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An Evaluation of Plotless Sampling Using Vegetation
Simulations and Field Data from a Mangrove Forest
Renske H ijbeek1'2*, Nico K oedam 1, Md Nabiul Islam Khan1'5, Jam es Gitundu Kairo3, Johan S ch o u k en s4,
Farid D ah d ouh -G u eb as1'5
1 Laboratory o f P lant Biology a n d N atu re M an ag em en t, Vrije U niversiteit Brussel, Brussels, Belgium , 2 Plant P ro d u ctio n S ystem s, W a g en in g en U niversity a n d R esearch
C entre, W a g en in g en , T h e N etherlands, 3 M om basa R esearch C entre, Kenya M arine a n d Fisheries R esearch Institute, M om basa, Kenya, 4 D e p a rtm e n t o f F u n d am e n tal
Electricity an d In stru m e n tatio n , Vrije U niversiteit Brussel, Brussels, Belgium , 5 Laboratory o f S ystem s Ecology a n d R esource M an ag em en t, U niversité Libre d e Bruxelles,
Brussels, Belgium
Abstract
In vegetation science and forest management, tree density is often used as a variable. To determ ine the value o f this
variable, reliable field methods are necessary. When vegetation is sparse or not easily accessible, the use o f sample plots is
not feasible in the field. Therefore, plotless methods, like the Point Centred Q uarter M ethod, are often used as an alternative.
In this study we investigate the accuracy o f different plotless sam pling m ethods. To this end, tree densities o f a mangrove
forest were determ ined and com pared w ith estimates provided by several plotless m ethods. None o f these m ethods proved
accurate across all field sites w ith mean underestim ations up to 97% and mean overestim ations up to 53% in the field.
Applying the m ethods to diffe re nt vegetation patterns shows th a t when random spatial distributions were used the true
density was included w ith in the 95% confidence lim its o f all the plotless methods tested. It was also found that, besides
aggregation and regularity, density trends often found in mangroves co n trib u te to the unreliability. This outcom e raises
questions about the use o f plotless sampling in forest m on itorin g and managem ent, as w ell as fo r estimates o f densitybased carbon sequestration. We give recom m endations to m inim ize errors in vegetation surveys and recom m endations for
furthe r in-depth research.
C ita tio n : H ijbeek R, K oedam N, Khan MNI, Kairo JG, S choukens J (2013) An Evaluation o f Plotless Sam pling Using V eg etatio n Sim ulations a n d Field D ata fro m a
M angrove Forest. PLoS ONE 8(6): e67201. doi:10.1371/journal.pone.0067201
E d ito r : Bruno H érault, Cirad, France
R e c e iv e d February 20, 2012; A c c e p te d May 15, 2013; P u b lis h e d J u n e 27, 2013
C o p y r ig h t: © 2013 H ijbeek e t al. This is an o p en -ac cess article d istrib u ted u n d e r th e te rm s o f th e C reative C o m m o n s A ttrib u tio n License, w h ich perm its
u n restricted use, distrib u tio n , a n d re p ro d u c tio n in an y m ed iu m , p ro v id ed th e original a u th o r a n d so u rc e a re cred ited .
F u n d in g : This s tu d y w as financially s u p p o rte d by th e V laam se Interu n iv ersitaire Raad (VLIR-UOS) a n d F onds N ationales d e la R ech erch e S cientifique. T he fu n d ers
had no role in s tu d y d esig n , d a ta collection a n d analysis, decisio n to p u blish, o r p re p a ra tio n o f th e m an u scrip t.
C o m p e tin g In te re s ts : T he au th o rs h av e d ec lared th a t n o c o m p e tin g in terests exist.
* E-mail: renske.hijbeek@ w ur.nl
Introduction
M e th o d s Available for Quantifying Biomass
Q uantifying the a m o u n t o f biom ass in the tropics can allow for
b e tte r deforestation estim ates a n d w ould allow calculation o f the
am o u n t o f carb o n lost. C urrently, for m ost tropical forests, neith er
the averages n o r the spatial distribution o f forest biom ass are
know n [5].
