The Statistical Analysis of Chaparral and Other Plant Communities by Means ofTransect Samples

Harry L. Bauer

Ecology, Vol. 24, No. 1. (Jan., 1943), pp. 45-60.

Stable URL:

http://links.jstor.org/sici?sici=0012-9658%28194301%2924%3A1%3C45%3ATSAOCA%3E2.0.CO%3B2-0

Ecology is currently published by Ecological Society of America.

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/esa.html.

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.

The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academicjournals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers,and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community takeadvantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org.

http://www.jstor.orgWed Nov 21 09:44:24 2007

http://links.jstor.org/sici?sici=0012-9658%28194301%2924%3A1%3C45%3ATSAOCA%3E2.0.CO%3B2-0http://www.jstor.org/about/terms.htmlhttp://www.jstor.org/journals/esa.html

THE ST.\TISTICA'IL AAN:\I,YSIS OF CHXP,IIIIIAAI, . 4 S I ) OTHI. 111 making both the labo- ratory and the fieltl tests much help was given

tleziretl matter5 are calculated. The methods of sampling vegetation ant1 of ~xesent ing the results have constitutetl 3erio~is problems eyer since Pound and C'letiients ('98) pro110seetl the quadrat as aii accurate means of - thecleter~ni~iing bunda dance of species in 11lailt associations.

There are several tlistinctly different col~cel~ts q~~ant i ta t ive Theseit1 rclatioiis. are :

( I ) Numerical a1)untlalice. in \vliicli all tlie sl~eci~iietlsare cc~untetl. 11ut tlie indl- vidual pla~its are not meabured ill any \\-a!.. The iml~ortance of a given q~ecies may 11c expressetl as its I1ei.ce1ltag.e of all intli-vitlual.; of all tlie species recordetl ; that ib. "percentage of vegetatioll."

(2 ) Frequency inclex or percentage, a btutly of clistril~ution in \\-liicli the presence of the sl~ecies is ~iotetl, Imt intlividual lllatits are neither measuretl 1101- countetl. Tlie iml~ortance of a given sllecies is ex- ~ ~ ~ - e > b c das tlie pel-centage of saml~les ill \vliich it occurs, talcell on tlie area inves- tigated.

( 3 ) Covel-age extent, in which tlie area of grountl covered hy the cro\\-n, or other portion, of eacli intlivitlual plant is meas- uretl. The importance o f a given species is assumed to be expressed by either the per cent of the total grouiid surface that it covers or as its percentage area in the total area covered by vegetation recorded.

(4) Volumes for eacli species. (5 ) Dry weight and per cent of total

dry weight for each species ~~rocluced per unit of time.

REVIE\\-OF TIIE LITI;K.\TUKG Methods of lrlaki~ig statistical analyses

of vegetation have been discussed exten-sively and ably by a number of ecologists.

great deal of the discussion has centered f)). ~~b~~~ E ~ H~~~~~~ ~ ~ ~ k ~ l l ,~ ~ ~ ~ ~ ~~ ~ ,l d I>ilit, H a r r y Tllorn~~hon ;~sountl Rnunkiaer's ('09.'18) frequencyant1 Da\-id Oshorri.

15

46 H A R R Y I..

method, antl attempts by various inveiti- gaiors to calculate abundance from for- mulae a11tl ot l le~ theoretical device,. Tlic size, shape, antl location of tlie sanlplc plots have also received attentioli

Among the early contributions to tlie subject \\-ere those of rlrrlie~lius ('21. '22. '23) ant1 Glea\on ('20. '22. '25) . ICenoyer ( '27). in his study of Ra~unkiaer's work. inclutletl an excellent summai-Y of tlie sta- tistical 111ethotls used up to that year. Hanson and Ball ( '28) applietl tile fre-quency mctliotl to grazing studies. Glea-son ( '29) sho\vecI that frequencj- per- centages var!. consitleral~ly \vith the size of the quadrat employetl. Nicl~ols('30) em~~hasizedtlie importance of quatlrat ant1 coverage tlata. Rotnell ( '30) cautioned- \ , against coml~aring statistics hnsed 011 different-sized sanq~le plots a~lrl pointed out the atlvantage of areal or covcrage ineasurements over frequency. FIanson and Love ( '30) ant1 tliscussed c o m ~ ~ a r e d the merits of five methods of quatli-atting. Cliristitlis ( '31) recommendetl tliat sam-ple plots l ~ e as long ancl narrolv as pos- sible to retluce tlie effect of hetel-cogeneit!..

I n an extensiye discussion of socio-logical concepts Cain ( '32) commentetl on the t e r m i ~ i o l o g uietl in analyzing antl de- ic r~bing vegetation and pointed out tlie error of species of highcon~ic ler~ng fre-rluenc) a \ neceyial ily being tloniinant. Hanson ( '34) compared ye~era l metliotl\ of analyzing tlie native prairie of NOI-th Dakota. AIcGinnies ( '34) tliscussetl both the theoretical aspects ant1 fieltl applica- tions of quadrat sampling ant1 frequency caiculations it1 several types of vegetation in Arizona.

