The Growth of Sphagnum: Experiments on, and Simulation of, Some Effects of Light Flux and Water-Table Depth Author(s): P. M. Hayward and R. S. Clymo Reviewed work(s): Source: Journal of Ecology, Vol. 71, No. 3 (Nov., 1983), pp. 845-863 Published by: British Ecological Society Stable URL: http://www.jstor.org/stable/2259597 . Accessed: 20/07/2012 08:50
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http://www.jstor.org Journalof Ecology (1983), 71, 845-863
THE GROWTH OF SPHA GNUM: EXPERIMENTS ON, AND SIMULATION OF, SOME EFFECTS OF LIGHT FLUX AND WATER-TABLE DEPTH
P. M. HAYWARD* AND R. S. CLYMO Departmentof Botany, Westfield College, London NW3 7ST
SUMMARY
(1) Experimentswere made to determinethe effects of bothshading and of water-table depthon the growthof threespecies of Sphagnum.The species(and theirusual habitats) were: S. capillifolium(hummocks); S. papillosum(lawns); and S. recurvum(pools and flushedlawns). (2) Water-tabledepth had littleeffect on growthmeasured as increaseof drymatter; shadingreduced growthand therewere specificdifferences associated withplant size. Therewere no significantinteractions between water-table depth and shading. (3) For growth measured as growth in length, there were highly significant interactions,individual species behavingdifferently in responseto shade and, to a lesser extent,in responseto water-tabledepth. (4) In Sphagnum lawns in two natural habitatsthere was a negativecorrelation betweendepth of the water-tableand surface-roughness.In experimentalconditions surface-roughnessincreased both as thewater-table was raisedand as shade increased. (5) A computersimulation of growthof Sphagnumin a lawn was able to reproduce theobserved variations in surfaceroughness. In mixedlawns oftwo species,the one in its 'natural'habitat out-grew the other.
INTRODUCTION
Most attemptsto measurethe growthof Sphagnumhave been concernedwith obtaining values of productivity(e.g. Leisman 1953; Overbeck & Happach 1956; Pearsall & Gorham 1956; Bellamy & Rieley 1967; Clymo & Reddaway 1974; Ilomets 1974; Pakarinen1978). Relativelyfew attempts have been made to measuregrowth in relationto the environment.Some of these (Chapman 1965; Clymo & Reddaway 1971; Boatman 1977) have entailedtransplanting Sphagnum from one positionto anotherin the field. Other studies,by Green (1968) and Clymo (1970, 1973) have includedlaboratory or gardenexperiments in whichthe environment was moreprecisely controlled, but only in a limitedway. The aim ofthe work presented here was to obtainmore precise details about the growth of Sphagnumin relationto itsenvironment. From this information, a quantitative model of thegrowth of a Sphagnumcarpet was developed. The earlierwork indicatedthat two environmentalvariables-light fluxand water supply-have an overridinginfluence on growth.Total lightflux is important,but so is the variationof incidentflux on a small scale, betweenone individualSphagnum plant and anotherin a singlelawn. These effectsmay be due to 'external'shading by larger,vascular plantsor to 'self-shading'by neighbouringSphagnum plants. Watersupply to the capitulum(the apical tuftof expandingbranches) has been shown to depend,in a complexway, on thestructure of the Sphagnum plant (which differs among * Presentaddress: Department of Botany, University of Leicester,Leicester LE 1 7RH.
0022-0477/83/1100-0845$02.00 (? 1983 BritishEcological Society 845 846 Effectsof light and wateron Sphagnumgrowth species)and on water-tabledepth (Hayward & Clymo 1982). In general,however, water supplyis inverselyrelated to thedepth of thewater-table and, for a givenwater content in thecapitula, the water-table will be at a greaterdepth below hummock species than it will be below lawn species.Thus, water-tabledepth can be used as a convenient,and easily measurableway, of expressingwater supply. Bogs have a water-tablewhich is, comparedwith most terrestrial habitats, relatively close to the surface.The distributionof speciesappears to be relatedto thedepth of the water-table(e.g. Ratcliffe& Walker 1958; Clymo & Hayward 1982). This impliesthat changesin the depthof the water-tablewill affect plants of differentspecies in different ways, complicatedby the fact that the water-tableis not a plane surfacebeneath the hummocks,lawns and pools ofthe microtopography (Popp 1962; Goode 1970; Boatman, Goode & Hulme 1981). Because thewater-table is close to thesurface, small changes in its depthhave a proportionallygreater effect on bog plantsthan they would if the water-table wereat a greaterdepth. Bothlight flux and water-tabledepth were therefore controlled in theseexperiments and were includedin the model of Sphagnumgrowth. The model had severalquantitative consequences.Of these,the one whichcan most easily be measuredin the fieldis the surfaceroughness of a Sphagnumcarpet. There is someindication (Clymo 1973) thatthis is negativelycorrelated with depth of the water-table.Here we reportmeasurements of surfaceroughness both in the field and in experiments.
THE SPECIES USED IN EXPERIMENTS
Plants of threespecies, S. capillifolium*,S. papillosumand S. recurvum,were used in experiments.These species are typicallyassociated with differentbog microhabitats. Sphagnumcapillifolium is naturallya species of drierareas such as hummocks,S. papillosumforms lawns at a heightintermediate between bog pool and hummock,at or just above thewater-table, and S. recurvumis foundin pools and wetflushed lawns.