M o n ito rin g forest stocks a n d forest a rea changes requires
reliable m ethods. D espite the necessity, quantifying biom ass in
forests rem ains a challenge [6], T exts on M onitoring, R e p o rtin g
a n d V erification reco m m en d a com b in atio n o f rem o te sensing a n d
gro und-based forest inventory a pproaches [7]. In ground-based
forest inventories one o f the variables often used is tree density.
D eterm in in g tree density is relatively straightforw ard w h en large
field plots can b e laid o u t in w hich trees are counted. A lternatively,
plotless sam pling (som etim es spelled plot-less), also called distance
m ethods, have b e en developed [8-11], b u t pro v en n o t to be
reliable in all cases [12,13]. Plotless sam pling m ethods calculate
the average a rea p e r tree by m easuring distances betw een points
a n d trees o r betw een trees. T hese techniques have the advantage
o f not req u irin g p lot bo u n d aries a n d are generally fast, since in te r­
tree distances ten d to be low in m angrove forests a n d therefore
rapidly m easured [14],
W h en en terin g a m angrove forest for research purposes, one has
to be aw are o f the tide schedule a n d progress is particularly
M angroves
M angroves are forests found in tropical a n d subtropical regions
w ith th eir tree roots partly o r com pletely in the saline substrate or
surface w ater. T h ey p re d o m in an tly grow in intertidal areas o f
shorelines, exhibit a m arked degree o f tolerance to high salt
concentrations a n d soil hypoxia a n d have propagules th a t a re able
to survive a n d exploit dispersal b y seaw ater [1], U nlike m ost
tropical forests, m angroves have a very low species diversity [2].
Besides the in tern al value a n d b eau ty o f m angroves, th ey provide a
n u m b e r o f services [3]: i) A ct as a n atm ospheric CCD sink; ii) A re
a n essential source o f oceanic carb o n iii) S upport fisheries; iv)
Buffer for seagrass beds a n d coral reefs against the im pacts o f
river-borne siltation v) P ro tect coastal com m unities from sea-level
rise, storm surges, a n d tsunam is; vi) Provide essential food, fibers,
tim ber, chem icals, a n d m edicines for com m unities living close to
m angroves.
H ig h po p u latio n pressure in coastal areas has led to the
conversion o f m an y m angrove areas. It has b e en estim ated th at
betw een 1980 a n d 2000 the w orld m ight have lost 5 m illion h a o f
m angroves, o r 25 p e r cent o f the extent found in 1980 [4],
N um bers how ever, have to be taken w ith caution as m on ito rin g is
scarce a n d not com prehensive.
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An Evaluation o f Plotless Sam pling
difficult w hen trying to get deep er into the forest as often clim bing
over tree roots is required. L aying plots in a m angrove forest can
range from bein g extrem ely tim e consum ing up to unfeasible.
M easuring distances b etw een trees is com paratively m ore easy a n d
fast. F or these reasons one ploüess sam pling m eth o d - the P oint
C e n tre d Q u a rte r M e th o d (PC Q M ) - has b e en re co m m e n d e d for
m angrove research [14] a n d since th en b e en used for a variety o f
purposes [15-19]. Besides P C Q M , a n u m b e r o f o th er plodess
sam pling m ethods exist.
while site 3 a n d 4 w ere in a m onospecific Avicennia marina stand.
T o g eth er, site 1 a n d 2 stretched from the shore to land, form ing a
com plete section o f the m angrove zonation. Site 3 was chosen in
a n a re a w ith closed canopy a n d site 4 in a n a re a w ith o p en canopy.
