The Growth of Sphagnum: Methods of Measurement
Author(s): R. S. Clymo
Reviewed work(s):
Source: Journal of Ecology, Vol. 58, No. 1 (Mar., 1970), pp. 13-49
Published by: British Ecological Society
Stable URL: http://www.jstor.org/stable/2258168 .
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13
THE GROWTH OF SPHAGNUM: METHODS OF
MEASUREMENT
BY R. S. CLYMO
College,London,N. W. 3
BotanyDepartment,
Westfield
INTRODUCTION
Peat coversa largepartof theearth'sland surfaceto thenorthof 60?N latitude(map in
Sjors 1961). In Finland,forexample,about a thirdof the land is peat covered.South
estimateputsthearea coveredby
of 60?N peat is stilllocallyabundant.A conservative
peat at about 1% of thetotalland surfaceof theearth(Taylor 1964). Sphagnumplants
Any attemptto accountfor
are, by mass,probablyamongsttheprincipalpeat formers.
and presentsurfacefeatures,is
the rate of peat formation,or for peat stratigraphy
on therateof Sphagnumgrowth.
likelyto requireinformation
therefore
ingrowthstudies
Some specialfeaturesof Sphagnumof importance
Sphagnumhas severalfeatureswhichare rareor absentin vascularplants,and which
of drymatterproduction.The plantsare able
mightbe expectedto affecttheefficiency
of inorganic
to flourishin habitatsin whichthereare uncommonlylow concentrations
of thesein the plants
of N and P compounds.The concentration
solutes,particularly
mirrorsthatin thehabitat;0.6% N and 0.0300 P by weightare reportedby Malmer &
Sjors (1955). The habitatsare, moreover,oftenunusuallyacid; pH values below 4 are
frequent.
two-thirds
of thedrymatterof
The structure
of Sphagnumis unusual.Approximately
is containedin an open networkof
theplantsis in the leaves. Most of the chlorophyll
cells only at the ends. The interlong narrowcells whichadjoin otherchlorophyllose
largepores (5-15 ,udiameter)and theleaves are only
veningemptycells have relatively
cell is effectively
freelysuspended
one cell thick,so that each chlorophyll-containing
betweena
intermediate
of fixedform.Sphagnumis, therefore,
but is held in a structure
of chloroplanktonicalgal populationand a vascularplant,not only in distribution
phyllosecells but also in dependenceon liquid waterand perhaps limitationby the
in water.
low rateof CO2 diffusion
relatively
unit.
A Sphagnumcommunityis, in some respects,a veryconvenientexperimental
Individualspecies occur in different
rangesof chemicalconditionsin the habitat; S.
squarrosum*may be foundin moderatelycalcareous conditions,whilstS. papillosum
thrivesonly in places wherethe calcium concentrationis low. Species differtoo in
rarelyoccursmorethan a fewcentimetres
toleranceof drierconditions;S. cuspidatum
is usuallyfoundin drierplaces.
above thewatertable,whilstS. rubellum
The plants are easilyhandled,and usuallygrowwiththeirstemsnearlyparallel to
in estimating
the amount
one another.Thereare no roots,so thatthereis no difficulty
of underground
parts,whichcan forman appreciablepart of higherplantproduction
(Westlake1963).
* Nomenclature
followsRichards& Wallace(1950).
14
Thegrowthof Sphagnum
Growthis predominantly
apical and indeterminate,
so thatthe main axis in space is
also an axis in time.
Lastly,since the plants are primarilyaquatic, experiments
may be made in water
culture,withall its advantagesovermixedsolid/liquidculture,withsome hope thatthe
resultsmaybe relevantto fieldbehaviour.
In otherrespectsthis systemis less convenient.One of the main difficulties,
arising
fromthegrowthhabit,is thatboundariesbetweenpartsof theplantare eitheruncertain
or inconvenient.
It is rare,forexample,to finda sharpboundarybetweenliveand dead
partsof the plants,or even on a practicalbasis betweengreenand brownparts.The
sharpestdivisionsare of leaf frombranch,whichprovidesinconveniently
small units.
More usefulpracticaldivisionsare of branches(withattachedleaves) fromstem,and
of capitulumfromtherestof theplant.
The amountof growthis an importantparameterin any attemptto accountforthe
concentrationof cations, and particularlyof H+, around the plants (Clymo 1967).
During a period of growththe numberof new ion exchangesites (and probablythe
amountof exchangeableH+ too) are directlyrelatedto the amountof drymatterproduced. The reportedvalues forgrowthvaryfrom077 g dm-2 year-' (fora mixtureof
at 300 m altitudein northernEngland; Chapman
S. papillosumand S. magellanicum
2
in northernGermany;Overbeck &
1965) to 16-6 g dm year-' (for S. recurvum
Happach 1956).
The meaningattachedhereto growth
The term'production',withits allies and derivatives,is acquiringa fairlyprecise
thaneverit was, though
meaning.Growthappearsto be no neareran agreeddefinition
an elementof irreversible
increaseis usuallyinvolved.The methodsto be describedhere
do notall measurethesamething,and cannotalwaysbe relatedto theproductionterms,
thoughmostare concernedwithan increaseof some kind.Growthis used as a neutral
termforall thequantitiesmeasuredhere.
Because thereis no clear divisionbetweenlive plant, dead plantand peat, theterms
'standingcrop' and 'biomass' have no usefulmeaningwhenappliedto Sphagnum.
The measurement
ofgrowth
The main problemin measuringanythingas complexas growth,particularly
in field
conditions,is thatthereis no yardstickwithwhichto assess accuracy.Precisionof any
one methodmay be estimatedwithstandardstatisticaltechniques,but a highlyprecise
estimateis not necessarilyhighlyaccurate;in the game of dartsthe shotsmay be close
togetherbut all a long way fromthe point aimed at. Close agreementbetweenmean
resultsis thenthe best evidenceof accuracy.The morediversethe methods,the better
theirmutualsupport.
In thispaperthemethodsavailableformeasuringSphagnum
growthare firstdescribed,
withnoteson theirrangeof application.Tests of themorepromisingmethodsare considerednext.These testsincludesome in fieldconditions.The limitationsrevealedin
thesetestsare discussedas theyoccur.
Conversionof resultsto an area basis needs additionalmeasurements,
and theseare
considerednext. Lastly are discussedthe constancyof Sphagnumcarpet density,the
of a Sphagnum
bearingof the resultson estimatesof accumulation,and the efficiency
carpet.
R. S. CLYMO
METHODS
OF MEASURING
15
GROWTH
In orderto comparemethodsofmeasuringgrowthin massitis usefulto referto a simple
model system(Fig. 1). The boundariesin thismodel are the outersurfaceof theplant,
and a specifiedtimeinterval,since growthwill not usuallybe at a constantrate. A
pass one or more times
particularatom may, duringthe course of the experiment,
betweenthecompartments.
For example,a carbon atom mightbe assimilatedby a live
cell duringthe day, releasedby respirationat night,and reassimilatedthe nextday by
matter.An
anotherleaf. Onlyits positionsat the beginningand end of the experiment
period. During the
amount of materiala is presentat the startof the experimental
an amount,Bof growthis made. This correspondsto grossprimaryproducexperiment
processes
tion. Duringthe same timethereare losses: ar and f1r due to selfdestructive
and
due
to
(mainly'apparentrespiration'),
'predation',includinglossesdue to animal
ap
f,p
Growth
a~~~~~~~~~~~~~a
Can+ ar+ ap
Start
ap
Finish
at
FIG. 1. Fractions
intowhichweightmaybe apportioned.
The parta is materialpresent
r
thestartofthegrowth
period.The partfiis growth
duringtheperiod.Partssubscripted
are lostin respiration;
thosesubscripted
p are lostfromothercauses.
thatdue to
attack,physicalremovalbywindand waterand,perhapsthemostimportant,
microbiologicalattack.The net growthis thenf,n. The quantityf,B+ f,pcorrespondsto
theusual definition
of netprimaryproduction.
It is probablytrue,in general,that aj/ac fi./fi.
This is partlybecause the original
biochemicalstate)fromthe
environment
plantmaterialis in a different
(and a different
new growth.In particular,therateof loss of matterfromdead Sphagnumis affected
by
its positionrelativeto the watertable (Clymo 1965). Nor are the ratiosan/aand 13n/j
constantwithtime.It is forthisreasonthatthelossesin thismodelare shownas amounts
(whichhave dimensionsand mustbe relatedto a particulartimeinterval)ratherthan
as dimensionless
fractions.If longtimesare involved,fl,p
maycome to be a largepropor-
tionoff,.
If theresultsare presentedper unitarea, thereis a good reasonforusingthe sample
of a resultgivenas 10 mg cm-2 would be verydifferent
size as unit.The interpretation
16
Thegrowthof Sphagnum
fromthatgivenas 1 tonneha- , thoughwhenreducedto a commonarea theseare the
same. The same argumentapplies to the unitof time,withthe complicationthatthere
are heretwo conspicuouscyclicchangesin habitatconditions(diurnaland annual),and
were
may depend on knowingin what part of the cyclemeasurements
interpretation
made. The obvious solution-using sample area and time as units-is not always
possible.First,interestoftenlies in comparingresults,and forthispurposea common
unit is necessary.Secondly,for the Sphagnumwork,almost all the estimatesso far
reportedhave been made on samplesof undefinedarea, and have to be convertedto an
theunitof g dm-2 has beenadopted,and where
therefore,
area basis. As a compromise,
relevantthe timegiven.
The ten methodswhichhave been used formeasuringgrowthof Sphagnummay,for
convenience,be separatedinto fourgroups.
The firstgroupcontainsmethodswhichmake use of an innatemarkerof time.The
use of naturalcyclicchangesof branchlengthand spatial densityof branches,and of
['4C]-dating,are examples.
In methodsof the second group,referencemarksare put outsidethe plants,and
growthin lengthis measuredagainstthese.
In the thirdgroup,plantscut to a knowninitiallengthare used.
The fourthgroupcontainsmethodsin whichdirectestimatesare made of changein
weightover a periodunderthecontrolof theexperimenter.
The use of innatetimemarkers
may sometimesbe foundin thelengthof Sphagnumbranches
(a) Cyclicfluctuations
have beenused to measuregrowth
in
their
and
spatialdensity.Similarcyclicfluctuations
with
and
morelimitedsuccessThuidium
the
1953),
of
splendens
(Tamm
moss,Hylocomium
and
schreberi
(Tamm 1953), RhacoPleurozium
Ptilium
crista-castrensis,
tamariscinum,
mitrium
(Tallis 1959) and Acrocladiumcuspidatum(Streeter1965). In all
lanuginosum
thesecases the cycle was shown,or assumed,to be annual. Cyclic patternsare concommune.
too, forexample,Polytrichum
spicuousin otherbryophytes
The causes of this behaviourhave been examinedby Hagerup & Petersson(1960),
who state that most of the extensiongrowthoccurs in the autumn.Malmer (1962)
avoidsdescribing
papillosumshowingthreeor fourcycles,butcarefully
figuresSphagnum
themas annual. If thesecyclesare annual,theyprovidea simplemethodof measuring
growthrate.The quantitymeasuredis fl.(Fig. 1), or simplyincreasein lengthover a
year.Wheregrowthis rapidthemethodmightbe used overtimesshorterthana year.
Using thismethodMalmer(1962) foundgrowthof about 3 g dm-2 segment-'. The
values of 2-3-9-6g dm-2 reportedby Pearsall & Gorham(1956), for'standingcrop' of
Sphagnumforseveralsitesin Englandwereprobablyobtainedwiththismethod.In the
presentworkthe methodhas provedof limitedvalue, forthe reasonsgivenbelow. In
two cases, however,clear resultswereobtained.At ThursleyCommon,ten samplesof
1 dM2 of S. recurvum
in a wet flushgave a mean value of
growingwithJuncuseffusus
12 g dm-2 forthe currentcycle.The plantswereharvestedin December.Polytrichum
commune
close by,butin purestand,gave a meanvalue (tensamples)of 8 g dm-2. The
otherclear case was of Sphagnumgrowingin furrowsploughed7 yearspreviouslyat
A minimumestimateof fl. over 7 yearswas available
Coom Rigg, Northumberland.
usingthe whole accumulatedmass, but a more likelyestimatewas givenby the cyclic
branchpattern.The resultsaretshownin Table 1. Theyare the moreremarkablewhen
R. S. CLYMO
17
comparedwithestimatesof0 77 g dm2 (Chapman 1965),fora mixtureof S. papillosum
and S. magellanicum
about 300 m away.
in
In a fewcases the cyclicchangeis of pigmentdensity.An exampleis S. rubellum
some habitatsin England.The redpigment,relatedto theanthocyanins,
is an aglycone,
productionofwhichis increasedat low temperatures
(Rudolph 1964,1965).The pigment
is difficult
to separatefromthe cell walls (Goodman & Paton 1954) and oftenremains
conspicuousafterotherpigmentshave disappeared.An estimateof 2-7 g dm-2 for'net
annual production'of S. fuscumat one sitein northernEnglandwas obtainedby this
means(Bellamy& Rieley1967).
with
The principaladvantagesof thistypeof methodare thatthereis no interference
the naturalhabitatbeforemeasurement,
and the methodis simple.
