potentials from bottom-up models: Population dynamics and the Hubbert peak theory Arnaud Helias, Reinout Heijungs

To cite this version:

Arnaud Helias, Reinout Heijungs. Resource depletion potentials from bottom-up models: Population dynamics and the Hubbert peak theory. Science of the Total Environment, Elsevier, 2019, 650, pp.1303-1308. ￿10.1016/j.scitotenv.2018.09.119￿. ￿hal-02625523￿

HAL Id: hal-02625523 https://hal.inrae.fr/hal-02625523 Submitted on 26 May 2020

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Copyright Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal journal pertain. be it manuscript a This doi: from Please Accepted date: Revised date: Received date: T Reference: DOI: PII: Arnaud Hélias,ReinoutHeijungs dynamics andtheHubbertpeaktheory Resource Accepted Manuscript o appearin: is service Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 discovered 10.1016/j.scitotenv published is bottom-up cite a PDF depletion to this will our in which file article under models: customers its of Comment citer cedocument: potentials final could go as: an .2018.09.1 Population copyediting, unedited Arnaud form. af we 9 September2018 7 September2018 6 July2018 Science oftheT ST doi: S0048-9697(18)33561-7 from fect

Please are OTEN 28623 19 10.1016/j.scitotenv Hélias, the manuscript bottom-up dynamics providing typesetting, content, note Reinout that otal Envir models: and that this and during Heijungs and the has early all .2018.09.1 Hubbert review Population legal onment been the version , production Resource disclaimers accepted of peak 19 the of resulting theory the depletion for process that manuscript. publication. . Stoten proof apply errors potentials (2018), before to may The the As Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal accurately estimates assessment, cycle life in abioticthecase. theoryfor ecological we resources biotic for factors characterization for proposal original the confirmed expert wa proposals of series a depletion, impact environmental so uses assessment impact cycle Life Abstract E Address : Montpellier SupAgro, 2place Pierre Viala, 34060 Montpellier Cedex 1, France Corresponding author: 1105, 1081 e Einsteinweg 2,2333 d c France b a

Sustainable Engineering, Technische Universität Berlin, Berlin, Germany. Department Econometrics of and Operations Research, Vrije Universiteit Amsterdam, De Boelelaan L - Institute of Environmental Sciences (CML), Sciences Environmental of Institute E Resource from potentials bottom depletion mail: BE, Montpellier SupAgro, INRA, s, eerh ru fr niomna Lfcce n Ssanblt Assmn, Montpellier, Assessment, and Lifecycle Environmental for group Research lsa, trace the milestones of of milestones the trace - based models based Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119

[email protected]

- based

HV Amsterdam, The Netherlands

foundation for the biotic case, and extend it by a novel analysis of the Hubbert peak Hubbert the of analysisnovel a by it extend and case, biotic the for foundation ACCEPTED MANUSCRIPT

CC Leiden, The Netherlands from

(e.g. climate change, particulate matter, land use…). land matter, particulate change, climate (e.g. ACCEPTED MANUSCRIPT

Arnaud Comment citer cedocument:

relevant research areas. research relevant We the show Arnaud Hélias

Hélias ; ruet and arguments Phone : +334 99 61 2765 s based on heuristic and formal arguments, but without the use of use the without but arguments, formal and heuristic on based s

Univ that

Hubbert peaktheoryHubbert -

ald hrceiain atr t ades ifrn tps of types different address to factors characterization called the

Montpellier, Montpellier, France original .

a

[email protected] , Department of Industrial Ecology, Leiden University, Leiden Ecology, Industrial of Department b a ,c , Reinout Heijungs . agnl elto caatrzto factor characterization depletion marginal

1 the A recent study in using fish population models has models population fish using in study recent A

- up models: dynamics the population up and abiotic depletionabioticpotential, two decades for used ein o rsuc depletion, resource of designs ; FAX no :

d , e

fax numberfax

For the topic of resource of topic the For

of the nineties the of

eieig an delivering

obtained . Here . Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal mo convergence a such to attention draw we communication, short this In electromagnetism. into light and magnetism electricity, on theories A theory. general more a into theories original mutual converge, suddenlyinvestigation theoretical of strands different Sometimes, to shown be correspond to those disciplinary models. can proposals “heuristic” existing the of some surprisingly, moreover, and mining, av models disciplinary are there paper, this in show will we as slightlyembarrassingbut,facta situation, in “heuristic”considerations.on basedis This aredepletion the form to acceptedgenerallyare etc.) science, toxicology,(environmentaldisciplinesatmospheric specific from 2016) Jolliet, and (Frischknecht address to importantissue an resources, is generalmechanism, encompassingall a on based pathways 2017) al., et (Sonderegger concern of areas two first the for metrics (JRC of area three the over consequences global assess to approaches multidisciplinary includes This human changes. environmental from to interventions mechanisms causal of understanding the with chains value of description technical products and policies, in asystem activities, human of drawbacks environmental the quantifies (LCA) Assessment Cycle Life 1. abiotic resource, biotic resource Keywords published data. from Introduction - I, 2011) EIS, a Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 dynamic Lf Cce Impact Cycle Life :

ai o te seset oes te urnl pplr seset oes o resource for models assessment popular currently the models, assessment the of basis

Wis guidelines Whilst . ACCEPTED MANUSCRIPT model ACCEPTED MANUSCRIPT

f h aalbe reserve available the of Comment citer cedocument:

and remains the least consensual area of concern. The modeling of impact of modeling The concern. of area consensual least the remains and