In site 1 a n d 2 all trees higher th a n 1.30 m w ere recorded, w hile in
site 3 a n d 4 all trees h igher th a n 0.50 m w ere recorded. B oth
heights rep resen t phases o f survival a n d targ et trees th a t are m ost
likely to b e recru ited into the a d u lt tree layer. Figure 1 shows all
the coordinates o f the trees in the four sites.
Research Q uestions
S im ulation-based Study
T his research tries to find the accuracy o f P C Q M in relation to
o th er plodess sam pling m ethods. T h e objectives are threefold: i)
T o evaluate the accuracy o f P C Q M b o th w ith field a n d sim ulation
data; ii) T o co m p are the accuracy o f P C Q M w ith o th er plodess
sam pling m ethods; iii) T o relate results o b tain e d from field d a ta to
different vegetation patterns.
F ro m previous studies it is know n th a t errors in plotless
sam pling can be (partly) ascribed to the degree o f n on-random ness
o f a vegetation p a tte rn . [23]. In vegetation analysis, two basic types
o f spatial p attern s a re know n besides random ness: regular a n d
aggregated dispersion, w here dispersion refers to the a rra n g e m e n t
o f points in a p lan e [24]. In m angrove forests a n ad ditional spatial
p a tte rn exists: species show a differential distribution p e rp en d ic­
ular to the coastline (parallel to elevation). T his p a tte rn is p ro bably
due to the different physiological adap tatio n s a n d different
tolerance levels to, for exam ple, salinity, resulting in different
optim al grow th conditions a n d hence position (Saenger 2002). T h e
p a tte rn has b e en referred to as zonation, w hich can be discrete or
gradual.
T o gain m o re insight into how the accuracy o f the m ethods
varies w ith the vegetation pattern s, six spatial p attern s w ere
created in M A TL A B : a regular, ra n d o m a n d aggregated p a tte rn
a n d each o f these th ree w ith o r w ith o u t a distributional g radient
(zonation).
First, ra n d o m , aggregated a n d sem i-regular p a tte rn w ere
generated: for the ra n d o m p a tte rn the M A T L A B function randQ
was used. T his function draw s p se u d o ran d o m values from the
sta n d ard uniform distribution. T h e aggregated p a tte rn was
g en erated b y clustering trees a ro u n d uniform ra n d o m spots. O n
average these clusters co n tain ed 10 trees. T h e trees w ithin the
aggregates h a d a uniform ra n d o m distribution. T h e semi- regular
p a tte rn was g e n era te d by placing points a t regular distances along
the x- a n d y-direction in the plane. Second, a grad ien t (density
trend) was applied to all th ree p attern s in the y-direction w ith a
n a tu ra l logarithm , creating th ree new spatial p a tte rn s w ith
zonation.
T r e e d e n s ity o f th e v e g e ta tio n p a tte r n s . In o u r 4 field
sites, densities w ere found b etw een 0.08 a n d 1.22 tr e e s /m 2. T o test
the effect o f different vegetation p attern s we used a density o f 0.2
tre e s /m 2 w ith plo t sizes o f 100 m by 100 m . T h e a cq u ired d a ta
sets w ere used to test a n u m b e r o f plotless sam pling m ethods.
T hese large plo t sizes allow ed us to also co m p are higher ord er
m ethods (for w hich the field sites w ere too small). A visualisation o f
the resulting six p attern s w ith tree densities o f 0.2 tre e s /m 2 is given
in figure 2.
T h e question is if relative errors will change if this density w ould
vary. T o find the effect o f the density itself o n the accuracy o f the
density estim ations we m ad e a n ad ditional analysis in w hich we
v aried the density o f each vegetation p a tte rn s b etw een 0.05 a n d 1
tre e s /m 2.
S et-up of t h e Study
T his study consists o f two parts: i) a n observation-based study
a n d ii) a sim ulation-based study. In the first p a rt, the locations o f
all trees w ere m ap p e d in four sites in a m angrove forest. In the
second p a r t tree p attern s w ere sim ulated using M A T L A B T M
(student version 7.7.0 R 2 0 0 8 b T h e M athw orks). As such, two
different types o f d a ta sets w ere a cq u ired o n w hich different
plodess m ethods w ere tested. In each o f the follow ing sections, first
the observation-based study a n d th en the sim ulation-based study
will be discussed.