The main disadvantagesare, first,that it is suitablefor use only over a long time
interval,unlesstheplantsare growingveryfast.Secondly,and moreserious,it appears
thatin theEnglishclimatethecyclicchangesin growthpatternare oftennot sufficiently
markedforit to be possibleto make clear separationof segments.Eitherthe change
occursand is gradual,or no distinctchangecan be seen at all. There mustalways be
some subjectiveelementin decidingwherea cycleends, but Tamm (1953) judged the
Table 1. Net annualgrowthin dryweightinfurrowsat Coom Rigg Moss,
Northumberland,
England
Minimumestimate Probableestimate
No. of
samples (g dm2 year-1)
(g dm2 year-1)
7
5
Sphagnum
papillosum
2-6
S. recurvum
15
9
3-2
is an averageofall
For methodofestimation,
see text.The minimum
estimate
is basedon thecurrent
materialremaining
after7 years.The probableestimate
cycleofgrowth.
Species
errorin decidingwherethe boundarylay in Hylocomium
splendensto be seldommore
1 dM2
than 1-2% of the segmentweight.By contrastin twenty-eight
out of forty-two
collectedduringthecourseof thisworkfroma varietyof sitesin
samplesof Sphagnum,
of the
at all could be seen in morethan three-quarters
England,no cyclicfluctuations
plants.The rate of extensiongrowthis correlated,amongstotherfactors,withwater
table height(Overbeck& Happach 1956). It may be that the cyclicchangesin morphology,and more particularlyof changes sufficiently
sharplydefinedto be of use,
or watersupply(or both) show sharpseasonalchanges.
appear onlywheretemperature
Hagerup& Petersson(1960) do, however,reporta similardifficulty.
It is possible that some furthergrowthmay occur on a particularsegmentin the
sinceMalmer(1962)
secondor subsequentyears.It seemsunlikelythatthisis important,
reports,and such observationsas have been possible here confirm,that all but the
currentsegmentshave usuallylost theirgreencolour.
(b) In specialcases, '4C datedpeat profilesmayproduceresultswhichare interesting
becausetheyare averagesoverperiodsof severalhundredyears.It mustbe demonstrable
thatSphagnumis the main constituent
of thepeat and, sincedrymattercontentis not
oftenpublishedfor '4C-dated samples,assumptionsmayhave to be made about this.
The quantitymeasuredis f,n, overthetimebetweensamples.
As an examplethedata of Turner(1964) forTregaronBog maybe used. Two samples
from169 to 171 cm depthgave dates of 2669 and 2624,each + 110 yearsBP. A sample
18
Thegrowthof Sphagnum
from82 to 84 cm gave a date of 2354+110 yearsBP. Turnerwrites'The Sphagnum
imbricatum
peat between82 and 171 cm,however,is veryweaklyhumidified
and differs
littlefroma contemporarySphagnumhummock;the leaves and branches,although
thoseof a livingplant.It is fairlyuniform
brownratherthangreen,closelyresembling
in structure
. . .'. No drymattercontentsare availablebutpublishedvaluesforpeat are
about 100+30 g litre-' (e.g. Malmer 1962; Clymo 1965; Gore & Olson 1967). These
data givea mostprobableestimateof 3 g dm- 2 year-' overa periodof about 300 years,
butthestatisticalerrorsin "C countinggivelimitsforP = 0-05of 1-10 g dm year-1.
The value of ,Bor of ft.+ 13pover shorterperiodswould have been higher,thoughby
how muchis unknown.
The use of reference
marksoutsidetheplant
(c) Leisman (1957) measuredthe depthto a wire whichwas originallylaid on the
surface.Over 3-4 yearsthemean growthratewas 1P4cm year-' in thesedgemat zone
of a bog in Minnesota.
(d) The disadvantageof a buriedwireis thatconsiderabledisturbanceis caused in
locatingit. This problemis largelyavoided by usingmanyseparatecrankedstainless
steel wires(shaped like a car startinghandle). One end of the wire,whichcan conbe about 10 cm long,is pushedintotheSphagnumcarpetvertically
(or parallel
veniently
to the stemsif theseare not vertical).The horizontalsection,about 1 cm long,is level
withthecapitula,whilstthefreeend, whichmustbe of exactlyknownlength,projects
intotheair.
The Sphagnumplantsgrowup aroundtheverticalfreeend of thewireand thegrowth
is measuredfromtheamountof wirestillprojectingabove the surface.The crosspiece
increasesresistanceto verticalmovementof thewireamongtheplants.No decreaseof
growtharound the wireshas been observedin the 4 yearsthatthismethodhas been
in use.
The quantitymeasuredis an increasein length.To estimate/Bn(Fig. 1), thislength
mustbe multipliedby the averagemass of plantsin unit depthof Sphagnumcarpet.
This pointis consideredlater.The methodhas provedusefulforannual measurements
wherethegrowthin lengthwas about 2 cm.
It is difficult
to testwhetheror notverticalmovementof thewirerelativeto theplants
occursin spiteof thecrosspiece. In Fig. 2 is showna comparisonof growthestimated
by crankedwire withthat estimatedfromgrowthof plants of knowninitiallength.
seemsto be satisfactory,
butthemethodmustbe suspectin verywethabitats,
Agreement
wherethe Sphagnumcarpetis liable to move. In such situationstheplantsoftengrow
almost horizontallyand thismethodis thenof littlevalue in any case. The principal
errorsarise in the estimationof wherethe surfacelies. They are least for the closely
and greatestin wethabitats.Theseerrorsmaybe reduced
packedcapitulaon hummocks,
by usinga glass tube,about 2 mm bore,witha perforatedplasticdisc 2 cm diameter
fixedto the end. The tube,disc end first,is slid over thefreeend of the wire,and the
disc servesto definethesurface.
This methodis simple,and can be used on a large scale. It has some disadvantages.
The wiresare oftendifficult
to findunlessa markerthreadis used or detailednotesmade
locatingthe positionto within10 cm. The wiresare also a potentialhazard to grazing
animals.Both thesedifficulties
are reducedif the freeend of the wireis doubled over
and the top centimetre
coveredin colouredPVC.
R. S. CLYMO
19
Overbeck& Happach (1956), followingearlierauthors,used a threadtiedroundthe
stemas a markeragainstwhichto measurethe growthin lengthof aquatic Sphagnum
plants. They recordedgrowthof up to 44 cm betweenMay and mid-Octoberby S.
in usingthismethodin habitats
cuspidatum
growingin a ditch.Theywereunsuccessful
whichwere not fullyaquatic, because the monthlydisturbancefor measurements
was
too severefortheplantsto survive.The plantstendedto dryout,mainlybecauseitwas
in anything
like theoriginalgrouping.
impossibleto rearrangethemaftermeasurements
but
with
Chapman(1965) used thesame principle,
onlyone disturbanceat finalharvest,
to checkthatthestemsbelow themarkerswerenot lost. This methodwas testedduring
the presentwork.It involvesmoredisturbancethanthe use of crankedwires,and was
therefore
abandoned at an earlystage,even forsituationswherea singleharvestwas
intended.
10
1
E
I
V
0
E
C
/
0
0
Oa
I
.
I
5
Direct measurementof growth
(cm)
I
10
FIG. 2. Comparison of growthin lengthby directmeasurementon plants of known initial
length,withestimatesby cranked wire. For details of methods see text.Values are mean
of ten (containersnear laboratory,o) or twenty-five
(field,o) measurements.Bars are ?
twice the S.E. of the mean. The line of slope+ 1 0 is that on which the points would fall
if the methodswere in exact agreement.
The use ofplantscut to knownlength
base to
(f) Overbeck& Happach (1956) used cylindersof celluloidwitha perforated
containSphagnumplantscut initiallyto a lengthof 8 cm. The plantswereremovedat
intervals,the extensionmeasured,and theplantscut back to 8 cm and replacedin the
fromthat
cylinders.Withsuch multipleremovals,the growthmay have been different
of undisturbed
plants,thoughthereis no reasonwhythe same procedurecould not be
used,butwithonlyone harvest.Anotherpotentialerroris due to thephysicalseparation
of the sampleplantsin the cylinderfromthe restof the Sphagnumcarpet.Whilstthe
but one
watertable remainsabove the base of the cylinderthismay not be important,
mightexpectit to become moreso if the watertable drops below the cylinder,though
Overbeck& Happach did not see visibledifferences
in plants inside and outsidethe
cylinders.
20
Thegrowthof Sphagnum
of growthin length,conversionto growthin dryweight
As withothermeasurements
requirestheuse of values forspatialdensityand individualplantweight.
cut to a length
(g) Chapman(1965) used plantsof S. papillosumand S. magellanicum
of 5 cm. Samples were taken for dryweightdetermination
and the restof the plants
replacedin the bog surface.Aftera year,the extensionand dryweightof the whole
A
o0
(a)
_(b
0
10
00
0
A
-20
0
0
00
1
0
0 0
5 -
0A
0
00A
5
A
to
A
08
.k
DS~~~
o~~~~~~~~~~~~~
E
~520 (c)
-
15-
SQ/
2
3
V
I
1
1
2
3
A:
45678
(d)
....V
I Is
I
fi
I
3
4
15~~~~~~~~~~~~~~~~~~~~~5
2Dryweight
3 3 cm ofstem(mg) 2
of
I
FIG. 3. Relationship
ofdryweightofcapitulum
to thatof3 cmofstemforfourspeciesof
Opensymbolsare values for a largesampleof individualplantsfromthe
Sphagnum.
lot used in the containerexperiments.
The calculatedstraight
line of bestfitforthese
pointsis shown.Filledsymbolsare meanvaluesforothersampleseachfrom1 dm2.(a) S.
rubellum:y = 3 25x-07, r = 0-84; (b) S. papillosum: y = 2 7x+0 4, r = 0-89; (c) S.
cuspidatum:y = 7 6x-1-8, r = 0 94; (d) S. recurvum:y = 4-3x-0 9, r = 0-97.
plantsweremeasured.Chapmanreportsthat'it was foundthatleavesand brancheswere
lost fromthebases of theshootsduringthecourseof theexperiment.. .' so thatdirect
estimatesof dryweightincreaseswereunreliable.Markerthreadsshowed,however,that
wholepiecesof stemwerenot lost,and'. . . increasein lengthprovideda moreaccurate
measureof growth.. .'. Fromgrowthin length,thegrowthin dryweightwas calculated,
usinga graphrelatingdryweightto length.The increasein dryweightper unit area,
fln(Fig. 1), was thencalculatedusingthemean spatialdensityof plants.
21
R. S. CLYMO
notveryprecise,because
For smallamountsof growththisestimateis, unfortunately,
and variabilityis large.
weight
a smallproportionof the total
the growthis, relatively,
5
cm
long was about 3700
of variationforweightsof S. magellanicum
(The coefficient
fora sampleof twentyplants.)
(h) An obvious modificationof Chapman's methodwould be to cut offand weigh
the new growthdirectly.This mayintroduceerrors,however,because some partof the
materialin the new growthhas been carriedthereby internodeextension;it is not
formedduringthe growthperiod.The errorwill be largestwheregrowthis small,and
is largein manycases,wherethecapitulummayweigh5 mgwhilstthenetannualgrowth
cannot be used because
is only 10-20 mg (Fig. 6). The easy solutionsto thisdifficulty
when
placedin a markedfor
example,
considerably,
change
size
itself
may
thecapitulum
it
The
can, however,
in
which
formed.
problem
than
that
ly drieror wetterenvironment
Weight
of
capitulum
of 3cm
_Weight
ofstem
Sample for
stem/capitulu
relation
}
J
cm
3c\
}3cm,
branchesremoved
Icm,rejected
I
(x+l)cm,
+ original
growth
copitulum
==
______
Start
3 cm used|
forestimate
oforiginal
5cm
Most
______plants
_____tomain
______experiment
______
_____
cpitulum
weight
cm,rejected
End
in weight.
growth
methodformeasuring
FIG.4. The 'capitulumcorrection'
be avoidedusinga rathermorecomplicatedtechnique.Thereis a fairlyclose relationship
(Fig. 3) betweenthe dryweightof the capitulum(definedfor convenienceas the top
of the Sphagnumplant) and thatof a unitlengthof stem,afterthebranches
centimetre
have been strippedoff.From the weightof stemat harvest,an estimatemay therefore
be made of thecapitulumweightat thestartof theexperiment.
of stemis rejected,
The procedureused is shownin Fig. 4. The bottomcentimetre
because it sometimesbecomesfrayed,withthe dangerof losingsmall pieces. A check
made withmarkerthreads1 cm fromthe bottomof the stemconfirmedChapman's
(1965) observationthatgrosslosses are rare; in fiveout of 200 plantsmarkedin a field
six there
thethreadswerenot recoveredat all aftera year,and in a further
experiment
was some loss.