METHODS Growthin relationto lightfluxand water-tabledepth An experimentwas made withplants of the above threespecies collected from Moor House N.N.R., Cumbria,from the areas aroundBurnt Hill and Bog End (NationalGrid referencesNY 753329 and NY 765329 respectively)growing in pots in a gardenin London.It includedtreatments, for each species,of factorial combinations of five depths to the water-table(0, 3, 6, 10 and 14 cm below the surface)and fivedegrees of shade (absorbanceof 0, 0.54, 0.80, 0.91 and 0.96 of incidentlight). We choseto use shade,with the consequentfluctuations in irradiance,rather than constantartificial light partly for convenience,and partlybecause we wanted to be able to relatethe resultsto field behaviour. Plantswere cut initially to (known)length, sufficient to allowall cutends to be at least 1 cm underwater at thestart of the experiment (Table 2). The lowest1 cm ofeach plantwas stainedwith a cationicdye (crystalviolet) so thatany loss duringthe experiment could be detected.There were no losses. All plantsof the same size and taxon werewell mixed
* Nomenclatureof Sphagnumfollows that of M. 0. Hill (1978); thatof vascularplants follows Clapham, Tutin& Warburg(1981). P. M. HAYWARD AND R. S. CLYMO 847 beforebeing allocated, forty plants to each treatment.The fortyplants were tied into loose bundles,so thatthey could be recoveredeasily, surrounded by othercut but unmarked plants(to reduceedge effects)and packed at naturaldensity into pots made fromsquare section2-litre plastic bottles by cuttingoff the top partleaving a 10-cmsquare, 20-cm tall containerwith straight sides. The shorterplants were placed on an underlyingbed of choppedSphagnum to bringthe capitula of the plants in all treatmentsto thesame level in thepot. The apparatusshown at thetop of Fig. 1 was used to pack theplants in thepots. The leftcontainer was a slidingfit inside the right one. The plantswere packed as shown and theleft container plus plantsslid into the right container. The leftcontainer was then withdrawnwith the string while the piston held the plants in positionin theright container. The filledpots wereclose packedon a flatlevel surface and weresurrounded by a 'guard ring' of otherpots filledwith Sphagnum on whichno measurementswere made. The experimentlasted for 77 days from17 June.During this time the orientation and position ofthe pots was changedrandomly each weekaccording to a Latinsquare arrangement. The waterlevel in each pot was maintainedthrough a tubeinserted into its base (Fig. 1). The tubewas attachedto a devicewhich kept the water level constant either by allowing excess rainto runaway or by addingdistilled water. With this arrangement there was no obvious accumulationof evaporitesat the surfaceof the plants.As the plantsgrew, the pots werelowered to maintainthe water-table at a constantdepth below the surface of the Sphagnumlawn in each pot. The potswere individually shaded by coveringthem with 0, 1, 2, 3 or 4 layersof black polyestergauze. The absorbanceof lightby this materialwas measuredon a recording
String Ofherplants 40 plants Homogenized cut to length dead plants
Sphagnum surface Water-table
4l-Air
FIG. 1. Methodused to maintaina constantwater level in pots duringthe growthexperiment. Onlytwo of thefive levels are shown.Water was cycledby raisingit on a streamof air bubblesin a verticalglass tube.The 25-litreMariotte bottle was refilledwith distilled water as required.The upperdiagram shows the apparatus used to pack plantsin containers. 848 Effectsof light and wateron Sphagnumgrowth spectrophotometer.Between wavelengthsof 350 nm and 1000 nm it was nearly independentof wavelengthwith an averagevalue, between 400 nmand 700 nm,of 0.337. The absorbanceof multiplelayers was close to additive.The gauze did affectthe rate of evaporationof water;the ratewith gauze was about 20% belowthat without gauze. But therate at whichwater moves up Sphagnumis high(Clymo & Hayward1982) so it seems unlikelythat the water supply to thecapitula was muchaffected. The size of the experiment(seventy five pots, 20 000 plantsof which3000 were cut accuratelyto size) precludedreplication, so second orderinteractions were used as an estimateof error. If anything,they should tend to over-estimateerror. However, in orderto obtainmore information about the typesof errorinvolved, a furtherfifteen pots wereset up. All thesecontained S. capillifolium,all had a water-table3 cm belowthe surfaceand all had one layerof gauze shading.Three harvests were made; after5, 36 and 45 weeks. At harvest,two typesof measurementof growthwere made: lengthand mass. Increase in lengthwas measureddirectly with a ruler.Increase in drymass was measuredusing the 'capitulumcorrection method' of Clymo(1970). The newgrowth was cutoff together with an extra1 cm to includeall theoriginal capitulum. From the dry mass ofthis material was subtractedan estimateof the mass of theoriginal capitulum based on a linearregression betweencapitulum mass and themass of a unitlength of stemimmediately below it. This methodallows for changesin the size of the capitulumduring the experimentand for materialcarried upwards by internodeextension within the original capitulum. The resultsof growthin mass wereexpressed in two ways: as growthper plant and as growthper mass of unitlength of fully elongated stem (the section from 1-4 cm belowthe apex whenthe experimentbegan). The latterwas used as a means of comparingplants, particularlythose of differentspecies, with different sized apices; stemmass is correlated withcapitulum mass and hencewith apex size (Clymo 1973). Thisprocedure also reduced variabilitybetween individuals.During the experimentsa few plants forked.The proportiondoing so was about 0*01, and the two axes of such plantswere treated as a singleindividual.
Fittingsurfaces to results Whererequired, multi-dimensional surfaces described by polynomialequations (detailed in the relevantplaces) werefitted to experimentalresults by minimizinga badnessof fit function,g. The functionwas the sum of squareddeviations from the measuredvalues. Arbitraryvalues of thepolynominal coefficients are chosenand thevalue ofg calculated. New values of thecoefficients are thenchosen in such a way as to reducethe value ofg. The processcontinues until no furtherreduction. of g can be obtained.A moredetailed descriptionis givenby Clymo (1978). The SIMPLEX option(Nelder & Mead 1965) of the CERN programMINUITS (libraryD506, D516) was used to locate minimaand the MIGRAD option(using Davidon's 1968 method),which is extremelyfast near a minimum, to refinethe estimate.
