Basic principles of temporal dynamics

Review

Basic

Principles

of

Temporal

Dynamics

Masahiro

Ryo

,

* Carlos

A.

Aguilar-Trigueros,

Liliana

Pinek,

Ludo

A.H.

Muller,

and

Matthias

C.

Rillig

Allecologicaldisciplinesconsidertemporaldynamics,althoughrelevant

con-cepts have been developed almostindependently. We here introducebasic

principlesoftemporaldynamicsinecology.Wefiguredoutessentialfeatures

thatdescribetemporaldynamics byfindingsimilaritiesamongabout60

eco-logical concepts and theories. We found that considering the hierarchically

nestedstructureofcomplexityintemporalpatterns(i.e.hierarchical

complex-ity)canwelldescribethefundamentalnatureoftemporaldynamicsby

express-ing whichpatterns areobserved at each scale. Across allecological levels,

driver–responserelationshipscanbetemporallyvariantanddependentonboth

short-andlong-termpastconditions.Theframeworkcanhelpwithdesigning

experiments,improvingpredictivepowerofstatistics,andenhancing

commu-nicationsamongecologicaldisciplines.

TheNeedforBasicPrinciplesofTemporalDynamics

Allecologicaldisciplinesconsidertemporaldynamicswithmajorparadigmsshiftingfromoneto another:equilibrium(seeGlossary)tononequilibrium,andstationarytononstationary(Box 1).UnderstandingtemporaldynamicsisbecomingmoreimportantintheAnthropocene.Several time-relatedconceptsandstatisticshaveemergedrecently[1–4].Nevertheless,ecologystilllacks basicprinciplesthatunderlieallstudiesrelevanttotemporaldynamics[5],andtheexchangeof knowledgeabouttemporaldynamicsamongsubdisciplinesislimited[6,7].

Recentlydevelopedconceptsinclude,forexample,temporalecology[5],abruptshifts in ecologicalsystems[8],ecologicalmemory[3],laghypothesisforcommunitydynamics[9],

and asymptotic environmentally determined trajectories [1]. These were proposed

almostindependentlyofeachother.However,theyallconsiderthatdriver–response relation-shipsarenotnecessarilyconstantthroughtime,buttheydependontherecentandhistorical past.Thisperspectivebringstogethervariousconceptstofigureouttheessenceoftemporal dynamicsacrossecologicalandtemporalscales.

Wehereintroducebasicprinciplesoftemporaldynamicsinecology.Ourprimarychallengewasto

figureoutessentialfeaturesthatdescribetemporaldynamicsbyfindingsimilaritiesamongabout 60ecologicalconceptsandtheories.The examplesare takenlargely frompopulation,community, andevolutionaryecology, butmoreexamplescanbefoundinTable S1(see supplemental informationonline).Wealsosummarizethevalueoftheconcept,rangingfromimprovingstudy designtocatalyzingknowledgeintegrationamongdisconnectedsubdisciplines.

HierarchicalComplexity

Weapplied the concept ofhierarchy[10–12] fordescribing temporalpatterns(i.e., driver– responserelationshipsintimeseries)touncoveruniversalfeaturesacrosstheexisting time-relatedconcepts.Theconceptofhierarchyoftenconsidersanestedstructureofhierarchical scales including absolute scale (seconds<minutes<hours) and relative scale (period

Highlights

Temporal dynamics are inherently complex.

Conceptsandtechniqueshavefl our-ishedtounderstandecological tem-poraldynamicsinrecentyears. Akeyfindingofrecentstudiesisthat driver–responserelationshipsarenot necessarily constant through time, butrather,thattheyareconditioned bytherecentandhistoricalpast. Basicprinciplesoftemporaldynamics needtobesummarizedtoincreasethe understanding and predictability of complextemporaldynamicsin ecol-ogyandevolution.

1

FreieUniversitätBerlin,Instituteof

Biology,D-14195Berlin,Germany

2

Berlin-BrandenburgInstituteof

AdvancedBiodiversityResearch

(BBIB),D-14195Berlin,Germany

*Correspondence:

[email protected](M.Ryo).