Blacl\man ( '35) recommended the "l>el-- centage of absence" of speciei a i a mealit o f stutlying changes in tlenhity. i\slil)!. ( '35 ) criticizetl much of the \\orli in sta- tistical ecology as being based on uil-satisfactory absumptions, such as that o i complete ranclom clistribution it1 p la~l t communities. Sitlgli ancl Das ( '39) stutl- ied the relation between frequency percent- ages and density in weed flora. Pechanec and Stewart ('4O), in an inyestigation of

RAUEK l ' co loq~ .Voi. 2-4 xu. 1

tlie .agebrush range of Idaho, found that long narrow sample plots were generally so~ne\vhatmore efficient than square ones of the sanie size, antl conclutletl that in selecting sampling tlevices a l~alance must 11e struck hetween sa~npling accuracy and such practical consitlerations as the timc ant1 effort required.

-\ltliough numerou, in\ eitigatio~ls in-\-olving t1u;uititative analysis of vegeta-tion have heen carrietl out in liei-baceous and forest comniunities. very f c ~ v stutliei have 1)een reporter1 fol- ,ic~-uh or brusli commu11itie.s. Selson ( '30) tlescrihetl a mcthotl of charting sIirub11~- vegetation for 11l;inirnetei- measurements. Aclamso~~ ( '31) . in stutlying the brush cciver of South .Africa, f o ~ m d tliat saml~les locatetl at rantlorn gave allout the a m e I-est~lts a i those locatetl in straight lines. FIorto~i ('11 ) i ~ ~ n t l estatistical analyses of the Cali- fornian chanarral a~i t l conclu(lec1 tliat the milacre plot is a suital~le size sample for l~ringing ottt important ecological relation- sllips in this type of vegetation. hut calls attention to the great amount of time 1.'-cluiretl to comljlete tlie fieltl and office \\ orl,.

Until recently ~)r:~ct~cnlly ~epor tb of no qu;mtitative analybes of yegetation basetl on transect sampling I-atliel- than on quad-rat i , haye appeared in the l i te ra tu~e Bauer ('36, pp. 4 2 2 1 2 6 ) , in an ill\ eitiga- tion of the Californian c l i a l~a~ra l , agaye brief account of transect sampling i l l ivhicli tlie d i~ tance that each indiyitlual plant s1xc:~tI over the line 11as recorded ant1 uietl as the 11a\1s for vnriou, calculat~ons Hayel ( '41) , in a study of reproductio~i in forests, usecl a metliocl of linear meas- u i -m~ent as a sul~stitute for mapping. Canfieltl ('31 ) tlescril~etl the line inter-ception metliotl as al)plietl to range stutlies.

~ -

Since transect sarnl~ling has been usetl so seltlom in the past, it is apparent t !~at tlie ~vorkers either assume that transect data are not valid or that t h e haye over- lookecl its atlvantageh. The writer (Bauer, '36) , in attempting to make a quatlrat study of the brush cover of tlie Santa Monica BIountains, encountered so many

January, 1943 STATISTICAL -1SALYSIS OF CHAP.4RRAL 4'7

difficulties that he was forced to conclude that extensive quadratting in a dense thicket was impractical. As a result, the transect method was adopted and much more satisfactory results were obtained.

Although small two-dimensional sample l~lots can be located quickly in l~erbaceous vegetation by dropping a wire or iron frame on the ground, this is not true of vegetation made up largely of shrubs or trees. In scrub and forest communities a transect can be run and the desired data recorded in a snlall fraction of the time required to establish a quadrat and make corresponding records. This is especially true if direct measurements of the indi- vidual plants are to be made as a .means of determining ground coverage from which the relative importance of the spe- cies can be computed. However, ques- tions may be raised as to the representa- tiveness and accuracy of transect data as compared wit11 quadrat data. The chief purpose of this paper is to compare the efficiency of the transect and the quadrat nlethods of sampling vegetation, and also to compare several different methods of expressing a given set of measurements.

In order to get information as to the relative accuracy of the transect and quad- rat methods of sampling, and also as a means of comparing the accuracy of sev-eral methods of expressing data, a series of laboratory tests was carried out. I n these, cardboard discs of various colors were spread out on a specially prepared board or table top of one square meter. in such a \tray as to simulate a plant com- munity. Each color represented a species and each disc an individual plant. The discs were cut to definite sizes and the nunlber ubecl was such that the area cov- ered and the percentage of the whole wai known for each color. The sizes and pro- portions were intended to approximate roughly those found in the Californian chaparral.

Before the samples were taken the discs were thoroughly nlixed and spread on the

board by hancl. No conscious effort was made to place any particular disc or color in any particular place. An attempt was made to distribute the discs over the sur- face with fair uniformity, by avoiding pile-ups and noticeably large bare spaces. The total area covered by all the discs was in every case the same as that of the board, namely 10,000 square centimeters. Since the discs were circular, there was some overlapping and there were some interstices among them. Each disc within the sa111ple area was recorded completely. even though it might be partly covered by another disc. The bare spaces were not recorded.

After the discs were scattered over the board, the assenlblage ("community") was sampled by means of four transects and four quadrats. The sa~~lples were lo- cated at random, but one transect and one quadrat were taken somewhere near each corner of the board. The transects were talcen along the edge of a transparent 30 cm. celluloid ruler. The distance that each sampled disc extended along the transect line was measured and entered nn a specially prepared form.

