This page intentionally left blankThe DiatomsApplications for the Environmental and Earth SciencesSecond EditionThismuchrevisedandexpandededitionprovidesavaluableanddetailedsummaryof themanyusesof diatomsinawiderangeofapplications intheenvironmental andearthsciences. Particularemphasis is placed on the use of diatoms in analyzing ecologi-cal problems related to climate change, acidication, eutroph-ication, and other pollution issues. The chapters are dividedinto sections for easy reference, with separate sections cover-ingindicators indifferent aquatic environments. Anal sectionexplores diatomuseinother elds of study suchas forensics, oiland gas exploration, nanotechnology, and archeology. Sixteennew chapters have been added since the First Edition, includ-ing introductory chapters on diatombiology and the numericalapproaches used by diatomists. The extensive glossary has alsobeen expanded and now includes over 1000 detailed entries,which will help non-specialists to use the book effectively.John P. Smol is a Professor in the Department of Biology atQueens University (Ontario, Canada), with a cross appoint-ment at the School of Environmental Studies. He is also co-director of the Paleoecological Environmental Assessment andResearchLab(PEARL). Since 1990, he has wonover 25researchawardsandfellowships, includingthe2004NSERCHerzbergCanada Gold Medal as Canadas top scientist or engineer.Eugene F. Stoermer is a past-President of the PhycologicalSocietyofAmericaandtheInternationalSocietyforDiatomResearch. He has worked at the University of Michigan (AnnArbor, USA) since 1965, where he is currently Professor Emer-itus in the School of Natural Resources and Environment. Hedirectedthephyto-lab,whichundertookawidevarietyofresearchtopics, specializingindiatomsystematicsandecology.The DiatomsApplications for theEnvironmental andEarth SciencesSecond editionEdited byJohn P. SmolEugene F. StoermerCAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town, Singapore,So Paulo, Delhi, Dubai, TokyoCambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UKFirst published in print formatISBN-13978-0-521-50996-1ISBN-13 978-0-511-90814-9 Cambridge University Press 20102010Information on this title: www.cambridge.org/9780521509961This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any partmay take place without the written permission of Cambridge University Press.Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.Published in the United States of America by Cambridge University Press, New Yorkwww.cambridge.orgeBook (EBL)HardbackThis book is dedicated to the memory of our friend and colleague,Dr. John Platt Bradbury (19352005), a leader in the application ofdiatoms to the study of earth and environmental issues.Dr. John Platt Bradbury, sampling peat in Tierra del Fuego (photo byVera Markgraf ).ContentsList of contributors page ixPreface xviiPart I Introduction1 Applications and uses of diatoms: prologue 3John P. Smol and Eugene F. Stoermer2 The diatoms: a primer 8Matthew L. Julius and Edward C. Theriot3 Numerical methods for the analysis of diatomassemblage data 23H. John B. BirksPart II Diatoms as indicators of environmental change inowing waters and lakes4 Assessing environmental conditions in rivers andstreams with diatoms 57R. Jan Stevenson, Yangdong Pan, and Herman van Dam5 Diatoms as indicators of long-term environmentalchange in rivers, uvial lakes, and impoundments 86Euan D. Reavie and Mark B. Edlund6 Diatoms as indicators of surface-water acidity 98Richard W. Battarbee, Donald F. Charles, Christian Bigler,Brian F. Cumming, and Ingemar Renberg7 Diatoms as indicators of lake eutrophication 122Roland I. Hall and John P. Smol8 Diatoms as indicators of environmental change inshallow lakes 152Helen Bennion, Carl D. Sayer, John Tibby, and Hunter J. Carrick9 Diatoms as indicators of water-level change infreshwater lakes 174Julie A. Wolin and Jeffery R. Stoneviiviii Contents10Diatoms as indicators of hydrologic and climaticchange in saline lakes 186Sheri C. Fritz, Brian F. Cumming, Franc oise Gasse, andKathleen R. Laird11 Diatoms in ancient lakes 209Anson W. Mackay, Mark B. Edlund, and Galina KhursevichPart III Diatoms as indicators in Arctic, Antarctic,and alpine lacustrine environments12Diatoms as indicators of environmental change insubarctic and alpine regions 231Andre F. Lotter, Reinhard Pienitz, and Roland Schmidt13Freshwater diatoms as indicators of environmentalchange in the High Arctic 249Marianne S. V. Douglas and John P. Smol14Diatoms as indicators of environmental change inAntarctic and subantarctic freshwaters 267Sarah A. Spaulding, Bart Van de Vijver, Dominic A.Hodgson, Diane M. McKnight, Elie Verleyen, and Lee StanishPart IV Diatoms as indicators in marine andestuarine environments15Diatoms and environmental change in largebrackish-water ecosystems 287Pauline Snoeijs and Kaarina Weckstrom16Applied diatom studies in estuaries and shallowcoastal environments 309Rosa Trobajo and Michael J. Sullivan17Estuarine paleoenvironmental reconstructionsusing diatoms 324Sherri Cooper, Evelyn Gaiser, and Anna Wachnicka18Diatoms on coral reefs and in tropical marine lakes 346Christopher S. Lobban and Richard W. Jordan19Diatoms as indicators of former sea levels,earthquakes, tsunamis, and hurricanes 357Benjamin P. Horton and Yuki Sawai20Marine diatoms as indicators of modern changes inoceanographic conditions 373Oscar E. Romero and Leanne K. Armand21 Holocene marine diatom records of environmentalchange 401Amy Leventer, Xavier Crosta, and Jennifer Pike22Diatoms as indicators of paleoceanographic events 424Richard W. Jordan and Catherine E. Stickley23Reconsidering the meaning of biogenic silicaaccumulation rates in the glacial Southern Ocean 454Christina L. De La Rocha, Olivier Ragueneau, and Aude LeynaertPart V Other applications24Diatoms of aerial habitats 465Jeffrey R. Johansen25Diatoms as indicators of environmental change inwetlands and peatlands 473Evelyn Gaiser and Kathleen Ruhland26Tracking sh, seabirds, and wildlife populationdynamics with diatoms and other limnologicalindicators 497Irene Gregory-Eaves and Bronwyn E. Keatley27Diatoms and archeology 514Steve Juggins and Nigel G. Cameron28Diatoms in oil and gas exploration 523William N. Krebs, Andrey Yu. Gladenkov, and Gareth D. Jones29Forensic science and diatoms 534Anthony J. Peabody and Nigel G. Cameron30Toxic marine diatoms 540Maria Celia Villac, Gregory J. Doucette, and Irena Kaczmarska31 Diatoms as markers of atmospheric transport 552Margaret A. Harper and Robert M. McKay32Diatoms as non-native species 560Sarah A. Spaulding, Cathy Kilroy, and Mark B. Edlund33Diatomite 570David M. Harwood34Stable isotopes from diatom silica 575Melanie J. Leng and George E. A. Swann35Diatoms and nanotechnology: early history andimagined future as seen through patents 590Richard GordonPart VI Conclusions36Epilogue: reections on the past and a viewto the future 611John P. Smol and Eugene F. StoermerGlossary, acronyms, and abbreviations 614Index 655ContributorsLeanne K. ArmandQuantitative Marine Science (CSIRO-University of Tasmania)and the Antarctic Climate and Ecosystems CooperativeResearch CentreHobart, Tasmania, AustraliaCurrent address:Climate Futures at Macquarie Department of BiologicalSciencesMacquarie UniversityNorth Ryde, NSW, 2109AustraliaRichard W. BattarbeeEnvironmental Change Research Centre (ECRC)Department of Geography, UCLGower StreetLondon WC1E 6BTUnited KingdomHelen BennionEnvironmental Change Research Centre (ECRC)Department of Geography, UCLGower StreetLondon, WC1E 6BTUnited KingdomChristian BiglerDepartment of Ecology and Environmental ScienceUmea UniversitySE-90187 UmeaSwedenH. John B. BirksDepartment of BiologyUniversity of BergenThormhlensgate 53Aixx List of contributorsN-5007 BergenNorwayandEnvironmental Change Research Centre (ECRC)Department of Geography, UCLGower StreetLondon, WC1E 6BTUnited KingdomNigel G. CameronEnvironmental Change Research Centre (ECRC)Department of Geography, UCLGower StreetLondon WC1E 6BTUnited KingdomHunter J. CarrickThe Pennsylvania State UniversitySchool of Forest Resources434 Forest Resources BuildingUniversity ParkPA 16802USADonald F. CharlesPatrick Center for Environmental ResearchThe Academy of Natural Sciences1900 Benjamin Franklin ParkwayPhiladelphia, PA 19103-1195USASherri CooperBryn Athyn CollegeBryn Athyn, PA 19009-0717USAXavier CrostaUMR-CNRS 5805 EPOCUniversite Bordeaux 1Avenue des Facultes,33405 Talence CedexFranceBrian F. CummingPaleoecological Environmental and Assessment andResearch Laboratory (PEARL)Department of BiologyQueens UniversityKingston, Ontario, K7L 3N6CanadaChristina L. De La RochaInstitut Universitaire Europeen de la Mer (IUEM)Universite de Bretagne Occidentale (UBO)Technop ole Brest-Iroise, Place Nicolas Copernic29280 PlouzaneFranceGregory J. DoucetteNOAA/National Ocean Service219 Fort Johnson RoadCharleston, SC 29412USAMarianne S. V. DouglasDepartment of Earth and Atmospheric Sciences,University of AlbertaEdmonton, Alberta T6G 2E3CanadaMark B. EdlundSt. Croix Watershed Research StationScience Museum of Minnesota16910 152nd St. NorthMarine on St. Croix, Minnesota 55047USASherilyn C. FritzDepartment of Geosciences and School of Biological SciencesUniversity of Nebraska LincolnLincoln, NE 68588-0340USAEvelyn GaiserDepartment of Biological Sciences and SoutheastEnvironmental Research CenterFlorida International UniversityMiami, FL 33199USAFranc oise GasseCEREGE, UMR 6635Marseille University-CNRS-IRDBP 8013545 Aix-en-Provence cedex 4FranceAndrey Yu. GladenkovGeological InstituteRussian Academy of SciencesPyzhevskii per., 7Moscow 119017RussiaList of contributors xiRichard GordonDepartment of RadiologyUniversity of ManitobaWinnipeg, Manitoba R3A 1R9CanadaIrene Gregory-EavesDepartment of BiologyMcGill University1205 Dr. PeneldMontreal, Quebec H3A 1B1CanadaRoland I. HallDepartment of Biology,University of Waterloo,200 University Avenue West,Waterloo, Ontario N2L 3G1CanadaMargaret A. HarperSchool of Geography, Environment and Earth SciencesVictoria University of WellingtonPO Box 600 WellingtonNew Zealand 6140David M. HarwoodDepartment of GeosciencesUniversity of Nebraska-LincolnLincoln, NE 68588-0340USADominic A. HodgsonBritish Antarctic SurveyHigh CrossMadingley RoadCambridge, CB3 0ETUnited KingdomBenjamin P. HortonDepartment of Earth and Environmental ScienceUniversity of PennsylvaniaPhiladelphia, PA 19104USAJeffrey R. JohansenDepartment of BiologyJohn Carroll University20700 North Park Blvd.University HeightsOH 44118USAGareth D. Jones3 Meadowlands DriveWesthill, Aberdeenshire AB32 6EJUnited KingdomRichard W. JordanDepartment of Earth & Environmental SciencesFaculty of ScienceYamagata UniversityYamagata, 990-8560JapanSteve JugginsSchool of Geography, Politics and SociologyNewcastle UniversityNewcastle upon Tyne NE1 7RUUnited KingdomMatthew L. JuliusAquatic Toxicology LaboratoryDepartment of Biological SciencesSt. Cloud State UniversitySt. Cloud, MN 56301USAIrena KaczmarskaDepartment of BiologyMount Allison University63B York St.Sackville, NB E4L 1G7CanadaBronwyn E. KeatleyDepartment of BiologyMcGill University1205 Dr. PeneldMontreal, Quebec H3A 1B1CanadaandDepartment