The stemsthemselveslose weightslowly,so that if the correctionfor the original
capitulumis largecomparedwiththenew growth,it is necessaryto estimatetheloss in
500 in a year; this
theselosseswereapproximately
weightof stems.In a fieldexperiment
is smallerthanthelossesfromwholeplants(Clymo 1965).
22
Thegrowthof Sphagnum
Growthin both lengthand dryweightcan be measuredby this method.The dry
weightincreaseestimatedis P. (Fig. 1). The assumptionthatthereis no largeamountof
materialtranslocatedhas proveddifficult
to check.There is certainlysome movement
of '4C fromolder parts to new growth,probablyoutside the plant as 14C02. The
reverseprocessseemsto be of littleimportance.The methodis sufficiently
sensitiveto
make samplingat monthlyintervalsuseful,althoughtwenty-five
samples,or more,are
neededon each occasion.
to estimatethesize of somepossibleerrorsare describedlater.
Experiments
Althoughtherelationship
betweencapitulumweightand stemweightis usefullyclose
to linearfor a particularsample of plants(Fig. 3), thereis considerablevariationfor
samplesfromdifferent
seasons,habitatsand localities.Withoutindividualmeasurements
for all thesesamplesit is impossibleto know whetherthe variationin mean values is
due to differences
in slope and positionof the line, or to greatlydifferent
variances.
Variancesso different
are unlikely,
so itis important
to takeall theplantsfora particular
experiment
fromone area, and fromthesame habitat,and to determine
therelationship
fora sampleof thesein each gathering.
It is arguablethata polynomial,givinga betterfitto thedata, could validlybe used
here,because the object of thisstep is purelyto estimatecapitulumweightfromstem
weight.In practicethe reductionin errorvarianceby usingeven a second orderpolynomialis so smallas to be notworththeextratrouble.The closenessof fitto a straight
line throughthe originis also usefulbecause groupsof plantsof varyingsize maythen
be treatedas units.
This methodneedsmoreworkthanmost,but givesa fairlydirectestimateof growth
in dryweightas well as of growthin length.It can also be used in experimental
(transplant)situations.
Directestimatesof changein weight
(i) The variabilityof weightforSphagnumplantsof equal lengthis so greatthatthe
obvious methodof takinga sample of plantsfordryweightmeasurement
at the start
of the experiment
is imprecise,unlessgrowthis severaltimesthe initialsize. Estimates
of total plant dry weightcan be made fromlinear dimensionsbut, so far,no high
correlationbetweendryweightand lineardimensionshas been found.
A different
approach is more successful.The plant is weighedfirstunderwater.A
secondweighingis made underwaterat harvest,and theplantis thendriedand weighed
a thirdtime.
If specificgravity= d, weightunderwaterat the start= Ws,weightunderwaterat
harvest= Wh,dryweightat thestart= Ds, dryweightat harvest= Dh and growth=
G, then
d = Dh!(Dh- Wh)
Assumingthatd does not changeduringtheexperiment,
Ds= Wsd/(d-1)
and
G= Dh-Ds
=
Dh(l-WslWh)
The quantityestimatedis f. - Or- OCp (Fig. 1). This methodis the most sensitiveyet
withcare,growthof 2 mg maybe detected.
testedextensively;
There are severalpracticaldifficulties.
Trapped gas bubblesmustbe removedfrom
betweenthe leaves, and fromthe hyalinecells. This is done by evacuatingthe plants
23
R. S. CLYMO
submergedin water.It is possible to 'boil' S. papillosumat 250 C for at least 1 min
withoutserious harm to the plants: they continuegrowingafterwards.In normal
on subsequent
of thistreatment
practiceonly5 sec evacuationis necessary.The effects
been experitrouble
has
later).
No
described
(see
tests
growthare apparentlyverysmall
such
bubbles are
(though
enced fromgas bubbles reappearingdue to photosynthesis
is made
if
the
weighing
commonin fieldconditions),and none should be anticipated
and the
temperature,
at
a
known
shortlyafterevacuation.Weighingsmust be made
C
was
used.
work
250
In
this
before
weighing.
reach
this
temperature
plantsallowed to
a
use
either
necessary
to
then
it
is
are
made
directly
to
be
If weighingsunderwater
immersedin water,or some formof suspension(betweenplantand
balance completely
to build a
balance) whichpasses throughthewater-airinterface.It has proveddifficult
balancewiththenecessaryprecision(0aI mg),rangeand robustness.
immersed
completely
The simplersolution,usingan OertlingH03 balance, witha cradle suspendedin the
Table 2. Specificgravity(at 250 C) of Sphagnum
Species
Partand origin
Wholeplants,endofexperiment
S. rubellum
S. cuspidatum Wholeplants,endofexperiment
New growthduringexperiment
S. papillosum Wholeplants,endofexperiment
New growthduringexperiment
Wholeplantsfromfield
Capitulumfromfield
Stem1-3 cmfromfield
Stem3-5 cmfromfield
Branches+leaves1-3 cm
Branches+leaves3-5 cm
S. recurvum Wholeplants,endofexperiment
No. in
sample
48
47
24
47
24
10
10
5
5
5
5
48
Specific S.E. of
gravity mean
0 009
1-65
0-046
1-54
0 040
1-55
0 008
1-61
0-014
1-62
0 007
1-61
0 012
1-60
0 021
1 60
0 018
1-63
0 010
1-62
1-62
0.031
0 046
1-57
waterwas therefore
adopted. The air-waterinterfaceproducesa relativelylarge error
in the balance reading,due to surfacetensioneffectson the suspension.The observed
weightmay,however,be correctedforthiserror(see Appendix).
The validityof the assumptionof constantspecificgravitywas examinedin experimentsdescribedlater: the resultsare shownin Table 2. Thereis no indicationthatthe
fromthatof theoriginalplants,nor thatthere
specificgravityof thenewgrowthdiffers
is any difference
betweenpartsof S. papillosum.Thereis some indication,thoughnot
at P = 005, thatthespecificgravityof S. papillosum(1.61) and, particularly,
significant
(1.54) and S. recurvum
S. rubellum(1.65) is slightlygreaterthan thatof S. cuspidatum
(1.57).
It seems,therefore,
thatthebasic assumptionof themethodis not seriouslyin error.
from
This methodinvolvesweighingthe whole plant. Loss of branches,particularly
the lowerpart of the stem,is therefore
a seriouspotentialsource of error.Because of
thisthemethodhas not been testedin fieldconditions.
in a
St'alfelt
(1938) and Romose (1940) have measuredchangesin CO2 concentration
gas streampassed overmoss plantsin a closed container.It is also possibleto use "C
are, however,
eitherin laboratoryor fieldconditions.The problemsof interpretation
naturefromthose of the othermethods
considerable,and are largelyof a different
be consideredhere.
describedhere.Theywillnot therefore
24
Thegrowthof Sphagnum
'LABORATORY
TESTS' OF SOME METHODS
The followingtestsweremade in conditionsin whichthe plantscould be protected
and the environment
controlled.Field testsare describedlater.
Four speciesof Sphagnum
weregrownin opaque cylindrical
containers
25 cm
polythene
diameterand 10 cm deep. The specieswereS. rubellum,
S. cuspidatum,
S. papillosumand
S. recurvum.
The unitformost measurements
was a group of ten plants,but in some
cases individualsweremeasured.All plants of one speciesweregroupedtogether,the
bundles being randomized,and surroundedby guard rows of plants on which no
measurements
weremade. The plantaxes wereverticaland parallel.
The containerswereput in a courtyardoutsidethe laboratory.In two of themthe
waterlevelwas keptabout 1 cm below thecapitulaand thetop coveredby nylongauze
.
-
020
a)
a
A
10
A
v
A
v
0
0
10
20
30
40
Mean growthIn weight
50
5. Relationship
betweenmean growthin weight(fin, Fig. 1) and samplestandard
deviation,of plantsgrownin containers.
Each samplecontainsfortyindividuals.Open
symbolsindicateestimates
as mgplant-'; filledsymbolsare estimates
as mg (mgcm-'
largesymbols
stem)-'; smallsymbolsare forplantsgrownin drierunshadedcontainers;
are forplantsgrownin wettershadedcontainers.*, o, Sphagnum
rubellum;v, v, S.
cuspidatum;
A, A, S. papillosum;*, o, S. recurvum.
FIG.
so that the radiationreachingthe plants was, on average,about 3000 of that in the
unshadedcontainers.
In the two unshadedcontainersthe watertable was kept at about 5 cm below the
capitula.These treatments
weredesignedto producedifferences
in growthagainstwhich
differences
due to errorsin themethodsofmeasuringit could be compared.The orientationand positionof thecontainerswerechangedrandomlyeach week.
The experiments
werebegunin June1965. One harvestwas made in thefirstweekof
August1965,and themainharvestin thefirstweekof January1966.
There were six main experiments
in this seriesusing threeof the methodsalready
described.For conveniencetheseare referred
to as the crankedwire(d), the capitulum
correction(h), and theweightunderwater(i) methods.
R. S. CLYMO
25
results
and selectionof a basisfor expressing
Thepatternof variation,
For each speciesand containerfortyplantswerecut to 5 cm at thestartof theexperiment.At harvestin Januarythe growthin lengthand in dryweight(by the capitulum
correctionmethod)weremeasuredon individualplants.Resultsforthe growthin dry
weightare shownin Fig. 5. The growthis expressedper plant,and also per weightof
unitlengthofstem.This lastneedsexplanation.Thereis considerablevariationin growth
of variation(ratio of standarddeviationto mean
expressedper plant. The coefficient
value) is about 05, whichis undesirablylarge. This variationoccurredboth withina
speciesand betweenspecies.It seemedthatthismightreasonablybe related,to some
extent,to variationsin the growthpotentialof theplants.This growthpotentialcould
in the size of the
be relatedto the size of the apex, and the size of the apex is reflected
stem
(Fig.
3). If growth
In
the
the
capitulum
and
the
apex,
the
larger
stem. general, larger
to reduce
hope
therefore
of
of
stem
one
might
unit
length
were expressedper weight
variabilitywithinspecies,and probablybetweenspeciesas well,thoughinterpretation
Such expressionimplies that the growthpotentialis
mightthen be more difficult.
proportionalto the cross sectionalarea of the stemand hencethe cross
approximately
sectionalarea of theapex.
filledsymbolsindicates
In Fig. 5, comparisonof theopen symbolswithcorresponding
is
for
two
methods
of expression.
similar
the
in
coefficient
of
variation
the
that general
if
resultsare
is
greater
the
coefficient
actually
is
indication
that
the
a
slight
Indeed,there
in
For
practical
of
unit
of
stem
for
drier
conditions.
plants
length
expressedper weight
of stem
weight
of
unit
length
by
using
there
is
nothing
to
be
gained
therefore,
purposes
results.The immediatecause ofthisis theverylow correlation
as thebasisforexpressing
betweenweightperunitlengthofstemand growth.This mightbe becausegrowthpotential is relatedto some functionotherthan the square of the stemradius.The lack of
correlationholds, however,even whenthe logarithmof the data is used (whichmight
be expectedto expose a power relationshipif it existed).For example,the correlation
forthefortyplantsof S. papillosumin drierconditions
coefficient
(aftertransformation)
is as low as 009. It appearsmorelikelythattheexplanationlies in theaccommodation
whichwill be the same
of apex size to the detailedconditionsof its microenvironment,
as its originalenvironment
in thefieldonlyby chance.This suggestionis supportedby
the observationin the fieldexperiments
(describedlater) that the correlationof stem
weightand growthis rathergreaterin theearlystagesaftertransplanting.
is imporThese resultsagain lead one to suspectthatthe detailedmicroenvironment
tant, and hence throwdoubt on resultsfromany methodwhich involvesrepeated
disturbanceof theplants.