. But while for human health and ecosystem quality, impact models impact quality, ecosystem and health human for while But . - seset (LCIA) Assessment wide perspective

concerns: human health, ecosystem quality and natural resources natural and quality ecosystem health, human concerns:

rvd mi picpe ad h crepnig assessment corresponding the and principles main provide

eet n h ae o te mat seset f resource of assessment impact the of area the in vement (Verones et al., 2017) al., et (Verones

famous . 2

(ISO, 2006a,2006b) hs s lutae fr 9 ea resour metal 29 for illustrated is This ,

hrceiain factor, characterization 1 9th century 9th ial fo fed lk fsey and like fields from ailable , the resource issue is still debated still is issue resource the , example is the merging of the the of merging the is example . An LCA study combines the agnl approach marginal ly reaffirming the the reaffirming ly e using ces such as such , Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal (BDP). potential depletion biotic a and (ADP) potential depletion abiotic an of basis the on resources (1995) Heijungs and Guinée 3.1 3. Resource depletion assessment: ahistorical survey ocean acidification and from for CFs of sets are there Nowadays, published were flows elementary of number increasing an for and categories impact different for CFs of Lists region. and/or compartment by differentiated are that CFs have to wa fresh (air, compartment categories impact of number the 1 or thousandsor1 against(hundreds than larger much is flows elementary of number the Usually, unit elementaryof flow DALY).or yr (in humanhealth or equivalent) m as such where contribution to an impact. The general structure was defined as characterization factors (CFs) that convert a like publications through cycl Life 2. and then move unification. their to depletion General impact assessment framework (199

Resource d 푚 Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 푓 , which is taking place now place taking is which , ipc assmn (CA ws ocpuly eeoe i te al nnte, mainly nineties, early the in developed conceptually was (LCIA) assessment impact e

3 is theis size of

or MJ) and MJ) or epletion potentials ( ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT the emission/extraction of type 퐼 푓 푐

Comment citer cedocument:

to to a c Fava et al. (1991, 1993) (1991, al. et Fava is the impact category indicator result, such as climate change (in kg CO kg (in change climate as such result, indicator category impact the is ter, etc.) and/or region (FR, NL, etc.), and as a consequence, it is possible is it consequence, a as and etc.), NL, (FR, region and/or etc.) ter,

respiratory diseases to loss of ecosystem services published a published ontribution to impact category

1992 . We will start by briefly sketching the different partial theories partial different the sketching briefly by start will We . 0

). As a further detail, the elementary flows may be specified by elementaryspecified thedetail, mayflows further be a As ). dozens - 1995) 퐼 “ 푐 proposal

= quantified

∑ f mat aeois rnig rm lmt cag to change climate from ranging categories, impact of 퐶 푓 퐹 1 푐 퐶 - 3 ,

1993 푓 ” 퐹 and

푐 is then the characterization factor that connects 1connects characterization thatfactor the then is for the construction of CFs for abiot for CFs of construction the for , 푓

푓 elementary (emission flow extraction) or into a

×

) Heijungs et al. (1992) al. et Heijungs

(usually kg, in occasionally but i 푚 푓

.

. . It relied on the use of use the on relied It .

fro tee as on. days these m ic and biotic and ic n other units ( 2 1 - )

Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal Oers and Guinée e.g. (see, part biotic the than more far elaborated and resourcesthey biotic For for recommendedapproach Sb kg in expressed then was score resulting The 푐표푛푠푡 where Guinée and Heijungs (1995) (1992) suggestion”, practical “a as made with In on fact, squared thein denominator: production) to (similar deaccumulation they seriousnes the indicating ... equation an ( reasoning heuristic on Based offer offer 푦 , they used used they ,

퐼 Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 and > 퐴퐷 0

a formula for assessing resource depletion on the basis of a characterization factor that has that factor characterization a of basis the on depletion resource assessing for formula a formal arguments, they argued that expressionthe

s h s the is , Fava et al. (1993) ol mk sne Te choice The sense. make would ( the same the 2016) ACCEPTEDand depletion abiotic for core MANUSCRIPT ACCEPTED MANUSCRIPT ) .

did not did Comment citer cedocument:

expression

the the

developed .

“ environmental both reserves and deaccumulation ... should somehow be included in included be somehow should ... deaccumulation and reserves both

propose a concrete referenconcrete a propose “ confirming

for a reference flow which was antimony for abiotic depletion. abiotic for antimony was which flow reference a for

퐶 { this approach s of depletion of s 푃 퐶 퐼 퐼 퐹 푓 퐵퐷 퐴퐷 퐹 푅퐷

in the numerator, and reserve (measured in som in (measured reserve and numerator, the in 푅퐷 , = = 푓 , 푦 푓 product = ” ∑ ∑ = =

- the more speculative schemes from schemes speculative more the 푐표푛푠푡 퐶 퐶 equivalent 4 퐼 1 푐표푛푠푡 퐵퐷 퐹 퐹

laig o the to leading , 퐴퐷 퐵퐷 both for abiotic and for biotic resources ” Guinée (1995), Hauschild et al. (2013), and (2013), al. et Hauschild (1995), Guinée

) and formal mathematics ( mathematics formal and ) s cr fr itc elto. o te constant the For depletion. biotic for score is , , footprint in in footprint 푓 푓 × × × × 푅 푚 ce. Indeed, ce. 푃 푚 푅 푃 푓 푦

푓 . This . 푦 푓 푓 + 2 푓 푓

1

an EU an is 푃 often / the abiotic part was cited, usedcited, was abioticpart the 푅 2 context

ye f oml ws then was formula of type used in LCA in used unit independence unit (Fazio et al., 2018) al., et (Fazio