The quadrat samples were taken by means of a square (10 cm. on each side) marked on a transparent piece of cellu-loid. The area of each disc, or portion of a disc, inside the quadrat was recorded. In order to get complete coverage, all pieces were recorded, even though the cen- ter of the disc was outside the square. Where only a portion of the disc was in- side the quadrat, its area was ineasured by matching with previously prepared pieces of known size.

After the eight samples (four tran-sects and four quadrats) were posted, the discs were picked up, thoroughly mixed, and redistributed over the board. Two hundred assemblages ("communities" j were sanlpled in each of the four tests made.

Test 1

I n the first test all the discs were of the same size, each having an area of ten

e ~

--

r discs of ( ~ 1 ~ 1 1 plete coverage of the line or i l l t l ~ e cluarl- I i 0 1 i c I ~ L I I I ( ~ I - ~ Y ~ three cn11cep1.i. "Coverage" i t l ~ c co~ir-

color wel-c uied. ant1 c.;lcli o i the t c ~ i color^, t l ie~~ciorc,cc)nstitute~l tcli pel- rat, beilig based on mcasllrellirlits of eacli cent of the entire assemblage. individual disc. I n the "numerical abun-

Table I shows the results of the 1nea.s- dance" part of the table, the lumber of uretnents 111atle ill the first test. The fig- discs of each color n a s used as n basis for ul-es given are percentage5 of all the discs the percentage calculations, rather than I "vegetation") recostit.cl for eacll of the 'the measurements of the indivitlual clisc.;.

7 .

1 I I . Percentages of colors ("species ") i n 200 cl.ssotiblnges (" con~iiiir?iities") co~izposedo f dissc

("pl i in ts") which e'er? (ill qf tile sciiiie size and i n z 'h ich each color ='as equally uhilndant

~ ~

- - -- ~-~..~ - ~ -

I ' D a t a based on rneasnrements D a t a based on rneasnrement< ' I\ctrlai per cent by tile transect metiiod by tile quadrat method ' oi all colors -

I"\-egrtatlon ") J--- t~er cent as ! I ' measured 1 Deviation ; r ~ ~ e Deviation~ ~ ~ ~

Data hased o n cotterage ~rieasurenlents ~--- -- - -- -- .- -. ---

\-iolet

Indigo

Grecn

Orange 10.00 1 10.42 0.42 9.91 0.06 Ited 10.15 0.15 10.20 0.20 \\.hit? 9.75 0.25 10.00 0.001

I -.\\.cragc 0.293 ~ ' 0.202

I - -- -- .. . ~

Dntci based on nzr tiicr iccll ( I bundiince - - -- - .- - -~ - ....~

I3lack 10.00 0.56 Brown 0.35 Hluc 10.00 10.24 0.24 10.34 0.311 \.iolet

I

10.00 9.16 10.04 1 0.01 Indigo 10.00 1 10.08 10.37 0.37 Green : 10.00 9.80 0.20 9.93 , 0.07 \-cllo\v 10.00 10.10 ' 0.10 Orange 10.00 10.16 0.16 9.79 0.21I Red 10.00 ' 10.34 0.34 10.40 0.40 \\'llitc. 9.77 0.23 9.93 ! 0.071 -- -

.\vcragc, 0.328 I 0.251 I-- -.- -.-

Datcz basrd on frequency -~ - ~ - --

I

13lacl; 10.00 10.11 0.11 10.07 0.07 Rrown 10.00 10.18 0.18 9.92 , 0.08 Blue 10.00 ' 10.02 0.02 9.91 0.06 \'iolet 9.55 0.45 9.79 0.21 Indigo 1 10.00 9.76 ' 0.21 Green 10.00 0.09 9.95 0.05 Yellow ' 11:; 9.6.3 0.3; 10.01 0.019.91 Orange 10.00 10.32 0.32 9.91 0.06I Iied 10.00 1 10.27 0.27 10.25 , 0.25 \\'hit? 9.88

riverage 0.255 1 0.087 -.

In thc "frequency" part of thc tal~le. neither nleasurement nor counting of tlle individuals was used. The percentages given are based on the frequency of occur-rence of a given color in all the samples taken. I11 tabulating frequency, several discs of a certain color are not weighted any more heavily than a single one of the sar-ne color that touches sollle part of the 30 cm. transect or is fount1 inside the 10 em. quadrat.

The most noticeable thing about table I is the close agreement betn-een the t ~ v o methods of sampling and also between the three methods of expressing tile results. The percentages basecl on quadrat s a n -ples, especially ~vhere basecl on frequency, are slightly more accurate than those based on transect samples. I n the case of cover- age, the average amount of deviation of the composition percentages as ~neasured. from the actual percentages is 0.29 for the transects ancl 0.20 for the quadrats.

The slightly better sho\\.ing of the quad- rats is probably due to the fact that tlle set-up favored the quadrats. The tran-sect used was rather short, being only three tirnes longer than the side of the quatlrat. In order to be equivalent, two sampling devices should yield about the sanle nurnber of statistical items. In this test tlie quadrats included about 38 per cent more items than did the transects. I t should also be remembered that in a natural con~munity of mixed species not all of the plants will have the same size body, and the species will not be of equal abundance.

Test 2

I n the second test tlle procedure was the same as in tlle first except that the colors were not equally abundant. Tlle black and the b ro~vn each co~lstituted 25 per cent of tlle entire assemblage, but the red and the white only 1.5 per cent. The total surface covered by the ten colors was the same as in the first test. The pur- pose \\-as to find out xvhich method of sam-pling xvould give better results in the case

of the colors ("species") present in sn~all percentages.