Surfaceroughness in thefield Surfaceroughness was estimatedby the point frame('shoe-box') technique,as the varianceof height(Harper, Williams & Sagar 1965; Boorman& Woodell 1966) after removalof largerscale (5-10 cm) topographicsurfaces (Clymo 1973). A setof thirty-two light-weight10 cm long pointers(culms of Deschampsia cespitosa) were supported verticallyand parallelin holesin two horizontal pieces of stainlesssteel gauze. The pointers werearranged 8 mmapart in each directionin a 4 x 8 rectangulargrid. Measurements of P. M. HAYWARD AND R. S. CLYMO 849 surfaceheight were made by photographingthe tops of thepointers against a graphpaper background.Pointers and camerawere mounted on an aluminiumframe incorporating a mirrorat 450 angle which allowed the camera to be pointeddownwards to record horizontalviews of the pointers. The resultsgiven are ofresidual variance in heightafter fitting a surface, with 25 degrees offreedom, of thegeneral form z = a + bx + dX2 + ey2 + fxyto theheights of the pointers (x andy are thetwo axes ofthe rectangular grid; z is theheight above an arbitraryzero; a to f are parameters).A surfaceof thisnature was fittedfor two reasons:the frame holding thepointers did nothave to be horizontal,and topographicfeatures on a scale of about 10 cm were ignoredwhilst keeping the small scale (1 cm) roughness(Clymo 1973). Each framethus gave a singlevalue of roughness. Field measurementswere made at randompoints within an area chosenbecause it was occupiedby a carpetof the requiredspecies of Sphagnumat about the requiredheight above the water-table.Garden measurementswere made on the centreof experimental cores.
Surfaceroughness in experiments Cores, 30 cm in diameter,of S. capillifolium,S. papillosumand S. recurvumwere collectedwith a stainlesssteel cutter from Coom RiggMoss N.N.R., Northumberlandand BrishieBog on theSilver Flowe N.N.R., Galloway(National Grid references NY 690796 and NX 447833, respectively).Care was takento disturbthe cores as littleas possible,and surfacedisturbance was negligible.The cores weremaintained outdoors, as describedfor thegrowth experiment, with factorial combinations of two depths of water-table (3 cm and 15 cm belowthe surface) and twodegrees of shade (absorbanceof 0 and 0.80, from0 and 2 layersof gauze respectively).Two cores (one in thecase of S. recurvum)were allocated randomlyto each treatment,one corefrom each site.No subsequentdifferences in surface roughnessattributable to originwere observed. Vascular plants growing above thelevel of the Sphagnum capitula (mainlyCalluna vulgaris,Eriophorum angustifolium and E. vaginatum)were cut offperiodically and measurementsof surfaceroughness made, with theapparatus already described, at intervalsfor a year.
RESULTS Growthin mass and lengthin responseto shade and water-table The growthof plantsin theextra fifteen Sphagnum rubellum pots is shownin Table 1. Variabilityin measurementsof growthin bothlength and mass was relatedto theamount of growth.For thesepots and all theothers in theexperiments (ninety in all) therewas an
TABLE 1. Growthof S. capillifoliumplants in pots (see text).The experimentbegan in September.Harvests were made in October(after 5 weeks),May (after36 weeks) and July(after 45 weeks).Values are themean for five pots except those for growth in lengthwhich are themean for all individualplants in fivepots (about 200 in all). Values in bracketsare standarderrors of the mean. Harvestafter (weeks) 5 36 45 Growthin length (cm) 1.30 [0-04] 3 48 [0.06] 6.53 [0-21] Growthin drymass (mg) 1.62 [0-38] 4-10 [0-50] 8.17 [1.47] Etiolation(cm mg-') 0.97 [0-25] 0.91 [0-15] 0.97 [0-15] 850 Effectsof light and wateron Sphagnumgrowth approximatelylinear relationship (r = 0.81) betweenstandard deviation and meangrowth in lengthof plants.A log transformationwas thereforeapplied to all the resultsbefore statisticalanalysis. This transformationhad theincidental effect of reducingthe coefficient ofvariation from a meanof 35% to 17%. A second importantresult from the extrapots was thatthe morphology of theplants, measuredas etiolation(quantified as growthin lengthdivided by growthin mass),did not changebetween harvests. This impliesthat the time scale of themain experiment was not critical;the same relativeresults would have been obtainedwith experiments of different length. Dry matterincrease in themain experiment is shownin Table 2. Water-tabledepth had littleeffect, shading reduced growth and therewere specific differences (associated with plantsize). None of theseeffects are surprisingas theyagree in generalwith the results of otherless detailedexperiments (Clymo 1973). Therewere no verysignificant interactions. Growthin lengthshowed highly significant interactions however (Table 2); individual species behaveddifferently in responseto shade and, to a lesser extent,in responseto water-tabledepth (Fig. 2). For all threespecies there was an 'optimum'shade and forS.