A<periodB).Yet,insteadofscale,weconsideranestedstructureofhierarchicalcomplexity: single-eventlevel,multiple-eventslevel,andthetrajectorylevel.Asingleeventisasubsetof multipleeventsoccurringwithinagivenperiodoftheentiretrajectory(i.e.,singleevent< mul-tiple events<trajectory; Figure 1). We refer to an event as an irregular change in either endogenous or exogenousconditions of the system within a limited period, inwhich the occurrenceperiodandsomeaspectsofthechangearedefinablegiven acertainrule(e.g., exceedingadefinedthresholdvalue).

Hierarchicalcomplexityisakeytosummarizingbasicprinciplesapplicableacrosstemporaland ecologicalscales.Forexample,weconsiderthatpulse-shapeeventsareconsideredtobelong tothesamecategory,irrespectiveofscale.Ifwehadreliedonscale,similarpatternsatdifferent scalescouldnotbecompared.Moreover,manygenerictermsdescribingtemporaldynamics (e.g.,pulseandpress)cannotbeattributedtoanyspecifictimescale.

Glossary

Asymptoticenvironmentally determinedtrajectory:trajectoryof apopulationprocessthatis approachedbyothertrajectories. Forexample,regardlessofinitial conditions,anytrajectoriesconverge eventuallyintoasingletrajectory thatisdeterminedbythe surroundingenvironmental

fluctuations.Thisconceptcan explainpopulationandcommunity dynamicsinanonstationary environment.

Carryover:interactioneffects (additiveornonadditive)ofmultiple driversthatoccursequentially. Ecologicalmemory:capacityof paststatesorexperiencestoexplain presentorfutureresponsesofan ecologicalsystem.Thelength, temporalpattern,andstrengthofthe memoryareimportantcomponents forquantification.

Equilibrium:stateofstable conditionsinwhichallforcescancel eachotheroutandthusallfactors remaintemporallystable.Thestate goesbacktothepreviousstable stateorreachesanotherstablestate afterperturbations.

Laghypotheses:Theno-lag hypothesis,incommunityecology, arguesthatacommunity

compositionisinequilibriumwiththe givenenvironmentatthatlocationat agiventime.Onthecontrary,thelag hypothesisarguesthatitisin nonequilibriumwiththe contemporaryenvironment[9]. Nonequilibrium:statethatdoesnot reachanequilibrium(see

Equilibrium).

Nonstationary:characteristicof time-seriesthatisnotstationary(see Stationary).Statisticalparametersof time-serieschangeovertime. Stationary:characteristicof time-serieswhosestatisticalparameters includingmean,variance,and autocorrelationaretemporally constant.Stationaryandequilibrium aresometimesinterchangeablyused. However,stationaryisastatistical term,whileequilibriumisatermto representthestateofasystem.A systemcanbeconsideredat equilibriumunderastationary condition,butanequilibriumstate doesnotnecessarilysatisfy stationarity.

Box1.ParadigmShiftsinUnderstandingTemporalPhenomena

Thestudiesabouttemporaldynamicsreliedhistoricallyontheequilibriumconcept.Theequilibriumconceptpositsthat anyecologicalsystemwillsoonerorlaterreturntoadeterminedstableconditionafteranyperturbations[68,69].The notionofabalancetracesbacktotheancientGreeks[70,71].Theconceptwasreformedinthe17thcenturywithmore mechanisticviews[72,73],andthe18thcenturygaverisetotheconceptofbalanceofnature[74].Thisconceptiswidely supportedbytheexistenceofself-regulatingmechanisms[18](e.g.,homeostasisofindividual,populationgrowth, negativefeedbackofcommunity,andresistance-resilienceandcompensatorydynamicsofecosystems). Theequilibriumconceptflourished,butatthesametime,wasalsocriticized[75–77].Negativeresultsreportingfailureto provideequilibriumstateswererarelyseen,untilPickett[69]andotherscalledforbroadattentiontothissituation.The needtoreconcilebothequilibriumandnonequilibriumparadigmshatchedthetheoryofmultipleequilibriainthe1970s and1980s[16,48,78].Anecologicalsystemcanshiftitsstatefromonestatetoanother,whenthedegreeofa perturbationexceedsanallowablecapacity[16,79–81].Together with thenotion ofthesenonlinear dynamics, consideringtemporaldynamicsalsopavedthewayforecologybeyondtheequilibriumconcept.Thenonequilibrium paradigmfocusesexplicitlyontimeseriestobetterdescribethetemporaldynamicsofecologicalsystems.Itassumes thatnostableconditionexists,andthepastexperiencesacrossvariousscalesinfluenceonthecurrentstateofasystem