M ethods
Ethics S ta te m e n t
F o r this study, fieldwork was cond u cted in a m angrove forest at
G azi b a y in the C oast Province o f K enya. F or this area, the
K e n y an M inistry o f Science a n d T echnology issued a research
clearance p e rm it (no. N C S T 5 /0 0 2 /R /1 5 8 ) . C onsequentiy, all
necessary perm its w ere o b tain e d for the described field studies.
O b serv atio n -b ase d Study
T o find the accuracy o f a sam pling m ethod, one should first
know the actual (true) density. W e established the tru e density o f
four sites in a m angrove forest in G azi bay, K e n y a (4°25 S a n d
39°30E) by counting a n d m ap p in g all trees in these four stands.
T his m eans th a t we could re p ro d u c e the forest stands o n a
co m p u te r to test the plotless sam pling m ethods as if they w ere
applied in the field. In plotless sam pling distances are m easured
between trees a n d therefore the tree location is the relevant variable.
W e digitized all tree locations a n d developed a n algorithm for each
plotless sam pling m ethod. T his allow ed num erous repetitions o f
the density estim ations a n d thus the calculation o f the m ean
estim ate a n d confidence intervals for each sam pling m ethod.
M a p p in g tr e e lo c a tio n s in th e fie ld . In the m angrove forest
in G azi b a y 10 m angrove species have b e en re p o rte d [20]:
A vicennia m arin a (Forssk.)Vierh., B ruguiera gym norrhiza (L.)
L am , C eriops tagal (Perr.) C.B. R obinson, H e ritiera littoralis
D ry an d , L u m n itzera racem osa W illd, R h izo p h o ra m u cro n a ta
L am , S o n n eratia alb a Sm , X ylocarpus g ra n atu m K o e n a n d
X ylocarpus m oluccensis (Lamk.) R o e m [21]. In this a rea
m angrove zonatio n has b e en previously described in detail [22].
In F eb ru ary a n d M a rch o f 2009, x- a n d y- coordinates o f single
trees w ere reco rd ed in four sites a t G azi Bay. T h is was done by
m aking field grids o f l O m by 10 m , 5 m b y 5 m , a n d 2 m by 2 m
a n d m easuring the distances from the trees to the grid borders. Site
1 a n d 2 w ere located in a n a re a w ith m ultiple m angrove species,
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Testing Plotless Sampling M e th o d s on th e Acquired Data
Sets
As far as we know , P C Q M is the only plotless sam pling m eth o d
used in m angrove research. T o investigate possible alternative
techniques, this evaluation is exten d ed w ith four categories o f
plotless sam pling found in the literature: the N earest N eighbour
m ethods, the Basic D istance m ethods, the O rd e re d D istance
m ethods, the V ariab le A rea T ra n se c t m ethods a n d the Angle
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June 2013 | V olum e 8 | Issue 6 | e67201
An Evaluation o f Plotless Sam pling
S ite 1
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Figure 1. Spatial d istrib ution o f m angrove trees in 4 field sites at Gazi Bay. The d o ts show th e location of each tree. The d iam eter o f th e
d o ts is proportional to th e d iam eter of th e stem above th e root. The colour of th e d o ts rep re sen ts th e tre e species: Dark blue is Avicennia m arina,
light blue is Bruguiera gym norrhiza, g reen is Ceriops tagal, o ran g e is Rhizophora m ucronata and brow n is Xylocarpus g ranatum . T ogether site 1 an d 2
form a co m p lete section of th e forest; from low tid e shore to terrestrial v eg etatio n (supralittoral level). The y-axis o f site 1 starts a t th e terrestrial
v eg etatio n an d en d s a t th e beginning o f site 2. The y-axis of site 2 en d s a t th e last tree a t th e creek side. Site 3 had closed canopy, while site 4 had
o p e n canopy.