Data for the second test are given in table 11. The average amount of devia-tion under the conditions of this test is considerably greater than in tlle first test, but there is still no appreciable tlifference between tlle transect and tlle quadrat meth- ods of taking the samples. Based on cov- erage, the average amount of deviation for tlle transects is 1.006 and that for the quadrats is 0.983. \Yl~en the percentages are based on nunlerical abundance the lesults are practically the sanle as \\-hel~ coverage is used.

Since all the discs used in this test were of the same size, the percentages in the samples should be directly proportional to the numbers used, and the mathematical expectancy \voulcl be, therefore, the same as the percentage composition of the en-tire assemblage ("community"), in the case of coverage ancl numerical abun-dance. I n tlle case of frequency, how- ever, this is not true because of the ele- ment of probability. The matl~ematical expectancies were calculated from the fol- lowing formulae : '

for t h e transects, F = 1 - (1 - P)'

for the quadrats, F = 1 - (1 - P')'.

I n these formulae. "F" is tlle frequency expected, ",V" is the number of discs of a given color used, "P" is the probability of a disc being included in a transect s a n - ple, and "Po'is the probability of a disc being included in a quadrat sample. The probability is calculated from the formulae,

2ar + rr2 for t h e transects, P =

A2

b2 + 4br + r r2 for the quadrats, P' = A'

I n these formulae, "a" is the length of the transect line, "r" is tlle radius of tlle

Z T h e formulae used for calculating the mathematical expectancies were provided by Dr. Paul G. Hoel, Assistant Professor of Mathematics, University of California at Los Angeles.

H A R R Y L. BAUER I

January, 1943 STA.I-IS'I'IC'.\I. ZISALYSIS OF CHAPARRAL 5 1

FIG.1. Diagram showing the shape and other details of the effective quadrat used in sampling simulated plant conimunities, and frdrn which the probabilities \\ere calculated. Formulae and esplanations in the test.

matical expectancies in the case of the transect is based on the fact that the proba- bilitj of a certain disc touching the tran- iect line i, the same as tlie probability of the center of that disc falli~lg within an area as long as the line, having a width of one diameter, ant1 having a half disc added at each end. Such an area is illus- trated in figure 2.

TVhen the percentages based on fre-quency data are coiiipared with the mathe- matical expectancies calculated according to the formulae given, a renlarkable agree- ment is noted in the case of both the tran- 5ect and the quadrat sampling, the aver-age deviations being 0.483 and 0.430 respectively.

In the case of both methods of sampling and of each method of expressing the re- sults, the percentages calculated from the measurements are some\vhat too low for

the colors constituting high percentages of the whole, and somewhat too high for the colors constituting lolv percentages of the \vhole.

I n tlie third test the discs tvere not all of tlie same size, but the area covered by each color was the same, namely 1,000 sq. cm., and each color, therefore, constituted 10 per cent of the total surface covered. The assemblage consisted of 10 black and 10 brown discs, each having an area of 100 sq. cm.; 13yt blue and 1354 violet discs, each having an area of 75 sq. cm. ; 20 indigo and 20 green discs, each having an area of 50 sq. cm. ; 40 yellow aiid 40 orange discs, each having an area of 25 iq. cm. ; and 100 red and 100 white discs, each having a n area of 10 sq. cm. The purpose of this test was to see if either of the two sampling devices had greater efficiency than the otlier in sampling colors ("species") which consisted of a com-paratively few large individuals rather than of numerous small ones. This ar - rangeme~lt, of course, resembles a natural community of mixed species Inore closelj than was the case in either of the previous tests.

Data for the third test are given in table 111. The mathematical expecta~lcies in the case of coverage data is the same as the percentage composition of the entire assemblage. The expectancies for the frequency data were calculated f roll1 the formulae given on page forty-nine. F o r the numerical abundance data, the ex-pectancies for the transect samples were calculated from the formula NP, and those for the quadrat samples from the

FIG.2. Diagram showing the shape and other details of the area used in calculating the probability of a disc touching the transect used in sampling assemblages of colored discs. For-mulae and explanations in the text.

j 2 TI.4RRJ. L. B.ZUER Ecology. Val. 21. S o . 1

ABLE 1I I . Percentages of colors (" species ") in 200 assemblages composed of discs ( "p lan t s ") o j z'arioz~s sizes but in which each color covered the same area

Data based on measurements Data based on measurements by the transect method by the quadrat method

hlathe- Per cent hlathe- Per cent matical as Deviation matical as Deviation1 I ( 1

expectancy measured expectancy measured I 1 I 1 I I

Data based o n coz8erage n~easurenzents

Black

Brown

Blue

Violet

I n d i ~ o

m re& Yello\v

Orange

Red

\\'hitc

Data based on nz~merical abz~ndance -

Rlack

Broa n

Blue

Violet

Indigo

Green

\-ello\\

Orange

Red

\I-hite

Data based on freqz~ency

Black

Rrov n

Blue

Violet

Indigo

Green

Yellow

Orange

Red

\\'bite

formula ATPI. In these formulae, ",Y"is iampling devices are about equally accu-the number of circles used, " P is the rate, but when coverage or nurnencal probability for the transects and "P"'tlie abundance was used the transects Lvere probability for the quadrats, these proba- Inore accurate than the quadrats. The bilities being calculated from the foriliulae advantage is especially marked in the case previously given. of tlie coverage data, the average deviation