TABLE 2. Mean values of growthof three species of Sphagnum in the pot experimentcarried out in a gardenin London,on the effectsof shade and water- table depthon growth.Values have been back transformedfrom logarithms. For detailsof treatments,see text.Values in parenthesesindicate length (cm) to which plantswere cut at thestart of theexperiment. Italic values in bracketsare F values froman analysisof variance.Mean values forthe main effects on growthin length are not givenbecause theinteractions are significant.The interactionmean values are shownin Fig. 2. Growthin Degreesof Mass Mass Length freedom (mgplant-1) (mg(mgcm-'stem)-') (cm plant-') Species 2 [85.2***] [40.1***] [52.7***] S. capillifolium 3.0 6.2 S. papillosum 8.5 7.3 S. recurvum 6.2 13.1 Shade Layers Absorbance 4 [39.2***] [32.7***] [26.2***] 0 0.00 9.2 14.4 1 0 54 7.4 12.0 2 0.80 5.8 8. 1 3 0.91 4.0 6 5 4 0.96 2.9 4.7 Water-tabledepth Plantlength 4 [1-1] [0-7] [18.8***] (cm) (cm) 0 (5) 4.8 7.6 3 (5) 5.4 8-7 6 (1 1) 5-4 8-4 10 (11) 5.9 9.1 14 (15) 5.6 8-4 Interactions: Species x shade 8 [1-6] [1-9] [13.2***] Species x water-table 8 [1-11 [2.9*1 [7.2***] Shade x water-table 16 [1-5] [1-91 [2.3*] Residualmean square 30 0.016 0 018 0.011 *0.01 (I) S. capiii1folium > q l~~~~~~~~~~~~~~5 5 (a) (b) N '''''.'.''-"tA" . Ng,'''.M , , >, R:... R....~...... ~~~~~~~~~~~~...... N ...... (1)Spapiiiosum se5 00 X::: 0:1 :::: E.X;o::::-...... ::::: *X:-....>n...,,... ::::::: w ( ...... (d) . . 1 I0~~~~~~~~0 (iii) S. recrvSum / 4 >~~~~~~~~~~~~~~~~~~~~~~~~SO .....,.,.. (c) d0 A 0 r0 2 (III) S. recurvum 5c 0 0 o (e-5) (f\ ::'e(Q 3X y \1 . ?er 4 141 \c>\tX((\ FIG. 2. Growthin lengthof Sphagnumin relationto shade and water-table:(a), (c), (e) growth (bars represent95% C.L.); (b), (d), (f0surfaces fittedto the results in (a), (c) and (e), respectively,by a leastsquares fit to thecubic equation L =a + bW + cS + dWS + eU'2 + fS2 + gWV3+ hS3 + iW2S + jWS2 whereL = growthin length(cm), W = depthof water-table(cm), S = absorbanceof gauze shade, a to j are parameterswhose value definesthe shape of the surface.The values are estimatedby theminimization procedure. 852 Effectsof light and wateron Sphagnumgrowth papillosumand S. recurvuma fallin thewater-table reduced the rate of growth in lengthat theshade optimum. In unshadedconditions, water-table depth had a largeeffect on rateof growthin lengthof S. recurvumand to a lesserextent of S. capillifoliumbut had relatively littleeffect on S. papillosum.These results are againconsistent with those of Clymo(1973) and also those of Sonesson et al. (1980) who measuredthe elongationof S. riparium (whichis in sectionCuspidata and relatedto S. recurvum)in differentdegrees of shade. It is clear that growthin mass and lengthvary in differentways in responseto the treatments.Stem length between branch fascicles increases and branchlength decreases (i.e. theplants became more straggling, or etiolated)with either or bothgreater shade and higherwater level. The effectsof shadeand waterdepth on etiolationare shownin Table 3. TABLE 3. Meanvalues of etiolation (growth in length/growth inmass) for the three speciesof Sphagnum used in a potexperiment, carried out in a gardenin London, on theeffects of shade and water-table depth on growth.Units of measurement are cm plant-'(mg (mg cm-'stem)-')-'.Values have been back transformedfrom logarithms.The maineffects of species,shade and water-tableare all highly significant(P < 0.001). Shade Layers Absorbance S. capillifolium S. papillosum S. recurvum 0 (0-00) 0.16 0.11 0.20 1 (0-54) 0.31 0.31 0.41 2 (0-80) 0.53 0.48 0.51 3 (0.91) 0.66 0.63 0.54 4 (0.96) 0.91 0.57 0 29 Water-tabledepth (cm) 0 0.55 0 49 0.65 3 0.56 045 0.51 6 043 0-41 0.37 10 0.37 0 27 0.28 14 0.32 0 24 0.20 Surfaceroughness measurements Naturalconditions Measurementsof surfaceroughness were made on lawns of S. papillosumin field conditionson Brishie Bog on the Silver Flowe N.N.R. and at a site in a pool- and-hummockcomplex between Bog Hill and SpurHill at Moor House N.N.R. (National Gridreference NY 771328). The resultsfrom both sites (there was no significantdifference betweenthe sites) are shownin Fig. 3. A negativecorrelation between variance and depth of water-tablewas foundbut the relationship was notlinear. A plotof log varianceagainst water-tabledepth was neara straightline but no functionalrelationship is implied. Experiments By themiddle of thegrowing season following that in whichthe cores were collected (44 weeks fromthe introductionof the waterlevel and shade treatments)values of surface roughnesswere as shownin Table 4. Therewere significant effects attributable to species, shade and water-tabledepth and therewas also a significantinteraction between species and shade. These trendscontinued throughout the growingseason; both shadingand P. M. HAYWARD AND R. S. CLYMO 853 S2O E E 10 o8 >6 -00 4 - LO 10 _ Lo L 2 I I I I fi I 0 10 20 30 Depth of water-table(cm) FIG. 3. Surface roughness of natural lawns of Sphagnumpapillosum in relation to depth of water-table. The line shows the regression: log10 (y) = 1.33- 00297 x; r2 = 0.90, where y is the residual surface variance (mm2) and x the water-table depth (cm). (a), Moor House; (0), Silver Flowe. TABLE 4. Surfaceroughness, assessed by residualvariance (mm2) of lawnsof three speciesof Sphagnumgrown in controlledconditions for 44 weeks.Values are the mean of duplicates,but for single measurementsfor S. recurvum.Values in parenthesesare lightabsorbance by shadingmaterial. Italic values in bracketsare F values froman analysisof variance.The F-value of the interactionspecies x shade was [12.3*]. Water-table Shade depth (cm) Species [39**] [1 72***] [35**] S. capillifolium S. papillosum S. recurvum Shaded (0-80) 3 17 33 26 15 13 27 23 Unshaded (0-0) 3 9 12 19 15 2 7 10 *0.01 A MODEL OF THE GROWTH OF A SPHAGNUM CARPET The variousinfluences on Sphagnumgrowth are generallyconsidered in isolation.If their overalleffect is to be studiedthey must be appliedto the systemtogether and allowedto act together.Two sortsof effect may be imagined: (i) wherethe overall effect is thatof the applicationof morethan one factorin a simple additiveway; or (ii) wherethe factorsmay interactin such a way as to producea resultwhich is not predictablefrom the main effects alone. 