doi:10.1371/journal.pone.0067201 ,g001
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Figure 2. V eg etation patterns. Spatial point p attern s representing 6 possible v eg etatio n distributions (from left to right and from to p to b ottom ):
Random , sem i-regular, ag g re g a te d , random w ith a density tren d , sem i-regular with a density trend and a g g re g a te d with a density tren d .
doi:10.1371/journal.pone.0067201 ,g002
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June 2013 | V olum e 8 | Issue 6 | e67201
An Evaluation o f Plotless Sam pling
T a b le 1. An o v e r v ie w o f t h e p lo tle s s s a m p lin g m e th o d s e v a lu a te d in th is s tu d y .
M e th o d
D e s c r ip tio n o f d is ta n c e (s ) m e a s u re d
E q u a tio n
N earest n e ig h b o u r
T he d is ta n c e b e tw e e n a tre e an d th e n e a re st tr e e is m e asu red .
L ite r a tu r e s o u rc e
[8], [12], [13]
b =
2 .7 7 S * ( E iW A T
Basic d ista n ce
T h e d is ta n c e b e tw e e n a p o in t an d th e n e a re st tr e e is m e asu red .
O rd ered d ista n c e 1
T he d is ta n c e b e tw e e n a p o in t an d th e n e a re st tr e e is m e asu red .
[8]
1
,
4 * ( E Rw / n y
[9], [28]
f)
> E *O rd ered d ista n c e 2
T h e d is ta n c e b e tw e e n a p o in t an d th e s e c o n d n e a re st tre e
is m e asu red .
O rd ered d ista n c e 3
T he d is ta n c e b e tw e e n a p o in t an d th e third n e a re st tre e
is m e asu red .
PCQM 1
T h e d ista n ces b e tw e e n a p o in t a n d th e n e a re st tre e in
e a c h q u a d ra n t a ro u n d th e p o in t a re m e asu red .
[9], [28]
h
2” ~ '
-
377 — 1
[9], [28]
4 (4 « —1)
[9], [11]
^ _
~
n
4
* £ £ V
i = ly = l
PCQM 2
T h e d ista n ces b e tw e e n a p o in t a n d th e s e c o n d n e a re st
tr e e in ea ch q u a d ra n t a ro u n d th e p o in t a re m e asu red .
^ _
~
4 (8 « —1)
n
[9]
4
* £ £ % 2)2
Ulj=l
PCQM 3
Variable A rea T ransect
T h e d ista n ces b e tw e e n a p o in t a n d th e th ird n e a re st tr e e in
e a c h q u a d ra n t a ro u n d th e p o in t a re m e asu red .
^ _
T h e d is ta n c e from a p o in t to th e g th individual in a g iven
direction w ith a certain w idth (a tran sect) is m e asu red .
^ _
4 (1 2 « —1)
« 4
[9]
n i£= i j £= i Rm
gn—1
u 'E - L s ii
[10]
D = e stim a te d density, R = d ista n ce m e asu red in th e field, ¡ = n u m b e r o f sam p lin g po in t, j = n u m b e r o f q u a d ra n t, g = th e g th individual, L is le n g th o f tra n se c t an d W is
w idth o f tra n se ct, N or n = n u m b e r o f sam pling points.
doi:10.1371 /journal.pone.0067201 .t001
O rd e r m ethods o f w hich P C Q M is p a rt. In each m eth o d distances
are m easu red b etw een trees o r b etw een points a n d trees to
estim ate tree density. F or each category a description, equation
a n d reference c an be found in table 1.
F o r each m eth o d a n algorithm was developed using M A TL A B .
T h e algorithm s w ere used to test the plotless sam pling m ethods on
the d a ta sets a cq u ired th ro u g h b o th the field-based a n d the
sim ulation study.
