Methods Ecol Evol. 2018;9:457–459. wileyonlinelibrary.com/journal/mee3  | 457© 2017 The Authors. Methods in Ecology and Evolution © 2017 British Ecological Society

Received:17July2017  |  Accepted:19September2017DOI: 10.1111/2041-210X.12906

F O R U M

Adaptive parental effects and how to estimate them: A comment to Bonduriansky and Crean

Leif Engqvist1  | Klaus Reinhold2

1BehaviouralEcology,InstituteofEcologyandEvolution,UniversityofBern,Bern,Switzerland2EvolutionaryBiology,BielefeldUniversity,Bielefeld,Germany

CorrespondenceLeifEngqvistEmail:leif.engqvist@iee.unibe.ch

HandlingEditor:MatthewDavey

Abstract1. Tofullyunderstandtheevolutionofadaptiveparentaleffectsweneedtoreliablyestimatetheirmagnitude.

2. Recently,we(Engqvist&Reinhold,2016,Methods in Ecology and Evolution, 7, 1482) highlightedsomeimportantproblemswhenestimatingthemagnitudeofanticipa-toryparentaleffectsintheso-calledmatch/mismatchexperiments.Asthesigna-tureofsuchparentaleffectsisastatisticalinteractionbetweenparentalenvironmentand offspring environment, it will be difficult to disentangle these effects fromothereffectsdependingonacombinationofparentalandoffspringenvironment,suchascontext-dependentsilver-spoon(=condition-transfer)effects.

3. Inarecentarticle,BondurianskyandCrean(2017,Methods in Ecology and Evolution) suggestedtomanipulateenvironmentalqualityonacontinuousscaleandusingageometricframeworkasawayoutofthisdilemma.

4. Here,wehighlightanddiscussthebenefitsandpotentialdrawbacksof thesug-gestedmethod.Weconcludethatusingthisapproach,onemayextractmorede-tailedinformationbutunfortunately,itwillnotresolvetheinterpretiveambiguityinherentinthisexperimentaldesign.

K E Y W O R D S

adaptiveparentaleffects,condition-transfer,silver-spooneffects,statisticalinteractions

Intheirarticle,BondurianskyandCrean (2017)makesomevery im-portantand insightful remarkson the studyofparentaleffects.Wecertainlyagreewiththetenorofthearticlearguingthatthestudyofparentaleffectswillgainbyfocussingmoreonthepotentialadaptivevalueofwhattheyrefertoascondition-transfereffectsandwelcomethisscientificdiscussion.Nevertheless,asweidentifiedafewpoten-tiallyconfusingissuesregardingthefinalpartofthearticle,wheretheyintroducethegeometricframeworkasameanstostudyadaptivepa-rentaleffects,wefeelthatthiscommentisnecessary.

Very recently,we highlighted an important pitfall regarding theexperimental design aimed to study anticipatory parental effects(Engqvist & Reinhold, 2016). Such parental effects are similar tocondition-transfer effects—also referred to as carry-over effects orsilver-spooneffects (Uller,Nakagawa,&English,2013)—inthattheyboth constitute trans-generationally induced phenotypic plasticityinoffspring.However,thesetwoparentaleffectsarealsoinherently

different. Condition-transfer indicates that parent condition will induce higher offspring condition irrespective of offspring envi-ronmental quality (yet importantly, themagnitudemay be context-dependent).Anticipatoryeffects,ontheotherhand,cruciallydependonamatchbetweenparentandoffspringenvironmentalquality.Theconcernweexpressedinourarticle(Engqvist&Reinhold,2016),isthatinatwo-factorialdesignvaryingparentalandoffspringenvironmentalquality,thetwoparentaleffectswillbestatisticallyconfounded.Forafulltreatmentofthis,wereferthereadertoouroriginalarticle.Shortlystated, the problem is that this experiment cannot disentangle be-tweenanticipatoryparentaleffectsandcontext-dependentcondition-transfer-effects. For example, it may signify anticipatory effects ifoffspringaredoingrelativelybetterinagoodqualityenvironmentiftheirparentscamefromasimilarenvironment,butitmayequallywellindicatethatcondition-transfereffectsaremorepronouncedingoodqualityenvironments.