Anotherfeatureof the resultsin Fig. 5 is that,withthe possible exceptionof S.
line; theerror
in wetterconditions,thepointsall lie close to a singlestraight
cuspidatum
removesmost of this
transformation
is proportionalto the mean value. A logarithmic
of variationto about 0-15. All subsequent
relationship,and reduces the coefficient
data. Similarfeaturesare shownby
been made on transformed
analyseshave therefore
as for
is not so satisfactory
growthin length,althoughthe logarithmictransformation
growthin weight.
The behaviourof the speciesin relationto watertable (and shade) is verysimilarto
oftheplants:S. rubellum
thatwhichmighthavebeenpredictedfromthefielddistribution
grewbetterin thedriercontainers,as did S. papillosumforwhich,however,theproporand S. cuspidatum
tional difference
was smaller.S. recurvum
grewbetterin the wetter
26
Thegrowthof Sphagnum
more
was proportionally
containers,eventhoughthesewerealso shaded.The difference
markedforS. cuspidatum.
and of the'weightunderwater'manipulations
The effects
ofdisturbance
All theplantswerecutto 5 cm and weighedunderwaterat thestartof theexperiment
(June1965). In each containerthreegroups(of each species)wereremovedin August,
re-weighed
underwaterand replacedin thecontainers.Anothertriowas removedat the
same time,thebundleof plantstakenapart,thenreassembledand replaced.A thirdset
underwaterand after
of threewas not disturbed.In Januaryall plantswerere-weighed
Table 3. Analysisof varianceof growthin lengthand of growthin weight
procedures
(boldfigures)of Sphagnumsubjectedto threehandling
df
Treatment
Mean
square
F
Handling(A)
(2)
1
05
06
Untouchedvshandled
0-16 0 36
1
06
07
Typeofhandling
0-22 0 41
Container(B)
(3)
1 13-3 14 6
38.8*** 25.4***
Highwatertablevslower
2
17
21
0.59 1-2
Replicates
3
1 52 34.7
44** 61***
Species(C)
6
0.23 0 29
07
05
Interactions
AB
6
AC
17
08
0-58 048
BC
9
0 43 0-80 1-3
1-3
1.0
18
ABC
09
0-36 052
96
0 343 0 574
Error
of theoriginaldata were
For detailsof treatments,
see text.The logarithms
usedin bothanalyses.
and ofgrowthin dryweight(bold
Table 4. Mean valuesofgrowthin length,
to
threehandling
of
Sphagnum
subjected
procedures
figures),
Treatment
Handling(at
firstharvest)
Weighed
Separatedbutnot
Untouched
weighed
62
68
76
70
86
90
Container
Highwatertable,shaded Low watertable,unshaded
87, 94
54, 69
45, 53
119, 111
S. rubellum
S. cuspidatum S. papillosumS. recurvum
Species
6-8 43
51 3-2
67 145
84
250
For detailsof treatments,
see text.Growthin lengthis in centimetres.
Growthin weightmeasuredby method(h), is in mg plant-', without
for losses duringthe experiment.
correction
Mean values have been refromlogarithms.
transformed
dryingat 1050 C. Growthwas calculatedby both the capitulumcorrectionand weight
underwatermethods.
By January,many of the lowestbranchesof some groupsof S. cuspidatum
and S.
recurvum
had become separatedfromthe stemsin the high watertable shaded containersand it was not alwayspossibleto associatethe brancheswiththecorrectstems.
Fortunatelythisdid not affectthe estimatesmade by the capitulumcorrectionmethod
and it is therefore
in thesetermsthatthe resultsare givenin Tables 3 and 4.
27
R. S. CLYMO
The analysis(Table 3) indicatesthat the handlingprocedureshave a small effect
and withthe differences
comparedwiththatof the watertable and shadingtreatment,
to
reduce
growth.
betweenspecies.Handlingtends
The growthin weightof speciesin relationto watertable (Fig. 5) is similarto thatin
BC but is of low significance.
1; it appearsas theinteraction
experiment
lowerforall speciesin the driercontainers.
Growthin lengthis consistently
Table 5. Analysisof varianceofgrowthin length,and ofgrowthin weight
initiallengths
(boldfigures)of Sphagnumcut to different
Mean
square
df
Treatment
F
Initiallength(A)
(2)
(2)
0 11 2-6
1
1
3-6
18-5***
3 cm vs5 and 7 cm
21
12
1
1
0-06 0-17
Rest
Container
(B)
(3)
(2)
4 04 2 2
1
1
1402*** 15-7***
High water table vs
lower
2
1
12 6*** 4.2*
0-36 0.59
Replicates
9 4*** 121***
0 27 16-8
3
3
Species(C)
6
0 04 015
1.5
1.1
AB
4
Interactions
6
6
005 062
44**
1-8
AC
2.4*
102***
012 14
9
6
BC
12
0037 034
18
1-3
2.4*
ABC
0 029 0139
46
36
Error
of theoriginaldata were
see text.The logarithms
For detailsoftreatments
of 3 cm vs. 5 and 7 cm is undesigned.
usedin bothanalyses.The comparison
Table 6. Mean valuesof growthin length,and of growthin weight(bold
initiallengths
figures)of Sphagnumcutto different
Treatment
Initiallength(A)
Container
(B)
Species(C)
S. rubellum
S. cuspidatum
S. papillosum
S. recurvum
7 cm
3 cm
5 cm
60
64
83
5-8 126
86
Highwatertable,shaded Low watertable,unshaded
5-8
70
5-6 7-3
7-7 8-1
8-9 10-4
22
2-5
22 0
26-2
4-7 4-7
5-7 5-3
42 45
5-4 4 9
69
53
96
27
22 0 20 2
22 7 21 2
Growth
For detailsoftreatments,
see text.Growthin lengthis in centimetres.
forlosses
inweight,
correction
bymethod(h),is inmgplant-', without
measured
fromlogarithms.
Mean valueshavebeenretransformed
duringtheexperiment.
method
The effectof initialplantlengthon growthmeasuredby the'capitulumcorrection'
The same fourspeciesand similarcontainerswereused. One set of plantswas cut to
5 cm long at the startof theexperiment.
Othersetswerecut to 3 cm and 7 cm. All the
capitulawerearrangedat the same level by supportingthe shorterplantson a bed of
homogenizedSphagnum.All were harvestedin January.The plants fromone of the
high watertable containerswere lost beforetheycould be weighed(duringremoval
fromone laboratoryto another),so onlythegrowthin lengthis availableforthem.
ofwatertableon growthin length
The resultsare shownin Tables 5 and 6. The effects
and weightare similarto those in the otherexperiments,
exceptfor a highvalue for
S. cuspidatum
in one of the driercontainers.No explanationis obvious; thismay be a
chanceresult.
28
Thegrowthof Sphagnum
There is some indicationthat the growthin lengthis inverselyrelatedto the initial
lengthand quite strongindicationthatgrowthin weightis similarlyrelated.The major
part of the effectis due to greatergrowthby 3 cm plants.This is a resultwhichwas
unexpectedand is noteasyto explain.For practicalpurposes5 cmplantsseemadequate,
and have beenused in therestof thiswork,because 7 cm ones are notso easilyobtained
undamaged,and losses are morelikelyto occur fromlongerplants.
20 -
(a)
0
0
0
0
10
t
C
0
_
%e 0X
/
0 -is.
E
/
00
/~~~*
*
0/
20 _
10
50
/
(b)
00
~
o~
U
*
o
O
40
0
-
20
0~~~~0
0
0
10
10
20
30
40
50
60
Growthwithcapitulumcorrection(mg plant-')
forchangein
6. Comparisonof growthin weight(fln)withand withoutcorrection
and (b) S. recurvum.
The
capitulumweightfortwospeciesof Sphagnum:
(a) S. rubellum
value. Open symbolsare for
singlelargesymbolin each graphis the meancorrection
filledsymbolsare forplantsgrownin wetter
plantsgrownin drierunshadedcontainers;
The line of slope+1 0 is thaton whichthepointswouldfallif the
shadedcontainers.
werein exactagreement.
estimates
FIG.
The effectof ignoring
thecapitulumcorrection
The same fourspeciesand containerswereused. All plantswerecut to 5 cm initially
and wereharvestedin January.In additionto the usual separationat 4 cm fromthe
base (Fig. 4) the sectionfrom4 to 5 cm was cut offand weighedseparately.It is thus
possibleto comparethegrowthestimatedaftercapitulumcorrectionwiththatestimated
simplyby removingeverything
beyond5 cm. The resultsfortwo speciesare shownin
wherethe mean of theestimatedinitialcapitulumsize is about
Fig. 6. For S. rubellum,
R. S. CLYMO
29
betweenthe estimatesis considerable,and is largerthe
halfthe growth,the difference
wherethegrowthwas muchgreater,and averaged
smallerthegrowth.For S. recurvum,
is muchsmaller.The othertwo
threeto fourtimesthecapitulumweight,thedifference
speciesfellbetweentheseextremes.
thatthe capitulumcorrectionmethodis accurate;
It is not, of course,demonstrated
results.It mightbe arguedthatthe methodcannot
onlythatthemethodsgivedifferent
true
be accuratebecauseit givessome negativeresults.This conclusionis not necessarily
3 -3
(a)
o2
o
-o
oY
E
0
0
o
m
I
vv
V
v
000
(O0
~~~~~0
0
v
t
Ss
0000
o
0
~~ ~ ~ ~ ~ ~ ~
0
-vV
0(b)
/
a~~~~~~
.C
E
I
0
00~~~AL
I
I
I
0
E
_
1
Cc)
(c)
2
2 3I
3
4
~~~~~~~lsm
Sd. cupiaum
usiatm
(dlou; c S
2
~ 2 ~3
3
4
d)Srcrvm
()S
recuvum
because no allowancehas been made forlosses (ir +fly),and some negativeresultsmust
be acceptedas the price of usinga correctionwhichrelieson a statisticalrelationship
whichis notperfect(Fig. 3). The negativeresultscould,however,raisea problemwhen
usinga logarithmic
transformation.
Fortunatelythishas not arisenin thepresentwork
since no negativevalues have been foundwiththe capitulumcorrectionmethodfor
groupsof plants,althoughtheydo occurwithindividuals.
methodwiththat
Comparisonof growthin weightestimatedby the'capitulumcorrection'
fromthe'weightunderwater'method
Plantsfromthe handlingexperiment,
togetherwithsome froma similarexperiment
not reportedhere,wereused forthiscomparison.If the methodsare to be compared
Thegrowthof Sphagnum
30
fromthelower5 cm of
directly,
some estimatemustbe made of thelosses,particularly
the plants,since one methodestimatesP. and the otherfB -?Cn-?Cr. These estimates
and
weremade on dead (air dried)Sphagnumwhichwas weighedbeforetheexperiment
thenplaced amongstthe live plants.At harvesttheseplantswere again air driedand
weighed.It is assumedinitiallythat the rate of loss was constantand applied to the
averagemass of materialinvolved:the mean total weightat firstand last harvestfor
the weightunderwatermethod,and halfthe correctedgrowthin the other.Losses are
forlive
probablyoverestimated
by thisprocedure,since theyare likelyto be different
and fordead material.
intologarithms.
The resultsare shownin Fig. 7, wherethedata have beentransformed
Some of theoriginaldata fortheweightunderwaterestimateswerenegativeand could
been omitted.Thereweretwo such cases
not be thustransformed.
Theyhave therefore
and one of S. recurvum.
This point is of some
of S. rubellum,
eightof S. cuspidatum
importance,since thesenegativevalues wereforgroupsof plantsafterallowancehad
one would expectnegativevalues to be
been made for losses. In thesecircumstances
rare and small. Those forS. rubellumcould perhapsbe acceptedas due to cumulative
small errorsin measurement
and loss estimates,sincethe growthwas small. Those for
are less easilyacceptedhowever.The
S. recurvum,
for S. cuspidatum,
and particularly
S.
shownas a solid symbol
negativevalues (and thewildlydeviantvalue for cuspidatum
methods
Table 7. Comparisonofgrowthin dryweightestimatedby twodifferent
P = 0-05
No. of Correlation
Mean
S.E. of
mean
samples coefficient difference 't'
confidence
of estimates
difference
limits
0 053
(0 92) to (1-14)
41
rubellum
Sphagnum
0-80
0-028(1-03) 0-52
S. cuspidatum
28
0 84
(1 08) to (1-34)
0-186(1-20) 3-60** 0-052
47
0 85
S. papillosum
(0 94) to (1-09)
0-012(1 01) 0-32
0-038
41
0-071(1-07) 2-83** 0 025
(1 02) to (1-12)
S. recurvum
0-86
The methodsusedwerethecapitulum
correction
method(h) and theweightunderwatermethod(i).