Heijun

and e way) e

gs et al. et gs it is va the 푅 ( ( ( 4 3 2 ), 푓 n . ) ) )

Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal impacts two into resources technical the in stored system). materials (raw one anthropogenic the reserve ultimate the to addition in curr with resources (available base reserve the whereas element the of content crustal the reserve, ultimate the was concern of point In 3.3 unreasonable Perhaps it validis within a limited range of values not is it believe we but here, assumption strong a course of is shape parabolic The From this 퐷 damage some is response the denominator. the in reserve the of square the and such about assumption reasonable approach ADP the of foundation disciplinary a provide C derive type a In 3.2 = response . Other related work (1997 Depletion potentials as derivatives (1997) 퐷 university oe fr eciig h rlto bten eore s ad elto ipc cn e sd to used be can impact depletion and use resource between relation the describing for model ( Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 푃 Fs. 1 Another Another general ( , 푃

This is the first proposal to use a partial derivative for resource impact assessment and to and assessment impact resource for derivative partial a use to proposal first the is This 2 o these to , …

report, report, ) . Non non proposed ACCEPTED MANUSCRIPT

the considered reserve considered the nta dvlpet, eea cags ee rpsd by proposed were changes several developments, initial - ACCEPTED MANUSCRIPT - Heijungs et al. (1997 p. 34 p. (1997 al. et Heijungs LCA linea Comment citer cedocument: .

S ) - rity is introduced avery in simple way: as a parabolic function:

change ee 2017) relation, CFs van Oers & Guinée (2016) Guinée & Oers van 퐷 퐶

a

u t ttl production total to due 퐹

푅퐷 model would to a CF with with CF a to lead would model is is

, 푓 h splitting the = for use in LCA 퐷 . 휕 휕퐷

푃 Guinée and Heijungs and Guinée

ent practices). ent 푓 = = ∑

. In our notation, the notation, our In 5

2 푓 푅

- 푃 36) ( 푓 2 푓 푅 푃 Or e a. 2002) al., et (Oers = 푓 푓

) icse o non a how discussed 2 푐표푛푠푡

. are derivedare as partial derivatives:

ad h “dose the and , for details. for n atclr te soe hw quite a how showed they particular, In

Schneider et al. et Schneider × JRC 푅 푃 ( 푓 푓 2 1995

-

EIS “dose” is the production the is “dose” the extraction in the numerator the in extraction the These changes have important havechanges These ) and ) (

2011) f iea ad energetic and mineral of -

epne i a function a is response” ( - 2015, 2011) 2015, Oers et al. al. et Oers linear linear various

decided considering decided “ dose

authors (

2002) considered -

response 푃 . 푓

used

One and ( ( 6 5 ” . ) )

Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal 3. 2015) CFs determining way consensual the domain relevant the from knowledge the on based context this In marginalthe change and determining the CFs. depletion). stock (the impact the to extraction) resource th linkingmathematicalrelationship a define to possible thus is It literature. simulating t illustrates 1 Figure 3. this paper, we will further restrict the focus to the 2015) of term based is principle different completely a of ore of amount Müller 2001; Spriensma, of decrease the account into applied the within variations such Besides extractionthe but results, the for consequences 4 4 .1 . Characterization factors from bottom Population dynamics (2 ) .

. All of this supports the use of this approach. Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119

exergy Dewulf et al. et Dewulf to assess resource assess to

the evolution of the exploitation rate, stock dynamics models dynamics stock rate, exploitation the of evolution the

to to reserve squared ratio. , . A third example is the is example third A . mined per additional unit of resource extracted resource of unit additional per mined

ACCEPTED the of model new development of the MANUSCRIPT he approach used to define CFs from bottom from CFs define to used approach he

( ACCEPTED MANUSCRIPT 2015 - Comment citer cedocument: wenk, 1998) wenk, depletion ) and ) ore grade and grade ore 018)

Sonderegger et al. et Sonderegger the 푅 푃 issues 2 Insert FigureInsert 1about here mathematical

,

framework, completely different completely framework, supply risk supply associated cost increase cost associated Fickeh ad ole, 06 Hucid n Huijbregts, and Hauschild 2016; Jolliet, and (Frischknecht - up models . corresponding

For instance, For on

hroyai accounting thermodynamic 푅 푃 6 . 2

based on the on based

In addition, t addition, In relationship remains identical in all these works: these all in identical remains relationship approach.

( 2017) involved mechanisms is not needed not is mechanismsinvolved T

he partial derivative is is derivativepartial he surplus energy requirement energy surplus t he

provide more comprehensive more provide future effort future

(Vieira et al., 2017) al., et (Vieira

criticality conceptcriticality (Goedkoop et al., 2013) al., et (Goedkoop he marginal approach is now one of one now is approach marginal he - up model. Based on empirical data empirical on Based model. up methods were methods s have been have

e human intervention (the humanintervention e were

(Dewulf et al., 2007) al., et (Dewulf then addressed (Sonnemann et al., et (Sonnemann . Another example Another

used expressing used proposed in the in proposed (Goedkoop and (Goedkoop proposed and proposed , or ,

, reviews so

by taking by the extra the CFs are CFs .