458  |    Methods in Ecology and Evolu on ENGQVIST aNd REINHOLd

TosolvethisproblemBondurianskyandCrean(2017)suggesttoexpandthelevelofmeasurementssothatbothparentaloffspringen-vironmentalfactorsspanabroadrangeoflevels.Byanalysingthedatawithinageometric framework, theyarguethat itwillbepossibletodetectcomplexinteractionsandnonlineareffects.Theyfurtherassurethereaderthat“[…]assessingoffspringperformanceacrossmultipleenvironmentswillmakeitpossibletodetectconditiontransfereffectsaswellasanticipatoryeffects,andtodeterminehowtheestimatedmagnitudesoftheseeffectsvarywithparentalandoffspringenviron-ment.”Theysummarizetheirargumentbystating“[…]parentalcondi-tion canbemanipulated simultaneouslywithoffspringenvironmentquality,providingadetailedpictureofhowparentalcondition-transfereffects interactwithoffspring condition.This approach canmake itpossible to detect condition-transfer effects, anticipatory effects,andcombinationsofbothtypesofeffects.”This isaverystrongar-gument,andassuch,thiswouldindeedbeatremendousprogressto

thecurrentstate-of-the-art.Unfortunately,BondurianskyandCrean(2017) providevery little details to support their argument andwethereforedecidedtoexamineitindetail.

In abstract theoretical terms, we can express parental carry-over effects combined with immediate offspring environmental ef-fects.Assumingclonal reproductionandnegligiblegeneticvariation,the expected offspring phenotype (Y) can be written as follows:Y= fP

(

xp)

+ fO(

xO)

+ fP×O(

xP, xO)

(cf. e.g. Kuijper & Hoyle, 2015).Here, xp and xO describes theparental andoffspring environmentalquality,respectively;thefP and fOarefunctionsthatdescribethephe-notypic effect of these, that is, the parental condition-transfer andimmediateoffspringenvironmentaleffects.Finally,fP×O isafunctionthat describes inwhichway the magnitude of potential condition-transfereffectsdependsontheoffspringenvironment.Ifweaddtheinfluenceofanticipatoryparentaleffects,weendupwithaverysimilarexpression: Y= fP

(

xP)

+ fO(

xO)

+ fP×O(

xP, xO)

+ fAE(

xP, xO)

. Here fAE

F IGURE  1 Schematicillustrationsoffourdifferentoutcomes,usingageometricframework.Coloursdepictincreasingoffspringfitnessfromlow(blue)tohigh(red).Linesareiso-fitnesslines.In(a)aspotlessanticipatoryparentaleffectscenarioisillustrated.Offspringarealwaysdoingbestthemoresimilartheenvironmentistotheoneexperiencedbytheirparents.In(b)asituationisdepictedwheremoderatecondition-transfereffects(seenasasubtleriseonthehorizontalplane)andstrongimmediateoffspringenvironmentaleffects(seenasanobviousriseontheverticalplane)actadditively.In(c)theeffectsfrom(a)and(b)arecombined.Theanticipatoryeffectsarelessobviousbuttheinteractionisstillvisibleasconcaveiso-fitnesslinescausingaridgeinthexy-plane.In(d)therearenoanticipatoryparentaleffectsandthecondition-transfereffectsarecontext-dependent,beingstrongerifoffspringenvironmentalqualityispoorthanwhenoffspringenvironmentalqualityisgood.Thisinteractionisvisibleasconvexiso-fitnesslinescausingadepressioninthexy-plane.Clearly,suchcontext-dependentcondition-transfereffectswillstatisticallyobscuretrueanticipatoryparentaleffects.Parametervalues:(a)fP= fO= fP×O=0, fAE=2 ⋅xPxO−x2