[1,19,44,82].Understandingsuchnonequilibriumdynamicshasbeenatthecenterofmodernecology[82]. Collectively,thisparadigmshifthasgivenrisetoarangeofquestionsabouttemporaldynamicsofecologicalsystems. Theseincludehowdotemporalchangesinenvironmentalconditionsdeterminesystemstates,andhowhasthecurrent stateofthesystembeenreachedthroughtime?

Figure1.HierarchicalComplexity.Theideadealswithdriver–responserelationshipsintime-seriesacrossthreelevels ofcomplexity.Thelevelsarehierarchicallynested,assingle-event(i.e.,onedriverandoneresponse)isasubsetofmultiple eventsthatareapartofthetrajectory.Thekeypropertyisthatdriver–responserelationshipsarenotnecessarilyconstant throughtime,buttheycanchangeovertimeduetorecentandhistoricalpastexperience.Hierarchicalcomplexitycanbe observedatanyscale.Temporaldynamicsateachofthelevelsaffecteachother.

Temporalecology:emergingfield inecology,whichisfocusedon understandinghowtimeinfluences ecologicalsystemsbeyondthe prevalentknowledgeabouttemporal dynamics.Temporalecologyhas beenproposedtointertwinewith spatialecology,whichisan integrativemultidisciplinaryfieldto addressissuesacrossspatialand ecologicalscales.

BasicPrinciplesof Temporal Dynamics

Basicprinciplesoftemporaldynamicsaredescribedateachlevelofcomplexity(Figure2).Some ecologicalconceptscancovermultiplelevels(TableS1;seesupplementalinformationonline),but forsimplicity, wesorttheminto onelevelinthe following.When lookingacross scales,the proposedhierarchiescanbefurthernested(e.g.,atrajectoryatasmallscalecouldbeasubsetofa singleeventatalargerscale).Thisnestednessisafundamentalnatureoftemporaldynamics,and alevelofcomplexitymaydependonhowcloselythedynamicsareobserved(i.e.,notthescalebut theresolution).Alevelofcomplexityforanobservedpatterncanbereasonablyassignedby clarifyingwhichfeatureofthebasicprinciples(discussedindetailbelow)isstudied.

SingleEventLevel

Types

Asingleeventcharacterizesbothdriverandresponse.Forthesakeofbrevity,adriveranda responsearerepresentedbyasingleattributeeach(e.g.,temperatureasdriverandfitnessas response),althoughmultivariateattributesarepossible[13].

Drivertypesareclassifiedintopulse(transient),step(includingpress),orramp[5,8,14].Afterthe emergence,apulsereturnstothepreviousconditionafterreachingapeak,astependsupata differentmagnitude,andarampmakesatrend(upperleftofFigure2).Nochange(constant) can beadditionally considered. Anypairings of driverand responsetypes are possible (4 driver4responsetypes).

Characteristics

Driverandresponsearecharacterizedbymagnitude,duration,andrateofchange(middleleft ofFigure2;[15]).Thesecharacteristicsallowvariouscomparisons:normversusextreme(any characteristic); low versus high (magnitude); transient versus persistent (duration); abrupt versusgradual(rateofchange);fastversusslow(rateofchange);acuteversuschronic(rate ofchangeandduration);andpulseversuspressversusramp(rateofchangeandduration). Patterns

Threshold;Thresholdsareattributabletothecharacteristics.Aminimalexceedancethreshold representsthevalueofadrivercharacteristictotriggeraresponse,whileamaximal exceed-ancethresholdrepresentsthevalueatwhichthedrivercharacteristiccausesanirreversible response(cf.regimeshift;lowerleftofFigure2).