In in Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal the of purpose The availability. resource assess to stock) the of characteristics internal and (size and properties (catch) constraints external represent in used models dynamics Population 3. constant may per differ well) as resources biotic other for conjecture, CF dynamics, population in model standard a from words, other In T a decrease of indicator damage t introducing by done deaccumulation between see respectively, habitat the of dynamicspopulationliterature Here equation (1954) Schaefer to stocks fish of dynamics population Recently, he characterization factor thenis derived from the resulting 4 .2

Hubbert peak ( 푟 푓 Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119

and éis t al. et Hélias 푅 퐾 푓 푓

. a of change of rate the expresses

. In

r species are The associated elementary flow elementaryassociated The

ACCEPTED MANUSCRIPTsteady this paper he depleted stock fraction (DSF, in bracket in equation 7 equation in bracket in (DSF, fraction stock depleted he ACCEPTED MANUSCRIPT population (2018) Comment citer cedocument: ( - 푃 state ( state 푓 ) -

and maximal regeneration ( regeneration maximal and

eedn prmtr (h symbols (the parameters dependent ) 퐶 and correspond to the intrinsic growth rate and to the carryingthecapacity and to growth intrinsicthe rateto and correspond

applied 퐹 푑 éis t l (2018) al. et Hélias 퐹퐷 푑푡

푅 of of fish. 푓 , 푓 푑 = 푑푡 = 푅

derive an expression for CFs of fish. The standard model by model standard The fish. of CFs for expression an derive 푓 this 0 − ) =

we have 휕퐷푆 − 휕 procedure 퐷푆 푅 푃 퐹 푓 푓 푓 퐹 which + 푓 =

7

population size ( size population = is a ma a is : 푟

푓 푟 푓 푃 푅 푟

푓 푓 푃 eae like behave 푓 o details for 2 o boi resources. biotic for 푅 푓 ( 푓 = 1

ss of fish removed from the sea, that means that sea, the fromremoved fish of ss 푟 − 푓 푐표푛푠푡 푅 expression: 퐾 푅 푓 푓 푓 ) ) , the limitation of the habitat the of limitation the ,

푓 ). × 푅 푃 s hs oe ad i te balance the in adds model This

푓 푟 / 푅 푃 can be derived for fish (and, we (and, fish for derived be can ) of fish type fish of )

푅 푓 푓 2

and 2

.

n sal oe s ht the that is note small One 퐾 They used used They

) r csoay n the in customary are

which 푓

as

is taken as the as taken is

the theory of of theory the a differential a . This

( ( ( is 9 8 7 ) ) )

Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal (2017) Scholz adapt). to easier it makes flexibility market's the (where ones driven demand or threat) the issue situation the of urgency the highlight authors some When topic. discussed highly a is availability resources of estimation The equivalence between steady at one Schaefer the to similar is equation Hubbert the that Note reserve) resource. given the of parameter parameter The resource since the beginning exploitation the of ( rate extraction the model, curve Hubbert the In 1956) 1981, t in usedrelation the also is economics. This and biology, chemistry ecology, management, stock as such domains many in applied is curve logistic the centuries, two i an describes SchaeferThe population dynamics model based is onthe very common logistic function. relationThis current production and stock description.It is interesting look to at parallelthe we draw. can estimation the similar: is resource abiotic for modeling

an rvr f h pouto rts ewe spl die rsucs wee h dpein s a is depletion the (where resources driven supply between rates production the of driver main (Tilton et al., 2018) al., et (Tilton Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 , this is rewritten as follows

and it is remarkable that the Schaefer and Hubbert models date back to the same period. same the to back date models Hubbert and Schaefer the that remarkable is it and nitial exponential increase, which is then slowed down to a limit value. In use for nearlyfor use Invalue.limit a todown slowed then is exponentialwhichincrease,nitial

d 푈 iscuss this point and underline that a Hubbert shape model hardly predicts peak time peak predicts hardly model shape Hubbert a that underline and point this iscuss 푏 Hubbert model defines the spreadingthe defines model Hubbert 푓 푓

is the initial ultimately extractable reserve extractable ultimately initial the is

ACCEPTED MANUSCRIPT time (in extraction cumulative of rate growth intrinsic the is 퐾 푓 ACCEPTED MANUSCRIPT

(Ali et al., 2017) al., et (Ali (viewed as Comment citer cedocument: . All These positions can be roughly synthetize through the establishing of establishing the through synthetize roughly be can positions These All .

the maximalthe size the of population) and 푃

푓 = 푃

others are less pessimistic, without d without pessimistic, less are others 푓 푑 푑푡 = 푄 푓 푏 = 푓 푄 푅 푃 푏 푓 푓 8 푓 푓 ):

( 푄 cumu the of function a is

1 푓 over the time the over − ( 1

푈 푅 frsuc aalblt i acrac with accordance in availability resource of − 푓 푓 ) 푈 푄

. With . 푓 푓 )

he Hubbert peak theorypeakHubbert he of the curve the of 푄 푓 = - state state 푈 푈 푓 푓 lated mass of extracted of mass lated . − ismissing the depletion the ismissing

when

푅 and 푓

( 푅 is constant for a for constant is − 푓 1 osdrn an considering . hs shape This ).

is the current the is Wellmer and Wellmer

(Hubbert, ( ( 10 11 ) )

Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal 4 Hubberton the peak theory. subscript thechanged have we where Hubbert theory: derivative partial of use The inventory. the of change marginal the to according impact the of change marginal reservecurrent removedresource,fromthe extracted 퐷푅 about correspondences between PAF andPDF). species of fraction of area quality ecosystem species is there that Note depletion. the with one towards tends and resource exploited never a for zero to equals fraction This depleted stock low therefore with mines of type each describe mine to dedicated from silver necessary as independently sometimes is it (although consumptions resource peak. extraction the of year ultimate the predict to model Hubbert the of interest the nothere discussing are We fitting. good for passed be to has peak the that or reserve the of knowledge a without . Empirical comparison classicalof 퐹 푓 is taken is Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 (PAF) resource therefore makes it possible to define the CF of the resource depletion on the basis of the of basis the on depletion resource the of CF the define to possible it makes therefore as the impact to assess for the resource depletion. The inventory flow is then a mass of mass a then is flow inventory The depletion. resource the for assess to impact the as n idrcl wt te oeta di potential the with indirectly and