P−x2

O;(b)

fP=xP, fO=2.5xO, fP×O= fAE=0;(c)fP=xP, fO=2.5xO, fP×O=0,fAE=2 ⋅xPxO−x2P−x2

O;(d)fP=xP, fO=2.5xO + fP×O=−xPxO, fAE=0;seetextfor

furtherdetails

Parental environment quality

Offs

prin

g en

viro

nmen

t qua

lity

Parental environment quality

Offs

prin

g en

viro

nmen

t qua

lity

Parental environment quality

Offs

prin

g en

viro

nmen

t qua

lity

Parental environment quality

Offs

prin

g en

viro

nmen

t qua

lity

(a) Anticipatory parental effects only

(c) Anticipatory parental plus moderate condition-transfer and strong immediate environmental effects

(b) Moderate condition−transfer and strongimmediate environmental effects

(d) Context dependent condition−transfer effects

     |  459Methods in Ecology and Evolu onENGQVIST aNd REINHOLd

describesthephenotypiceffectattributabletothematch/mismatchof parent-offspring environments, that is, the anticipatory parentaleffects.

What is important is thattheeffectoffP×O and fAEwillbesta-tistically confounded within the parent-offspring-environment-interaction.They are both bivariate functions of the parental andtheoffspringenvironmentalqualityanditisthereforenotpossibleto vary them independently from each other in a straightforwardmanner.Ascanbeseenfromtheequationabove,thisdoesnotde-pendonthescaleofmeasurementofeitherparentalenvironment(xp)noroffspringenvironment(xO).Itthusdoesnotmatterforourargumentwhetherenvironmentalqualityismeasuredonadiscretescale(suchasgood/bad)oronacontinuousscale.InEngqvistandReinhold(2016),weillustratedtheproblemusingthediscretecase.The problem remains for the continuous case (see Figure1), con-trastingBondurianskyandCrean’s(2017)argumentthatthiswouldsolvetheproblem.

Insummary,wedonotwanttodiscourageresearchersinterestedinadaptiveparentaleffectstousethegeometricframeworkasout-linedbyBondurianskyandCrean(2017).Certainly,amorefine-tunedexperimentalvariationinparentalenvironmentalqualitywillallowforamore fine-tuned investigationof itseffects, suchas thedetectionofnonlinearpatterns,notfeasiblewithasimpletwo-factorialdesign.Nevertheless,itwillnotbyitselfresolvetheproblematicissueprevi-ouslyoutlinedbyus(Engqvist&Reinhold,2016).Itmaybepossibletorevealcomplexinteractionsusingthegeometricframework.However,it cannot reveal causality, that is, whether anticipatory effects orcontext-dependentcondition-transfereffectsarecausing the statis-tical interaction.We argue that sophisticated experimental controlsarenecessary for thispurpose, asoutlined indetail inEngqvist andReinhold(2016).

AUTHORS’ CONTRIBUTIONS

L.E.andK.R.togetherdiscussedtheargumentsandthegeneralout-line.L.E.draftedthefirstversionofthemanuscriptandK.R.providedcommentsandfinalisedit.

DATA ACCESSIBILITY

Thismanuscriptdoesnotincludeanydata.

ORCID

Leif Engqvist http://orcid.org/0000-0002-9434-7130

REFERENCES

Bonduriansky, R., & Crean, A. J. (2017). What are parental condition-transfereffectsandhowcantheybedetected?Methods in Ecology and Evolution,https://doi.org/10.1111/2041-210X.12848.

Engqvist,L.,&Reinhold,K.(2016).Adaptivetrans-generationalphenotypicplasticityandthelackofanexperimentalcontrol inreciprocalmatch/mismatchexperiments.Methods in Ecology and Evolution, 7, 1482–1488.

Kuijper,B.,&Hoyle,R.A. (2015).When to relyonmaternaleffectsandwhenonphenotypicplasticity?Evolution, 69, 950–968.

Uller,T.,Nakagawa,S.,&English,S.(2013).Weakevidenceforanticipatoryparentaleffects inplantsandanimals.Journal of Evolutionary Biology, 26, 2161–2170.

How to cite this article:EngqvistL,ReinholdK.Adaptiveparentaleffectsandhowtoestimatethem:AcommenttoBondurianskyandCrean.Methods Ecol Evol. 2018;9:457–459. https://doi.org/10.1111/2041-210x.12906