Data weretransformed
to logarithms
foranalysis.Values in parentheses
are retransformed
to the
originalunits,and aretherefore
theratiooftheestimate
bymethod(h) to thatbymethod(i).
Species
in Fig. 7) are notobviouslyassociatedwithparticularly
smallvaluesof growthestimated
by the capitulumcorrectionmethod(whichmighthave indicatedthatthe logarithmic
was inappropriatefor verysmall values). The simplestexplanationof
transformation
thesefeaturesis thatthereis some grosserrorin some of the estimatesby the weight
under water method.The most likelyis that gas bubbles were trappedbetweenthe
plantsduringweighing.This is particularly
likelyto happenwithS. cuspidatum,
because
thebranchestendto flexoverbubblesand preventtheirrelease.Of thenineS. cuspidatum
samplesshowingtheselarge deviations,fourwereweighedat the intermediate
harvest
as well,and all show growthsince the firstharvest,but a large apparentloss between
second and finalharvest.
Thereis some indicationthatthismayhave happenedto a fewplantsof S. rubellum
and S. papillosumas well.
Assumingthatthe errorsin each methodare random,it is possibleto calculatethe
difference
betweenthe two estimatesforeach sample and testthe hypothesisthatthe
mean difference
is zero (Table 7).
Thereis no reason to suppose,fromthesedata, thatthe two methodsgive different
resultswhenapplied to S. rubellumand S. papillosum,forwhichthe mean differences
R. S. CLYMO
31
is lessgood fortheothertwospecies:7 and 20% difference.
are 3 and 10. The agreement
Apart fromthe possibilityof errorsdue to small gas bubbles (not large enough to
producegrossanomalies)forwhichthereis no real evidence,the mostlikelysourceof
the discrepancylies in the correctionforlosses, whichis largerfor thesespecies than
of theestimatesto changesin thevalue
and S. papillosum.The sensitivity
forS. rubellum
taken for proportionlost is not the same. For the weightunder water methodthe
correctionmustbe applied to the averagetotalmass,includingthe originalplants.For
the capitulumcorrectionmethod,the allowanceforloss is made primarilyon the new
growth(witha separateand less importantcorrectionforloss of originalstemmaterial).
Where growthin weightis large compared to the weightof the originalplant, the
relativelyinsensitiveto errorsin the estimates
difference
betweenmethodsis therefore
is, of course,altered.Wheregrowthin weight
both
of
value
absolute
the
though
loss,
of
betweenmethodsis
plant,thedifference
weight
of
the
original
to
the
is smallcompared
was about 1-5,
weight
dry
original
to
of
growth
the
ratio
which
for
larger.S. recurvum,
0 3, showsthe
of
about
ratio
with
a
S.
cuspidatum,
showsthefirstof theseconditions;
second.
to errorsin loss estimatescan easilybe shown.It is possibleto calculate
The sensitivity
betweenthe methods
theproportionalloss necessaryto make the sum of the difference
value
of 0-23measured.
the
with
compared
is
0-28,
this
S.
cuspidatum
For
equal to zero.
the loss would have to be 0 50, comparedwith0-25 measured.It has
For S. recurvum
been assumedthatthelosses wereuniformin timeand thattheywerethesame forlive
and dead partsof theplant.These assumptionsare almostcertainlyuntrue,and add a
of thegrowthestimatesforS. cuspidatum
The sensitivity
elementof uncertainty.
further
(by theweightunderwatermethod)to such a small changein estimatesof losses is so
of2000 shouldprobablynotbe takento indicate
greatthattheobservedmeandifference
thatthe two methodsof growthestimationdisagree,althoughwhenthe errorsin loss
though
theremaybe real disagreement,
estimationare added theydo. For S. recurvum
thesize of thisis muchsmaller:700.
In conclusion,it seemsthat,iflosses are large,or ifgrowthis small,theweightunder
open to error,and greatcaremustbe takento avoid trapped
watermethodis particularly
gas bubblesin all situations.If growthand losses are large,thetwomethodsmayagree,
but theaccuracyof theestimatesof fln+,fpdependsmuchmoreon theaccuracyof loss
thetwomethodsmutuallysupporttheconclusion
estimation.In theirgeneralagreement
alreadymade. Sincetheweightunder
thatbothare fairlyreliable-withthereservations
and proneto accidents,thecapitulumcorrecmoredifficult
watermethodis technically
thoughless sensitive.
tion methodis usuallypreferable,
Comparisonof directand 'crankedwire'estimatesofgrowthin length
These estimateswere made on crankedwiresin the containersand on the plants
immediatelyaround the wires.The resultsare shownin Fig. 2. Agreementwas satisfactory.
'FIELD
TESTS' OF TWO METHODS
Methodswhichare practicablein theprotectedconditionsjust describedare not necessarilysuitablein fieldconditions.
The main object of the followingexperimentwas to test the capitulumcorrection
method(h) and the crankedwiremethod(d) in fieldconditions.The testswere more
B J.E.
32
Thegrowthof Sphagnum
satisfactory
than anticipatedand gave resultswith widerapplicationthan expected.
siteswereat Moor House National NatureReserve,Westmorland,
The experimental
England (on the area, at about 575 m altitude,knownto workerson the Reserveas
BurntHill) and on the bog at ThursleyCommon,Surrey(at about 30 m altitudeand
now a local NatureReserve).
area is to the south of the
BurntHill is coveredby blanketbog. The experimental
pool and hummock
centre.It is about 300 m across,verywet,and witha well-developed
?
Thursley
16
~~i0
E10
~
.2
8
0
13
6
?
9
12
20
5
17
21
23
I 19
4
[0E
6
IC
I
MoorHouse
*
.a 20
a.
0
F21
21
17
16
26
>
,[
20
0~~~~~
15 0
E
a,
L
<
House
_Moor
5|
j~~~~~~~~~~Alc
Holt
O 0
A
M
J
J
A I
1963
S
O
N
D
J
F
IM
1964
AI
Common(Surrey)
FIG. 8. Someclimaticand habitatvariablesforthefieldsites,Thursley
meantemperature.
are monthly
and Moor House (Cumberland).
The lowerhistograms
For Moor House, thetemperatures
wererecordedat 09.00 hoursdailyat 30 cm in the
Commonthenearestcomsite.For Thursley
groundabout 1 kmfromtheexperimental
about13 kmfromtheexperimental
site.
parablerecordsarefromAliceHolt (Hampshire)
on the
Recordsare for20 cm (thicklines)and 61 cm. Trianglesare spotmeasurements
are 'rainfall'at thesameMoor House
sitesat 30 cm.The upperhistograms
experimental
stationas temperature
about4 kmfromtheThursley
site.
and at Milford,
meteorological
are numberof days withmorethan 1 mm of precipitation.
Figuresin the histograms
Circlesshowthepositionofthewatertablein thepool on thesite,relativeto an arbitrary
datum.
fuscum).The edgesof thepeat are eroding,
complex(includinghummocksof Sphagnum
withgulliesas deep as 2-5 m. Bower (1959) consideredthatthe hill is in an earlystage
oferosion,and thatthegulliesare cuttingback intothecentralmass.The mostabundant
macroscopicplant species in the experimentalarea are S. papillosum,S. cuspidatum,
S. rubellum,Eriophorumvaginatum,E. angustifolium,
Scirpus cespitosus,Empetrum
nigrumand Cladoniaarbuscula(agg.).
ThursleyCommonis a valleybog, derivingits main watersupplyfroma catchment
of Lower Greensand(Folkestone beds). The surroundingarea is dry heath,mainly
R. S. CLYMO
33
and Ulex eurocoveredby Calluna vulgaris,Erica cinerea,Betula spp., Pinussylvestris
duringthe last
is
probably
grown
considerably
also
very
wet,
and
has
paeus. This bog
hundredyears,due to impeded drainage.Tracks shown on the 1870 (revised 1913)
OrdnanceSurveymap as crossingone arm of the bog are now coveredby up to 1+ m
sitelies in theotherarmof thebog, in an area shieldedfrom
of peat. The experimental
the main line of waterflow,in a similarway to thatdescribedby Newbould (1960) for
Cranesmoor-a New Forestbog. The peat in thisarea is about 90 cm deep. Thereare
a numberofpools in thearea, butfewerhummocksthanon theMoor House site.There
and
mainlyS. papillosum,S. recurvum
is, again,an almostcompletecoverof Sphagnum,
The pools within20 m ofthesitecontainratherlittleS. cuspidatum,
but this
S. rubellum.
heath,but do not
speciesis commonelsewhere.Fires are frequenton the surrounding
thebog surfacemuch.
appear to have affected
was primarily
to testthemethods,onlya fewspotmeasurements
Sincethisexperiment
profileto 30 cm and
of climaticvariablesweremade. At harvesttimesa temperature
the waterlevel in relationto a fixedpost wererecorded.At both sitesthe watertable
betweenspotmeasurecan fluctuate
by at least5 cm in 3 days.The maximumdifference
mentsat Thursleywas 8 cm,and at Moor House 9 cm. Thereis no obviousrelationship
(Fig. 8) betweenthe spot levelsand monthlyrainfall.This is not unexpectedsince the
rapidly.Thereis, however,a close connectionbetween
watertable fluctuatesrelatively
at 30 cm and thatat the meteorologicalstationsat about the same
mean temperature
in Augustin both bogs. The
depth,withthepossibleexceptionof highertemperatures
of the dailyfluctuations
30 cm depthwas chosenas a depthat whichsome integration
between
would be achieved(Geiger 1965). The mean difference
of surfacetemperature
The surface
sitesis about 20 C or about 2 monthsin theyearfora giventemperature.
are muchgreaterof course; up to 300 C at the surfacehas
of temperature
fluctuations
been recordedon a sunnywindlessday evenat Moor House, butin theabsenceof more
detailedrecordsthiswill not be consideredfurther.
werethesame fouras in thelaboratorytests.Theywere
The speciesin theexperiment
in the Sphagnum
all collectedat Moor House, and cut to 5 cm long beforereplacement
to Thursley.At each site,groupsof plantswere
carpetat Moor House, or transplanting
in termsofheight
placedin each ofthreehabitats.Thesecould notbe definedbeforehand
relativeto thewatertable,so the Sphagnumplantswerethemselvesused as indicators,
lawn (S. papiland S. recurvum),
and thethreehabitatsdefinedas pool (S. cuspidatum
losum and some S. recurvum)and hummock(S. rubellum).There were six harvests
throughthe courseof a year(at 10, 14, 20, 30, 41 and 51 weeks) afterthe startin late
precludedharvestingat both sites on the same day,
April 1963. Transportdifficulties
and mostlymuchless. For statistical
but the intervalwas nevermore than a fortnight
The harvestedplantswere
purposestheseharvestshave been treatedas contemporary.
stored at - 16? C until it was convenientto measurethem. (Storage at 20 C is not
to preventextensiongrowthin some cases.)
sufficient
was a groupof tenplantstiedroundlooselywitha nylon
The unitformeasurements
weremade ofgrowthin length
Measurements
thread,to helplocationand identification.
and in mass, by the capitulumcorrectionmethod.Concurrentestimatesof losseswere
made on dead Sphagnumin nylonbags (Clymo 1965),allowingan estimateto be made
of the quantityfln+ fp (Fig. 1). The correctionfor losses was about 2000 of growth,
dependingto some extenton species.
During the experimentthreegroups of plants were not recoveredfor a varietyof
reasons.They have been treatedas 'missingplots' in the analyses(Snedecor 1956). A
Thegrowthof Sphagnum
34
Table 8. Analysisof varianceof growthin lengthand of growthin weight
(boldfigures)of Sphagnuminfieldconditions
Treatment
df
Mean
square
3-3
40
1.1
7-4
5-6
4-2
15-4
2-9
0-33
0-42
0-23
0-021 0-060
F (all ***)
160 66
5
Time (A)
2
361 19
Habitat(B)
205 93
1
Site
(C)
142 255
3
Species (D)
16
2
BC
Interactions
3
21
CD
11
ABC
10
27
Error
140
Total
see text.Growthwas transformed
For detailsoftreatments,
withPO0-001 are
in bothcases. Onlyeffects
to logarithms
shownhere.
Table 9. Mean valuesof growthin lengthof Sphagnuminfield conditions
Habitat(B)
Samplingtime(A)
Carpet(amongst
(weeksand approximate Hummock(amongst
S. papillosum)
S. rubellum)
calendardate)
Site(C) ThursleyMoor House ThursleyMoor House
1-2
1-5
2-3
0-8
10 Last weekJune
4-4
2-4
30
1-7
15 FirstweekAugust
4-6
3-4
20 SecondweekSeptember 3-5
1-9
44
19
30 ThirdweekNovember 4-1
4-7
3-8?
3-2?