Theequilibriumparadigmassumes nomaximalthresholdandtransientresponses [16,17]. Negativefeedbackisakeymechanismforequilibrium,irrespectiveofecologicalscales[18]:for example,individualhomeostasis,populationdensitydependence,communitycompensatory dynamics,andecosystemresilience.Thenonequilibriumparadigmexplicitlyconsiders persis-tentresponses beyond the maximalthreshold,including mode switching of individual and regimeshiftsofecosystems[16,17,19,20].Regimeshiftsinanecosystemcanoccurnotonly basedonthemagnitudeofadriver[21],butalsotherateofchangeofadriver[22],theduration ofapulseddriver,andtheirinteractions[13].

Lag;Lagsalsocausenonlinearpatterns;forexample,laggeddynamics,legacy,antecedent effects,orecologicalmemory[3,23,24].Lagpatternsarequantifiablebylatentduration(the intervalbetweentheoccurrencetimingofthedriverandtheemergenceoftheresponse)and timetopeak(lowerleftofFigure2).

Inphysiologicalecology,lagpatternsthathavetheiroriginearlyindevelopmentbutthatarefirst seeninjuvenilesoradultsareknownas latenteffects [25].In individualecology,carryover

Figure2.BasicPrinciplesofTemporalDynamics.Ateachlevelofcomplexity,someuniquepropertiesaresummarized.Atsingle-eventlevel,forinstance,there arefourdifferenttypesofpatterns,threequantifiablecharacteristics,andtwoimportantnonlinearpatterns.Foralldrawings,thehorizontalaxisistimeandthevertical axiscanbeanymeasurablequantity.Driverandresponsearecategorizedbytheirshapebasedontype(upperpanels),andtheircharacteristicsarequantitatively measurable(middlepanels).Byconsideringthecombinationofdriverandresponse,driver–responserelationshipsmaygiverisetosomelevel-dependentpatterns (lowerpanels).

effectsarereferredwhenanonlethaleventduringapreviousseasonaffectsthecurrentstatus ofan individual ([26];notethat this definitiondiffers from ourdefinition ofcarryover which appearsinthefollowingsection).Storageeffects,linkingpopulationandcommunityecology, areamechanismthatexplainsspeciescoexistenceinachangingenvironmentbecauseeach species can benefit from a transient opportunity for increasing fitness [27]. In community ecology,a‘ghostofcompetitionpast’isinvokedwhenavoidanceofcompetitioninacurrent community is attributed to previous competition having led to niche separation [28]. In ecosystemecology,‘afterlifeeffects’and‘legacyeffects’describethepersistentimpactsof aspeciesandindividualonabioticorbioticprocessesofanecosystemaftertheir disappear-ance[29].Theirunderlyingcommonideaisthataneventinthepastpartiallyexplainsthecurrent behaviorofthesystem[3,9].

MultipleEventsLevel

Types

Multipleeventsarecombinationsoftwoormoreevents.Dependingonthenumberofdrivers andresponsesandtheirrespectiveeventtypes,weconsiderthefollowingfourtypes: single-typeunivariable,multitypeunivariable,single-typemultivariable,andmultiple-typemultivariable (uppermiddleofFigure2).Single-typeownsonlyoneeventtype(e.g.,repeatedpulses),while multitype owns more types such as pulse and press. A variable with various temporal characteristics belongs to multitype univariable (e.g., hydrologic regimes in a river where theflowshowspulse-typefloodsandpress-typedroughtsovertime[15]).Multivariable,for example,studiesmultiplestressors.