of Natural Resource SciencesMcGill University21,111 Lakeshore RoadSte. Anne de Bellevue, Quebec H9X 3V9Canadaxii List of contributorsGalina KhursevichM. Tank State Pedagogical UniversityDepartment of Botany18 Sovetskaya StreetMinsk 220809Republic of BelarusCathy KilroyNational Institute of Water and Atmospheric ResearchPO Box 8602ChristchurchNew ZealandWilliam N. KrebsPetronas Carigali SDN. BHD.Petronas Twin TowersKuala Lumpur, MalaysiaCurrent address:2506 Plumeld LaneKatyTexas 77450USAKathleen R. LairdPaleoecological Environmental Assessment andResearch Lab (PEARL)Department of BiologyQueens UniversityKingston, Ontario K7L 3N6CanadaMelanie J. LengNERC Isotope Geosciences LaboratoryBritish Geological SurveyKeyworthNottingham NG12 5GGUnited KingdomandSchool of GeographyUniversity of NottinghamNottingham NG7 2RDUnited KingdomAmy LeventerDepartment of GeologyColgate UniversityHamilton, NY 13346USAAude LeynaertUMR CNRS 6539Institut Universitaire Europeen de la Mer (IUEM)Techn opole Brest-Iroise, Place Nicholas Copernic29280 PlouzaneFranceChristopher S. LobbanDivision of Natural SciencesUniversity of GuamMangilaoGuam 96923USAAndre F. LotterInstitute of Environmental BiologyLaboratory of Palaeobotany and PalynologyUtrecht UniversityBudapestlaan 43584 CD UtrechtThe NetherlandsAnson W. MackayEnvironmental Change Research Centre (ECRC)Department of Geography, UCLGower StreetLondon WC1E 6BTUnited KingdomRobert M. McKayAntarctic Research CentreVictoria University of WellingtonPO Box 600 WellingtonNew Zealand 6140Diane M. McKnightINSTAAR1560 30th StreetUniversity of ColoradoBoulder CO 80303USAYangdong PanEnvironmental Sciences and ManagementPortland State UniversityPortland, Oregon 97207USAList of contributors xiiiAnthony J. PeabodyMetropolitan Forensic Science Laboratory109 Lambeth Rd,London SE1 7LPUnited KingdomReinhard PienitzAquatic Paleoecology LaboratoryCentre for Northern Studies2405 rue de la TerrasseUniversite LavalQuebec (Quebec) G1V 0A6CanadaJennifer PikeSchool of Earth and Ocean SciencesCardiff UniversityMain Building, Park PlaceCardiff, CF10 3YEUnited KingdomOlivier RagueneauUMR CNRS 6539Institut Universitaire Europeen de la Mer (IUEM)Techn opole Brest-Iroise, Place Nicholas Copernic29280 PlouzaneFranceEuan D. ReavieCenter for Water and the EnvironmentNatural Resources Research InstituteUniversity of Minnesota Duluth1900 East Camp StreetEly, Minnesota 55731USAIngemar RenbergDepartment of Ecology and Environmental ScienceUmea UniversitySE-90187 UmeaSwedenOscar E. RomeroInstituto Andaluz de Ciencias de la Tierra (IACT-CSIC)Facultad de Ciencias, Universidad de GranadaCampus Fuentenueva18002 GranadaSpainKathleen R uhlandPaleoecological Environmental Assessment andResearch Laboratory (PEARL)Department of BiologyQueens UniversityKingston, Ontario K7L 3N6CanadaYuki SawaiGeological Survey of JapanNational Institute of Advanced Industrial Scienceand TechnologySite C7 1-1-1 HigashiTsukuba, Ibaraki, 305-8567JapanCarl D. SayerEnvironmental Change Research Centre (ECRC)Department of Geography, UCLGower StreetLondon WC1E 6BTUnited KingdomRoland SchmidtInstitute for LimnologyAustrian Academy of SciencesMondseestrasse 9A-5310 MondseeAustriaJohn P. SmolPaleoecological Environmental Assessment andResearch Lab (PEARL)Department of BiologyQueens UniversityKingston, Ontario K7L 3N6CanadaPauline SnoeijsDepartment of Systems EcologyStockholm UniversitySE-10691 StockholmSwedenSarah A. SpauldingUS Geological SurveyINSTAAR, 1560 30th StreetUniversity of Coloradoxiv List of contributorsBoulder CO 80303USALee StanishINSTAAR1560 30th StreetUniversity of ColoradoBoulder CO 80303USAR. Jan StevensonCenter for Water SciencesDepartment of ZoologyMichigan State UniversityEast Lansing, Michigan 48824USACatherine E. StickleyDepartment of GeologyUniversity of TromsN-9037 TromsNorwayandNorwegian Polar InstitutePolar Environmental CentreN-9296 TromsNorwayEugene F. Stoermer4392 Dexter RoadAnn Arbor, MI 48103USAJeffery R. StoneDepartment of GeosciencesUniversity of Nebraska LincolnLincoln, Nebraska 68588-0340USAMichael J. SullivanSt. Andrewss North Campus370 Old Agency RoadRidgeland, Mississippi 39157USAGeorge E. A. SwannNERC Isotope Geosciences LaboratoryBritish Geological SurveyKeyworthNottingham NG12 5GGUnited KingdomEdward C. TheriotTexas Natural Science CenterThe University of Texas at AustinAustin, TX 78705USAJohn TibbyGeographical and Environmental StudiesThe University of AdelaideAdelaide SA 5005AustraliaRosa TrobajoIRTA-Aquatic EcosystemsCrta de Poble Nou, Km 5.5PO Box 200E- 43540 Sant Carles de la R`apitaTarragona, CataloniaSpainHerman van DamConsultancy for Water and NatureP.O. Box 377771030 BJ AmsterdamThe NetherlandsBart Van de VijverNational Botanic Garden of BelgiumDepartment of Cryptogamy (Bryophyta & Thallophyta)Domein van BouchoutB-1860 MeiseBelgiumElie VerleyenGhent UniversityProtistology and Aquatic EcologyKrijgslaan 281 S8, B-9000GentBelgiumMaria Celia VillacDepartment of BiologyMount Allison University63B York St.Sackville, NB E4L 1G7CanadaList of contributors xvAnna WachnickaSoutheast Environmental Research CenterFlorida International UniversityUniversity Park OE 14811200 SW 8th StreetMiami, FL 33199USAKaarina Weckstr omGeological Survey of Denmark and Greenland (GEUS)Department of Marine Geology and Glaciologyster Voldgade 10DK-1350 Copenhagen KDenmarkJulie A. WolinDepartment of Biological, Geological andEnvironmental SciencesCleveland State UniversityCleveland, Ohio 44115USAPrefaceIf there is magic on this planet, it is contained inwater. (Loran Eiseley, The Immense Journey, 1957)Diatoms are being used increasingly in a wide range of appli-cations, and the number of diatomists and their publicationscontinuestoincreaserapidly. Althoughseveral bookshavedealtwithvarious aspects of diatombiology, ecology, andtaxonomy,the rst edition of this volume, published over a decade ago,was the rst to summarize the many applications and uses ofdiatoms. However, many new and exciting papers have beenpublished in the intervening years. This, coupled with the factthat research on environmental and earth science applicationsof diatoms has continued at a frenetic pace, prompted us toundertake a major revision of our rst edition.Our overall goal was tocollate a series of reviewchapters thatwould cover most of the key applications and uses of diatomsin the environmental and earth sciences. Due to space limita-tions, we could not include all types of applications, but wehope to have covered the main ones. Moreover, many of thechapters could easily have been double in size, and in fact sev-eral chapters could have been expanded to the size of books.Nonetheless, we hope material has been reviewed in sufcientbreadth and detail to make this a valuable reference book for awidespectrumof scientists, managers, andother users. Inaddi-tion, we hope that researchers who occasionally use diatoms intheir work, or at least read about how diatoms are being usedby their colleagues (e.g., archeologists, forensic scientists, cli-matologists, engineers, etc.), will also nd the book useful.Compared to our 1999 volume, the current edition is signif-icantly expanded and revised. It includes 16 new chapters, andan extensive revision and expansion of the original chapters,including the addition of many new co-authors.Thevolumeisbroadlydividedintosixparts. Followingour brief prologue, there is an introduction to the biology ofdiatomsandachapteronnumericalapproachescommonlyxviixviii Prefaceused by diatomists. Part II contains eight chapters that reviewhowdiatoms canbe usedas indicators of environmentalchange in owing waters and lakes. Part III summarizes workcompleted on diatoms from cold and extreme environments,such as subarctic and alpine regions, Antarctica and the HighArctic. These ecosystems are often considered to be especiallysensitivebellwethersofenvironmentalchange.PartIVcon-tains nine chapters dealing with diatoms in marine and estu-arine environments. The nal part (Part V) summarizes mostother applications (e.g., using diatoms as indicators in sub-aerial, wetland and peatland environments, and other applica-tions such as tracking past wildlife populations, archeology,oil exploration and correlation, forensic studies, toxic effects,atmospheric transport, invasive species, diatomites, isotopes,andnanotechnology). We conclude witha short epilogue(PartVI),followedbyamuchexpandedglossary(includingacronyms and abbreviations) and an index.Many individuals have helped with the preparation of thisvolume. We are especially grateful to Martin Grifths (Cam-bridge University Press), whoshepherdedthis project through-out muchof its development. As always, the reviewers providedexcellent suggestions for improving the chapters. We are alsograteful toour colleagues at Queens University andthe Univer-sity of Michigan, and elsewhere, who helped in many ways tobring this volume to its completion. And, of course, we thankthe authors.These are excitingtimes for diatom-basedresearch. We hopethat the following chapters effectively summarize how thesepowerful approaches can be used by a diverse group of users.John P. SmolKingston, Ontario, CanadaEugene F. StoermerAnn Arbor, Michigan, USAPart I Introduction1Applications and uses ofdiatoms: prologueJOHN P. SMOL AND EUGENE F. STOERMERThis bookis about theuses of diatoms (Class Bacillario-phyceae),agroupofmicroscopicalgaeabundantinalmostall aquatic habitats.Thereisnoaccurate countofthe num-ber of diatom species; however, estimates on the order of 104areoftengiven(Guillard&Kilham, 1977), althoughMann& Droop (1996) point out that this number would be raisedtoat least 105byapplicationof modernspeciesconcepts.Diatomsarecharacterizedbyanumberoffeatures,butaremost easily recognized by their siliceous (opaline) cell walls,composed of two valves, that, together with the girdle bands,form a frustule (Figure 1.1). The size, shape, and sculpturingof diatom cell walls are taxonomically diagnostic. Moreover,because of their siliceous composition, they are often very wellpreserved in fossil deposits and have a number of industrialuses.The main focus of this book is not the biology and taxonomyofdiatoms,althoughJulius&Theriot(thisvolume)providea primer on this subject, and a number of chapters touchon these topics. Other books (e.g. Round et al., 1990) and thereview articles and books cited in the following chapters, pro-vide introductions to the biology, ecology, and taxonomy ofdiatoms.Instead,ourfocusisontheapplicationsandusesof diatoms to the environmental and earth sciences. Althoughthisbookcontainschaptersonpracticaluses,suchasusesof fossilized diatom remains in industry, oil exploration, andforensic applications, most of the book deals with using theseindicators to decipher the effects of long-term ecological per-turbations, suchasclimaticchange, lakeacidication, andeutrophication. As many others have pointed out, diatoms arealmost ideal biological monitors. There are a very large num-berofecologicallysensitivespecies,whichareabundantinnearly all habitats where water is at least occasionally present.Importantly, diatom valves are typically well preserved in thesediments of most lakes and