1.9
3-7?
41 Last weekJanuary
5-2
4-7
4-2
1.9
51 SecondweekApril
Species(D)
Pool (amongst
S. cuspidatum)
ThursleyMoorHouse
24
2-8
40
3-3
5-4
5-5
56
7-4
4-7?
7-3
5-8
8-3
Site(C)
ThursleyMoor House
30
1-8
4-8
40
S. rubellum
S. cuspidatum
4-1
2-4
S. papillosum
4-3
3-8
S. recurvum
Mean valueshavebeenretransformed
For detailsof treatments,
see text.Growthis in centimetres.
fromlogarithms.
Table 10. Mean valuesof growthin weightof Sphagnuminfieldconditions
Samplingtime(A)
(weeksand approximatecalendardate)
Habitat(B)
Site(C)
Species (D)
14
20
51
10
30
41
Last week Firstweek Secondweek Thirdweek Last week Secondweek
June
April
August
September November January
55
10-3
12-3
14 0
15-3
16 7
Hummock(amongst Carpet(amongst
Pool (amongst
S. papillosum)
S. rubellum)
S. cuspidatum)
13 7
11-4
101
Moor House
Thursley
142
9.5
S. rubellum
S. cuspidatum
S. papillosum
S. recurvum
44
15-3
14 4
18-7
For detailsof treatments,
see text.Growthis in mgplant-'. Mean valueshave beenretransformed
fromlogarithms.
35
R. S. CLYMO
is thesporadicoccurrence
moreseriousproblem,whichhas notbeensolvedsatisfactorily,
of individualdead plants,and in six cases (out of 141) of wholegroupsof dead plants.
All theseweremeasuredseparatelyfromthe live ones. The sporadicdead plantswere
not obviouslysystematicin occurrence,so were leftout, the growthper plant being
fourwereS. cuspidatum
The wholegroupsweremoresystematic;
correctedaccordingly.
in the
two
wereS. recurvum
other
and
the
in thelast threeharvestsin thedrierhabitats,
species
of
these
further
growth
of
Absence
last two harvests,again on the hummocks.
in thesame
be interpreted
mustnottherefore
in dryhabitatsat theend oftheexperiment
live
plants.
way as for
5T
M
(a)
(b)
0
M~~~~~~~~~
/~~~~~~~~~C
O
M J
J A
S O
1963
N
D
J
F M A
1964
M JJ
(d
A S O
1963
N D
J F M A
1964
speciesat twosites.The capituFIG.9. Growthin lengthduringa yearforfourSphagnum
methodwas used. Filledsymbolsindicatethatall plantsat thisharvest
lum correction
foranalysis,so theS.E. varieswiththe
to logarithms
weredead. Data weretransformed
mean.As a graphicaid, theS.E. ofthey valueis shown(bythesteeplyslopingline)as a
fromthex = 0 axis. The unitsof thisare, however,thoseof they axis.
displacement
(a) S. rubellum;(b) S. cuspidatum;(c) S. papillosum; (d) S. recurvum.T, Thursley; M,
Moor House.
Estimatesofgrowthin lengthwerealso made at Moor House, usingcrankedwires(d).
Resultsare shownin Tables 8-10 and in Figs. 9-12. The mainpurposeof theexperimentwas achieved.With the exceptionsalreadymentionedthe capitulumcorrection
methodappearspracticableforfielduse, thoughrathertedious.
The analysesof variancegive threegroupsof results.
The
forboth measurements.
The firstgroupincludesall but one of the main effects
significanceof these is high-variabilitywas far less than had been expected. The
but theresultsare hardly
estimateof errorwas takenfromthehighestorderinteraction,
are used. The second groupincludethe
affectedif second and thirdorderinteractions
These are all
in the lengthmeasurements.
main effectof habitatand threeinteractions
Thegrowthof Sphagnum
36
butbecauseof thedeathof someplantsmay,in reality,
statistically,
significant
highly
in thefifth
due to fouroftheresults
ABC is mainly
The interaction
be lessimportant.
and thereis reasonto thinkthat
veryunlikely
(Table9). Thesearebiologically
harvest
1 cmshort.
Theremaining
recorded
weremistakenly
someatleastofthesemeasurements
in growth
in lengthof themore
to thedifference
CD, is due principally
interaction,
at thetwosites.The thirdgroupare
and S. papillosum,
terrestrial
species,S. rubellum
whichneednotbe discussed.
ofmuchlowersignificance,
results
are:
Theprincipal
results
on
whichhasa summer
temperature
(Figs.9 and11)atThursley,
is greater
(a) Growth
(a)~~~~~~~~~~~b
p~~~~~~~~~~~~~~~~~~~~~~
5
h~~~~~~~~~~~~~~
0
o'
(c)
(d)
o~~~~~~~~~~
M J
J
A S O
1963
N D
J
F M A
1964
M J J
A S
1963
0
N D
J F
M A
1964
(h) (withSphagnum
FIG. 10. As Fig. 9 butshowingresultsforthreehabitats:hummocks
as originalcover);lawns(1) (withS. papillosumas originalcover);pools (p)
rubellum
as originalcover).The harvestdateshave been shownas halfway
(withS. cuspidatum
betweentheactualdatesat thetwosites.
number
andgreater
rainfall
thanat MoorHouse,despitethehigher
average4? C higher
of Thursley
valleybog, the
of wetdaysat Moor House. Becauseof thehydrology
In theabsenceof somesystem
of theregionis notmanifested.
waterdeficit
potential
cannotsurvivein the
the rainwatersupply,Sphagnum
and buffers
whichamplifies
A setof tenestimates
was madeon S.
climateoftheThursley
area,however.
present
ofabout750m.
Mineat an altitude
at MoorHouse,butneartheStakebeck
papillosum
habitat
with23-6mgplant-1in a comparable
Thesegave12-5mgplant-1, compared
fortheDun Fellmeteorotemperature
on themainsite175mlower.Themeansummer
and 3 kmawayis about20 C lowerthanthat
logicalstationat aboutthesamealtitude
at Moor House.
in thesummer
months.
rateoccurs,as mightbe expected,
growth
(b) The greatest
37
R. S. CLYMO
byOverbeck
Thereis no indication
ofa midsummer
'restperiod'suchas thatreported
& Happach(1956).Theyworked,
however,
on a raisedbog wherethewatertablefell
waterlevel,theyfoundno suchcheck
20-35cmin summer.
In cultures
witha constant
ofwatersupply.
in growth.
Thepresent
siteswerenotsubjectto suchextremes
ofplantsin pools,particularly
in weight
(c) It appears(Figs.10 and 12) thatgrowth
thewinter
months
whileotherspecies,
ofspeciesnormally
foundthere,
continued
during
measurehad almoststoppedgrowth.
Temperature
and thesespeciesin otherhabitats,
ments
in thepoolsmight
be informative.
in thethreeenvironments
is leastforthemost
ofgrowth
in weight
(d) Thedifference
to the mostaquatic(S.
and increasesprogressively
terrestrial
species(S. rubellum)
Thismaybe interpreted
to showthatS. rubellum
can growwellin a very
cuspidatum).
(b)
(
(a)
5T
-~~~~~~~~~~~3
0~~~~~~~~~~~~~~~1
EC
0
30
20 -2
MD
J0
Ac J
A30
MJJASOd
10
10
1963
1964
1963
1964
FIG. 11. As Fig. 9 but showingthe netgrowthplant-' (fin+,8p,Fig. 1). (a) Sphagnum
T, Thursley;M, Moor
rubellum;
(b) S. cuspidatum;
(c) S. papillosum;(d) S. recurvum.
House.
wetenvironment,
cannotgrow
thoughit is notusuallyfoundthere,butS. cuspidatum
wellin an environment
occupies.Thisis confirmed
bythe
muchdrierthanit normally
to
ofdeathsalreadydescribed.
inlength
doesnotshowthesedifferences
pattern
Growth
thesameextent.
willbe madein a laterpaper.
Further
comment
on thesefactors
Growthin lengthcan be compareddirectly
between
different
species.The difference
for
between
in lengthis leastforthedrierenvironment,
and greater
speciesof growth
thewetterones.Thishas beenconfirmed
whichare reported
in cultureexperiments,
and is bestconsidered
separately,
withthem.The crankedwireand directestimates
(Fig.2) arein satisfactory
agreement.
Thegrowthof Sphagnum
38
ofgrowth
in weight
fordifferent
to compareestimates
species,because
It is difficult
ofstem
perplant,andthesizeofplantsvaries.A basisofunitweight
theyareexpressed
specialized
one.
butthisunitis a highly
forreasonsalreadydiscussed,
mightbe better,
perunitarea.The conversion
fromplantto areabasis
It is simpler
to comparegrowth
is nowconsidered.
(a )
(b)
p~~~~~~~~~~~~~
20
-
L
0~~~~~~~~~~~~~~~~1
a'
(a
30
20
I0
1
<1
M J
1
1
1
J A S O
1963
1 0
1
N D
J F M A
1964
1
M J
1
1
J
1
A S
1963
1
0
N D
J
F M A
1964
netgrowth
rubellum;
12.AsFig.10butshowing
Fig. 1). (a) Sphagnum
plant- (6ni+,fi,
p, Pool; 1,lawn; h. hummock.
(c) S. papillosum;(d) S. recurvum.
(b) S. cuspidatum;
FIG.
CONVERSION OF RESULTS TO AN AREA BASIS
speciesand habitats-for
areas are oftena mosaicof different
Sphagnum-dominated
forthewhole
ofproduction
Anyestimate
and hollowtopography.
examplehummock
areawilltherefore
needgrowth
on an areabasis.
estimates
Overbeck& Happach(1956) estimated
growthin length,the averagenumberof
Chapman(1965)
plants/dm2,
and thedryweightof a lengthequal to a year'sgrowth.
and unlessthesampleson
variations,
useda similarmethod.Bothreportconsiderable
area,a ratherlargeerrorcouldbe
was measured
occupya well-defined
whichgrowth
was therefore
introduced.
between
numbers
The relationship
and,averageplantweight
Allplantswithin
froma widerange
examined.
squareplotsofside10cmwerecollected
of sitesin England.The sampleswererequired
to be morethan9500 ofonespeciesof
vertically.
They
nearly
to containfewotherplantspecies,andto be growing
Sphagnum,
weretakenfromas widea rangeofhabitats
notmerely
fromthecommonest
as possible,
one forthatspecies.The number
and eachplant
ofplantsin thesamplewas counted,
was separatedintocapitulum
(0-1 cm),and in mostcases,thenext3 cm (1-4 cm).
39
R. S. CLYMO
fromthestems,and thedryweightof these
plusleaveswerethenseparated
Branches
in branch
periodicity
where
therewasdistinct
In thosecases
determined.
threefractions
1-4cm
of
wastaken(instead thearbitrary
thewholeofthesegment
andlength,
density
four
species
the
same
1
for
Results
of
cm
length.
arerelatedto a unit
Allresults
section).
reported
byGreen(1968)all
as beforeareshownin Fig. 13.Themeanspatialdensities
leadsto a very
and
weight
fallwithinthelimitsshownhere.The use of log numbers
of
-1.
Thesearelines
slope
lines
with
diagonal
parallel
to
the
attaching
simplemeaning
of equal mass areat depth 1.
2
E
3
o
0o
0
Cypitulo(
( -1cm)
A
AAAf
E
00~~~~~~~~~~~~~
a
V
0
0 102051
oL
~~~
A
E
V2
U-
-0 5
0
VVE
E
0o
2f u
ar
0
20
I0
loglo dryweight(mg)
A
2-0
0
10
(mg cm-')
logli dryweight
V
0 20
weig0h.5
1.0
Stems
0
0
2dm O
~
U
05
log10 branchdryweight(mg)
30
Branches +stem
EVA
00
*
0~~~~~
5
15
30 -
0
0
0
dw
t
A
V-
gdm2
02
10
0
logatdry
weight(mgcm-')
andmeandryweight
FiG.13.Relationship
between
spatialdensity
perplantforvarious
of thesameplants.o, S.
stemsandbranches
plants,andbetween
partsof Sphagnum
linesof slope- 1 0
Straight
u, S. recurvum.
A, S. papillosum;
V, S. cuspidatum;
rubellum;
was
section
cm' On somesamples
onlythecapitulum
arelinesofequalweight bran
weighed.
in thesegraphs.
Thereareseveralnotablefeatures
(a) Althoughit is in generaltruethatthelargerstemscarrya greaterweightof
thegreatvariability
theconnection
withina speciesis tenuous.Thisreflects
branches,
withmuch
ingrowth
form.Someplantshavemanylargebranches
closely
packed,others
arefoundeven
thesamesizeofstemhavefewbranches
widely
spaced.Thesedifferences
in theabsenceofdistinct
cyclicvariations.
