peter Harper, and the editors of this
manual (Downing and Rigler) considerably improved an earlier draft of this
chapter.
R.H.Peters. Conversations with many scientists added immeasurably to
this 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 with
data analysis and manuscript preparation, J.O.Murie,
P.A.Murtaugh,
T.Reynoldson, and C.J.Strobeck for reviewing the manuscript, J.A.Downing
and
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 Science
and Engineering Research Council of Canada 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
and
G.G.Winberg. The meeting had been preceded by much correspondence, and
preliminary drafts of most of the book were written i n advance. At the meeting
the participants worked in groups to examine the material, and made
recommendations of changes and additions. After the meeting, most of the
manuscripts were revised in accordance with the recommendations of the
working groups. Some material was requested from people who did not attend
the working meeting. Inevitably, some duplication occurred, and some topics
were 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 of
overlap 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 some
have been greatly changed to fit them to the purpose of the book as the editors
see it. An attempt has been made to indicate the primary authorship of the
various 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. The
editor regrets any errors or omissions of attribution that may have been made.
It should be understood that this book has a somewhat transitory and
ephemeral character. During the process of production, a steady stream of
pertinent contributions has appeared in the scientific literature, and as the
book goes to press, papers are about to appear that will make some sections of
this book obsolete. Further, there is disagreement about the merits of certain
methods 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 imperfectly
developed.
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 extensively
revised for the special purposes of the book. For the very effective meeting at
Liblice, thanks are due the organizer, Dr Jaroslav Hrbacek. The persons who
agreed 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 Edition
many who helped, the work of Dr K.H.Mann and Dr F.H.Rigler at the
meeting and later was especially useful to the editorial work. The indefatigable
Dr Julian Rzoska has contributed more to the production of this book than
meets the eye or can ever be defined and expressed.
Finally, a special word of thanks goes to the late Professor Vittorio Tonolli
who, 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 on
zooplankton sampling in the book, was written when the end of his life was in
sight.
W.T.Edmondson, Editor
G.G.Winberg, Co-editor
Abbreviations
Abbreviations are listed by chapter. Where a single abbreviation is used for
more than one term, the meaning of the abbreviation is described in text.
Chapter 1
a, 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 duration
of embryonic development, or development time,
g: instantaneous growth rate.
*m: mmax-mmin-
m{: mean body mass of an individual.
mraax: mmaximmajti: upper size limit of stage i.
mmin: mmini
mmini: 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
Abbreriaiions
P: secondary production.
P;: production in size class or developmental stage T
r: 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 a
stone.
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 an
emergence 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
xxi
Ezi: 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 7
B: 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 of crustacean 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.
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Abbreviations
Chapter 8
A: 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
Aal: 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 10
C: carbon content of animals.
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xxiv
Abbreviations
Cp Ca, Cc: oxygen concentration of the initials, bottles with animals, and
controls.
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 10°C.
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.
/<: activation energy.