T h e algorithm s can be found in File S I a n d on the w ebsite o f
the Lhiiversité L ibre de Bruxelles [25].
Preventing edge effects. T h e d a ta sets acq u ired (both from
the field-based a n d sim ulation-based study) are enclosed a n d thus
c ontain borders. W h en a sam pling p o in t is lo cated close to the
b o rd e r o f a d a ta set, the n earest tree m easu red m ight be farther
aw ay th en w ould be m easured in the field (for exam ple, in the field
th ere m ight be a tree right a t the o th er side o f the b o rd e r, causing
a sm aller distance m easured). T his effect has b e en described by
P eter Flaase [26] a n d called edge effects. T o p rev en t edge effects in
this study, th ree actions w ere taken:
3. Fligher o rd e r m ethods w ere n o t analysed for the field d ata, b u t
only for the sim ulation-based study, w hich h a d large areas o f
100 m . by 100 m.
Replications. E ach m eth o d was used to estim ate tree density
using 5, 10, 15, 20, 25 a n d 30 ra n d o m sam pling points. T hese
calculations w ere re p ea te d ten tim es for each field site a n d p a tte rn
to allow for the m ean a n d sta n d ard deviation calculation. T h e
sta n d ard deviation was calculated w ith the follow ing equation:
sd = ^
.
\
y
—.v)2^ , w here
the
m ea n
is given by
.\'= —N
Xi. B oth the estim ated m ea n a n d sta n d ard deviation
fi
l
did n o t change m u ch above 15 sam pling points. T h erefo re in this
article only the results for estim ations w ith 30 ra n d o m sam pling
points are presented. T h e v a riation in m ean estim ation a n d
sta n d ard deviation w hen using 5 to 30 sam pling points c an be
found in File S2.
Results
1. T h e sam pling points w ere located at a m inim al distance from
the site bo u n d aries (0.05*surface a rea " for sites w ith m ore
th a n 128 trees a n d 0.1*surface a re a 0'5 for sites w ith 32 to 127
trees, correspon ding to at least the average distance betw een
two trees).
C lark a n d E vans [27] developed a n aggregation index as a
crude m easure o f clustering or ord erin g o f a po in t p a tte rn . A value
R > 1 suggest regularity, R < 1 suggests clustering a n d R equals 1
suggests random ness. T h e sta n d ard range is 0 < R < 2 .1 4 9 1 .T o
co m p are the degree o f clustering b etw een the field sites a n d the
vegetation p atterns, the R index was calculated for each o f these.
T ab le 2 a n d 3 show the aggregation indices for b o th the field
sites a n d the p atterns: T h e p a tte rn s o f the field sites vary betw een
clustered a n d close to ra n d o m . Sites 3 a n d 4 have p attern s m ost
closely ap p ro ac h in g random ness w ith aggregation indices o f 0.85
2. W h en a m eth o d m an d a te d th a t a tree across the site b o u n d a ry
should be used for co m putation, the relevant sam pling point
was om itted (this applied only for P C Q M a n d the V ariable
A rea T ran sec t m ethod).
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(
4
June 2013 | V olum e 8 | Issue 6 | e67201
An Evaluation o f Plotless Sam pling
a n d 0.92 respectively. T h e trees in site 1 a n d 2 show a m ore
diverse p a tte rn w ith aggregation indices betw een 0.56 a n d 0.67.
T h e sim ulated vegetation p attern s show a w ider range, w hich
provides the o p p o rtu n ity to test the p erfo rm an ce o f plotless
sam pling in cases o f m o re extrem e regularity o r aggregation.
T ab le 4 a n d 5 give a n overview o f the results for each m ethod,
field site a n d p a tte rn . T h e results from the observation-based study
show the e rro r one can get w hen sam pling in the field; the
sim ulation-based study relates the spatial p a tte rn to the errors.