Inspection of the table shows that when for the transects being 0.579 ant1 that for the data are based 011 frequency, the two the quadrats 1.368. As sampled by tran-

- -

sects ant1 expressed as coverage, the per- centages sllo~v about the same tleviation for all colors. Hon-ever, as sampletl b ~ . quadrats, there is a nlarketl tendency f o r the percentage. of those cotors present a-: a few large tliscs to be too low a ~ l d f o r

SIS OF CIIAPARRAT, 53

T:IB~.EIV. -Yil?nbers i i x d nrecIs of discs irsrd ii1

T e s t I I", and t h e percentages qf t n f c ~ l

sur face c n x r e d

---- --.--.-, ,

o f oiC o l ' l r c 1 disc. ! used 1 Sq. crn.

tliose of the colors present as numerous Black ,mall disc.; to he too Iligh. 7'liis may 1)e clue to the fact that the tralisect has greater linear extent and reaches into more of tlie entire area being hampled.

111 tlie fourth t c t the colors vnrietl a. to tlie amount c ~ i SLII-face covered. a11t1 cnch color consistetl of three tliffcrcllt-sizctl tliscs. There Iva. also vnl-iatio~i alllong tlie cc~r101-> :I> to tllr :ive~-agc. hizc o t tlie thrce tlix-i. Iletails of the cc~r~iipcjsi- tion of this a~ , c~ i i l~ l age arc give11 in table TV. 'I'lie plan Ivas to .,imuiate n i nearly :rs pcjssil~le tile co~itlitic-111s ill a natural cotii- munity of inixetl s1,ecies. I n such a COI~I- ~ i iu~ l i tythe specie5 ilc~t only vag- as to the amount of gi-c~untl surface coverctl hut :ilso ns to the characteristic size, o f tllc. plants.

Resulrs !!i tlle fourth test are give11 in table 1'. ' fhe mathematical exl~ect:i~lcie-ior the covel-age tlata are tlie same as the i~ercentage conlposition of the entire as-hemhlage. The expecta~icies for the nu-merical al~untlance data were computetl fr1-1111the following forn~ulae :

for the t ranwcts , YIPi+ S2P?+ -X73P1 for the quatlrats, S ~ P ' I+SZP':!+ A\-"is'~.

T h e expectancies for the frequenc? d a t a were computed from the follo\ving formulae :

for the transects, F = 1 - ( 1 - PI)', x (1 - Pz)'? X ( 1 - P,)'d

for the quadra ts , F = 1 - (1 - P'l)ll X (1 - P'z)r X (1 - P':i)-'a.

I11 the above formulae the* subscript.; refer to each of the three sizes of discs of which each color is composetl in this test. The symbols are the sanie as in the fol-- lnulae previously gi\.en.

-~-- - .----, I .\rc;t , : ixe oti ro i r red total

I co\ erage

1 2 4 1 IOrange 10

Exainination of table \* s110\\ that tlie results of the fourtli te,t arc allout the same in principle as those oi~tained in tlie third test Transect and cluatlrat ,ampling are about equally accurate n-lien tile per- centages are based on frequency ant1 011 nunlerical al~undance. I-To~veves. the 11-an- sect has a clistiiict advantage ~vlieil cover- age data are con;jitleretl, the avc.1-age clevia- tion being 0.719 for the transect a i ~ d 1.181 for the quadrat. The tendency of both methods t o give percentagcs too 101v i o ~ the inore abundant ccjlors aiiil too high ioi-the less al~untlant one is apparent.

In tablr. I , IT, TI1 and V, tlie tlata,

--

j4 HARRY L. BAUER Ecology, Val. 24, No. 1

TABLEV. Percentages of colors ("species ") i n 200 assemblages of discs ("plants ") i n which the color3 varied as to the amount of surface covered, and i n which each color

consisted of discs of three different sizes

Data based on measurements Data based on measuretnents Actual made by the transect method made by the quadrat method

per cent of all colorsColor I 1 I 1(" Vege- Mathe- P e r z n t Mat,he- P e z n t

tatlon ") matical Deviation matical Deviation expectancy measured expectancy measured

Data based on cozlerage measurenzents

Black / 24.00 1 24.00 1 22.61 1 1.39 1 24.00 1 21.09 1 2.91 Brown Blue Violet Indigo Green Yellow Orange Red \Vhite

Average

Data based on numerical abundance

Black

Brown

Blue

Violet

Indigo

Green

Yellow

Orange

Red

\Vhite

Average

Data based on frequency

Black 17.04 1 16.68 1 0.36 Brown 17.04 16.23 0.81

Blue

Violet

Indigo

Green

Yellow

Orange

Red

White

Average

regardless of whether the measurements the two-dimensional quadrats truly repre- were recorded as numerical abundance, sent the entire community, the percentage frequency or coverage, were given as "per of coverage within the quadrats is also cent of vegetation," in order to make valid the percentage of coverage in the larger comparisons. I n the case of coverage area. In the case of the transect, how- measurements, the data might better be ever, it might be questioned whether or presented as the actual area covered. If not the percentage of the sample line cov-