854 Effectsof light and wateron Sphagnumgrowth In themodel of a Sphagnumcarpet, which is now described,measured interactions were included,but all othereffects were simple additive ones. The modelallows an examination of the consequencesof puttingthe pieces togetherin a situationwhere a sufficiently detailedfactorial experiment would be too largeto be practicable.It also providessome calculatedeffects which can be checkedindependently-values for surface roughness are themost obvious. The modelis shownpictorially to theleft of Fig. 4 whereSphagnum plants are shown growingvertically in a pure lawn which is flat and horizontalwith a well defined water-tablebelow it. The capitulaare notalways all at thesame level,however, and so the questionmust be considered:What happensto an individualif its capitulumis not at the generalsurface but is eitherabove or below it? To the rightof Fig. 4 are shownthe radiantflux and the watersupply to whichthe capitulumof such an individualmight be subject.Both of theprofiles have two distinctparts: one above,the other below the mean surface. Incident radiation Capitulum / Surface Wateravailability Watertable Increasing FIG. 4. A conceptualmodel of a Sphagnumlawn with, to theright, profiles of lightflux and water availabilityto the capitulumof an individualwhich is notgrowing level withthe rest of thelawn and whose capitulumis eitherabove or belowthe mean surface.The partof themoisture profile shownby thebroken line is speculativeand has notbeen demonstrated by experiment. For shortdistances above the surface,incident radiant flux is constantat a value determinedby the generalclimate and 'external'shading from vascular plants (Calluna vulgaris,etc.). Below the surface,flux falls exponentially with depth or, moreprecisely, withcumulative dry matter, i.e. Beer's Law can be applied.The slope of the attenuation linedepends on thespecies involved and on theprevious history of shadingand water-table (Clymo & Hayward 1982); shaded conditionsand a high water-tableboth reduce absorbance,i.e. absorbanceis inverselyrelated to 'etiolation'(see above). The moistureprofile between the surface and thewater-table depends on severalfactors includingspecies and theprevious position of thewater-table. Both hydraulic conductivity and densityof thepeat also affectsupply. There is consequentlyno simplemathematical descriptionof water supply analogous to Beer's Law for light,although in specific conditionsthe moistureprofile can be described(Hayward & Clymo 1982). Fortunately, P. M. HAYWARD AND R. S. CLYMO 855 thisproblem can be avoided by usingthe resultsfrom the growthexperiment described above as growthwas relatedto depthof thewater-table, not to watersupply. Polynomial equationsfitted to those resultshave thusbeen used in the modelto describegrowth in termsof both lengthand dry matterby substitutingvalues for shade (calculatedfrom Beer'sLaw) and thedepth of the water-table below a particularcapitulum. The effectof theheight that an individualplant is exposedabove thegeneral surface on watersupply to, or on growthrate of, the plant, has notbeen investigatedexperimentally and is indicatedby a brokenline in Fig. 4. In thecomputer model therefore, the amount of growthcalculated fromthe heightof the capitulumabove the water-tablehas been modifiedby multiplyingit by a value whichwas variedto simulatedifferent exposure effects.The exposureeffect, E, was determinedfrom a simpleexponential function: E = exp (k *DL) wherek is a constantand DL is theheight of an individualabove the averagelevel of the six surroundingplants (Table 5). (Capitals denote names of variables used in the computerprogram.) With k = 0, therate of growthwas unaffected.By makingk positive or negative,the rate of growth could be increasedwith exposure or decreased. The componentsof themodel and theirinter-relationships are shownin Fig. 5. Most of the model,that part withinthe box, concernsindividual Sphagnum plants in the lawn separately.Five parametervalues are requiredbesides those describing growth rate and the attenuationof light.These fiveparameters are listedin Table 5 togetherwith typical values. In the followingresults the numberof plants,n, was set at 25 throughout.These plantswere arrangedin a 5 x 5 gridwith alternate rows offset by halfa columnso that each plant was surroundedby six equidistantothers. The whole array was wrapped aroundtoroidally to minimizeedge effects; i.e. theplants at theleft edge are consideredas adjacentto thoseat theright edge, and thoseat thetop as adjacentto thoseat thebottom. TABLE 5. Parametersrequired in the model of Sphagnum growth shown in Fig. 5. Symbol Description Typicalvalue(s) Units Chosen beforeeach run C(1) Numberof plants, n, in thelawn 25 C(2), C(3) k in theequation: E = exp (k.DL) for -1.39 (growthhalved cm-l effectof exposureon elongationand whenDL = 0.5 cm) productivityrespectively* C(4) Externalabsorption of lightby 0 and 0-3 (testedup to 1.0, Calluna vulgarisetc. i.e. 10% transmission) C(5) Depth of water-tablebelow mean 0-14 cm surfacelevel Builtinto the model GL(1.. 10) Parametersfor growth function See Table 6 cm plant-' determiningelongation (foundfrom growth experiment) GM(1.. 10) Parametersfor growth function See Table 6 mgplant-1 determiningproductivity (foundfrom growth experiment) AC(1 .4) Parametersfor function See Table 6 determiningextinction coefficient (fromHayward 1980) * DL is thedistance of an individualabove themean heightof thesix surroundingplants (SRND). In Fig. 5, DL = X(j) - SRND. The effectoperates only when DL is positive,i.e. theindividual is emergent. 