T a b le 2 . The aggregation Indices (R) for the field sites.
Observation-based Study
In figure 3, the results for the observation-based study are
show n in a graph. U sing the plotless sam pling m ethods, large
underestim ations w ere fo und for the density o f the sites, especially
in site 1 a n d 2. T h e largest underestim atio n (97%) was found in
the estim ation w ith the O rd e re d D istance M e th o d (O l) in site 2
w ith the tree Ceriops tagal. O verall, the V ariable A re a T ran sec t in
the y-direction (VY) a n d the N earest N eig h b o u r (NN) m eth o d
perfo rm slightly b e tte r in the field d ata, b u t still g enerate errors as
large as 80% in som e sites.
D u e to the size o f the plots (see previous section ab o u t
prev en tin g edge effects), P C Q M (denoted P I in figure 3) was only
tested in sites 3 a n d 4. In these sites, it has a n underestim atio n o f
31% a n d 24% respectively. T hese errors are larg er th a n the errors
o f the o th er m ethods for these two sites.
S ite
A g g r e g a tio n in d e x (R)
Site 1 (Avicennia marina)
0.67
Site 1 (Ceriops tagal)
0.56
Site 2 (Ceriops tagal)
0.59
Site 2 (Rhizophora m ucronata)
0.64
Site 3 (Avicennia marina)
0.85
Site 4 (Avicennia marina)
0.92
doi:10.1371 /journal.p o n e.0 0 6 7 2 0 1 .t002
D iscussion
Observation-based Study
In the field, m ea n underestim ations a n d overestim ations u p to
97% a n d 53% respectively w ere found. T hese errors c an result in
estim ated densities up to 30 tim es below the real value. O u r
findings confirm a n d extend results from o th er a u thors [12,13,28],
E rrors as large as fo u n d here, based on actu al field d ata, w ere
how ever n o t yet reported. T his is p ro b ab ly due to the species
zonatio n presen t in the m angrove forest. O n e should rem em b er
though, th a t density gradients do occur outside m angroves. O ften
these gradients d e p en d on changes in the env iro n m en t like
altitude. T herefore, these results apply to m ore types o f vegetation.
Simulation-based Study
In figure 4, the results for the sim ulation-based study w ith tree
densities o f 0.2 trees/m ~ are show n in a graph. In the ra n d o m
p atterns, all m ethods score relatively well: T h e tru e density was
included w ithin the 95% confidence lim its o f all plotless m ethods
tested.
In the aggregated p atterns, all m ethods p erfo rm w orse w ith no
m ea n e rro r sm aller th a n 45 %. T h e sign o f the e rro r in aggregated
p attern s is negative: the estim ated density is m u ch low er th a n the
exact value. F or ra n d o m sam pling points, the chance is h igher to
fall outside a cluster th a n w ithin: the distance m easured, w hich will
also b e squared, becom es larg er w hen the sam pling p o in t falls
betw een clusters a n d the estim ated density will be low er th a n the
exact density. F o r the N earest N eighbour m eth o d the exact
opposite m echanism operates: in a n aggregated p a tte rn the chance
o f a ra n d o m tree falling w ithin a cluster becom es larger while the
distances w ithin a cluster betw een trees a re m u ch sm aller: the
estim ated density will b e h igher th a n the exact density.
In regular p atterns, the N earest N eighbour m eth o d gives an
underestim atio n w hile the others overestim ate the density. In
regular p attern s the variatio n in errors is m ixed: the h igher ord er
m ethods (O rd ered D istance 2, O rd e re d D istance 3, P C Q M 2,
P C Q M 3 a n d V A T X a n d Y) perform relatively well w ith m ean
errors low er th a n 20% . O n average, the g radient increases the
e rro r for all th ree p attern s a n d m ethods selected.