many areas of the oceans, as wellas in other environments.Precisely when and how people rst began to use the occur-rence and abundance of diatom populations directly, and tosense environmental conditions and trends, is probably lost inthe mists of antiquity. It is known that diatomites were used asa palliative food substitute during times of starvation (Taylor,1929), and Baileys notes attached to the type collection of Gom-phoneis herculeana (Ehrenb.) Cleve (Stoermer & Ladewski, 1982)indicate that masses of this species were used by native Ameri-cans for some medicinal purpose, especially by women ( J. W.Bailey, unpublished notes associated with the type gatheringof G. herculeana, housed in the Humboldt Museum, Berlin). It isinteresting to speculate how early peoples may have used thegross appearance of certain algal masses as indications of suit-able water quality (or contra-indications of water suitability!),or the presence of desirable andharvestable shor invertebratecommunities.However, twogreat differences separate humanunderstand-ing of higher plants and their parallel understanding of algae,particularly diatoms. The rst is direct utility. Anyone can quitequickly grasp the difference between having potatoes and nothaving potatoes. It is somewhat more difcult to establish theconsequences of, for example, Cyclotella americana Fricke beingextirpated from Lake Erie (Stoermer et al., 1996).Thesecondisperception.Atthispointinhistory,nearlyanypersonlivingintemperatelatitudescancorrectlyiden-tifyapotato. Somepeoplewhoseexistencehaslongbeenassociated with potato culture can provide a wealth of infor-mation, even if they lack extended formal education. Almostanyuniversitywillhaveindividualswhohaveknowledgeofaspectsof potatobiologyor, at aminimum, knowwherethisrichstoreof informationmaybeobtained. Ofcourse,knowledgeisneverperfect, andmuchresearchremainstoThe Diatoms: Applications for the Environmental and Earth Sciences, 2nd Edition,eds. John P. Smol and Eugene F. Stoermer. Published byCambridge University Press.c Cambridge University Press 2010.34 J. P. Smol and E. F. StoermerFigure 1.1Scanningelectronmicrographsofsomerepresentativediatoms: (a) Hyalodiscus; (b) Diploneis; (c) =Surirella; and (d) Stephano-discus. Micrographs a, b, andc courtesy of I. Kaczmarska andJ. Ehrman; micrograph d courtesy of M. B. Edlund.bedonebeforeour understandingof potatoesapproachescompleteness.Diatoms occupy a place near the opposite end of the spec-trumofunderstanding.Earlypeoplescouldnotsenseindi-vidual diatoms, and their only knowledge of this fraction ofthe worlds biota came from mass occurrences of either living(e.g. biolms) or fossil (diatomites) diatoms. Even in todaysworld, it is difcult to clearly and directly associate diatomswith the perceived values of the majority of the worlds popu-lation. The consequences of this history are that the impetusto study diatoms was not great. Hence, many questions con-cerning basic diatom biology remain to be addressed. Indeed,it is still rather rare to encounter individuals deeply knowledge-ableaboutdiatomsevenamongstuniversityfaculties.This,however, is changing rapidly.What isquiteclearisthat peoplebegantocompileandspeculateupontherelationshipsbetweentheoccurrenceofcertain diatoms and other things which were useful to knowalmost assoonasoptical microscopesweredeveloped. Inretrospect,someofthetheoriesdevelopedfromtheseearlyobservations andstudies may appear rather quaint inthelight of current knowledge. For instance, Ehrenberg (seeJahn, 1995) thought that diatoms were animal-like organisms,andhisinterpretationof their cytologyandinternal struc-ture was quite different from our modern understanding. Fur-ther, his interpretations of the origins of airborne diatoms (hethoughttheyweredirectlyassociatedwithvolcanoes)seemratheroutlandishtoday. Ontheotherhand, Ehrenbergdidmake phytogeographic inferences which are only now beingrediscovered.Aswill bepointedoutinchaptersfollowing, knowledgeabout diatoms can help us knowabout the presence ofpetroleum,ifandwhereadeceasedpersondrowned,whenstorms over the Sahara and Sub-Saharan Africa were ofsufcient strengthtotransport freshwater diatomremainsto the mid-Atlantic, and indeed to the most remote areas ofGreenland, as well as manyother applications and uses. Aswill be reected in the depth of presentation in these chapters,diatoms provide perhaps the best biological index of annual tomillennial changes in Earths biogeochemistry. As it becomesincreasinglyevident that humanactionsareexercisingevergreater control over the conditions and processes that allowforour existence (Crutzen & Stoermer, 2000), fully exercising allthe tools which may serve to infer the direction and magnitudeof change, and indeed the limits of change, becomes increas-ingly imperative. This need has fueled a considerable increasein the number of studies that deal with diatoms, particularly asapplied to the problems alluded to above.The primary motivation for this much-revised and expandedsecondeditionis tocompile this rapidly accumulatingandscat-tered information into a form readily accessible to interestedreaders. Aperusal of the literature will showthat the authors ofthedifferent chapters areamongst theworldleaders inresearchon the topics addressed.The perceptive reader will alsonote that, despite theirgreatutility,thestoreoffundamentalinformationconcern-ing diatoms is not as great as might logically be expected fora group of organisms that constitute a signicant fraction ofEarths biomass. For example, readers will nd few referencesto direct experimental physiological studies of the species dis-cussed. Sadly, therearestill only afewstudiestocite, andpracti-cally none of those available was conductedonthe most ecolog-ically sensitive freshwater species. Readers may also note thatthere are some differences of opinion concerning taxonomiclimits, even of common taxa, and that naming conventions arepresently in a state of ux. These uncertainties are real, anddevolve from the history of diatom studies.Asalreadymentioned, thestudyofdiatomsstartedrela-tively late,compared withmostgroupsofmacroorganisms.Diatomshaveonly beenstudiedinany organizedfashionfor about 200years, andtheperiodof effectivestudyhasonlybeenabout 150years. It isalsotruethat thehistoryof studyhasbeenquiteuneven. After thedevelopment offully corrected optical microscopes, the study of microorgan-isms in general, and diatoms in particular, attracted immenseApplications and uses of diatoms: prologue 5interest and the attention of a number of prodigiously ener-getic and productive workers. This grand period of explorationand description produced a very substantial, but poorly assim-ilated,literature.Diatomistswhoworkedtowardtheendofthisgrandperiodofgrowthproducedremarkablyadvancedinsights into cytology and similarly advanced theories of bio-logical evolution(Mereschkowsky, 1903). This, andthefact thatsophisticated and expensive optical equipment is required fortheir study, gained diatoms the reputation of a difcult groupof organisms to study effectively. Partially for this reason, basicdiatom studies entered a period of relative decline beginningc. 1900, although a rich, if somewhat eclectic, amateur tradi-tion ourished, especially in England and North America. Thearea that remained most active was ecology. As Pickett-Heapset al. (1984) have pointed out, Robert Lauterborn, an exception-ally talented biologist who was well known for his studies ofdiatomcytology, could also be appropriately cited as one of thefounders of aquatic ecology.The people who followed often did not command the degreeof broad recognition enjoyed by their predecessors, and manyof them operated at the margin of the academic world. As ex-amples, Friedrich Hustedt, perhaps the best known diatomistin the period from 1900 to 1960 (Behre, 1970), supported him-self and his family as a high-school teacher for much of hiscareer. B. J. Cholnoky(Archibald, 1973) wascaught upinthe vicissitudes of the Second World War, and produced hisgreatest works on diatomautecology, including his large sum-mary work (Cholnoky, 1968), after he became an employee ofthe South African Water Resources Institute. Although manyworkers of this era produced notable contributions, they wereperipheral to the main thrusts of academic ecological thoughtand theory, particularly in North America. Although this conti-nent hadnumerousindividualswhowereinterestedindiatoms,and published on the group, most of them were either inter-ested amateurs or isolated specialists working in museums orother non-university institutions. For example, when one of us(E. F. S.) decidedtoundertake advanceddegreeworkondiatoms in the late 1950s, there was no university in the UnitedStates with a faculty member specializing in the study of fresh-water diatoms.One of the most unfortunate aspects of separation of diatomstudies fromthe general course of botanical research was sub-stantial separation fromthe blossoming of newideas. The fewpublishedgeneralworksondiatomshadacuriousdatedquality, andrelatively littlenewunderstanding, except fordescriptions of new species. The main impetus that kept thissmall branch of botanical science alive was applied ecology,and this was the area that, in our opinion, produced the mostinteresting new contributions.The above situation began to change in the late 1950s, par-tially as a result of the general expansion of scientic researchinthe post-Sputnikera, andpartially as the result of technologi-cal advances, particularly inthe area of electronics. The generalavailability of electronmicroscopes openedneworders of mag-nitude in resolution of diatom structure, which made it obvi-ous that many of the older, radically condensed, classicationschemes were untenable. This released a virtual ood of new,rediscovered, and reinterpreted entities(Round et al., 1990),which continues to grow today. At the same time, the generalavailability of high-speed digital computers made it possibleto employ multivariate statistical techniques ideally suited toobjective analysis of modern diatom communities and thosecontained in sediments (Birks, this volume).The history of ecological studies centered on diatoms canbe roughlycategorized as consistingofthreeeras. Therstis what we might term the era of exploration. During thisperiod (c. 18301900), most research focused on diatoms asobjects of study. Work during this period was largely descrip-tive, be it the topic of the description of new taxa, discovery oftheir life cycles and basic physiology, or observations of theirgeographic and temporal distributions. One of the hallmarksof this traditionwas the indicator species concept. Of course,the age of exploration is not over for diatoms. New taxa havebeen described at a rate of about 400 per year over the pastfour decades, and this rate appears to be accelerating in recentyears. Basic information concerning cytology and physiologyof some taxa continues to accumulate, although at a lesser ratethan we might desire.The second era of ecological studies can be termed the eraof systematization (c. 19001970). During this period, manyresearchers attemptedtoreduce the richmosaic of informationandinference concerningdiatoms tomore manageable dimen-sions. The outgrowths of these efforts were the so-called sys-tems and spectra (e.g. halobion, saprobion, pH, temperature,etc.). Such devices are still employed, and sometimes modiedandimproved.Indeed,thereareoccasionalcallsforsimpleindices as a means of conveying information more clearly tomanagers and the public.We would categorize the current era of ecological studiesfocusedondiatoms as theageof objectication.Giventhecomputational toolsnowgenerallyavailable, it ispos-sible todetermine more accurately whichvariables affectdiatom occurrence and growth and, more importantly, do soquantitatively,reproducibly,andwithmeasurableprecision.6 J. P. Smol and E. F. Stoermer(a)Figure 1.2Some of the diverse ways that diatoms are collected foruse in environmental and earth science applications. (a) Collecting asediment core from Lake of the Woods. Photograph by K. R uhland.