856 Effectsof light and wateron Sphagnumgrowth LEVNGTe MTTE average e o n A(6 A() J e prodAuc7tvityJ_ ,f-- Ge~~rjpeatbox for each of j =I fo n plant i Xt etiolation /elongation _THGROWTHe -kNCTIONI k~~~~~J FUNCIONproductivity - - ~~~~~~~ ~R(j in) exposure exposure effect water-tabledepth fl effect (EE) belowindividual \I (EE) (W) ~~--~ A length shadingon -- plant (S) (D L) A(j + 1) lengthabove m- / mattera above datum Rmean lengthof 6 /tum X(j surroudingplant X/ /n (SRND) / / TL ~~~~water-tal extinction C4 vrg TL heightabo dtum coefficient se If-shad ((EXT)A I A(9)3 I surfacerioughness varianceverageng average mnter ( oof matter A'' ~~A(2 bB(i A5) FIG. 5. Flow diagramrepresenting a model of Sphagnum growth.Flows of 'matter'and of 'length'are representedby solid arrows and causal relationships('flows of information')by broken lines. The conventionsare those of Forrester(1961): 'X' representsa measurable physicalquantity, 'R' a rate,'A' some otherauxiliary variable and 'C' a constant.Letters in parenthesesare othernames used in the model. Everythingwithin the large rectangularbox is repeatedfor everyplant in a carpet. (A flowof 'length'indicates that the particularvalue of lengthgrowth of the plantsin a giventime interval, determined by the variablesand constants shown,is handedon unchangedduring subsequent time intervals.) It is theoreticallypossible for these edge constraintsto cause wave-likepropagation of effects,but there was no signof this happening in thesesimulations, For each plantin thelawn, growth in bothlength and mass was calculatedas indicated by the solid arrowsin Fig. 5. The rateof growthwas determinedby a 'growthfunction' and dependedon the shade ('external'and 'self')and depthto thewater-table as already described.The growthfunctions were the polynomial equations describing fitted surfaces such as thosein Fig. 2. The parametersof these equations are givenin Table 6 forthe two speciesused in themodel. Mixed lawns of different species could be modelledby specifying theappropriate parameters. The water-tablewas keptat a specifieddepth below the mean surface,i.e. bothrose at thesame rate as theplants grew. The amountof shadingon the individual(S) had two components:the amountof externalshade, C(4), and the amountof 'self-shade'.The latterwas zero unless the capitulumwas belowthe meanlevel of its six nearestneighbours when DL was negative (Fig. 5). The effectsof self-shadewere calculated from Beer's Law. If theplants were rigid structures,as impliedby themodel, and thesun wereoverhead at all times,this would be incorrect.However, for most of thetime the light falls obliquely, so thepath length is at least proportionalto DL (path lengthequals DL dividedby the sine of the angle of incidence).Also, theplants are not rigidstructures and tendto crowdover each otherso thateven if overhead, the sun mustoften penetrate a canopyof neighbouring plants before reaching a shorterindividual. Thus Beer's Law, in practice, seems a reasonable approximationfor estimated self-shade. Depth in the carpetwas used in the calculation P. M. HAYWARDAND R. S. CLYMO 857 TABLE 6. Values for parameters(estimated from measurements, see text) of equationsused in the model of Sphagnumgrowth. The two species in the model were:(i) S. capillifoliumand (ii) S. papillosum Length,Z* Mass,Z* (cmplant-') (mgplant-') EXTt Parameter (i) (ii) (i) (ii) (i) (ii) a 0.79 1-5 1.7 10.9 0.89 0.71 b(W) 0 57 0.097 0.72 1.3 0.085 0.022 c(S) 5-1 10.6 5.5 3.5 -0 73 -0-58 d(WS) 0.057 -0.77 -0-60 -3.6 -0.093 -0-027 e(W2) -0 082 -0-014 -0-028 0.027 f(S2) -3.8 -7.2 -9.0 5.2 g(W3) 0.0030 0.00026 -0-00030 -0-0069 h(S3) 1.2 0.30 3.9 -4-4 i(W2S) 0-018 0.018 0-031 0.13 j(WS2) -0-28 0.36 -0-046 1.22 * 'Growthfunctions' were polynomial equations, fitted to theresults of the growth experiment. They were of the form:Z = a + bW + cS + dWS + eW2 + fS2 + gW3 + hS3 + iW2S + jWS2 whereW= depthof water-table(cm), S = absorbanceof shading plant material, and a to j areparameters whose value defines the shapeof the surface. The valuesare estimated by the minimization procedure. The equations were valid over theranges 0-14 forW and0-1 .3 forS. t 'Extinctioncoefficient' equations (from Hayward 1980) were of the form: EXT = a + bW + cS + dWS. The equationis validonly within the range 3-15 forW and 0-0.8 forS. Outsidethese limits EXT was assumedto remain constant. ratherthan cumulativedry matter(Hayward 1980) in orderto avoid complicatingthe model.The extinctioncoefficient (EXT) was calculatedfrom the mean water-table depth, C(5), and theexternal shade, C(4) (Hayward1980). The parametersof these equations are givenin Table 6. Whenthe length of an individualwas greaterthan that of itsneighbours (DL positive) the rate of growthwas modifiedto take account of increasedexposure as previously explained. The measurementsof surfaceroughness described above are particularlyimportant in the contextof the model because the value of surfaceroughness is independentof the assumptionsmade in the model and can be calculatedfrom it. The model calculates surfaceroughness as thevariance of thelengths of all theplants in themodel carpet. This measureis similarto thatused in thefield but not identical;the lengths measured in real lawnswere not necessarily those to theapices of discreteindividual plants. The completemodel was writtenin FORTRANand run as a subroutineof a general programSYSFLO written by one of us (R.S.C.). It controlsinput, manages iterations for a series of time steps and produces printedand graphicaloutput. Forrester's(1961) conventionswere followed.At each iteration,all new values of variables(lengths and weights)were calculated before any rates.The orderof individualplants and theorder in whichthe new value of variables was calculatedwere thus of no importance. Resultsfrom the computermodel The model describedin the previoussection does not allow forindividual variation betweenplants; all behavein thesame way in a particularset of conditions.It couldeasily be made stochastic,but thereis too littleknown at presentto make thisworthwhile. The modelwas therefore'forced' at thestart to simulateindividual differences by choosingthe initialvalues so thatthe lengths(distributed at random)followed a normaldistribution witha meanof 0 cm (datumlevel) and a standarddeviation of 0 5 cm.The onlyexception 858 Effectsof light and wateron Sphagnumgrowth was thattwo plantswere set at -1 cm and + 1 cm respectively(2 S.D.) and theeffect of shadingand exposurewas subsequentlyrecorded in detailfor