- -- --

-

--

January, 1913 ST.I\TISTIC.I\L ASALYSIS OF C I ~\I' \KK \ I 5 5

I'IBLLVI. Kelatzon of the percentage of the lzne covered zn the transect savzples and the percentage'

of the wr face area covered zn the quadrat s a n ~ p l e s to the true percentage of

cooerage zn the large assemblage (" comnz2~nzty")

1 / Transect sampling 1 Quadrat sampling True per cent I

of coverage in larger Per cent per cent /

assemblage of line _ l e i i t i o n of area Deviation1 I

covered covered

Discs of ziniform size; colors equally abzindazt

Black Brou n Blue \'lolet Indigo Green Yellou Orange Red \Vhite

Dzscs of unz form szze, colors zot equally abundant

Black Brou n 1

25.00 25.00

I 19.89 19.66 1 5.11 5.31 19.43 19.98 1

--

5.57 5.02

.. -Violet Indigo Green

Orange l ied

1 3.50 1.50 1 3.24 1.22

\Vhite

Average

I

I

1.50 I

1.74

Discs of various sizes; each color cooering same area

Black Bro\vn Blue Violet Indigo Green Yellow Orange Red \Vhite

Average

Discs of various sizes; colors varying a s to area covered I

Black / 24.00 23.66 0.34 21.08 1 2.92 F3r;wn Blue \:iolet Indigo Green Yellow Orange Red \Vhite

1 56 H A R R Y

ered is also the percentage of the surface area covered in tlie larger area.

Tahle \'I is a coiliparison of the true percentage of the surface covered by tlie colored discs with the percentage of the line covered in the case of tlie transects and tlie percentage of tlie area covered in the case of the quadrats. I t is apparent that tlie transect samples and tlie quadrat salriples indicate the actual percentage of coverage with about equal accuracy in the case of those assemblages composetl of individuals of uniform size ( a situation rarely fo~mtl in natural vegetation). I t is rather surpri>ing to note that in the assei-ublages coillposed of intlividuals of various sizes (the usual condition in natu- 1-a1 plant communities) tlie tl-atisects indi- cate coverage in the larger area with con- siderably more accuracy than quatll-ats. 111 the assemblage tliat 1110st nearly re-semhles a tiatural commuility, tlie average tleviatioil for tlie transects was 0.655) antl that for tlie quatlrats 1 .lS2.

The itiforinatioti derivetl from the labo- ratory tests oil sitllulated plant communi- ties, tlescribetl 111 the precetling pages, may liave some practical applicatioili 111 field studies ~tivolving the detel-mination of tlie compositiotl of tlie vegetatiotl or other chal-acteristics of plant communities. Tlie tratisect niethod of sampling appears to have some definite advantages over quad- 1 at sampling it1 certain types of vegeta-tion, such as scrub or forest, where tlie iildividual platits are large etiougli and sufficiently well-defined to be measured quickly and accurately. Data hased on trailsect\, \vhicl~ involve ~ileasuring the plants in one diii?ension only, can be oh- tailled it1 a small fraction of the time re- quired to establish atid make chart quad- rats. lloreovel-, ~vlien coverage of the ground is cotisitlered or is taken as a basis for calculating percentage colnpo-sitioti, data hasetl 011 transect sampling appear to be more accurate, especially in niixed communities wliere ~ndividuals vary considerabl!. a i to size

L. BAUER ~ C C C ) ~ ~ I ~ J ,vrjl.24, 1-0,

111 ordel- to test the transect method of sampling vegetation unrlel- field conditions. it was tried out on certain plots in thc San Dimas Experimental Forest of the California Forest antl Range Experiment Station, located near Glentlora, California. At this forest, extensive studies of the relations between chaparral vegetation antl illoisture conditions are 1,eing made. The experimental work being done here is de- scribed ll!- Kraebel and Siiiclair ('30). The area used to make tlie test was a set of nine "liun-off antl Erosio17 Plots" lo-catetl on a northeasterly exposure with a slope of allout 20 to 25 per cent. Tlie chaparral vegetation here is tall ant1 tlie statid so tlense tliat much of it can be traveisetl only 011 hands antl k1iee.s. Eacll plot is 10 ft. xvitle by 125 i t . long.

This area \\-as selectetl l>ecause inteilsive quadrat studies of its floristic composition have heen carried 011 for some years, antl its percentage composition of species is probably knon-n with tilore exactness than that for any other available al-ea. In making the study the Forest Service has charted the entire surface of the nine plots grapliicallj- and to scale. Almost ailnually since 1935 this area has 1)een careft~lly antl completely ineasuretl. T o tlo this requires. fo r each chal-ting, about t\venty man-day. or 160 1lot11-s of time. Ol~sei-vations of herbage and litter are matle as \yell a. observations on the shrubby cover.