(b) Epilithic diatoms being sampled froma rock substrate froma HighArctic pond. Photograph by J. P. Smol. (c) Scuba divers collectingmarine diatoms near Guam. Photograph by M. Schefter.Thus, applied studies based on diatoms have been raised froma little-understood art practised by a few extreme specialists,to a tool that more closely meets the general expectations ofscienceandtheusersof thiswork, suchasenvironmentalmanagers.The result is that we now live in interesting times. Diatomshave proven to be extremely powerful indicators with whichto explore and interpret many ecological and practical prob-lems.Theyareusedinavarietyofsettings,usingdifferentapproaches (Figure 1.2). The continuing ood of newinforma-tion will, without doubt, make the available tools of appliedecology even sharper. It is also apparent that the maturationof this area of science will provide additional challenges. Goneare the comfortable days whenit was possible to learnthe char-acteristics of most freshwater genera in a fewdays and become(b)(c)Figure 1.2(cont.)Applications and uses of diatoms: prologue 7familiar with the available literature in a fewmonths. Althoughwe might sometimes wish for the return of simpler days, it isclear that this eld of study is rapidly expanding, and it is ourconjecture that we are on the threshold of even larger changes.The motivation for producing this updated volume is to sum-marize recent accomplishments and, thus, perhaps make thenext step easier.ReferencesArchibald, R. E. M. (1973). Obituary: Dr. B. J. Cholnoky (18991972).Revue Algologique, N. S., 11, 12.Behre, K. (1970). FriedrichHustedts LebenundWerke. NovaHedwigia,Beiheft, 31, 1122.Cholnoky,B.J.(1968).Die OkologiederDiatomeeninBinnengewassern.Verlag von J. Cramer: Lehre.Crutzen, P. J. &Stoermer, E. F. (2000). The Anthropocene. The Interna-tional Geosphere-Biosphere Programme (IGBP) Global Change Newsletter.41: 1718.Guillard, R. R. L. & Kilham, P. (1977). The ecology of marine plank-tonicdiatoms. InTheBiologyof Diatoms. Botanical Monographs,vol. 13, ed. D. Werner, Oxford: Blackwell Scientic Publications,pp. 372469.Jahn, R. (1995). C. G. Ehrenbergs concept of the diatoms. Archiv furProtistenkunde, 146, 10916.Mann, D. G. & Droop, J. M. (1996). Biodiversity, biogeography andconservation of diatoms. Hydrobiologia, 336, 1932.Mereschkowsky, C. (1903). Nouvelles recherches sur la structure et ladivision des Diatom`ees. Bulletin Societe Imp`eriale des Naturalistes deMoscou, 17, 14972.Pickett-Heaps,J.D.,Schmid,A.-M.,&Tippett,D.H.(1984).Celldivision in diatoms: a translation of part of Robert Lauterbornstreatise of 1896 with some modern conrmatory observations.Protoplasma, 120, 13254.Round, F. E., Crawford, R. M., & Mann, D. G. (1990). The Diatoms:Biology and Morphology of the Genera. Cambridge: Cambridge Uni-versity Press.Stoermer, E. F. & Ladewski, T. B. (1982). Quantitative anal-ysis of shape variation in type and modern populationsof Gomphoneis herculeana. Nova Hedwigia, Beiheft, 73,34786.Stoermer, E. F., Emmert, G., Julius, M. L., & Schelske, C. L. (1996).Paleolimnologic evidence of rapid recent change in Lake Eriestrophic status. Canadian Journal of Fisheries and Aquatic Sciences, 53,14518.Taylor, F. B. (1929). Notes on Diatoms. Bournemouth: GuardianPress.2The diatoms: a primerMATTHEW L. JULIUS ANDEDWARD C. THERIOT2.1 IntroductionDiatoms havelongbeenlaudedfor their useas powerfuland reliable environmental indicators (Cholnoky, 1968; Lowe,1974). This utility canbe attributedtotheir highabundance andspecies diversity, which are distributed among most aquaticenvironments. Additionally, their remains are highly durableand well preserved inaccumulated sediments. Often, scientistsexploiting the groupsimply as environmental proxies give littlethought as to how and why the species diversity exists in theseenvironments. This may be a by-product of how diatoms arecollected and identied. Diatoms are most often recognized bythe presence of a siliceous cell wall, the frustule. This structurevaries considerably in shape and architecture among species(Figure2.1)andvirtuallyall taxonomicdiagnosisoftaxaisbased upon frustular morphology. To properly observe diatomfrustules for taxonomic identication, living and sedimentarycollections are typically subjected to various cleaning tech-niques designed to remove all organic materials (e.g. Battarbeeet al., 2001; Blancoet al., 2008), allowingunobstructedobserva-tionof thefrustuleinthemicroscope. Thisfrequent observationof inorganic components of the cell without reference to theorganicfeaturesallowsobserverstoforgetthat thespecimensseen in the microscope represent individual organisms com-petinginthe selective environments drivenby biotic andabioticecological pressures. The abundance and taxonomic diversitycan be attributed to the extraordinary success of diatoms in thecompetitive ecological arena.The casual observer frequently regards diatoms, like mostprotists, as primitive ancestral lineages to multicellular organ-isms.Whilesomeprotistsmaytthisdescription,diatomsdo not. Diatoms are a relatively recent evolutionary group withthe common ancestors origin considered to be between 200and 190 million years before present (Rothpletz, 1896, 1900;Medlin et al., 1997). As a point of reference, the origin of thisrst diatom is approximately 60 to 70 million years youngerthan the specialized teeth found in mammals, including thoseinthereadersmouth(Shubin, 2008). Datesfortheoriginof the diatom common ancestor are bracketed by molecularclock estimates (Sorhannus, 2007) and the oldest stratigraphicobservation (Rothpletz, 1896, 1900). Both of these estimatesareinherentlybiased. Thetemporal proximityofeachesti-mate to one another does, however, suggest a certain degree ofaccuracy, given the complimentary nature of the biases. Molec-ularestimatesrepresentanattempttoidentifytheabsolutemoment two populations diverged fromone another. The old-est stratigraphic observation represents a period where fossilremains were sufciently abundant to allow discovery. Giventhe expected disparity between the moment two populationsdiverged, and the time it would take divergent populations todevelopsufcientnumbersallowingpaleontologicaldiscov-ery, the 10 million year gap between the two estimates does notappear to be overly large in context of other estimates in thistemporal range.Discussion of when diatoms originated begs the question:what didtheyoriginatefrom?Diatomsshareancestrywithheterokonts.Heterokonts(orstramenopiles)areagroupofprotists withunequal agella(Leedale, 1974; Hoek, 1978)that includes both chloroplast-bearing and non-chloroplast-bearing representatives (Patterson, 1989) whose commonancestor is thought to have arisen 725 million years beforepresent(Bhattacharya&Medlin,2004).Thegroupcontainsanarrayofmorphologicallydiversegroupsincludinggiantkelps(>60m) at thelargeendof thesizespectrumandthe Bolidomonads and Pelagomonads (12m) at the smallend of the size spectrum (North, 1994; Andersen et al., 1993;Guillouet al., 1999). Theheterokonts may bepart of thelargerchromalveolateevolutionarygroup,whichincludesThe Diatoms: Applications for the Environmental and Earth Sciences, 2nd Edition,eds. John P. Smol and Eugene F. Stoermer. Published byCambridge University Press.c Cambridge University Press 2010.8The diatoms: a primer 9a b cdeghfFigure 2.1Variations in frustule morphology within diatoms species.(a) Amphicampa mirabilis, (b) Navicula cryptocephala, (c) Cymbella inae-qualis, (d) Hydrosera whampoensis, (e) Acanthoceras magdeburgensis,(f ) Cyclotella striata, (g) Cymatopleura solea, (h) Gyrosigma acuminatum.Scale bars equal 5 m.cryptophytes, dinoagellates, ciliates, apicomplexans, andhaptophytes (Yoon et al., 2002; Cavalier-Smith, 2003; Harper&Keeling, 2003; Ryall et al., 2003; Bachvaroffet al., 2005;Harper et al., 2005). This proposed relationship is controver-sial and highly debated (e.g., Falkowski et al., 2004; Grzebyket al., 2004; Keeling et al., 2004; Bachvaroff et al., 2005; Bodyl,2005). Within heterokonts, individual groups are well estab-lishedandeasilydiagnosable, buttherelationshipbetweenthese groups has yet tobe denitively identied(Saunders et al.,1995; Sorhannus, 2001; Goertzen & Theriot, 2003). Moleculartechniques utilizing multiple data sets have identied the boli-dophytes (Goertzen & Theriot, 2003) as the heterokont mostcloselyrelatedtodiatoms.Thebolidophytesareagroupofmarineunicellularagellatesthatwereunknowntosciencepriortothelate1990s(Guillouet al., 1999). Thisrelativelyrecent discovery of the diatoms sister group reects howmuchdiscovery and description-level science remains uncompletedin heterokont biology.This statement about heterokonts easily extends to diatoms.Onceanunderstandingof originisachieved, anapprecia-tion should be given to the speed of diversication. Currently,>24,000diatomspecies have validscientic names (Fourtanier&Kociolek, 2009a, b). Many of these have only been illustratedin the literature with light microscopy, and few have yet beenthe subject of any other genetic, ecological, or physiologicalstudy. Mann and Droop (1996) conservatively estimated thatthere are 200,000 diatomspecies. If these numbers are taken atface value, 12% of the diatom ora is currently described. Thismeans the modern diatomtaxonomic community has a major-ity of the 24,000 described species to observe in the electronmicroscope, and an additional 176,000 species to describe. Inaddition,completingaphylogenyforthese200,000speciesshould also be an objective. Julius (2007a) demonstrated thatthe rate of species descriptionindiatoms is approximately 183185 per year and that this rate has remained constant for nearlya century. At this pace it will take approximately 951 years todescribe diatom species completely!With this in mind, it is easy to understand why the diatomsystematics community is still grappling with the collection ofdetailed ultrastuctural information for most species, descrip-tion of species, and the proper way to analyze these data. Manymodern diatomsystematic studies deal with taxa at the genericor higher level, avoiding unresolved issues concerning ultra-structure and species concepts. Several recent studies suggestdiatomdiversityismuchgreater thanpreviouslyimagined(Theriot &Stoermer, 1984; Bourne et al., 1992), causingresearchers to suggest continued emphasis on species descrip-tion is most essential in developing phylogenetic hypotheses(Kociolek, 1997; Lange-Bertalot, 1997; Mann, 1997; Round,1997). In many instances, researchers also continue to argueabout what classes of data should be emphasized, valvemorphology or cytological features, in classication systems(Round, 1996) without regard to any sense of evolution.Systematicstudiesinthetwenty-rstcenturymustincor-porate all types of character information in some sort of ananalysis emphasizing the similarity between evolved features(cladisticanalysisiscurrentlythemostprominentsystem).This character information must be presented for individualspecies, not broad generic groups. This requires considerableadditional descriptive work. Gradually, a classication morereective of evolutionary history will develop. Simply put, thereis a great deal of work to be done. We are gradually developing10 M. L. Julius and E. C. Theriotamorestructuredwayof handlingtheproblemand, withluck, progresswill bemade. Oneindicationofthisactivityisthedistinctlynon-lineartrendseenintherateofgenericdescription over the last two decades (Fourtanier & Kociolek,1999). Generic descriptions increased at an exponential rateduringthistime, contrastingwiththelinear rateseeninspecies.This may indicate that existing taxa are being placed into newlycreatedhigher taxonomiccategoriesandagreater interestisbeingtakenintherelationshipbetweenonespeciesandanother.2.2 ClassicationModernsystematicsstrivestoachievenatural, or monophyletic,groups when designating categories above the species level.These natural groups contain an ancestral lineage and all ofitsdescendants(monophyly).Manytaxonomicgroupswereestablishedpriortotheacceptanceofmonophylyasagoal.Taxonomicdesignationsfordiatomsarenoexception, andresearchers have only recently begunattempts totest andadjustdiatomtaxonomic schemes toreect monophyletic groupings.Notallindividualsestablishinggeneraandothercategoriesfor diatoms view monophyly as a goal, despite its widespreadacceptance elsewhere in biology, and proceed in their endeav-ors inanevolutionary free context (Williams &Kociolek, 2007).Individuals utilizing taxonomic schemes for diatoms shouldbeawareof theunstablestatusof manyhighertaxonomiccategories(genusandabove).Speciesarefrequentlymovedinandoutofcategoriesandnewcategoriesarecontinuallybeing established. This process, hopefully, reects the gradualtransition to a monophyletic taxonomic system and the over-whelming level of species description remaining incomplete.Individuals utilizingdiatoms as indicator species oftenndthisuctuation in higher taxonomic categories frustrating. To cir-cumvent this taxonomic instability, identications should bemade to the species level whenever possible, because speciesnames can always be referenced back to the original popula-tion described no matter how many times a name is modiednomenclaturally.Diatoms are traditionally classied as one of two biologicalorders, the Centrales (informally referredtoas centrics) andthePennales (or pennates). Diagnostic features cited supportingthe two classes typically include (1) valve formation developingradially around a point in centrics, contrasted by depositionoriginating along a plane in pennates and (2) oogamous sexwith relatively small motile agella bearing sperm and a largenon-motile egg in the centrics, contrasted by isogamous sexwith ameboid gametes in the pennates. These features are notdistinctly distributed among bilaterally and radially symmetricmorphologies on the diatom evolutionary tree, but are insteaddistributed along a gradient moving from basal radially sym-metric groups to more recently diverged bilaterally symmetricgroups.Simonsen (1979) was the rst to discuss a phylogeny for alldiatoms in the context of a taxonomic system. While Simonsenpresentedanevolutionarytreefor diatomfamilies, hewasreluc-tant to deconstruct class and order designations in a mannerreecting monophyly. Most notable is the presentation of cen-tric diatoms as distinctly non-monophyletic while maintainingthe traditional taxonomic category for the group. Round et al.(1990) presented a taxonomic system for genera and higher-level groups. This work treated the diatoms as a division withthreeclassesconsistingof theradiallysymmetrictaxa, thearaphidpennatetaxa, andraphidpennatetaxa, suggestingthat evolution was along this line and that the centric diatomsprecededpennates.Thistextremainsthemostrecentcom-prehensive coverage for diatoms, but the classication systemwas not developed in an evolutionary context and many of thetaxonomic designations are being reconsidered and modied.A comprehensive evolutionary tree for the diatoms is cur-rently a popular research topic (summarized in Alverson et al.,2006andTheriotetal.,2009).Whilemolecularsystematicshas advanced rapidly in other areas of biology, only the smallsubunit of the nuclearly encoded ribosomal rDNA gene (SSU)hasbeenusedfor comprehensiveanalysesof diatomphy-logeny (other genes and morphology have generally just beenemployed selectively at the ordinal level or below). Trees pro-duced using the SSUmolecule have uniformly obtained a gradeof multiple lineages of centric diatoms generally with radialsymmetry of valve elements, thena series of lineages of centricswith generally bipolar or multipolar symmetry, then a series ofaraphid taxa and, nally, the clade of raphe-bearing pennates.The only exceptions to this are when only a few diatoms wereincluded in the analysis or the analytical techniques used wereimproperly applied (Theriot et al., 2009).Goertzen and Theriot (2003) noted the effect of taxon sam-pling on topologies generated in phylogenetic analyses of het-erokonttaxa. Diatomdiversitypresentsachallenge,inthiscontext, toattempts at reconstructingphylogenies for thegroup using molecular data. All attempts to date have sampled20) of seemingly signicantpartitions (e.g. Laird et al., 2003). Sucha large number of zonescan defeat the major purpose of zonation, namely as a tool indata summarization. High-resolution data often have a highinherent sample-to-sample variance (Birks, 1998). An effectiveand more useful summarization of such data may be achievedby using ordination methods, which, by design, concentratethe signal in a data set into the rst few ordination axes andrelegate the noise to later axes (Gauch, 1982).In the analysis of modern diatom data sets, it can be usefulto cluster or partition the data into a smaller number of groupsof samples with similar diatom composition or environmen-tal characteristics (Legendre & Birks, 2011a). There are manypotential uses of the results from such analyses, for exampledetectinggroupsof sampleswithsimilardiatomcomposi-tionorwithsimilarenvironmental features, detectingindi-cator species for the groups, relating biologically basedgroups to environmental variables, and assessing similaritiesbetween fossil diatom samples and groups of modern diatomsamples from known environmental settings. Besides impos-ing one-dimensional temporal or stratigraphical constraints,two-dimensional (geographical coordinates) constraints(Legendre&Legendre, 1998; Legendre&Birks, 2011a)canbe imposed to detect spatially contiguous groups of sampleswith similar diatom composition and/or environmental char-acteristics. The question of whether to apply such constraintsdepends very much on the research problem of interest dosimilarmoderndiatomassemblagesalloccurtogethergeo-graphically, or how can modern diatom assemblages be par-titionedintocoherentgeographical areasofsimilardiatomoras? In the rst question, unconstrained analyses would beappropriate; in the second case, spatially constrained analyseswould be required. The results of such clustering or partition-ing should be displayed as maps of the group membership ofsamples or on low-dimensional ordination plots of the sam-ple scores on the ordination axes. Clustering and partitioningtechniques are surprisingly little used in the numerical anal-ysis of diatom assemblage data, except in the partitioning ofstratigraphical sequences into assemblage zones.3.4.2.2Ordinationapproaches Incontrast tocluster andpar-titioning approaches, ordination techniques or indirect gradi-ent analysis are widely used in diatom research (Birks, 1998;Legendre &Birks, 2011b) to summarize patterns of variation incomplex modernor stratigraphical diatomdata sets andtopro-vide convenient low-dimensional representations of such data.ttEnvironmental variable (x)Abundance value (y)UCFigure 3.1The Gaussian response curve for the abundance (y) of adiatom taxon in relation to an environmental gradient (x). The esti-mated optimum for the species is shown as U, its tolerance is labeledt, and the maximum height of the response curve is designated C (terBraak, 1987b).The major ordination or dimension-reduction techniques fordata summarization, as distinct from constrained ordinationtechniquesusedindataanalysiswhereparticularnumericalstatisticsareestimatedfromdiatomdata(seebelow), areprinci-pal components analysis (PCA), correspondence analysis (CA),detrendedcorrespondenceanalysis(DCA),principalcoordi-nates analysis (PCoA) (=metric or classical multidimensionalscaling), and non-metric multidimensional scaling (NMDS).All these ordination techniques can provide a low-dimensionalrepresentation of the samples and the variables (indirectly inPCoA and NMDS) in the diatom data set so that the points inthe low-dimensional plot (usually two-dimensional) that areclose together correspond to samples that are similar in theirdiatom composition, and points that are apart correspond tosamples that are dissimilar in their diatomcomposition. Thereis, however, a second more ambitious purpose of an ordina-tion (ter Braak, 1987a), namely to detect the underlying latentstructureinthedata:inotherwordstheoccurrenceand/orabundances of all the species in the data set are assumed to bedetermined by a few unknown environmental variables (latentvariables) accordingtoasimplespeciesenvironment responsemodel (ter Braak & Prentice, 1988). If the aim of an ordinationis to detect the underlying structure in the data, we need toassume a speciesresponse model (e.g. linear or unimodal) apriori. The ordination problem is thus to construct the singlehypotheticalenvironmentalvariablethatgivesthebesttto the species data under the assumption of a linear or uni-modal response model. Principal components analysis relatestoalinearresponsemodel inwhichtheabundanceofanyspeciesincreasesordecreaseswiththevalueofeachlatentenvironmental variable. Corresondence analysis and its DCArelative are related to a unimodal response model (Figure 3.1)Numerical methods for analysis of assemblage data 29inwhichany species occurs ina limitedrange of valuesforeachofthelatentvariables(terBraak,1987b).PrincipalcoordinatesanalysisandNMDSaresolelydimension-reductiontechniques andare not guaranteedtoextract the latent variablesthat give the best ts to the species data because they makenoassumptionsabout speciesresponsemodels. Theyonlyinvolve dissimilarities (PCoA) or rank dissimilarities (NMDS)between all