these two plants. The modelwas firstrun with pure lawns of each of S. capillifoliumand S. papillosum and variouscombinations of theconstants C(2) to C(5). The modelwas testedwith depths to thewater-table of between0 cm and 14 cm withabsorbance ('external' shade) up to 10 (10% transmission;equivalent to a path lengththrough Calluna vulgarisof 6-9 cm (Grace & Woolhouse1972)). The most noticeablefeature of these runswas thatthe model Sphagnumpopulation tendedtowards one of two statesdepending on the particularcombination of parameters used. The populationeither went into a steadystate withthe averagerates of growth constantand surfaceroughness stabilized, or it became unstablewith some plantsfalling irrevocablybehind and othersgrowing at an increasingrate away fromthe mean surface. Two typicalresults, showing stable and unstablebehaviour, are shownin Fig. 6. There were two sets of conditionsunder which the model became unstable.The firstof these occurredin cases withno externalshade, C(4) = 0, and withcombinations of high water-tableand onlya smallnegative exposure effect. The instabilitywas increasedwhen the exposureeffect was made zero or positive(i.e. withincreased growth above the surface).These unstableconditions were mainly caused by longplants growing away from thesurface. This consequenceis expected,but such plants are neverobserved in nature,so itis probablethat k is in realitynegative. The modelalso becameunstable when there was some externalshade and thedepth to thewater-table was great.Changing the value of k (positiveor negative)in the equation for exposureeffect made littledifference. In thiscase the instabilitywas largelydue to short plantsbeing 'left behind'. The modelwas notdesigned to respondto suchevents and plants whichbehaved in thisway (and whichwould have diedin reality)simply left a 'hole' inthe model lawn. In naturethis hole would be filledby sidewaysmovement or growthof neighbours,or by the splittingof apices to producetwo plants where before there was one (Clymo& Hayward1982). Some of the model resultsof surfaceroughness are shown in Fig. 7. The resultof changingthe exposureeffect with no externalshade is shown in Fig. 7 (a) for S. capillifolium.As expected,the resultsshow a decreasein surfaceroughness with more negativevalues of k and also withlower water-tables, with exception of a small(the graph is plottedon a log scale) increasewith the lowest water-tables in combinationwith the most negativevalues of k. It is improbablethat an effectof this size couldbe detectedin thefield orin experiments. The effecton surfaceroughness of depthof the water-table down to 6 cm and ofshading withabsorbance of from0 to 1I0 forboth S. capiltifoliumand S. papillosumis shownin Fig. 7(b) and (c). Sphagnumcapillifolium behaved much as it did in realityin the experimentallawns describedabove (see Table 4). Water-tabledepth had a similareffect on the surfaceroughness of S. papillosumalthough it was in generalsmaller with lower water-tables.Shade had a largereffect, generally increasing roughness, except where the absorbanceof lightwas 0.3 whenit was apparentlyat a minimum.These resultsdo not conflictwith those of Table 4 wherethe effect of shadeon S. papillosumwas muchgreater thanwas thatof water level. The modelwas nextrun with mixed stands of differentspecies. For thesetests the model was arrangedwith one ofthe species forming a flatcarpet in whichwere placed twoplants of theother species. In varioustests these plants were arranged to be eitherlevel with the generalsurface or 1 cm above or below the surfaceas in previousruns. Figure 8 shows P. M. HAYWARD AND R. S. CLYMO 859 (a) A(O0) 8 , -\\\/ A(3) 6 / A(8). , 6. A A2 ) 4 / / A(17) ,, 2 ...... A( . _, s 2 ..(6) cn cv 0 10 (b)- / AO)- .h-- t - - A A(17) . ... 8 o / A() -- 8-2 A ~~~ V A(7)~~~~~~~~~~~~~~A8 > 6 < ) 100G 200 300 400 500 600 Time (days) FIG. 6. Resultsof computersimulation for the growthof Sphagnumcapillifolium run for600 timesteps of one day: (a) withno externalshade and thewater-table 3 cm belowthe surface; (b) withabsorption by externalshade of 0-3 and water-tableat 12 cm. Variable names are those used in Fig. 5 and theirvalues have been scaled on a commonaxis by multiplyingby theitalic values shown below in brackets:A(2), average length(cm) [0-40]; A(3), average mass (mg) [0-25]; A(4), variancein length(surface roughness) (cm2) [20]; A(5), variancein mass (mg2) [1.0]; A(6), averagerate of elongation(cm day-') [40]; A(7), averagerate of production(mg day-') [401; A(8), averageetiolation (cm mg-1) [101. Growthin lengthof plantsinitially 1 cm above and below the mean surfaceis shownby shadingaround A(2). Exposureeffect with k = -1 39, A(10) [10], and shade, A(17) [2 51, are shownfor these two plantsrespectively. After 600 days,the value of A(5) in (b) was 35 mg2. some of theresults obtained as themean growth in lengthof the second species in relation to thatof themain species. Both of thesegraphs show similareffects. In bothcases, when there was no external shade, S. papillosum grew fasterthan S. capillifoliumdid when the water-tablewas near the surface.With the water-table below 2 cm,the rate of growthin lengthof thetwo specieswas aboutthe same, although S. capillifoliumgrowing in a lawn of S. papillosumgrew slightly faster when the water-table was betweenabout 2 cm and 8 cm depth.In all these cases the model reacheda steadystate. Plants initially above or 860 Effectsof light and wateron Sphagnumgrowth a) 0 0 (a) S.capo///fo/wum o 4 ~910480, E~ k C I _ \ / * ~~~-139 a) C _J~ ~I I I I I I Water-table depth(cm) U) 0 0>- .3 (b ) S. capi///ifo/niJm ( c) Sp,apoi//osum u 0 6 1010 0 ,-,1002 \ 20 7 000 0~~0 0 15 0? C,r V FIG. 7. (a) Surface roughness(log scale) of model lawns of Sphagnumcapilitfolium with a varietyof water-tabledepths and no externalshade. Each set of pointswas recordedwith a differentexposure effect. Values at theright are k in theequation of exposure effect (see Table 4). (--O--), indicates conditionswhere the model was unstable (plottedpoints are then the minimumvalues attained);*shows the surfaceroughness of the lawn at the startof a runwhen