, from , fraction (

ACCEPTED MANUSCRIPTin the ecosystem (PDF) missing in the nature (see nature the in missing (PDF) ecosystem the ACCEPTED MANUSCRIPT a Comment citer cedocument: conceptual point of view, an analogy with the potential affected fraction of fraction affected potential the with analogy an view, of point conceptual concern 퐷푅

hs model This 퐶 퐹 푓 퐹 - 퐻퐷 = grade ores). We use the shape of the model to describe the current the describe to model the of shape the use We ores). grade . They represent the represent They , 1 푓 퐴퐷 −

=

and Hubbert 푈 푅 −

푓 푓 from the classical abiotic depletion todepletion abiotic classical the from ) 휕퐷푅 shape

휕 퐷푅 푅 wt high with s 푓 퐹 푓 퐹

푓 = is el numerous well fits 9 = apae fato o species of fraction sappeared

푏 - 푃 푓 based ADP 푏 푅 푅 푓

푃 푓 푓 fraction 푓 2 푅 푓 .

푓 = The use of the ofuse The

- rd oe ad ivr s co as silver and ores grade 푐표푛푠 of individuals of species (PAF) or the or (PAF) species of individuals of 푡

푓 × 푅 푃 Woods 푓 푓 2 observed

marginalapproach ly recoverable reserve or the or reserve recoverable ly

et al., (2017) al., et 퐻퐷 yais f abiotic of dynamics (PDF)

for the one based one the for - rdc from product sd o the for used

relatesthe for details for ( ( 12 13 ) )

Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal parameters two these by determined t between are values reserves in estimates peak extraction the (e.g. magnitudes yr 푈 parameter shape this model, Hubbert the In value visually correlation, parameter a with equations between difference The (4) in 3 expected the from (2017) extracted cumulative o amount reservesrecoverableultimate of computation which of work the used we data, shared with approaches both for CFs compute To × ) 푓 − , with the relation the with , yr , 1

a value ten tim ten value a − for to to platinum for 1

≪ Sverdrup et al. , Table 2) Table , for for Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 rvds consistent provides 0 ( re quality grading” by grading” quality re 푅 . 001 푏 푓 elru and tellurium 푓 ) and the and )

vrrp t l (2017) al. et Sverdrup for for

(based on the Pearson correlation between the logarithms the of two sets of CFs) , both

퐶 and allows to determine to allows and ie (antimony fixed es bigger means a depletiontimestenfastera bigger means es 퐹 ACCEPTED MANUSCRIPTmaximum

퐻퐷 2.7 in Figure in 푏 ( extraction rates ( rates extraction 2014) 7.7 amount 푓 classical ACCEPTED MANUSCRIPT . × = The two CF two The 10 × Comment citer cedocument: h two the 1.3 10 4 푈 4 푀 ).

estimates 푓 −

t 푓 × (URR) 2 production rates production

2 푄

10 for obtained from the logistic model equation model logistic the from obtained , and statistically through the the throughstatistically and , yr 푓 ADP Sverdrup et al. (2017) al. et Sverdrup 9

“prxmtl aon dg p eoe 2010” before up dug amount (“approximately approach - 1 emnu and germanium t based) based)

× . Therefore, while theoretically Hubbert theory Hubbert theoreticallywhile Therefore, . oe the over )

o tnse. So, tungsten. for s estimated are used as as used are estimated yr values

푃 f ecitr fr 9 iea reserves, mineral 29 for descriptors of and − f resources of 푓 1 Figure ) for for

are spread over seven orders of magnitude (the boundaries (the magnitude of orders seven over spread are the u es Hubbert i conversion nit are thus not thus are 푏 , 푓 rn for

current ( 퐶 gives the intrinsic speed of the depletion the of speed intrinsic the gives e of set 푀 2 퐹

10 푓 about here 퐴퐷

, also , 2.4

-

, 푓 ae ADPs based il cu i dcds r centuries or decades in occur will

× resources reserve , see Table 2) Table see , and 푏 푃 10

푓 푓 directly comparable. But we can study their study can we But comparable. directly provided

). That means the the means That ). 11 푈 ais vr o oe hn w odr of orders two than more no over varies 퐶 factor

t correlation coefficient correlation

. (named “URR estimated by extractableby estimated “URR (named 푅 for for 퐻퐷 Values are distributed are Values between

푓 considered . The . ,

푓 rn for iron by for rm h sm dt suc. The source. data same the from le i the in lies , , it also gives estimations of of estimations gives also it , these authors these 퐶 푏 퐹 푓

퐴퐷

(see for example Equation example for (see parameters are determined are parameters 푅 I cnrs, the contrast, In .

푓 n a and

, Sverdrup et al. (2017) al. et Sverdrup CF

n between and constant and by value - , “P , based ADPs based 푟 resource

vrrp t al. et Sverdrup = allow MAX s 0 : for a given a for :

. part of of part are se peak see , 99 ” s

- in Table in

1.2 specific with with o the for current mainly 5 .