Characteristics

Thejointcharacteristicsofthedriversandresponsesaredefinable:forexample,theorder,the intervalperiod,andthefrequencyofoccurrences(centerofFigure2).Theorderofoccurrence canoftencausesignificantconsequencesinecologyandevolutionashistoricalcontingency

[30–34]. Patterns

AccumulativeCarryover;Carryoverpatterns,theeffectofadrivercanchangeaccordingto theprevious events,are about lags butemergeat the multiple-events level.Accumulative carryoveroccurs whentheeffects ofsequentialeventsadditivelyaccumulateovertime[8], becauseofashortintervalbetweenevents(lowermiddleofFigure2).Frequentdisturbances areacauseofdisequilibrium[9,17,35].Accumulativecarryovercausesinterestingdynamicsin whichathresholdismetbytheaccumulativeeffectsoffrequent,smalldisturbances. Interactive Carryover; Interactive carryover occurs when the preceding driver changes an internalparameterormechanismofasystem,suchthatthesystemrespondstoafollowing driverdifferentlyfromhowitwouldhaverespondednothavingexperiencedthefirstdriver.An antecedentdriver may amplify some characteristics of the responseof the system to the followingdriver(i.e.,synergism)orweakenthem(antagonism)(lowermiddleofFigure2).While accumulativecarryoverresultsfromashortintervalbetweenevents(addingup),interactive carryoverdoesnotnecessarilyfollowthisandcanhappenduetoadistantpastmemory. Interactivecarryovereffectsare oftenreported as physiologicalresponsesof organismsto sequentialtransientstresses as a defensivemechanism: for example, learning,imprinting, priming,andacquiredresistance[36,37](TableS1;seesupplementalinformationonline).Even organismslackinganervoussystemsuchasmicrobesandplantsshowinteractivecarryover

[36–38].Theinteractivecarryoveroccurring attheindividuallevel mayinfluence population

TrajectoryLevel Type

Trajectorylevelrepresentsthelong-termvariabilityofasystem,includingalargenumberof events:forexample,life historystrategy,community assembly,and succession.Trajectory typescan beclassifiedbasedonstatistical properties[8,41](4driver4responsetypes): Stationary, trend stationary, cyclostationary, and nonstationary (upper right of Figure 2). Stationaryassumestime-invariantmeanandcovariance,whichmayadditionallyfollowatrend (i.e., trend stationary) or cyclic pattern (cyclostationary; e.g. seasonality in temperature). Nonstationarydynamicschangemean,variance,and/orautocorrelationintime[42].Regime shiftsareanexampleofsuch[43].Yet,nonstationaryisfarlessstudiedthanstationarybut beingrecognizedasanimportantfeature[1,44,45].

Characteristics

Statisticalpropertiescharacterizetrajectorypatterns,includingmean,variance,and autocorrela-tion[5,8].Avarianceisoftenusedtoevaluatetheseverityofasingleevent(normorextreme). Age,thetimesincethesystememerged,isanotherkeycharacteristic(middlerightofFigure2). Several properties of single and multiple events may depend on the system age (e.g., emergenceor terminalphases). Ecosystemschange infunctional performancedepending onthesuccessionalstageofthecommunity(e.g.,youngandoldforestsdifferinginresource useefficiency[46]).Many systemsare the most sensitive to perturbations throughoutthe lifetimewhentheyareemerged.

Ecologists’interpretationsofthesamedriveralsovaryaccordingtosystemage:forexample,at thepopulationlevel,theeffectofindividualarrivaliscalledfoundereffectsattheestablishment phase of a local population [47] and called rescue effects at the terminal phase. At the communitylevel,speciesarrivalisstudiedaspriorityeffects ifalocalcommunityis sparse

[34]andstudiedasspeciesinvasionifthecommunitywasalreadyestablished.Consideringage clarifiesmanyecologicalcontexts.

Patterns

Divergence;Smalldifferencesmaycompletelychangethedynamicsofasystemandthusthe futuretrajectory[48](lowerrightofFigure2),knownasbutterflyeffectsinchaostheory[49]. Divergencepatterns have been often studied in the context of geneticsand evolution as historicalcontingency[33].Examples arematernaleffects attheindividual level,wherethe maternal genotype orphenotype influences the offspring phenotype [50]. Founder effects occuratthepopulationlevel,wheretheestablishmentofanewpopulationbyasmallnumberof individualsfroma larger populationdetermines thegenetic variationwithin the established patch[51]. Priorityeffects are at the community level, where the first arrivalof a species influences establishment success of the later-arriving species [34]. In evolution, adaptive radiationexplainsaprocessinwhichorganismsdiversifyfromanancestralspeciestoavariety offormsatanexceptionallyhighspeedwhenspeciesarriveinanovelenvironment.Contraryto adaptiveradiation,phylogeneticnicheconservatismistheresultofprocessesthatinhibittrait divergenceinrelatedlineages[52,53].