For
constant.
themassdm-2ofcapitulais remarkably
(b) For all butS. cuspidatum,
to find
uncommon
S. cuspidatum
thevaluesarelower.Thismaybe becauseit is rather
Evenwherethe
vertically.
muchabovethewatertable,or growing
thisspeciesgrowing
40
Thegrowthof Sphagnum
verticalconditionwas satisfiedthe sites were usually verywet, and oftenthe plants
appearedto be spreadinginto a previouslyopen sitein veryshallowwaterat the edge
of a pool. The capitulawereusuallyverylax, and thewholelawnvery'open' in structure.
Althoughthe capitula are close to a constantmass area-' depth-', the stemsand
branchesare not. Each specieshas itscharacteristic
regionon thegraph.The volumetric
densityof S. recurvum
below the 'standard'capitulumis onlyabout 03-O 5 thatof S.
This is almostexactlybalanced,however,
bythelargervertical
papillosumandS. rubellum.
on thesesamples,the depthof green
extentof greenbranches.Wheredistinguishable
and only2 cm in S.
canopy below thecapitulumwas on average6 cm in S. recurvum,
rubellumand S. papillosum.In all threespecies,the total mass of greenbranchesplus
stemsis almostthe same-2 g dm2 -and the same as themass of capitula.
It is not immediately
apparenthow thisparticularlimitis imposed.Tinbergen(1940)
and Overbeck& Happach (1956) have shownthatmorethan0 90 of theincidentlight
(measuredwitha photocell)is absorbedin the top 2 cm of the Sphagnumlawns which
theyexamined,althoughless for S. recurvum
than for otherspecies. The volumetric
ofmatterappearsto be ratherlow (Table 11) butis notso whencompared
concentration
withmostplantcommunities,
whichspreadtheirphotosynthetically
activepartsthrough
a greaterverticalrangethan does Sphagnum.
Table 11. Volwmetric
concentration
of matterin blanketbog at Moor House
Depth(cm)
Dryweight(g 1')
ml organicmatter1I
0-1
20
12
6
1-4
10
45-50
75
120
= 1-6 has been used in thecalculation.The
Specificgravity
data for0-4 cm depthweretakenfromFig. 13,thosefor45-50
cm fromClymo(1965).
(c) For converting
growthresultsto a unitarea basis, the quantityrequireddepends
on the method.If growthin weightper plant is measured,thenthe spatial densityis
thestandarderrorof themeanvalue of spatial densneeded. For all but S. cuspidatum
ityis about 100 ofthemean value. If howevergrowthin lengthis measuredthenthe
weightof plantsper unitarea and depthof lawn are needed.
The appropriatequantityis the 1-4 cm sectionratherthanthecapitulum,because the
whichproducesa continuousproductcapitulummaybe consideredas the-machinery
thestemand branches.The quantityrequiredis theamountof product,not theamount
of machinery.The standarderrorof the mean for the standard3 cm depth of this
is also about 10%4of themean. (The scale on thediagonalaxis of Fig. 13
measurement
is only0 7 thatof theverticaland horizontalones.) Use of thisconversionassumesthat
and forthis
therehas been no changein thesize of thecapitulumduringtheexperiment,
reason alone mustoftenbe inaccurate.
More seriousis thatweightarea-' is not constantwithdepth-the extremeexample
is cyclicpatternof branchspacing.For periodsof less thana yeartheremaytherefore
be seriouserrorsin assumingit to be constant.
The other major inaccuracyis likelyto occur when the fielddata are applied to
in conditions
situations.A plantmay survivefora yearin an experiment,
experimental
In thesecircumstances
thefielddata
in whichit would not naturallyforma community.
are used outsidetheirrangeof application.Whilstthe spatial densityof plantscan be
41
R. S. CLYMO
method,
thatthefirst
cannot.It seemstherefore
responses
themorphological
controlled,
the
than
objections
open
to
fewer
is
conversion,
density
for
needingonlythespatial
workers.
previous
second,thoughthesecondis theonewhichhas beenusedby
havebeenconverted
to
ofthefieldexperiment
Results(/3 + fl,)fromthelastharvest
on
of
variance
analysis
12.
An
in
Table
are
shown
and
an areabasisbybothmethods
betweenthe
of a difference
showssomeindication
of thedifferences
thelogarithms
and S.
for
S.
cuspidatum
method
by
the
first
larger
estimates
due
to
the
species,mainly
errorofabout8?., but
forall is 9 5y4,witha standard
The meandifference
recurvum.
beas thedifferences
in length,
fromgrowth
iftherearelargeerrorsin theconversion
thenthelackofsigniFigs.10and 12wouldsuggest,
tweenFigs.9 and 11,andbetween
and due to thepositiveand negativeerrors
coincidental,
is entirely
ficantdifferences
used.
rangeofconditions
equalsizein theparticular
beingofapproximately
Table 12. Estimatesof growth(g dm-2 year-'), by two methodsfor four species of
Sphagnumat two sites and in threehabitats
Species
Site
Habitat
Hummocks Thursley
Moor House
Thursley
Lawn
Moor House
Pool
Thursley
Moor House
No. ofplantsdm 2
Mean g dm-2
S. rubellum S. cuspidatumS. papillosum S. recurvum
4 3 (3 7)
2 4 (1-3)
3-2 (3 6)
2-4 (2 3)
4 3 (6 8)
24 (3-8)
450
36
18
36
1.9
79
79
(3 4)
(1 2)
(2 6)
(2-3)
(5 0)
(4-1)
150
3-1 (4 6)
2-4 (1 9)
4-0 (5-1)
3-3 (4 4)
6-1 (8 2)
21 (45)
125
3-6 (3 2)
2-3 (1 1)
4.8 (2 6)
4-8 (3 3)
5 4 (4 4)
60 (4-1)
150
cm'1
+
(stems+ branches
05
1.0
05
1.0
leaves)
Estimatesare made on plantsfromthelast harvestonly,fromgrowthin weightperplant
inlengthperplanttimesmean
andfromgrowth
perunitarea (boldfigures)
timesmeannumber
in parentheses).
The constantsforS.
weightper unitarea per unitlengthof plant(figures
havebeenassumedthesameas thoseforS. recurvum.
cuspidatum
ofdifferences,
butifonemethod
indication
In summary,
thereis no strong
statistical
correction
method,
workitshouldbe thecapitulum
forexperimental
has to be preferred
inTable12fittheusual
theresults
toit.Usingthisestimate
as therearefewer
objections
all speciesshowgreatest
(or equal
ofthefourspecies.Although
ecologicaldistributions
at MoorHouse),thetwo
ofS. papillosum
in pools(withtheexception
growth
greatest)
in thedifferent
habitatsare:
bestgrowth
speciesshowing
and S. papillosum
(Thursley)
Hummocks S. rubellum
(MoorHouse)or S. recurvum
Lawn
Pool
S. papillosumand S. recurvum
(Moor
and S. papillosum
S. cuspidatum
(Thursley)or S. recurvum
House)
of fieldbehaviourmust
is anothercase whereany explanation
Here,apparently,
ofplantinteractions.
includesomeconsideration
GENERAL DISCUSSION
The accuracyofgrowthestimates
and comes
theonlyavailableevidenceofaccuracyis indirect
As alreadymentioned,
For
this
reason
diverse
as
methods
as
possible.
between
of
fromthecloseness agreement
42
Thegrowthof Sphagnum
and
correction
(to within2000 or less) of thecapitulum
thegeneralcorrespondence
Additional
is important.
habitats,
usedin widelydifferent
weight
underwatermethods,
comesfromtheagreement
support,thoughof muchless value becausequalitative,
between
ratesandecologicalbehaviour.
fieldgrowth
of growth
in lengthare also in good
(crankedwire)estimates
Directand indirect
up to 10000, thoughaveraging
(individually
buttherearelargerdifferences
agreement,
in
correction
and growth
on an area basisderivedfromcapitulum
10%) forestimates
lengthmethods.
evidence
thatestimates
itseemsthatthereis at leastindirect
Takentogether
therefore,
ofgrowth
arefairly
accurate.
bythesemethods
The constancyof totalcapitulummassper unitarea
Where w = mean weightplant-', d = numberarea-', and c and k are constants,
lineon Fig. 13is:
thentheequationfora straight
w = cdk
or log w = k log d+log c
In thisparticular
case k = -10, and c = totalmassarea-' cm-'. Thereis a formal
subterraneum
betweenthisresultand thoseof Donald (1951)forTrifolium
similarity
and in
(bothseparately
and of Harper(1961)forBromusrigidusand B. madritensis
aftertheplantsbegantointeract.
Thereare,however,
mixtures),
at thestagesin growth
in whichthisrelationship
heldforthehigher
in theconditions
important
differences
andhad
Thehigher
at different
densities,
plantsstarted
plantsandthoseforSphagnum.
in
Theplantweight
wasmeasured,
grownforthesametime,and thesameenvironment.
measurements
whilst
theSphagnum
on theamountofvertical
growth,
withno limitation
1
of
cm.
refer
to thearbitrary
depth
weedand forfour
Yoda etal. (1963)haveshownthatforfourspeciesofherbaceous
in
of
tree
natural
the
value
k
of
forest
approaches-15.
populations
species(orgroups)
so highthatall stands,whatever
theirage
wereprobably
In all casestheinitialdensities
meansize
and at theirlimiting
fortheparticular
or habitat,
wereselfthinning,
density
ofplant.
Ifs = meanareacoveredbya plant,then
S=d-=
is thattheplantswere,at all stagesofgrowth,
geometrically
Theirsecondassumption
to its volume)varieswithi3,
similar.The weightof a plant(assumedproportional
of12. Hence:
theareacoveredis a function
whilst
s oc w1.*
withlarger
than-10. Forthisto be truethelessdensestands,
andso k = 1-5 rather
result
would
vertical
dimensions
a
similar
also
have
must
(though
larger
individuals,
of
increased
the
volumetric
material
while
changed).
geometry
followifthe
density plant
on Amaranthus
showthatthe ratioof
For example,theirmeasurements
retroflexus
in leastdenseand mostdensestands(- 30) was morethantheratioof s05
heights
fixeddepth,as has beendone withthe
(- 6) forthesestands.Takingan (arbitrary)
ofYoda et al.
withthesecondassumption
is notconsistent
measurements,
Sphagnum
(1963).
thenecessary
measurement
on Sphagnum;
to devisea meansformaking
It is difficult
fromthe
howmanyofthepresent
at leastit wouldinvolvefinding
capitulaoriginated
ofa recognizable
mutation
or similar
sameplant.Theappearance
changeseemsto offer
R. S. CLYMO
43
the best possibility,but has not so far been reported.At one extremea whole carpet
mightbe the resultof vegetativespread of one plant. The otherextreme,with each
presentcapitulumthedirectand onlyproductofeach originalplant,seemsveryunlikely,
forkingoccurredsignisince forkingof main stemsoccurscommonly.In experiments
thanin theother
moreoftenin drierconditions,and less oftenin S. acutifolium
ficantly
threespecies.
The factthatcapitula of the threespeciesof drierhabitatshave the same value for
since each can grow in the habitatnormally
c (_ 2 g dm-2 cm-') is not surprising,
occupied by the other,as the fieldexperimentshave shown, and the similaritiesin
structure
and behaviourof all threespeciesare perhapsreasonablysupposedto be more
stronglyin
interacting
They are presumably,therefore,
importantthan the differences.
naturalconditions.
The rateofpeat accumulation
Althoughthecurrentrateof drymatteradditionat Thursleyis greaterthanat Moor
House, it cannotbe concludedthatpeat accumulationis morerapid. The rate of loss
of matterfromdead Sphagnumis also higherat Thursley(Clymo 1965). Nevertheless,
thenetadditionof matterat thesurfaceis greaterat Thursley(Fig. 11), but thesurface
layersof liveplantsformonlya smallproportion-probablyless than 1%-of themass
of peat at thesesites.Not onlyis therea muchgreaterdepthof peat thanof liveplants,
but thevolumetricdensityis greaterin thepeat (Table 11). Even thoughtherateof loss
of matterfromthepeat is lowerbyperhapsa factorof 100 thanfromthesurfacelayers,
the overallbalance may be much affectedby it. The presentdirectestimatesof losses
preciseor accurate(Clymo 1965) to allow any
fromthe lowerpeat are not sufficiently
firmconclusionto be drawn.