I n measuring this area by the transect sample method, a single thirty-meter tran- sect \vas rut1 through each of the ninc plots. .q steel tape was used. Tlle extent of crown projection along the line from either above or helow, was measured ant1 recorded in a specially prepared form. The san~pling device used simulated a vertical plane transect 1-ather than a liiir t ransect. A sui~?iiiary of the data obtained by the

two metliotls is given i l l Table ITIT. Tlie figures giveti are percentages of composi- tioti, antl are basetl oil coverage measure- ments. There is fair agreement between the four-year averages of the two t~iethotis of measuring. The percentages of most

-- --

January, 1943 STATISTICAL AIi‘;ALYSIS OF CHAPARRAL 57

B E 1 . Percentage composition of species i n the vegetation of n ine rz~n-of f plots of the S a n Dinzas

Experinrental Forest. Percentages are based o n corlerage

~

Plant species

. Idenoston~a fasczczilat~l~iz

. lrctostaphylos glazica Ceanothzls crass~folzus Ceanothzis olzganthzc 7 Cercocarpz~s hetzilozdes Plzotznza a r b z i t ~ f o l ~ a Przinzis zlzczfolza Qzierczcs dz in~osa R h a n l n z ~ scrocea \Tar. rlzczfolza Rhlrs ovata

. ldenostoma fasciczilatziii~

. I rctostaphylcs glaz~ca Ceanothz~s crassifolizis Ceanotlzz~s o l iganthz~s Cercocarpzis hetziloides Phol in ia arhz~t golia Przinzis ilzcifolia Qzierczis dunrosa Rha ,nnus crocea var. i l icifolia Rlzzis ovata

-~

l leasurements made in

1 1 I 4 year average 1936 1938 1939 ,941I

Data obtained f ro t t~ forest serz'ice qziadrats

7:;;, 1 25.46

10.00

I 12.58

' 2.22

0.74 46.58

1 0.34

I -

Data obtained f rom transect sanrples

of the species are surprisingly alike. I n the case of L4rcfostap1~ylos glaz~ca and Ccrcocarpzts brt7iloides (all plant names according to Jepson, '25) the difference is more noticeable, but still the percentages are close enough to have considerable ~ a l u e .

I n view of the short titlie required to take the transect samples, the similarity in the results of the two tliethods of meas- uring is remarkable. Otlly about three man-hours were required for the tran-sects, \vhereas ahout 160 mall-hours were ,pent in quadratting the area. I t is prob- able that a few more hours spent it1 taking additional transects \vould yield practically the same results as charting the entire ground surface. I t should be noted that in this field test, transect samples are not being compared with quadrat s a i n p l ~ sbut with a 100 per cent chartiilg of the entire area. Such complete chartiilg is an accu-

rate neth hod but 1s not practical oil a large area. I t can only he used on small areas ant1 \\.hen plenty of help is available. For nlost field investigations, a sampling method 111ust he employed.

I t should be remembered that the chap- arral plots in which the field test was made was a particularly difficult sample of vege- tation it1 which to work. The thicket was so dense that it could not be easily trav- ersed, and, because of the overlapping l~ranches, the linlitatioils of the individual plants were often not clear. AIoreover, the species \\.ere not uniformly distrib-uted, some of them having a tendency to occur in patches in certain parts of the area. I n spite of these handicaps fairly good results were obtained \\.it11 a com-paratively few transect iamples which required only a feiv hours to take. \Tit11 a more open type of vegetation, or a some- what larger ilunlber of transects, still nlore accurate results \vould be expected

1l:ZRRU

I ~ I S C U S S I ~ X

A stutly of the results of the laboratory tests slio\vs that percentages based 011 trailsect sampling compare fairly well wit11 percentages hased ojl quadrat salnpling in all cases, antl that in some instances the tl-ansects gave decitletlly more accurate results than the quadrats. Quatlrat sam-pling appears to have a slight advantage ill tlie assemblages coinposetl of incli-viduals of uniform size ( a contlitioil not generally fount1 in nature) antl in all cases iv11e1-e the perceiitagcs are l~ased on f I-equency . I11 those assemblages co11i-posed of inrlividuals of various sizes (the usual condition in nature) transect saln-pling appears to have a >light atlvantage 11-11eii the percentages are basetl on nu-nierical al~untlance, and a very tlecided atl- vantage when they are hased on coverage.

The advantages of the tt-ansect metliotl may be even more pronouncetl than is in- dicated, in view of the fact that the ex-11erimenta.l set-up used appears to favor the quadrat method. 111 ortier to make the fairest coil~parisons, the t\vo sampling devices should yield about tlie same num- 11er of itelils. The thirty centimeter tran- sect used tlid not include as many plants as the quadrat. 111 Tests 1 and 2. in which the assemblages consistetl of discs of uniform size, about 38 per cent more cntries were made in the quadrat record than in the transect record. In Tests 3 and 4, in wliicll the discs were of v~I.'lousc sizes including a nu~llber of coniparatively large ones, over 12 per cent more items were entered in the quadrat than in the transect record. I n spite of this advan- tage, the quadrats did not give markedly better results at any point, and in some cases, as noted above, were decidedly less accurate than the transects.

Nu~llerical abundance data do not take into account the fact that plant bodies vary as to size. In counting, a small plant is weighted just as heavily as a large one, although it obviously produces less vege- tation than a large one. This is an inl-portant matter in mixed communities

L. BAUER Ecology. Val. -71,No. 1

where ~ l a n t s varv consiclerablv it1 size. -A .pecies characterized by large individuals has greater importance in an association than a species composed of small plants. even though both species may have the same numerical abundance.