Convergence;Theideaoppositetodivergenceisconvergence,wheretherecentpastconditions mightbemoreinfluentialforthecurrentdynamicsofasystem,andthereforetheyareeventually independentofinitialconditions(lowerrightofFigure2;[1]).Convergenceisimplicitlyassumedin mostecologicalstudiesthatcorrelatedriversandresponsesasasnapshot,asthisassumption requiresonlycurrentorrecentpastinformationandallowsneglectingtheinfluenceoflong-distant past.Divergenceandconvergencejointlydeterminethedynamicsofasystem[31].

InteractionsacrossLevels

Recognizingthe inter-relatedness of single events,multipleevents,and trajectorylevelsis inevitabletounderstandtemporaldynamics.Forexample,theeffectofaphysiologicalstresson growthofanorganismisstudiedmostlyatthesingleeventlevel,butresultsmaygreatlydiffer dependingonbothrecentanddistant-pastexperiences[54].Thisisaretrospectiverecognition ofthe inter-relatedness. In this case, one can studythe possibility that lag and threshold patternsdependonwhatthesystemhasexperiencedpreviouslyandtheage.Onthecontrary, asaprospectiverecognition,onecanstudytheeffectsofastressorattheinfancystageonthe followingtrajectorydynamics.

Areviewemphasizestheneedofmodelingspeciesandcommunityresponsestoclimaticand ecological changes by taking paleo-information (i.e., trajectory) into account [55]. On the contrary, a single driver may determine multiple-event level consequences (e.g., warming determinesthedegreeofpriorityeffects[56]),andmultipleeventsdeterminetrajectory dynam-ics(e.g.,historicalhumanactivityinfluencesarcticvegetationdynamicsovermillennia[57]).Yet, theinter-relatednessofhierarchicalcomplexityisunderstudied.

Short-andLong-TermBenefitsofApplyingThisFramework

Short-TermGain:StudyDesignandImprovingPredictivePower

ThecomponentswesummarizeinFigure2 canbeusedas acomprehensivechecklistfor designingandevaluatingstudies(Box2).Referringtothesecomponentshelpswithplanninga time-relatedstudysystematically:whichlevelsofthecomplexityaretargeted;arecross-level interactionstested;whichaspectsoftemporalpatternsarequantified(e.g.,magnitude and interval);andwhatpatternsmayemerge(e.g.,lagandthreshold).Asareference,wehighlight someestablishedexperimentaldesignsandstatisticalanalysesinFigureS1(seesupplemental informationonline).Wealsoconsiderthatthepredictiveabilityto modeltheeffectsofpast conditionsonecologicalvariablescouldbesubstantiallyimprovedbydesigningstudiesand analyzingdatausingourapproach[3,58].

Thebasic principles we offer can promote the use of existing time-series data tobetter understand temporal dynamics [5,8]. Although many observations in ecology are either nonreplicatedor infrequently repeated [59], some databases and techniques are already available:forexample,theLongTermEcologicalResearchNetwork(https://lternet.edu/),the NationalEcologicalObservatoryNetwork(https://www.neonscience.org/),Ameriflux(http:// ameriflux.lbl.gov/),theglobalspeciestime-seriesdatabase[60],andanalysisof environmen-talDNA[61].

Short-toMedium-TermGains:ForIdentifyingGapsandTransferringConcepts

Similarconceptsmayhavedifferentnamesandareappliedindifferentfields.Identifyingsuch conceptual linkages can help transfer concepts from one ecological level to another. For instance:

Priorityeffects(i.e.systemcomponentsarrivingindifferentorder)atthecommunitylevel[34]

are conceptuallysimilarto founder effectatthe populationlevel[47].By transferringthe equivalentideatotheecosystemlevel,wecanaskifitplaysarolewhichcomponentofa nutrient cycleestablishesfirst(duringanew colonization)fordevelopingbiogeochemical dynamics.