The efficiency
of a Sphagnumcarpet
In boththeresultof a process
Thereseemto be two mainuses of thetermefficiency.
is considered.
is used to measurethe ratio of
(Slobodkin 1962), efficiency
First,and more strictly
outputto inputin a process.The same thingis measuredat both inputand output,so
in thisuse has no dimensions.Examplesare commonin energyflowstudies;
efficiency
food chain efficiency,
(Phillipson 1966). In a
ecological efficiency
growthefficiency,
disguisedformthesame conceptappearsin measuressuch as generationtime(timefor
numbersout to becometwicenumbersin).
of a processis described,but
The seconduse is moregeneral.Again theeffectiveness
insteadof input,some measureof the 'machinery'or capitalis used. The dimensionsin
thiscase maybe almostany.Examplesof thisuse are growthas g dm-2 year-' (dimensions m 12 t-1), wherethe capital is area and time,oxygenproductionper unitmass
althoughit could be expressedas
of chlorophyll
dimensionless,
(whichis fundamentally
into
This seconduse gradesimperceptibly
13 m-1 at a givenpressureand temperature).
at all; spatialdensity(numbers
measureswhichare not usuallythoughtof as efficiencies
per unitarea, 12) is an example.
fora process,and
It is usuallypossibleto make morethanone measureof efficiency
in one set of termsshould be correlatedwiththatin
thereis no reason whyefficiency
be
kindscannottherefore
of different
anotherset (althoughit may be so). Efficiencies
compared.
44
Thegrowthof Sphagnum
ca~~~~~~~~
C'
I
CH
j s ; z04
ct~~~~~~~~~~~~~~~4
t4
~~~~~~~~~~~~~~~~~~~~~Cd
9,
IO
11:
Iz,
E~~~~~~~~~~~~~~R
>
*.
Q
ce
.b.=el
?Z
Si0
at
3
^
3
g
3
3 ?
Z
~o 2
R. S. CLYMO
45
tool. The measure
is in mostcases used as a practicaland comparative
Efficiency
In
recentyearstwo
the
comparison.
selectedmustdependon thereasonformaking
energetic
These
are
first,
by
ecologists.
commonly
used
measures
havebeenespecially
energetic
capital.
The
area
and
time
as
based on
efficiencies
and second,efficiency
rather
low;
content
is
itself
4-114-32
is ratherlow.The energy
efficiency
ofSphagnum
kcalg-1 (Gorham& Sanger1967);4-21-446kcalg-1 forsixsamplesofthefourspecies
have not beenmade at eithersite,but
used in thiswork.Radiationmeasurements
is
of Sphagnum
radiation,
theefficiency
60 kcal cm-2 year-' forincoming
assuming
about0.2%. On an area basis, at leastin theuplandsite,Sphagnumseemsto be of about
and drierblanket
as thegrasslands
producer,
thesameefficiency,
as a netdrymatter
production
(Table 13)
bogsofthearea (Table 13). In thelowlandsite,netdrymatter
1957).
on sandysoil(Ovington
is onlyabouta thirdthatofpinewoodgrowing
thepositionis altered
is madeon basisofN or P capitalemployed,
If comparison
thanpine.Thatthismaybe
efficiency
has a higher
(Table13).In bothcasesSphagnum
is suggested
of biologicalsignificance
bytheworkofWatt& Heinselman
a difference
Minnesota,
and ofBrown,
ofPiceamarianaon a bogin northern
(1965)on thegrowth
on a bogin southern
ofPinussylvestris
Scotland.
Carlisle& White(1966)on thegrowth
treegrowth
rateandfoliarconcentration
between
In bothcasestherewas a correlation
withlowconcentration.
correlating
ofN andP, slowgrowth
the
in comparisons
of thiskind,eventhoseof whatis nominally
The uncertainties
smallcomparedwith
are considerable.
Theyare,however,
samemeasureofefficiency,
withaquatichabitats.
to comparethesemi-aquatic
An
thosewhicharisein attempting
appearsto be
at thisis shownin Fig. 13. On all basesthereshown,Sphagnum
attempt
by a factorof two cannotbe counted
thanthelake,but differences
moreefficient
an essentially
in comparing
becauseof thedifficulty
evergreen
community
important
oflivecellsfluctuates
so widely.Talling(1965)has prowithonein whichthenumber
to thoseusedin growth
in manyrespects
analysisofhigher
ducedconcepts
equivalent
neither
between
thempossible.Unfortunately
system
plants,whichmakecomparisons
can be appliedeasilyto Sphagnum.
CONCLUSION
ofSphagnum
is at leastcomparable
hereshowthatthegrowth
with
Theresults
presented
to knowmoreaboutthefield
fromthesamearea.It seemsdesirable
othercommunities
oftheplants.It is notpossible,forexample,
and abouttheresponse
microenvironment
as hummocks
of bog topography
forsuchobviousfeatures
to accountsatisfactorily
andpools.
ACKNOWLEDGMENTS
thisworkwasdone,
G. E. Fogg,F.R.S., inwhoseDepartment
to Professor
I amgrateful
on a draft
ofthispaper;to MrA. J.P. Goreforharvesting
someofthe
forcommenting
ofthework;to Dr E. Fordfortheenergy
samplesat MoorHouseandfordiscussions
toDr K. E. Clymo,Dr P. J.GrubbandtoMrE. J.F. Reddaway
content
measurements;
Mrs
on a draftofthepaper;to MissG. Sellers,MissS. Langsford,
fortheircomments
oftheNatureConserand Mr M. Parhamfortechnical
help;to thestaff
P. Ratnesar,
theworkthere;to
J.B. Craggforfacilitating
vancyat Moor Houseand to Professor
ofLondonComputer
oftheUniversity
thestaff
Service;andtotheNaturalEnvironment
forpartofthework.
ResearchCouncilforfinancial
support
46
Thegrowthof Sphagnum
SUMMARY
growthoverperiodsof a fewweeksto
Sphagnum
Methodssuitableformeasuring
severalyearsare described.
meanvaluesagree
Threeof themostusefulmethodsare comparedin experiments;
to be
on speciesand habitat.Accuracyappearstherefore
to within1-20% depending
in weightunless
withgrowth
Growthin lengthis notcloselycorrelated
satisfactory.
environment.
referred
to a particular
as thetop 1 cmofplant)perunitareais approxiofcapitula(defined
Thedryweight
of
(Fig.13).Thetotalweight
constant-2g dm-2 cm'1 forall speciesexamined
mately
in
2,
but
differences
there
are
to
2
dm
g
greenplantbelowthislevelalso approximates
thedepthto whichthegreenpartsextend.
averages
Englandvalleybogat 30 m altitude
(Table12)in a southern
Netproduction
about
bogat575maverages
Englandblanket
about4 g dm-2year-1,andin a northern
habitats
fordifferent
species,
byan orderofmagnitude
3 g dm-2 year- . Valuesdiffer
and timeofyear.
inpools,lesson lawnsandleastonhummocks
inweight
is greatest
In general,
growth
habitats
is least forthe hummockspecies(S.
difference
between
(Figs. 9-12). The
cuspidatum).
(S.
for
species
pool
rubellum)
and most the
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(Received10 January1969)
APPENDIX
in water
objectswhichare submerged
Weighing
froma balancein air
If theobjectrestsbelowwateron a cradle,whichis suspended
in
maybe introduced
thentwoerrors
thewatersurface,
bya wirewhichpassesthrough
appliesonlyto thosebalanceswhichuse
bythebalance.The first
theweightrecorded
fromthezeropositionas a measureforthesmallersubtheamountof displacement
by an optical
is less than20, and is magnified
divisions.(Usuallythisdisplacement
to thezero
is (usually)tiltedrelative
In suchcases,as thebeamat equilibrium
system.)
thanwouldbe ifthe
wireis submerged
position,thenmoreor lessof thesuspension
The growthof Sphagnum
48
becausesomeofthesuspension
weight,
theapparent
beamwerenottilted.Thisaffects
The
density.
in one fluid(airor water)is nowin theotherofdifferent
wirepreviously
is 3.2% ofthatpart
H03 balanceandtwo26 SWGwiresupports
errorwithan Oertling
decimalpartsofa gram
oftheweight
coveredbytheopticalscale:thethirdandfourth
withsufficient
accuracy.
Thiserrorcan be calculated
(up to 9 9 mgmaximum).
tensionforceson thewireat
andis dueto surface
The seconderroris muchgreater,
and a known
If thewatermeniscus
has reachedequilibrium,
theair-water
interface.
is
themeniscus
is addedto thebeamso thatthewiremovesdownwards,
smallweight
optical
is
a
smaller
The
result
of thewireis opposed.
and themovement
deformed,
No correction
/ tCorrectedfor suspension
irnmersion
7 0 -
6.0
Cumulativeno. of opticolreodings
300
400
100
5 0
043
0
t1o
v
2-
?
_
7
~~~~~~~position
~~~~~~~Equilibriumn
~
10
-2
0
2
6
4
Added weight(mg)
8
10
and surfacetensionerrorsin weightunderwater
curveforimmersion
FIG. 14. Correction
(see
method.The two straight
of suspensionimmersion
linesshowthecalculatedeffect
observeddeviations(0) shownby
text),whichis smallcomparedto theexperimentally
theexperimental
of A). The curveA through
curveA and B (whichis thecontinuation
showsthecumulative
pointsis thecalculatedcubicequationof bestfit.The histogram
of weights
ofunselected
objects(see text).
frequency
A similarerroris producedifthebeamrisesdueto removalof
readingthanexpected.
a smallweight.
Theseerrorscan be morethan100% oftheopticalpartoftheweight.
Sincetotalweights
thiserrorcannotbe ignored.
of about50 mghaveto be measured
in thewater,butthisseemsundesirable
It can be reducedbyputting
soap or detergent
whentheplantsareintended
coatofPTFE overthewire
growth.
A surface
to continue
is to accepta relatively
Onesolution
unstable.
also reducestheerror,
butis mechanically
the
and to standardize
correction
of theopticalpartof theweighing
largeempirical
is cleanedfrequently
thewiresuspension
carefully.
As partofthisprocedure
procedure
withacetone,and thewatersurfacesweptwithpaper.The emptycradleis weighedat
leasteveryfifth
to checkforanysuddenchanges.
weighing
meniscus
shape,and
The detailedmanipulations
toensurea reproducible
aredesigned
R. S. CLYMO
49
to ensurethatopticalreadingsare made withtheminimumdeparturefromequilibrium.
The procedureis:
to a standardposition.This is done becausetheoptical
(1) Set opticalzero adjustment
ofthemeniscus,notdirectly
readingis to be used as a measureofthelineardisplacement
zero
positionused in thiswork was a
as an estimateof weight.The standardoptical
theknifeedges.
on
rested
readingof 5 0 at thepointwherethebeamjust
(2) Find the approximateweight.
weightand releasethe beam. The
(3) Add about 20 mg too littlecounterbalancing
beam firstmoves down 0 3 mm withouttiltinguntil it restson the knifeedges, the
meniscusbeingtherebydepressedbut not slidingup thewire.The beam thentiltsand
about 0 5 mmmoreof thesuspendingwirepasses belowthewatersurface,themeniscus
slidingup thewire.
(4) Arrestthe beam. This removesabout 0-8 mm of wirefromthe waterand leaves
themeniscusextended.Steps2 and 3 ensurethatthemeniscusis in a reproduciblestate
beforetheweighingis made.
weightsand releasethebeam. Withtheparticular
(5) Add thecorrectcounterbalance
balance used, the correctweightsare such thatthe optical readingis between1-4 and
4-6 (curveA, Fig. 14). As the beam is lowered,the meniscusis depressedby 0 3 mm.
As the beam tiltstowardsloweroptical readings,the meniscusis extendedagain, and
(in theseconditions)is at equilibriumat an opticalreadingof2-4.At thispointthecurve
relatingopticalreadingto weightshould be steepest,and a changeof 0.1 unitsshould
be approximately
equal to 01 mg. Carefulexaminationof Fig. 14 showsthatcurveA
is indeedS-shapedin theregionof opticalreading2 4, thoughiftheexpected0.1 mg =
0-1 unitrelationship
is presentitmustbe so fora rangeof + 0 5 mgat most.For practical
purposesthe thirddegreepolynomialof best fit,whichis shownin Fig. 14, was used.
A checkon thiscurveis providedby a Monte Carlo method:thecumulativefrequency
is shownsuperimposedon curveA
of 432 opticalreadingsmade duringtheexperiments
exactness.
in Fig. 14. The histogramfollowsthemeasuredpointswithsatisfactory
In manycases a secondopticalreading(curveB) maybe obtainedforthesame object
on thecradlebyaddingan extra10 mgcounterbalance
weight.The meniscusis,however,
in a veryunstablestate,and reproducibility
is verypoor. The regionbetween4-6 and
7-5is therefore
of no practicaluse.