× have × 10 10 the the 푝 − - 2 3 ,

Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal Funding 2016) derivativesdose frompartial are CFs where LCIA, Moreover, paper). relevant 1992) al., et Heijungs 1995; Heijungs, nineties early the in ADPs the to lead that arguments heuristic The define. stock) (anthropogenic technopshere the in usable quantity the and environment the in reserve extractable the merging one, t and extraction the combining models, complex more on approach marginal a be could interest of point Another 2017) resources of depletion the assessing use model logistic concern of area resource ab and biotic is it like on based is design CF the that implies marginalADP asa approach ADP. theforfoundation new a addspaper averageapproachesclassification. This versus marginal the before reasoning, useful and pragmatic of basis the on proposed initially was ADP The 5 estimator a

. better Conclusion . .

Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 theoretical foundationtheoretical

disciplines, both for biotic resources biotic for both disciplines,

for other impact other for for the the oi resources iotic

he recycling dynamics. However, this changes the assessed stock: assessed the changes this However, dynamics.recycling he CF i te ubr pa theory peak Hubbert the in d the resource depletion potential design potential depletion resource the ACCEPTED MANUSCRIPT derived . ACCEPTED MANUSCRIPT hs prah a tu t b dsusd ute a further discussed be to thus has approach This , which is a hot topic in LCA in topic hot a is which , Comment citer cedocument:

categorie

. as a as applied onresource dynamicmo

ial, this Finally, than the more heuristic original ADPheuristicmoreoriginal the than marginal depletion s. , relating to damage cost cost damage to relating , The models we have discussed suggest discussed have we models The

a

r bce u b a epr hoeia fudto fo the from foundation theoretical deeper a by up backed are model

ol cnrbt t a oe osnul aha fr the for pathway consensual more a to contribute could (Hélias et al., 2018) al., et (Hélias

which was which 11 s lo used also is - response type of models of type response

characterization (Sonderegger et al., 2017) al., et (Sonderegger now fits better in the overall the in better fits now

developed in the relevant research fields research relevant the in developed dels dels n vr dfeet LCIA different very a in ae on based offers interesting perspectives. This

and and for abiotic resources (this resources abiotic for and and s,

factor the (Fava et al., 1993; Guinée and Guinée 1993; al., et (Fava original upu cost surplus from d h ascae models associated the nd

(Frischknecht and Jolliet,(Frischknechtand

a similar approach for approach similar a the Hubbertthe ADP is a is ADP it would be a wider a be would it . Interestingly, the the Interestingly,

Ver e al., et (Vieira framework of framework Considering method very curve good

. for

, Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal 2018. D., E, L., Zampori, M., Secchi, E.M., Schau, S., Sala, V., Castellani, S., Fazio, A 1991. A., Barnum, S.E.M., Selke, B., Vigon, M.A., Curran, B., Jones, R., Denison, J., Fava, 1993. B., Vigon, T., Mohin, K., Dickson, R.,Denison, F., Consoli, J., Fava, S., Hellweg, H., Langenhove, Van G., Vorst, Der Van B., Meester, De M.E., Bösch, J.J., Dewulf, J., Maes, M., Recchioni, F., Ardente, G.A., Blengini, S., Sala, L., Mancini, L., Benini, J., Dewulf, Enriquez, R., Durrheim, A., Demetriades, G., Brown, E., Nickless, N., Arndt, D., Giurco, S.H., Ali, References not or commercial, public, the in agencies funding from grant specific any receive not did research This - for requires resource governance. Nature 543, 367 for supply R., Mineral 2017. Schodde, N., Yakovleva, J., O., Salem, Vidal, G., R., Schneider, Oberhänsli, L.D., Meinert, A., Littleboy, J., Kinnaird, M.A., information to the characterisation factors of recommended EF Life Cycle Impact Assessment Impact Cycle Life EF recommended of factors characterisation the to information Chemistry and life for framework technical SETAC life for 5310 accounting. Environ. resource for method assessment environment impact natural cycle life the comprehensive 49, A from (CEENE): extraction exergy Cumulative 2007. M.A.J.J., Huijbregts, Technol. M.A Huijbregts, Sci. Environ. Assessment. https://doi.org/10.1021/acs.est.5b00734 Cycle t Rethinking 2015. D., Pennington, R., Pant, - Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 profit sectors.profit

-

yl ipc assmn. oit o Evrnetl oiooy n Ceity and Chemistry and Toxicology Environmental of Society assessment. impact cycle Foundation Environmentalfor Education, Pensacola, USA. ACCEPTEDSci. Technol. 41, 8477 MANUSCRIPT SETAC Foundation Environmentalfor Education, Pensacola, USA.

JJ, ese, . e Vrt G Vn e, agnoe H Vn Hlwg S., Hellweg, Van, H. Langenhove, der, Van G. Vorst, De, B. Meester, .J.J., ACCEPTED MANUSCRIPT Comment citer cedocument: - yl assmns Scey f niomna Txclg and Toxicology Environmental of Society assessments. cycle – 8483. https://doi.org/10.1021/es0711415

12 he Area of Protection “Natural Resources” in Life in Resources” “Natural Protection of Area he –