Primingeffects(i.e.,aninitialstimuluspreparesasystemforasubsequentmoredeleterious stressor;nottheprimingeffectwhichreferstostrongshort-termchangesinorganicmatter decompositioninsoilscience[62]),originallydefinedatthe individuallevel[37] andthen

arguedtobeapplicableatthecommunitylevel[40],canalsobeconsideredatpopulation andecosystemlevels.Forinstance,doesapriormilderstressprovidegreaterresistanceor resilienceinanecosystemprocessrate?

Long-TermGains:TowardKnowledgeIntegrationacrossEcologicalFields

Theidea of hierarchical complexity opens the door to comparing among organisms with completelydifferentlifespans,suchasmicrobesandmacrobes(i.e.,irrespectiveofbiological hierarchyandtemporalscale).Hierarchicalscalecapturesthemultiscalenatureoftemporal dynamicsbyexpressingwhathappenacrossscales(e.g.,forestfirescanlastfromhoursto years,fromahundredmeterstohundredsofkilometers)[5,59,63–65].Bycontrast,hierarchical complexity describes the fundamental nature of temporal dynamics by expressing which patternsareobservedateachscale.

Theconceptofhierarchicalcomplexityrealizesthevalueoforganizingdisconnectedfieldsof research,includingimprovingcommunicationamongscientistsindisparatefields.Nearly60 conceptswecollected(TableS1;seesupplementalinformationonline)canbeusedtomake inroadstowardsunifyingterminology:

Using the same concept regardless of scale. For example, resilience is an ecosystem concept,butcoulditalsobeappliedtoindividuals,whereitiscurrentlynotusedbutinstead describedintermsofrecovery,eventhoughresistanceisusedequivalentlyatbothlevels. Creatingahierarchyofconcepts.Atabroaderlevel,wealsofoundthatmanyconceptscan beorganized ina hierarchicalfashion. Suchhierarchies could beused to unifydifferent Box2.TheConceptasaChecklisttoContextualizeStudyDesigns

Weheredemonstratehowtheconceptofthebasicprinciples(seeFigure2inmaintext)canbeusedasachecklisttosystematicallycategorizetime-relatedstudies, byintroducingsomeexamples:alaboratoryexperiment,statisticalmodelingframework,andmeta-analysis.

(A) Experiment:Theexperimentalstudy[54]investigatedtheeffectsofpastinundationordroughteventsonthesubsequentgrowthresponsesofplantspeciesto thesame,oppositeormorefavorableconditions(cf.primingeffectsexplainthataninitialstimuluspreparesasystemforsubsequentmoredeleteriousstressor; cross-protection,whichisprimingwithdifferenttypesofstresses).Theyfoundthatthepastinundationwasmorebeneficialforspeciesfromwethabitatsthan forothers,whilespeciesfromdryhabitatsacquiredthestrongestdroughttoleranceafteradroughtevent.Therefore,thisstudywasaboutcarryovereffectsat themultiple-eventslevel,forwhicheffectsizeswerepartiallyexplainedbythehistoricalpastatthetrajectorylevel,assummarizedinTableI(A). (B) Modelingframework:Thestatisticalmodelingframeworkproposedin[3]takesrecentpastfluctuationsintoaccountforexplainingthecurrentstatusofany