pairs of samples. Detailed accounts of PCA, CA,DCA, PCoA, and NMDS are given by ter Braak (1987a; 1996),Legendre and Legendre (1998), and Leps and Smilauer (2003).As it is generally more useful ecologically toextract the latentvariables, andthus touse PCA, CA, or DCA, the questionimme-diately arises of which response model and hence which meth-ods are appropriate for a given data set. ter Braak and Prentice(1988)suggestthatthelengthoftherstgradientofvaria-tioninmultivariate biological data, suchas diatomassemblagedata, as estimated by DCA (in standard deviation (SD) units ofcompositional turnover) is a useful guide as to whether speciesresponses are primarily monotonic (gradient length3 SD). My experience with DCA withmany diatom percentage data sets is that turnover estimationshould be based on square-root transformed data and withoutdown-weighting of rare species (ter Braak & Smilauer, 2002).Which method should be used if the gradient length is 2.4 SD?My experience is that CA is remarkably robust with percentagedata and it can be safely used for data with gradient lengths aslow as 1.5 SD, whereas PCA is more erratic for data with gra-dient lengths >2.5 SD. If the nal ordination is based on PCA,square-root transformed data and a covariance matrix betweenspecies are reliable choices, whereas if the nal ordination isbased on CA or DCA, square-root transformed data and down-weighting of rare species are appropriate. In the constructionofordinationplotsforPCAorCA,careshouldbegiventothe choice of axis scaling. The choice of scaling focused oninter-sample distances is generally appropriate when the pri-mary interest is on the conguration of the samples, whereasthe scaling focusedoninter-species distance is generallyappropriate when the interest is on the conguration of thespecies. Symmetric scaling (Gabriel, 2002) is often a very goodcompromise.In general, in all uses of the unimodal-based methods of CA,DCA, and canonical correspondence analysis (CCA), down-weighting of rare species should be applied because individualsamples withrare species may distort the results of the analyses(ter Braak & Smilauer, 2002). In estimating gradient length orcompositional turnover along the rst DCA axis or along therst constrained axis (e.g. pH or age) in detrended canonicalcorrespondenceanalysis(DCCA),experienceshowsthatnodown-weighting of rare species is desirable as it usually leadsto more robust estimates of compositional turnover.Ordination results of analyzing diatom stratigraphical datacan usefully be plotted in a stratigraphical context with axis1 sample scores plotted against depth or age, axis 2 samplescores plotted in the same way, etc. The appropriate number ofordination axes to retain and plot can be assessed by compari-son with the broken-stick model (Jolliffe, 1986; Jackson, 1993;Legendre & Legendre, 1998). Such stratigraphical ordinationplots provide a useful summary of the major patterns of varia-tion and the nature of changes in the stratigraphical sequence.These plots allow the detection of trends and abrupt changeswithin the sequence which may be obscured in zonation wherethe primary aim is partitioning the data sequence into homo-geneous units or zones. Careful examination of the species(variable) scores or loadings on the ordination axes can revealwhich diatomspecies are most inuential to the sample scoresforagivenordinationaxis,therebyprovidinganecologicalinterpretation of the observed patterns in the latent variables(= ordination axes) (see Bradshaw et al. (2005) for a detailedexample of using DCA to summarize and compare patterns instratigraphical diatom and pollen data).Forsummarizingbiostratigraphicaldata,DCAismypre-ferredordinationtechniquebecausethesamplescoresarescaledinstandarddeviationunitsofcompositional changeor turnover (Hill &Gauch, 1980). It is thus possible to obtain agraphical summary of the magnitude of diatomcompositionalchange within the stratigraphical sequence. Other ordinationtechniques such as PCA and CA lack this ecologically attractiveand useful scaling of sample scores. Using PCoA and NMDS isnot really appropriate for stratigraphical plotting as their axesare not selected to capture the latent structure of the data.Ordinationof spatial moderndiatomdatasetscanusefullybedone withPCA, CA, or DCAdependingongradient length(PCAor CA) and research questions (CA or DCA). However, manymodern diatom data sets also include environmental variablessuchaslake-waterchemical dataand, inthesecases, con-strained ordination or direct gradient analytical techniques aremore useful. These are discussed below under data dnalysis.3.4.2.3Twoor morestratigraphical sequences Whentwoormore paleoecological variables (e.g. diatoms, pollen, chirono-mids) have been studied in the same stratigraphical sequence,numerical zonations based on each set of variables and a com-parison of the resulting partitions can help to identify commonanduniquechangesindifferentvariables(Birks&Gordon,30 H. John B. Birks1985). Separate ordinations (PCA, CA, or DCA) of the differentdata sets can help to summarize the major patterns within eachdata set, and these patterns can be compared by, for example,oscillationlogs (Birks, 1987). Incases where one data set canbeconsideredas representing response variables (e.g. diatoms)andanotherdatasetcanberegardedasreectingpotentialpredictor or explanatory variables (e.g. pollen, independentclimateestimates(e.g.StJacquesetal.,2009)),constrainedordinations such as redundancy analysis (RDA=con-strainedPCA), canonical correspondence analysis (CCA=con-strained CA), or detrended CCA (DCCA = constrained DCA)andassociatedMonteCarlopermutationtests(terBraak&Smilauer, 2002) canbeusedtoassessthestatistical relationshipbetween the two data sets (Haberle et al., 2006). This approachis discussed further in the data interpretation section.3.4.2.4Other datasummarizationtechniques An importantpart of datasummarizationis clear display of thedata. For fossildiatomassemblages with 50 or more species, it is important toplot their relative frequencies in basic stratigraphical plots ina way that displays the major patterns of variation within thedata as a whole. A very simple but effective way is to calculatethe weighted average or optimum of each species for age ordepth and to re-order the species in order of their optima, withspecies having high optima for age or depth being plotted rstat the bottom left of the stratigraphical plot and with specieshaving low optima being plotted at the top right of the plot(Janssen & Birks, 1994). Alternatively, species can be orderedon the basis of their modern weighted-average optima for aparticular environmental variable (e.g. lake-water pH see thesection on data analysis below) or on the basis of the speciesscores on the rst DCA or CA axis.Non-parametric regression techniques such as locallyweighted scatterplot-smoothing (LOWESS or LOESS) regres-sion provide useful graphical tools for highlighting the sig-nalor major patternsinstratigraphical sequencesof individualspecies in stratigraphical plots of sample scores on ordinationaxes, and of time series of reconstructed environmental vari-ables. The LOESS technique (Cleveland, 1979; 1993; 1994) canbe usedtomodel the relationshipbetweena response or depen-dent variable (e.g. abundances of Tabellaria binalis (Ehrenberg)Grunow) and an independent variable (e.g. age or depth) whenno single functional form such as a linear or quadratic modelis appropriate or assumed. The technique provides a graphicalsummarythathelpstoassesstherelationshipandtodetectthe major patterns of change within noisy data. Unlike con-ventional regression modeling, LOESS ts a series of locallyweighted regression curves for different values of the indepen-dent variable, in each case using data points weighted by theirdistances tothe values of interest inthe independent variable. ALOESS curve is a non-parametric regression estimate becauseit does not assume a particular parametric form(e.g. quadratic)for the regression (Cleveland & Devlin, 1988). It is conceptu-ally similar to running means except that LOESS takes intoaccount the uneven spacing of the independent time or depthvariable. In LOESS tting, the degree of smoothing or span canbe varied and lies between 0 and 1. As the span is increased, thettedcurve becomes smoother. Choosingthe appropriate spanrequires some judgment for each data set. The goal is generallytomake the spanas large as possible andthus tomake the ttedcurve as smooth as possible without distorting the underlyingpattern or signal in the data (Cleveland, 1994). The LOESStechnique canalsobe usedas a scatter-plot smoother when, forexample, the abundance of Eunotia exigua Brebisson ex K utzingRabenhorst (dependent variable) ina series of modernsamplesis plotted in relation to lake-water pH (independent variable).3.5 Data analysisDataanalysisisusedherespecicallyfor specializedtechniquesthat estimate particular numerical characteristics from mod-ern or fossil diatom assemblage data. Examples include taxo-nomic richness, rates of change, modern diatom assemblageenvironment relationships, species optima and tolerances forcontemporary environmental variables, inferred past environ-mental variables, andperiodicities andpower spectra indiatomstratigraphical data.3.5.1Taxonomic richnessRarefaction analysis (Birks & Line, 1992) estimates the taxo-nomicrichnesswithinandbetweenstratigraphical diatomsequences and within and between modern diatom data sets.It estimates how many species would have been found if allthe diatom counts had been the same size. The actual mini-mum count among the data set(s) of interest is generally usedas the base value. Examples of the use of rarefaction analysisin diatom research include Anderson et al. (1996) and Lotter(1998), whereas Weckstr om and Korhola (2001), Rusak et al.