372. https://doi.org/10.1038/nature21359

A Conceptualframework A utial development sustainable

Supporting

– 5317. Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal use, land and resources natural for categories Impact 1997. G., Huppes, J.B., Guinée, R., Heijungs, Hauschild,Assessment,ImpactCyclein: Introducing 2015. Huijbregts, Life M.A.J., M.Z.,Hauschild, M., Goedkoop, M.Z., Hauschild, usefor equivalencyresourcefactorsof definition the proposalfor A 1995. Heijungs,R., J.B., Guinée, life environmental the for methodology a of Development 1995. J.B., Guinée, Eco The 2001. R., Spriensma, M., Goedkoop, Goedkoop, M., 2016. (Eds.), O. Jolliet, R., Frischknecht, 2008 indicators https://doi.org/10.2760/671368 meth CML report 138.Leiden, The Netherlands. https://doi. ImpactCycleNetherlands,LifeAssessment. (Eds.), 1 Springer M.A.J.M.Z., Huijbregts,pp. https://doi.org/10.1007/s11367 68 Assess. Cycle Life J. Int. assessment. impact cycle life in modeling characterization 2013. S., Sala, A., Laurent, S., Humbert, De, A. Schryver, life https://doi.org/10.1002/etc.5620140525 product in products. With a case study on margarines. Leiden, The N Netherland. Methodology Assessment Impact Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 od. -

First editionFirst (revised)

— Heijungs, R.,Huijbregts, De M., Schryver, A., Zelm, Struijs, Van J., R., 2013.ReCiPe org/10.1007/978

volume 1.UNEP/SETAC Life Cycle Initiative, Paris. ACCEPTED MANUSCRIPT Ispra. JRC109369, Commission, European EN, 28888 EUR ACCEPTED MANUSCRIPT Comment citer cedocument: - yl assessment. cycle -

94 Guinée, J.B., Heijungs, R., Huijbregts, M., Jolliet, O., Margni, M., Margni, O., Jolliet, M., Huijbregts, R., Heijungs, J.B., Guinée, -

- Report I:Report Characterisation. TheHague, Netherland. -

017 012

- - 9744 0489 --

- - - indicator 99 A damage oriented method for method oriented damage A 99 indicator ehdlg Rpr. r Cnuat Amersfoort, Consutant, Pré Report. Methodology 3_1 5 lbl udne o lf cce mat assessment impact cycle life for guidance Global

13

nio. oio. hm 1, 917 14, Chem. Toxicol. Environ.

etherlands. Identifying best existing practice for practice existing best Identifying

- yl assmn of assessment cycle

Life Cycle Life 3 – – – 697. 925. 16. Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal deple resource Abiotic 2002. G., Huppes, J.B., Guinée, De, A. Koning, Van, L. Oers, Müller JRC managementEnvironmental 14044:2006 2006b. ISO, management Environmental 14040:2006, 2006a. ISO, Practice. Production and Drilling Fuels, Fossil the and Energy Nuclear 1956. M.K., Hubbert, 1007 49, Phys. J. Am. system. energy evolving world’s The 1981. M.K., Hubbert, Fréon J., Langlois, A., Hélias, H.A.,WegeneHaes, de UdoLankreijer, G.,R.M., Guinée, Huppes, R., J.B., Heijungs, - I, 2011. EIS, biotic biotic resources depletion. Fish.Fish press.in https://doi.org/10.1111/faf.12299 Leiden, Netherlands.The Assessment of Products Cycle Life Environmental 1992. H.P., Goede, de R., Duit, van P.G., Eggels, A.M.M., Ansems, Dutch LCA Handbook. new the in recommended as depletion resource abiotic for factors characterisation Improving gradelower deposits used in future. IWÖ Diskussionsbeitrag Nr. 57. Luxembourg. Union, European the https://doi.org/10.27 of Office Publications Commission. European 2011, EN 24571 EUR context European the in Assessment Impact Cycle Life for Recommendations guidelines, CEN Central secretariat. International Organization for Standardization. framework, CEN Cen American PetroleumInstitute, New York. https://doi.org/ - Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 ek R, 98 Dpein f boi rsucs egtd n ae f vrul ipcs of impacts ” virtual ” of base on weighted resources abiotic of Depletion 1998. R., wenk,

ACCEPTED MANUSCRIPT10.1119/1.12656 nentoa Rfrne ie yl Dt Sse (LD Handbook: (ILCD) System Data Cycle Life Reference International ACCEPTED MANUSCRIPT Comment citer cedocument: 8/33030 tral secretariat.tral International Organization for Standardization.

-

, P., 2018. P., , Vol1: Guide Vol1:

Fisheries in life cycle assessment: Operational factors for factors Operational assessment: cycle life in Fisheries -