ecologicalsystem(e.g.,stomatalconductance,soilrespiration,ecosystemproductivity,andtreegrowth).Theydemonstratedthatmodelswiththerecentpast effectsincludedexplainedanadditional18–28%ofresponsevariationcomparedtomodelswithoutthem.Thisstudywasaboutexplainingthevarianceofa trajectorybyincludinglageffectsatthesingle-eventlevelandbothaccumulativeandinteractivecarryovereffectsatmultiple-eventslevel,seeninTableI(B). (C) Meta-analysis:Themeta-analysis[58]revealedthatsurvivalofprimedmicrobeswasabouttenfoldhighercomparedwiththatinnonprimedmicrobesbased onthefindingsfromover250trials.Thisstudyisameta-analysisaboutaspecifictypeofinteractivecarryovereffectsacrossmicrobes[i.e.,priming;TableI(C)]. Wedemonstratedthatsuchcategorizationinthestandardizedrulemakescomparisonacrossstudieseasier.Forinstance,theexamplesAandCshareasimilar focusbasedonthecategorization,andsimilaritywasmoredifficulttonoticebeforecategorization.Inaddition,thechecklist(TableI)allowsresearcherstoidentify whichaspectsoftemporaldynamicsareinvestigated,andmoreimportantly,whichofthemhavenotbeeninvestigated.Thissystematicassessmenthelpswith

findingnovelandunexploredaspectsoftemporaldynamics.

TableI.TheProposedConceptasaChecklistforEvaluatingStudyDesigns.

(A)Experiment (B)Modelingframework (C)Meta-analysis

Single Multiple Trajectory Single Multiple Trajectory Single Multiple Trajectory

Types Multitype univariable Applicabletoany types Multitype univariable Characteristics Theorderof

occurrence

Differentmeans Quantifiable Theorderof

occurrence Patterns Carryover observed Lag modeled Carryover modeled Convergence assumed Carryover evaluated Themostrelevantlevelsareinboldtype.

concepts.Forexample,theconceptofcarryovereffectsinpopulationecology,initself,has beenbroadlydefinedtooccur‘... inanysituationinwhichanindividual’sprevioushistory and experience explains their currentperformance ina given situation.’ [66].Thus, this conceptencompassesarangeofdynamics.

ConcludingRemarks

We propose hierarchical complexity as a fundamental concept that describes temporal patterns of driver–response relationship, based on the collection of nearly 60 terms and conceptsacrosssubfieldsinecologyandevolution(TableS1;seesupplementalinformation online).Wethinkthatusingthisconceptwilladvanceecologyandevolutionintwomainways. First,itprovides acommonlanguageforbettercommunicationamongecologists studying analogousconceptsindifferentsubfields.Second,itstressestheneedtoconsiderpastevents foradequatelyconsideringthecurrentandfuturestateofecologicalphenomena.Acrossall ecologicallevels, fromindividualto ecosystem,theecologicaldriver–responserelationships canbetemporallyvariantanddependentonbothshort-andlong-termpastconditions. Finally,we posean openquestion: canhierarchical complexitybeanucleusfor the developmentof atemporalecology[5](seeOutstandingQuestions)?Suchafieldwouldbeanalogoustospatial ecology,forexample,wherelocalandregional-scaleprocesseswouldbetheequivalentof short-term(multiple-event)andlong-termpast(trajectory).Whilespatialecologyhasflourishedasafield tostudythespatialnatureofecologicalphenomena,noequivalentexistsforthestudyofthe temporalnatureofecologicalphenomena.Therearebooksonspatialecology[67]butnoton temporalecology.Inaddition,wefound300000versus10000Googlesearchhitsoftheterms ‘spatial ecology’ and ‘temporal ecology’, respectively(on March 7, 2019). This situation is paradoxical,giventhatthereisnoshortageoftermsandconceptsrelatedtotimeinecology andevolution.Wethinkthetimeisripeforthedevelopmentofsuchafield.

Acknowledgments

TheworkwasfundedbytheGermanFederalMinistryofEducationandResearch(BMBF)withintheCollaborativeProject

“BridginginBiodiversityScience(BIBS)”(fundingnumber01LC1501A),byDeutscheForschungsgemeinschaftthrough supportforSFB973“Primingandorganismalresponsestostress”,bytheERCAdvancedGrant“GradualChange”,and bytheGrant-in-AidforJSPSOverseasResearchFellowships.

SupplementalInformation

Supplementalinformationassociatedwiththisarticlecanbefoundonlineathttps://doi.org/10.1016/j.tree.2019.03.007.

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