Frequency index data are sul~ject to misleading itlterpi-etation>, such as assuin- ing that species of high frequency arc necessarily "domit~ant" (Cain. ' 32) . I t has been shoivn (Gleason. '29) (Keno! el-. '27) that whet1 the frequencies are gi-ouped in the five frequency classes (A. B, C, D. & E) as is often done, the resulting ratio5 tlepeiid in large measure on the size of the quadrat sa~ilple uqetl. I n ortlei- to demon- strate Raunkiaer's law, different-sizetl sat~iple plots iilust be used for different associations. For a given association quite different results are obtained ~ 1 i e 1 1 tlie size of the sample plot is varied. Thib brings into frequency index tlata at1 ele- ment of uncertainty that is unclesirahle in the quantitative analysis and comparison of different associations. Co~l l~a r i sonsot' vegetation cannot be made where different- sized quadrats have been used (Rol-uell. ' 30) . Frequency index tabulations are. however, useful to show uniformity, 01 lack of uniformity, in the distribution of species-that is, the degree of homo-geneity of an association.

Coverage data have some tlistinct ad-vantages. They provide a sound basis from ~vhicli tlie percentage composition of the vegetation can be calculatetl, because they take into account the fact that plant^ vary as to size. 111 addition, coverage can he ex~ressed as the actual amount of the ground surface covered, an important eco- logical character. I t is coverage rather than numbers of plants or frequency of occurrence 01- other quantitative concepts used in the analysis of vegetation that determines dominance and gives charactel- to a community. Because of these things coverage data may be thought of as more valuable and significant than other data intended to express the quantitative rela- tions among species.

The time and labor involved in record-

january, 1933 S T A T I S T I C A L A N A L Y S I S O F CHAI 'ARRAL 5 9

lng coverage data ill the past have tended to discourage its extensive use. IVhen quadrats are used as a basis for such corn- putations, the individual plants are some- ti~iies charted to scale and, later, the area of each tlieasured with a plani~iieter (Han- son and Love. '30). Even when tlie areas within the quadrats are estimated instead of actually measured, much t i~iie is re-quired and it may be doubted \vhether the results justify tlie labor.

The transect method of sa~iipling vege- tation, as described herein, offers a real a v i n g of time and trouble in obtaining data as to coverage or other ecological relations wit11 no loss of accuracy what- ever. Indeed, the laboratory tests carried out indicate that, in tliixed communities. transect sa~npling gave decidedly Illore accurate percentages of coverage than quadrat sampling. I t is not clear why this is true but it is probably due to the fact that the transect has greater linear extent than the quadrat and reaches into more of the entire area being sampled.

The transect is not only suitable for obtaining data as to coverage, ~ lu~ner ica l abundance and frequency, as discussed above, but can be adapted to show other structural characteristics of vegetation. By recording appropriate units or itellis in the field record, it is probable that such characters as density, openness, luxuriance and volu~ne can be ascertained nit11 coti- siderable accuracy. Since transects can be recorded in a s~nall fraction of the time required to ~iiake the corresponding records fro111 quadrats, investigators should give careful con side ratio^^ to the possibilities of this method of sampling.

X series of laboratory tests involving measurements of sitliulated plant commu- nities of known co~nposition was con-tlucted for the purpose of comparing the relative efficiency of the transect and the quadrat methods of sampling vegetation for statistical analysis. Comparisons were also made between three different con-

~ ~ 1 1 t ho i cluant it:ltive rclatio~l>. tlaniel!.. ( 1) coverage, (2 ) numerical ahunclance and ( 3 ) frequency, or percentage of oc-currence in the sa~iiples taken.

I t was found that in con~n~uni t ies in 1vhic11 the individuals were all of the same size (an unnatural condition) the transect and the quadrat ~iiethods of sampling were of about equal accuracy. Transect sam-pling, however, has the advantage of re-quiring 111~1cli less time. I n comniunities it1 \vhich tlie i~ldividuals were of various sizes (the usual situation in nature) the transects gave decidedly niore accurate results when the data were based on cover- age measurements. This \vas probably clue to the greater linear extent of the t t-ansects.

Con~parisons of data obtained from the laboratory tests showed that, in the case of assemblages co~liposed of intlividuals of various sizes, the per cent of the linc covered in the transect saniples was a considerably more accurate intlication o f the true areal coverage in the entire as-semblage than was the per cent of t11c area coveretl \vithin the quadrat samples.

X field test of transect sanlpling was made in the Californian chaparral, the main watershed cover in southern Cali-fornia. This shrubby thicket was so dense that much of it could be traversed only on hands and knees. The results, con-sidering the comparatively s~nall amount of t i~iie involved, compared very favor-ably with the results of a chart quadrat survey \vhich covered the entire area stucl- ied and which required a great deal of titlie to make.

I t is probable that transect sampling deserves,a n ~ u c h wider use t11an has been ~iiade of it in the past. I t appears to be well suited for use in scrub or other corn- munities where tlie extent of the indi-vidual plants can be clearly observed. I t is likely that tliost of the relations that can be determined from quadrat sa~nples can also be determined from transect samples by making the proper adaptations, without loss of accuracy but with a very consider- able saving of time.

1'01. 23, s o . 1 HARRY L. BAUER I < i ~ o ~ o g y .

1930. Comparison of n ~ e t h o d s of cluadr;lt- ting. Ecology, 11 : 733-738.

Adamson, R. S. 1931. T h e plant c o t ~ ~ ~ ~ ~ u t ~ i - Hasel, A. A. 1931. I