October 1992.October Centre Environmental of Science (CML),

14

— —

Life cycle assessment cycle Life

ie yl assessment cycle Life

Requirements and Requirements —

r Sleeswijk,A., r rnils and Principles tion in LCA in tion

– 1029. - -

Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal Humphreys, J.I., Guzmán, M., Ericsson, R.G., Eggert, J.H., DeYoung, P.C.F., Crowson, J.E., Tilton, rates, mining copper global the modelling On 2014. D., Koca, K.V., Ragnarsdottir, H.U., Sverdrup, as sustainabilitysupply metal of assessment An 2017. D., Koca, Ragnarsdottir,K.V.,H.U., Sverdrup, Sonnemann, G.,Gemechu, E.D., N., Adibi, De Bruille, Bulle, V., C.,2015. Vieira, F., Verones, F., Stoessel, S., Pfister, D.M., Souza, de P., Fantke, J., Dewulf, T., Sonderegger, depletion abiotic extended stock anthropogenic The 2011. M., Finkbeiner, M., Berger, L., Schneider, Schneider, L.,Berger, M., Finkbeiner, M., 2015.Abiotic resource depletion LCA in managementthe theof dynamicsimportantto populations ofthe ofSome aspects1954. M., Schaefer, potential ( AADP ) as a new parameterisation to model the depletion of abiotic resources 929 resources abiotic of depletion the model to parameterisation new a as ) AADP ( potential CycleLife Assess. J. Int. model. (AADP) potential depletion abiotic extended stock anthropogenic the of update commercial marine fisheries. Bu uue iea sple. eor Plc 5, 55 57, Policy Resour. supplies. mineral future Lagos, D., 174. https://doi.org/10.1016/j.resconrec.2014.03.007 158 87, Recycl. Conserv. Resour. reserves. copper of end the and price copper supply, market scarcity. J.Clean. Prod. 140, 359 sec policy: to input an Assessment. J. Clean. Prod. 94,20 criticali the integrating for framework conceptual https://doi.org/10.1007/s11367 cycle life in protection 2017. S., Hellweg, B., Weidema, M., 936. htt Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 ps://doi.org/10.1007/s11367 G., Maxwell, P., Radetzki, M., Singer, D.A., Wellmer, F.W., 2018. Public policyand Public 2018. F.W., D.A.,Wellmer, Singer, M., Radetzki,P., Maxwell, G., ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT 20, 709 Comment citer cedocument: rt o spl etato rts stocks rates, extraction supply of urity

– mat assessment. impact 721. https://doi.org/10.1007/s11367 - 017 ll. Inter –

372. https://doi.org/10.1016/j.jclepro.2015.06.085 – - 34. https://doi.org/10.1016/j.jclepro.2015.01.082 - 1297 011 - - oad hroiig aua rsucs s n ra of area an as resources natural harmonizing Towards American Trop. Tuna Comm. 1,27 0313 - 8

15 -

7

n. . ie yl Ass. 2 1912 22, Assess. Cycle Life J. Int. ty of resources into Life Cycle Sustainability Cycle Life into resources of ty

- 015 - in - - s, eyln, n rs of risk and recycling, use, 0864 From acritical review toa - 0 –

56. —

background and

– 1927. – 60. – – Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal Fant M., Damiani, J.S., Woods, mineral of history the from learn we can What minerals: Peak 2017. R.W., Scholz, F.W., Wellmer, Vieira, M.D.M., Ponsioen, Goedkoop,T.C., Huijbregts, M.J., M.A.J., 2017. Surplus Potential Ore as a Jolliet, A., Henderson, S., Hellweg, M., Hauschild, R., Frischknecht, C., Bulle, J., Bare, F., Verones, Potential: Depletion Abiotic The 2016. J., Guinée, L., Oers, van . Fnk, . 21. CA rmwr ad cross and framework LCIA 2017. P., Fantke, M., Vieira, C., Ugaya, S., Sala, R.K., Rosenbaum, B., Ridoutt, V., Prado, L., Posthuma, S., Pfister, D., Souza, de Maia J.P., Lindner, X., Liao, A., Laurent, O., Resources 5, 16.https://doi.org/10.3390/resources5010016 https://doi.org/10.1016/j.resourpol.2018.01.006 in press.in https://doi.org/10.1007/s11367 LCIA:quo,harmonization,status wayforward. andsuggestionsInt.for Life Ass the Cycle J. 73 in quality Ecosystem 2018. F., Verones, R.K., Rosenbaum, L., Posthuma,S., Pfister, D., 30, Souza, Econ. Miner. ? and gold of 381 cases https://doi.org/10.1007/s13563 21, the and Ecol. economics Ind. J. Extraction. Resource P for https://doi.org/10. Clean. Indicator Scarcity J. Initiative. Cycle https://doi.org/10.1016/j.jclepro.2017.05.206 Life SETAC Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT 1111/jiec.12444 Comment citer cedocument:

ke, P., Henderson, A.D., Johnston, J.M., Bare, J., Sala, S., Maia de Maia S., Sala, J., Bare, J.M., Johnston, A.D., Henderson, P., ke, - 016

- 0094 - 017 - 3

- 16

1422

- 8 -

utn ise giac wti te UNEP the within guidance issues cutting

Background, Updates, and Future. and Updates, Background, ihle, . Ptulad L., Patouillard, O., Michelsen, o. 6, 957 161, rod. – – 967. – 390. ess. 93. - Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal symbols on Figure Figure 1.Schematic of the CF CaptionFigure Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 2 Satrlt i log (in Scatterplot . the right

ACCEPTED MANUSCRIPT . For ACCEPTED MANUSCRIPT Comment citer cedocument: 퐶 퐹 퐴퐷 - derivation scale) of of scale) , we have taken

퐶 from bottom 퐹 퐻퐷

푐표푛푠푡 versus 17

- = up model. 퐶 1 퐹 . 퐴퐷

o 2 mnrl eore, e element see resources, mineral 29 for

Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal Highlights peak theory bottom from potentials depletion Resource     

Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 Abiotic resource assessment matches using Biotic resource assessment matches with this population dynamic assessment. based A 20 The historical developm The resource issue is relevant in life cycle impact assessment.

- ACCEPTED MANUSCRIPTyear speculation old on this is connected with a recent paper on fish stock. ACCEPTED MANUSCRIPT Comment citer cedocument: ent resource of depletion potentials presented.is

- up models: population dynamics and the Hubbert the and dynamics population models: up 18

the Hubbertthe peak theory.

Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal Figure 1 Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 Comment citer cedocument: Version postprint Hélias, A. (Auteurdecorrespondance), Heijungs,R. (2019).Resource depletionpotentials from bottom-up models:Population dynamics andtheHubbert peaktheory. Scienceof theTotal Environment, 650, 1303-1308. ,DOI :10.1016/j.scitotenv.2018.09.119 Figure 2 Comment citer cedocument: