Liebig's law of the minimum - Wikipedia

Dobenecks used the image of a barrel—often called "Liebig's barrel"—to explain Liebig's law. Just as the capacity of a barrel with staves of unequal length is ... Liebig'slawoftheminimum FromWikipedia,thefreeencyclopedia Jumptonavigation Jumptosearch Thisarticleneedsadditionalcitationsforverification.Pleasehelpimprovethisarticlebyaddingcitationstoreliablesources.Unsourcedmaterialmaybechallengedandremoved.Findsources: "Liebig'slawoftheminimum" – news ·newspapers ·books ·scholar ·JSTOR(February2017)(Learnhowandwhentoremovethistemplatemessage) Liebig'slawoftheminimum,oftensimplycalledLiebig'slaworthelawoftheminimum,isaprincipledevelopedinagriculturalsciencebyCarlSprengel(1840)andlaterpopularizedbyJustusvonLiebig.Itstatesthatgrowthisdictatednotbytotalresourcesavailable,butbythescarcestresource(limitingfactor).Thelawhasalsobeenappliedtobiologicalpopulationsandecosystemmodelsforfactorssuchassunlightormineralnutrients. Contents 1Applications 1.1Scientificapplications 1.2Proteinnutrition 1.3Otherapplications 2Liebig'sbarrel 3Biotechnology 4Seealso 5References Applications[edit] Thiswasoriginallyappliedtoplantorcropgrowth,whereitwasfoundthatincreasingtheamountofplentifulnutrientsdidnotincreaseplantgrowth.Onlybyincreasingtheamountofthelimitingnutrient(theonemostscarceinrelationto"need")wasthegrowthofaplantorcropimproved.Thisprinciplecanbesummedupintheaphorism,"Theavailabilityofthemostabundantnutrientinthesoilisonlyasgoodastheavailabilityoftheleastabundantnutrientinthesoil."Or,toputitmoreplainly,"Achainisonlyasstrongasitsweakestlink."Thoughdiagnosisoflimitingfactorstocropyieldsisacommonstudy,theapproachhasbeencriticized.[1] Scientificapplications[edit] Liebig'slawhasbeenextendedtobiologicalpopulations(andiscommonlyusedinecosystemmodelling).Forexample,thegrowthofanorganismsuchasaplantmaybedependentonanumberofdifferentfactors,suchassunlightormineralnutrients(e.g.,nitrateorphosphate).Theavailabilityofthesemayvary,suchthatatanygiventimeoneismorelimitingthantheothers.Liebig'slawstatesthatgrowthonlyoccursattheratepermittedbythemostlimitingfactor.[2] Forinstance,intheequationbelow,thegrowthofpopulation O {\displaystyleO} isafunctionoftheminimumofthreeMichaelis-Mententermsrepresentinglimitationbyfactors I {\displaystyleI} , N {\displaystyleN} and P {\displaystyleP} . d O d t = O ( min ( μ I I k I + I , μ N N k N + N , μ P P k P + P ) − m ) {\displaystyle{\frac{dO}{dt}}=O\left(\min\left({\frac{\mu_{I}I}{k_{I}+I}},{\frac{\mu_{N}N}{k_{N}+N}},{\frac{\mu_{P}P}{k_{P}+P}}\right)-m\right)} Theuseoftheequationislimitedtoasituationwheretherearesteadystateceterisparibusconditions,andfactorinteractionsaretightlycontrolled. Proteinnutrition[edit] Inhumannutrition,thelawoftheminimumwasusedbyWilliamCummingRosetodeterminetheessentialaminoacids.In1931hepublishedhisstudy"Feedingexperimentswithmixturesofhighlyrefinedaminoacids".[3]Knowledgeoftheessentialaminoacidshasenabledvegetarianstoenhancetheirproteinnutritionbyproteincombiningfromvariousvegetablesources.OnepractitionerwasNevinS.ScrimshawfightingproteindeficiencyinIndiaandGuatemala.FrancisMooreLappepublishedDietforaSmallPlanetin1971whichpopularizedproteincombiningusinggrains,legumes,anddairyproducts. Otherapplications[edit] MorerecentlyLiebig'slawisstartingtofindanapplicationinnaturalresourcemanagementwhereitsurmisesthatgrowthinmarketsdependentuponnaturalresourceinputsisrestrictedbythemostlimitedinput.Asthenaturalcapitaluponwhichgrowthdependsislimitedinsupplyduetothefinitenatureoftheplanet,Liebig'slawencouragesscientistsandnaturalresourcemanagerstocalculatethescarcityofessentialresourcesinordertoallowforamulti-generationalapproachtoresourceconsumption. Neoclassicaleconomictheoryhassoughttorefutetheissueofresourcescarcitybyapplicationofthelawofsubstitutabilityandtechnologicalinnovation.Thesubstitutability"law"statesthatasoneresourceisexhausted—andpricesriseduetoalackofsurplus—newmarketsbasedonalternativeresourcesappearatcertainpricesinordertosatisfydemand.Technologicalinnovationimpliesthathumansareabletousetechnologytofillthegapsinsituationswhereresourcesareimperfectlysubstitutable. Amarket-basedtheorydependsonproperpricing.Whereresourcessuchascleanairandwaterarenotaccountedfor,therewillbea"marketfailure".ThesefailuresmaybeaddressedwithPigoviantaxesandsubsidies,suchasacarbontax.Whilethetheoryofthelawofsubstitutabilityisausefulruleofthumb,someresourcesmaybesofundamentalthatthereexistnosubstitutes.Forexample,IsaacAsimovnoted,"Wemaybeabletosubstitutenuclearpowerforcoalpower,andplasticsforwood...butforphosphorusthereisneithersubstitutenorreplacement."[4] Wherenosubstitutesexist,suchasphosphorus,recyclingwillbenecessary.Thismayrequirecarefullong-termplanningandgovernmentalintervention,inparttocreatePigoviantaxestoallowefficientmarketallocationofresources,inparttoaddressothermarketfailuressuchasexcessivetimediscounting. Liebig'sbarrel[edit] Liebig'sbarrel Dobenecks[5]usedtheimageofabarrel—oftencalled"Liebig'sbarrel"—toexplainLiebig'slaw.Justasthecapacityofabarrelwithstavesofunequallengthislimitedbytheshorteststave,soaplant'sgrowthislimitedbythenutrientinshortestsupply. Ifasystemsatisfiesthelawoftheminimumthenadaptationwillequalizetheloadofdifferentfactorsbecausetheadaptationresourcewillbeallocatedforcompensationoflimitation.[6]AdaptationsystemsactasthecooperofLiebig'sbarrelandlengthenstheshorteststavetoimprovebarrelcapacity.Indeed,inwell-adaptedsystemsthelimitingfactorshouldbecompensatedasfaraspossible.Thisobservationfollowstheconceptofresourcecompetitionandfitnessmaximization.[7] Duetothelawoftheminimumparadoxes,ifweobservetheLawoftheMinimuminartificialsystems,thenundernaturalconditionsadaptationwillequalizetheloadofdifferentfactorsandwecanexpectaviolationofthelawoftheminimum.Inversely,ifartificialsystemsdemonstratesignificantviolationofthelawoftheminimum,thenwecanexpectthatundernaturalconditionsadaptationwillcompensatethisviolation.Inalimitedsystemlifewilladjustasanevolutionofwhatcamebefore.[6] Biotechnology[edit] Oneexampleoftechnologicalinnovationisinplantgeneticswherebythebiologicalcharacteristicsofspeciescanbechangedbyemployinggeneticmodificationtoalterbiologicaldependenceonthemostlimitingresource.Biotechnologicalinnovationsarethusabletoextendthelimitsforgrowthinspeciesbyanincrementuntilanewlimitingfactorisestablished,whichcanthenbechallengedthroughtechnologicalinnovation. Theoreticallythereisnolimittothenumberofpossibleincrementstowardsanunknownproductivitylimit.[8]Thiswouldbeeitherthepointwheretheincrementtobeadvancedissosmallitcannotbejustifiedeconomicallyorwheretechnologymeetsaninvulnerablenaturalbarrier.Itmaybeworthaddingthatbiotechnologyitselfistotallydependentonexternalsourcesofnaturalcapital. Seealso[edit] Bottleneck(disambiguation) Criticalchain Criticalpathmethod Ironfertilization Keystonespecies Limitingfactor Randomwalk Ratedeterminingstep Sustainability TheoryofConstraints References[edit] ^ThomasR.SinclairandWayneR.Park(1993)"InadequacyoftheLiebiglimiting-factorparadigmforexplainingvaryingcropyields",AgronomyJournal85(3):472–6doi:10.2134/agronj1993.00021962008500030040x ^Sinclair,ThomasR.(1999)."LimitstoCropYield".PlantsandPopulation:istheretime?.Colloquium.WashingtonDC:NationalAcademyofSciences.doi:10.17226/9619.ISBN 978-0-309-06427-9.Archivedfromtheoriginalon2011-07-03. ^W.C.Rose(1931)FeedingExperiments,JournalofBiologicalChemistry94:155–65 ^Asimov,Issac(1962)."Life'sBottleneck".FactandFancy.Doubleday. ^Whitson,A.R.;Walster,H.L.(1912).Soilsandsoilfertility.St.Paul,MN:Webb.p. 73.OCLC 1593332.100.IllustrationofLimitingFactors.TheaccompanyingillustrationdevisedbyDr.Dobenecksisintendedtoillustratethisprincipleoflimitingfactors. ^abA.N.Gorban,L.I.Pokidysheva,E.V.Smirnova,T.A.Tyukina.LawoftheMinimumParadoxes,BullMathBiol73(9)(2011),2013–2044 ^D.Tilman,ResourceCompetitionandCommunityStructure,PrincetonUniversityPress,Princeton,NJ(1982). ^Reilly,J.M.;Fuglie,K.O.(6July1998)."Futureyieldgrowthinfieldcrops:whatevidenceexists?".SoilandTillageResearch.47(3–4):275–290.doi:10.1016/S0167-1987(98)00116-0. vteEcology:Modellingecosystems:TrophiccomponentsGeneral Abioticcomponent Abioticstress Behaviour Biogeochemicalcycle Biomass Bioticcomponent Bioticstress Carryingcapacity Competition Ecosystem Ecosystemecology Ecosystemmodel Keystonespecies Listoffeedingbehaviours Metabolictheoryofecology Productivity Resource Producers Autotrophs Chemosynthesis Chemotrophs Foundationspecies Mixotrophs Myco-heterotrophy Mycotroph Organotrophs Photoheterotrophs Photosynthesis Photosyntheticefficiency Phototrophs Primarynutritionalgroups Primaryproduction Consumers Apexpredator Bacterivore Carnivores Chemoorganotroph Foraging 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