lengthswere normallydistributed random numbers with S.D. =0.5. (b) Surfaceroughness of model lawn of Sphagnumcapilifolium (with same unitsas (a)) withdifferent combinations of water-tabledepth and externalshade. The exposureeffect was set to -1.39. (c) As (b), but Sphagnumpapillosum. below the surfacetended to stabilizeat the same level as those startingat the general surfacelevel. Sphagnumpapillosum consistently produced greater growth in massexcept at thelowest water-tabledepths examined, where growth was similarto thatof S. capillifolium.This may simplybe a consequenceof thevalues of meanstem weight used to convertthe units of growthin mass to mg (mg cm stem-1)-1.The importantpoint is probablythat the differenceis greater the nearer the surface the water-table is. Withthe external absorbance of light set at 0.3, thedifferences in growthin lengthwere greater;S. papillosumnow grewfaster than S. capilifoliumwith the water-table down to 5 cm. A largeexposure effect prevented S. papillosumplants from stabilizing very far above thesurface of a S. capillifoliumlawn with a highwater-table but in the reverse situation, S. capilifoliumplants were some distancebelow the surfaceat theend of therun. With the water-tableat 0 cm,these plants were still slowly falling further behind at 200 days,so the model communitywas probablyunstable in these conditions.It was certainlyunstable when S. papillosum was grown with a low water-tablein a S. capillifoliumlawn, P. M. HAYWARD AND R. S. CLYMO 861 (a) S.cap/l/ifo/lumamongst Sopap/llosum (b) S.pap/llosum amongst Scap/l/ifolium E 10 0i5- M + L * S 03 ' C s * *-A--- @ ~~0------ff- 11/4D "Shade 0 J - ? 0 0 M 1 FIG.; 8. Resltso a moel ofphagnmgroth:theffetofntroduingasecon L i Shade -5~~ L ~ ~ - 0.0 -M~~~~~~~ 0 0 n 0ge03Shade ( -a-n ------,:, -25 0 5 L 0 \ i Depth of --- 15 o0) h20 fr0- p o 20 dy w capillifoliumgrowing0 a0 5 25 pillifolium.In (b), the S. papillosumplants initiallyDepth ofwater-table (cm) a' ~~~0 5 10 Depthof water-table(cm) j s FIG. 8. Resultsof a modelof Sphagnumgrowth: the effect of introducing a secondspecies into a Sphagnumlawn. Graphs show differencein growthbetween the second species and the restof the lawn whenall theplants started at the same level.The symbols+ and - show thedifference in growthof plantsinitially at 1 cm above or belowthe surface,at water-tabledepths of 0, 3, 8 patcual and 14 cm.whe In eachth plntgraph, difference wer intalin growthbeo in lengthth (L,sufae andIntblt in mass (M,case ----) by is dense shownfor a periodof 200 days withabsorbance by externalshade of 0.0 (g) and of 0.3 (0). The value of k in the equationfor exposure effect (see Table 4) was-1i39 throughout.(a) S. capillifoliumgrowing in a lawn of S. papillosum;(b) S. papillosumgrowing in a lawn of S. capillifolium.In (b), the S. papillosumplants initially at -1 cm, at water-tabledepths of 8 and 14 cm,both finished at -2e6 cm (shownby arrows). particularlywhen the plantswere initially below the surface.Instability caused by dense shade in associationwith a low water-tablehas been seen before,when lawns of single specieswere considered. DISCUSSION The existenceof a relationshipbetween water-table depth and surfaceroughness is confirmed,and it can be simulatedtoo. Thereare at least two mechanismswhich could account forthis observation. The firstconcerns the effectof watersupply on emergent plants.If the water-tableis near the surface,the rateof growthin lengthof a plantjust above thesurface will be high,despite the exposure effect. But as it growsaway fromthe surface,the exposure effect will cause therate to fallso thatin a steadystate the plant is growingat thesame rateas therest of the lawn but just above it (Fig. 2). Ifthe water-table is lowered,the rate of growthin lengthof an emergentplant is immediatelyreduced and the rest of the lawn catches up. Thus surfaceroughness is inverselyrelated to depthof water-table. The secondmechanism concerns the effect of shadingon a plantwhich falls behind, and mayreinforce the reduction of surfaceroughness where there is no externalshade. The rate of growthin lengthis greatestwhen the radiant flux incident on a lawnis highbut a plantis shadedby itsneighbours a fewmillimetres above. Such a plantwould then tend to returnto the surface,though with a reducedapex size, because growthin mass is reducedby shading.Another effect is also apparentfrom the results in Fig. 2. Whenthere is external shading,any increase in shadefrom neighbouring Sphagnum plants will tend to reducethe 862 Effectsof light and wateron Sphagnumgrowth rateof growthin lengthof a shorterindividual and itwill fall behind irrevocably. This effect was observedin themodel. Severalinteresting points arise fromthe modelruns with mixed lawns. First,the two species each appear to outperformthe otherin theirown 'natural' habitat.Even if individualsof one speciesare in a minority,they will grow better than those of theother species if the water-tableis eitherlow, for S. capillifolium,or near the surface,for S. papillosum.Whether such individualscould competeto the extentof eliminatingthe predominantspecies cannot be determinedwithout studying their branchingand reproductiveabilities. Secondly,the depthof the water-tableat whichthe growthof thetwo speciesis equal seemsto be about2 cm belowthe surface, with no externalshade, falling to 5 cm deepwith an absorbanceof lightby externalshade of 0.3. AlthoughS. capillifoliumis usually consideredto be a hummockspecies, it can grow successfullyin places wherethe water-tableis nearlyat thesurface (Ratcliffe & Walker1958; Clymo& Hayward1982). Nevertheless,this result does implythat S. papillosumgrowing on a hummock,where the water-tablemay be 20-30 cm belowthe surface, is at a disadvantage.This may,of course, be compensatedby otherfactors such as its ability,compared with S. capillifolium,to multiply. Thirdly,the differencesbetween the two species are greaterwhen they are shaded externally.Again, hummocks, which are oftenshaded more than open lawns,would seem to putS. papillosumat a disadvantage. ACKNOWLEDGMENTS We thankP. 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