(2004), Heegaard et al. (2006), Telford et al. (2006), and Vyver-manet al. (2007), highlight thepotential of exploringrigorouslyrichness patterns of diatom assemblages in space and time.The pioneering approach of Patrick and colleagues (Patrick,1949;Patricketal.,1954;Patrick&Strawbridge,1963)useddiatomassemblagestructuretoassessrichnessanddiver-sity of diatom communities. Pappas and Stoermer (1996) alsoNumerical methods for analysis of assemblage data 31exploited aspects of diatom assemblage structure to evaluatecountingaccuracy.Muchworkisneededinestimatingandinterpretingtaxonomicrichnessandbiodiversityof diatomassemblage data.3.5.2Rate-of-change analysisRate-of-change analysis (Jacobson & Grimm, 1986; Grimm &Jacobson, 1992) estimates the amount of compositional changeper unit time in stratigraphical data. It is estimated by calcu-lating the multivariate dissimilarity (e.g. Euclidean distance,chorddistance(=Euclideandistanceof square-root trans-formedpercentagedata))betweenstratigraphicallyadjacentsamples and by dividing the dissimilarity by the estimated ageinterval betweenthe sample pairs. Analternative approachis tointerpolate the stratigraphical data to constant time intervals,calculate the dissimilarity, and divide by a constant time inter-val. The data can be smoothed prior to interpolation. Althoughthebasic ideais attractive, inpracticethereareseveral problems(Lotter et al., 1992; Laird et al., 1998). Rate-of-change analysisis critically dependent on the time standardization unit used tostandardize the estimateddissimilarity betweenadjacent strati-graphical samples. As radiocarbon years do not equal calendaryears, a carefully calibrated timescale or an independent abso-lute chronology (e.g. from laminated sediments) is essentialfor reliable rate-of-change estimation. Rate-of-change analy-sis of ne-resolution data from annually laminated sediments(e.g. Lotter et al., 1995) is often dominated by the high sample-to-samplevariabilityincompositionthat commonlyoccursin ne-resolution data. This inherent variability is reduced incoarserresolutionstudiesasstratigraphicaldatafromsuchstudies are effectively time averaged and temporally smoothed.One approach is to summarize the stratigraphical data as therst few statistically signicant ordination axes or latent vari-ables and to use these composite summarizing variables onlyin the rate-of-change analysis (Jacobson & Grimm, 1986). Therationale here is that, as discussed above, ordinations like PCA,CA, or DCA generally represent the signal in complex datasuchas diatomassemblage data as the rst fewordinationaxesandrelegatethenoisetolater,non-signicantordinationaxes (Gauch, 1982; Birks, 1998). Examples of rate-of-changeanalysis with diatomdata include Lotter et al. (1995), Laird et al.(1998), Birks (1997), and Birks et al. (2000).3.5.3Constrained ordination methodsPrior to the development by Cajo ter Braak of constrained ordi-nationmethods suchas canonical correspondence analysis (terBraak, 1986), the classical approachto assessing what environ-mental variables might inuence modern diatomassemblageswas to do a PCA or CA of the diatom data and then relate theresulting ordination axes to particular environmental variablesby correlation or regression analysis. What ter Braak did wasto combine the ordination stage and the regression stage intoone technique that nds a weighted sum of the environmen-tal variables that ts the diatom species data best statistically,namely that gives the maximumregressionsumof squares. Theresulting ordination plots showthe patterns of variation in thespecies and the samples and the main relationships betweenthe species and the environmental variables. The ordinationaxes are constrained to be linear combinations of the environ-mental variables. The constrained version of PCAthat assumeslinearspeciesresponsesisredundancyanalysis(RDA) andthe constrained version of CA that assumes unimodal speciesresponses is canonical correspondenceanalysis (CCA). Inaddi-tion, the constrained version of DCA is detrended canonicalcorrespondence analysis (DCCA). Details of the mathematicsandhowtouseRDA, CCA, andDCCAarepresentedinter Braak,1986, ter Braak and Prentice (1988), ter Braak and Verdonschot(1995), Legendre and Legendre (1998), ter Braak and Smilauer(2002), and Leps and Smilauer (2003).Thecommonest way that RDAor CCAareusedintheanalysisof moderndiatomassemblage data suchas diatomcounts fromsurface sediments from a set of lakes with associated environ-mental data such as lake-water pH, specic conductivity, totalnitrogen, etc. is to analyze the two data sets together to estab-lishhowwell, ina statistical sense, the environmental variablesexplain the modern diatom assemblages. This is done, if weareusingCCA,bycomparingtheeigenvaluesofanuncon-strainedCAorDCAwiththeeigenvaluesoftheCCAwhichare measures of how well the species scores or optima are dis-persed along the axes. The speciesenvironment correlationsand the percentage variation of the species data should also becompared between the CA (or DCA) and the CCA. The eigen-values in the CCA will always be lower than the unconstrainedCA or DCA eigenvalues because of the constraint that the axesmust be linear combinations of the environmental variables,whereasthespeciesenvironmentcorrelationswillnormallybe higher in CCA. If the environmental variables are impor-tant in explaining the diatom data and are highly correlatedto the latent variables in the CA or DCA, then the eigenvaluesof the CA or DCA and the CCA should be fairly similar. Thesumof all the constrained eigenvalues (speciesenvironmentalrelationships)shouldbecomparedwiththesumofall theunconstrained eigenvalues (inertia) to assess how much of32 H. John B. Birksthe total variation in the diatom data is explained by the envi-ronmental data. Experience shows that a CCA eigenvalue >0.3suggests a strong gradient, and an eigenvalue>0.4 suggestsa good niche separation of species along the overall environ-mental gradient. A similar argument applies to PCA and RDAexcept that the eigenvalues quantify the sumof squares of ttedvalues to the latent variables (PCA) and to the linear combina-tion of environmental variables (RDA). RDA, CCA, and DCCAare multivariate direct gradient analytical techniques where allspecies and environmental variables are analyzed together, incontrast to simple direct gradient analyses (=regression anal-ysis) where one species and one or more environmental vari-able(s) are analyzed, and multivariate indirect gradient analy-ses where only the species data are analyzed as in PCA, CA, orDCA.As CCA, RDA, and DCCA are, in reality, multivariate regres-sions of complex diatom species response data in relation tomany environmental predictors, they are statistical modelingtechniques as well as graphical data-summarization tools. As abasic model is tted by RDA, CCA, or DCCA (species respondto the environmental predictors), it is essential to evaluate thestatistical signicance of the model, namely to do a conrma-tory or hypothesis-testing data analysis. This is done by MonteCarlo permutation tests. The environmental data are permutedmany times (usually 99 or 999 times) and test statistics for therst canonical axis and for all canonical axes are computed forthe observed and the permuted data. If the diatom species arestatistically related to the environmental variables, the statisticfor the observed data should be larger than most (e.g. 95%)of the statistics calculated for permuted data. If the observedstatistics are in the top 5%, one can conclude that the speciesresponse is statistically signicant to the environmental vari-able considered.In addition to the question of statistical signicance of thespeciesenvironment relationships, a critically important partof RDA, CCA, and DCCA is the graphical presentation of theresults (ter Braak, 1994; ter Braak &Verdonschot, 1995). Giventhat there are ten possible data tables that can be plotted, itis important to decide which aspects of the results are mostimportant ina particular researchproject. Inmost diatomstud-ies using CCA, the most relevant are the species scores, thecorrelations of the quantitative environmental variables (e.g.pH) with the ordination axes, the centroids of nominal envi-ronmental variables (e.g. presence or absence of fringing bogaroundthe lakes sampled), andthe sample (lake) scores. Whenthe emphasis is on the speciesenvironment relationships, aspecies-conditional plotorcorrelationbiplotisappropriatewhere the species are represented by the niche centre alongeach axis. If the emphasis is on the sample scores, a distancebiplot, possibly with Hills scaling so that distances betweenthesamplesarecompositional turnover distances, ismostuseful.TerBraakandVerdonschot(1995)describeindetailtheoptionsintheconstructionofCCAplotsandprovideaguide as to howto interpret such plots in terms of the centroid,distance, andbiplot principles. ter Braak(1994) discusses thesetopics in the context of RDA. One aspect in CCA and RDA thatcan cause some confusion is that there are two sets of samplescores one is the linear combination scores that are predictedor tted values of the multiple regression with the constrain-ing environmental variables, the other is the weighted averagesof the species scores. In general the linear combination scoresshould be used, except when all the environmental predictorvariables are presence/absence variables.A useful tool in diatomstudies where there are both moderndiatom and environmental data and fossil diatom data is to doan RDA or CCA of the modern data and to treat the fossil dataas passive or supplementary samples (ter Braak & Smilauer,2002). The fossil samples are positioned on the basis of thecompositional similarities with the modern samples that are,in turn, positioned in relation to the modern environmentalvariables. It is thus possible to trace the fossil diatomsequencethrough modern environmental space (e.g. Birks et al., 1990b),if the fossil samples are well tted, namely have a low squaredresidual distance from the plane formed by the rst two ordi-nation axes.TheRDAorCCAtechniquescanbeusedtoquantifytheexplanatorypowerofsingleenvironmental variablesonthemodern diatom assemblages by a series of constrained anal-yses with each environmental variable as the sole constraint(e.g. Lotteret al., 1997). TheDCCAtechniquecanalsobeused to estimate the amount of diatomcompositional turnoveralong specic environmental gradients (e.g. lake-water pH).Suchestimatesareaguidetothetypeofregressionproce-dure that should be used in the development of transfer func-tionsfrommoderncalibrationsetsforquantitativeenviron-mental reconstructions (Birks, 1995; 1998). In these analyses,DCCA should be based on detrending by segments, non-linearrescaling of the axes, and no down-weighting of rare species.The same DCCA approach can be used to estimate composi-tionalturnoverinfossildiatomassemblagesoveraspecictime period at many sites (Smol et al., 2005; Birks, 2007) or indifferent groups of organisms over a specic time periodat oneor more sites (Birks & Birks, 2008), thereby providing a com-mon basis for comparing the amount of compositional changeNumerical methods for analysis of assemblage data 33between sites, between organisms, or between different timeperiods.In addition to RDA, CCA, and DCCA, there are related par-tial techniqueswheretheeffectsof particular variablesornuisancevariables(e.g.differentsamplingdates)arefac-toredout statistically as inpartial regressionanalysis (terBraak & Prentice, 1988). Partial RDA or partial CCA providemeans of partitioningthe total variationindiatomassemblagesinto fractions explained by, for example, lake characteristics(size, depth, etc.) and lake-water chemistry, and the covaria-tion between lake morphometry and water chemistry, plus theunexplained fraction. This approach, pioneered by Borcard etal. (1992) has been expanded to three or more sets of predictorvariables (e.g. Jones & Juggins, 1995) and has recently beenput on a more rigorous statistical basis to obtain unbiased esti-mates of the fractions (Peres-Neto et al., 2006). Although rarelyused in diatom research, there is also partial PCA, CA, or DCAwheretheeffectsofparticularvariablescanbefactoredoutprior to an indirect ordination (ter Braak & Prentice, 1988).Ordinations of fossil diatomstratigraphical data, con-strained by sample depth or age, using RDA, CCA, or DCCA,can be valuable in identifying the major patterns of variation,the nature of the changes, and trends in the sequence (Birks,1987). For some research questions, it may not be useful toimpose the stratigraphical constraint and to use PCA, CA, orDCA (see above) and simply detect the major patterns of varia-tionirrespective of the orderingof the objects. Inother researchproblems, it may be relevant to partial out, as covariables, theeffects of variables not of primary interest, such as sample ageor depth in partial PCA, CA, DCA, RDA, CCA, or DCCA (e.g.Odgaard, 1994; Bradshaw et al., 2005).A basic principle of statistical modeling is the minimal ade-quatemodel,arealizationoftheprincipleofparsimonyinstatistics and of Ockhams principle of simplicity in science(Ockhams razor). Various aids in RDA, CCA, or DCCA suchas variance ination factors and forward selection and associ-ated permutation tests (ter Braak & Smilauer, 2002) can helpto derive a minimal adequate model with the smallest numberof signicant environmental variables that explains, in a sta-tistical sense, the diatom data about as well as the full set ofexplanatory environmental variables. Oksanenet al. (2008) havedevelopedexperimental unfoundedanduntested statistics inCCA and RDA that resemble deviance and the Akaike Informa-tionCriterion(AIC) (Godnez-Domnguez &Freire, 2003) usedin the building and selection of statistical regression models.These new statistics can help model building and selection inCCA and RDA. If the investigator is lucky there may only beone minimal adequate model but it is important to assume thatthere may not be only one such model.Important recent developments in the area of constrainedordinations are constrained methods that use samplesample proximity or distance measures other that thoseimplicit in RDA/PCA (Euclidean distances) and CCA/CA (chi-squareddistance).Distance-basedRDA(Legendre&Ander-son, 1999), canonical analysis of principal coordinates (CAP)(Anderson & Willis, 2003), and non-linear CAP (Millar et al.,2005)useproximitymeasuressuchastheBrayandCurtis,Jaccard, or Gower coefcients but in a constrained ordinationframework. Thesedevelopmentsconsiderablywidenthechoiceof proximity measures andalsoallow(non-linear CAP) for non-linear relationships between diatomassemblages and environ-mental variables. They warrant use in several areas of diatomresearch where aspects of both assemblage composition andspecies abundance need to be considered simultaneously andwhere the environmental variables show non-linear relation-ships, for example with increasing distance from a pollutionsource.ConstrainedordinationtechniqueslikeRDAarealsoveryuseful with eld or laboratory experimental data of diatoms(e.g. Pappas&Stoermer, 1995) becauseall speciescanbeanalyzed, interactions between variables can be included, andstatistical signicance can be assessed by permutation tests,thereby relaxing some of the demanding assumptions of clas-sical multivariateanalysis of variance. Several permutationtestsare available in the CANOCO software (ter Braak & Smilauer,2002) totakeaccount of particular samplingdesigns, e.g.timeseries,line-transects,rectangulargrids,repeatedmea-sures, and split-block with whole-plots containing split-plots.Whole-plots, split-plots, or bothcanbepermuted. Withinplots, samples can represent time series, line-transects, spa-tialgrids,orbefreelyexchangeable.Thusmultivariatedatafromdifferent designscanbeanalyzedandtested(Leps&Smilauer, 2003). Afurther development relevant in experimen-tal diatom studies involving a repeated-measure design is theprincipal responsecurve(PRC)technique(vanderBrink&terBraak,1998)developedinecotoxicology.Thistechniquefocuses on time-dependent treatment effects by adjusting forchanges across time in the control and provides a succinct andelegant way of displaying and testing (by Monte Carlo permu-tation tests) effects across time.3.5.4Estimating species optima and tolerancesInsome diatomstudies involvingmoderndata sets fromdiffer-ent geographical areas or fromdifferent habitats (e.g. Cameron34 H. John B. Birks302520157.5 7.0 6.5 6.0 5.5 5.0 4.5 4.07.5 7.0 6.5 6.0 5.5 5.0 4.5 4.07.5 7.0 6.5 6.0 5.5 5.0 4.5 4.07.5 7.0 6.5 6.0 5.5 5.0 4.5 4.01015129635030252015105001086420pHTabellaria binalis Achnanthes minutissimaAchnanthes marginulataAsterionella formosapHpHPercentagePercentagePercentagePercentagepHFigure 3.2FittedGaussianresponse curves for four diatomspecies inrelationtopH. DataarefromtheSWAPdataset of 167lakes inEngland,Wales, Scotland, Norway, and Sweden (Stevensonet al., 1991). Diatomnomenclature follows Stevenson et al. (1991).et al., 1999), it isuseful tocomparetherealizednicheof thesamediatomspeciesindifferentareasorhabitats(e.g. Stoermer& Ladewski, 1976). Such comparisons require statisticalmodeling of the diatom responses in relation to environmen-tal variablesofinterest.Therearemanytypesofecologicalresponse curves. A compromise is necessary between ecolog-ical realism and simplicity (ter Braak & van Dam, 1989); theGaussianresponsemodel withsymmetricunimodal curvesis a suitable compromise (Figure 3.1) (ter Braak, 1996). TheGaussian logit model is usually applied to presence/absencedata (ter Braak & Looman, 1986) but it can be used as a quasi-likelihoodmodel for proportions (Figure3.2) andas anapprox-imationtothemorecomplexmultinomial logit model (terBraak&vanDam, 1989). UsingGaussianlogit regression(GLR)(binomial error structure), onecanestimatetheoptimum,tolerance,andheightofitscurvepeakfromtheregressioncoefcients (Birks et al., 1990a), along with the approximate95% condence intervals for the estimated optimum and thestandard error of the estimated tolerance for each species inrelation to the environmental variable of interest (ter Braak &Looman, 1986). For each species, the signicance of the Gaus-sian logit model can be tested against the simpler linear-logit(sigmoidal) model, and the linear-logit model can be testedagainst the null model that the species has no statistically sig-nicant relationship to the environmental variable of interest.For species with estimated optima clearly outside the range ofsampled environmental variables (see Figure 3.3), and with asignicant linear logit model, the optimum can be assumed(asaminimalestimate)tobethelowestvaluefortheenvi-ronmental variable sampled for decreasing linear logit curvesand the highest environmental value sampled for increasinglinear logit curves (Birks et al., 1990a). Tolerances are dened36 H. John B. Birksbetween the diatom assemblages and pH are modeled numer-ically and the resulting model or transfer function is usedto transform the fossil diatom assemblages into quantitativeestimates of past lake-water pH.Therearenowmany numerical techniques for derivingtrans-fer functions (Birks, 1995; ter Braak, 1995; Birks, 1998, 2003;Telford et al., 2004; Guiot & de Vernal, 2007; Juggins & Birks,2011). Some have a stronger theoretical basis, either statisti-cally, ecologically, or both, thanothers. Some (e.g. simple two-way WA regression and calibration and its closely related tech-niqueofweighted-averagingpartial leastsquares(WA-PLS)regression and calibration and the more theoretically rigorousGLR and maximum likelihood (ML) calibration) fulll all thebasic requirements for quantitative reconstructions, performconsistently well with a range of data, do not involve an exces-sive number of parameters to be estimated and tted, involveglobalratherthanlocalparametricestimationfromthemoderndata,andarethusrelativelyrobuststatisticallyandcomputationally economical.3.5.2.1Basic approaches and assumptions Therearefourbasic considerations whenestimating transfer functions. First,thereis thechoiceof inverseor classical regressionapproaches.The classical approach is of the general form:Y = f (X) +errorwhereYarespeciesresponsesthat aremodeledasafunc-tion of the environment X with some error. The function f() isestimated by linear, non-linear, and/or multivariate regressionfrom the modern training set. Estimated f() is then invertedto infer the past environment fromYf, the fossil diatomassem-blage. Inversioninvolvesndingthepast environmentalvariable that maximizes the likelihood of observing the fossilassemblage in that environment. If function f() is non-linear,which it almost always is, non-linear optimization proceduresare required. Alternatively there is the simpler inverse approachofX = g(Y) +errorwherethedifcult inversionstepisavoidedbyestimatingdirectlythefunctionofg()fromthetrainingsetbyinverseregression of X on Y. The inferred past environment (Xf) givena fossil assemblage (Yf) is simplyXf= g(Yf).As ter Braak (1995) discusses, statisticians have debated therelative merits of the classical and inverse approaches. In thefewcomparisonsofthesetwomajorapproaches(terBraaket al., 1993; Birks, 1995; ter Braak, 1995; Telford &Birks, 2005),inverse models (WA or WA-PLS) nearly always performas wellas classical methods (ML). Inverse models appear to performbestifthefossilassemblagesaresimilarincompositiontosamples in the central part of the modern data, whereas clas-sical modelsmaybebetterat theextremesandwithsomeextrapolation, as in no-analog situations.Second, there is the assumedspeciesresponse model. Manytransfer-functionmethods assume a linear or a unimodalresponse whereas others (e.g. modern analog techniques, arti-cial neural networks) do not assume any response model. Itis a general law of nature that speciesenvironment relation-ships are usually non-linear and species abundance is often aunimodal function of the environmental variable (Figure 3.1).Each species grows best at a particular optimum value of theenvironmental variable and cannot survive where the value ofthat variable is too low or too high (ter Braak, 1996). Thus allspecies tend to occur over a characteristic but limited environ-mental range and within this range tend to be most abundantnear their environmental optimum.Third,thereisthequestionofdimensionality.Shouldallspecies be consideredindividually (full dimensionality) orshould some axes or components of species abundance (anal-ogous to principal components) (reduced dimensionality) beused?Fourth, thereis theestimationproceduretoconsider. Shouldaglobal estimationprocedurebeusedthat estimatesparametricfunctionsacrossthecompletetrainingset andthusallowssome extrapolation or should a local estimation procedure beadopted that estimates non-parametric local functions whichdo not allow any extrapolation?There are strong theoretical and empirical reasons for pre-ferring methods with an assumed species response model, fulldimensionality, and global parametric estimation. These rea-sons are:(1) It is possible totest statistically if a species has a statisticallysignicant relation to a particular environmental variableby GLR (see above).(2) Itispossibletodeveloparticialsimulateddatawithrealistic assumptions for numerical experiments (e.g. terBraak et al., 1993; ter Braak, 1995).(3) Such methods have clear and testable assumptions and areless of a black box than, for example, articial neuralnetworks(Raccaet al., 2001, 2003; Telfordet al., 2004;Telford & Birks, 2005).38 H. John B. Birks1000. Ineach, a subset of modernsamples is selectedrandomlybut with replacement fromthe training set to forma bootstraptra