Varying the tree density. T h e effect o f varying the tree
densities can be seen in c h ap ter three o f the supplem entary
m aterial. T h e tables presen ted show th a t the e rro r in the density
estim ate becom es (on average) sm aller w ith increasing density.
O nly w h en a tre n d is present, the accuracy becom es less w ith
h igher densities, p ro b ab ly because the ap p ea ran c e o f the tren d
also becom es stronger. U n d e r clustered p atterns, a low er density
seems to result in a larger erro r, p ro b ab ly because the degree o f
aggregation also increases. O verall the V ariable A rea T ran sec t
M e th o d (VAT) seems to p erfo rm best u n d e r varying tree density.
S im ulation-based Study
F o r alm ost all m ethods the sign o f the e rro r - over or
underestim atio n - depends o n the p a tte rn (aggregation or regular
pattern). T his m echanism will increase the e rro r w h en tree
densities o f two forests w ith differing vegetation p a tte rn s are
com p ared . T h e unreliability range th e n corresponds w ith the
entire e rro r range.
T h e p a tte rn s o f o u r field sites vary betw een clustered a n d close
to ra n d o m . Sites 3 a n d 4 have p attern s m ost closely a p p ro ac h in g
random ness. All m ethods give the highest accuracy for these sites
(figure 3), ju st like for the ra n d o m dispersion p attern s in figure 4.
T h e trees in site 1 a n d 2 show a m ore diverse p a tte rn w ith also less
accu rate density estim ations. Interestingly, the N earest N eighbour
m eth o d gives relatively good results in the field study, especially in
site 1, w hile it gives w orse results for the vegetation pattern s. A
possible explan atio n could b e th a t b o th Avicennia marina a n d Ceriops
tagal have a m ix o f vegetation p attern s (both aggregation a n d
regularity) in w hich the N earest N eighbour m eth o d h ap p en s to
p erfo rm well.
T a b le 3 . The aggregation indices (R) for the vegetation
patterns.
S p a tia l p a tte r n
A g g r e g a tio n in d e x (R)
R andom
1.03
R andom w ith g ra d ie n t
0.90
S em i-regular
1.89
S em i-regular w ith g ra d ie n t
1.46
A g g reg ate d
0.45
A g g reg ate d w ith g ra d ie n t
0.42
doi:10.1371 /jou rn al.p o n e.0 0 6 7 2 0 1 .t003
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An Evaluation o f Plotless Sam pling
T a b le 4 . Tree density estim ations using plotless sampling in fo u r field sites (30 sam pling points, 10 replicates).
E x act
d e n s ity
OD1
PCQM 1
VATX3
VATY3
Range o f m ean
B D ( n /m 2)
( n /m 2)
( n /m 2)
( n /m 2)
( n /m 2)
e r r o r (% )
0.08
0.02
0.01
-
-
0.06
- 8 7 to +5
0.02
0.01
0.01
-
-
0.01
0.20
0.02
0.01
0.07
0.01
0.01
-
-
0.16
0.05
0.04
0.14
0.10
0.02
0.02
0.07
0.11
0.11
0.07
0.07
0.08
0.07
-
-
0.05
0.33
0.18
0.19
0.15
0.21
0.21
0.24
0.03
0.07
0.05
0.06
0.04
S ite
( n /m 2)
N N ( n /m 2)
Site 1 (Avicennia m arina)
0.08
95% Cl
Site 1 (Ceriops tagal)
0.20
95% Cl
Site 2 (Ceriops tagal)
1.22
95% Cl
Site 2 (Rhizophora m ucro nata)
0.49
95% Cl
Site 3 (Avicennia m arina)
0.22
95% Cl
Site 4 (Avicennia m arina)
0.57
0.09
-
-
- 9 4 to +1
0.03
0.14
0.50
0.50
0.43
0.36
0.47
0.46
95% Cl
0.20
0.21
0.19
0.11
0.15
0.14
R a n g e o f m e a n e r r o r (% )
- 8 7 to +53
—9 6 to - 1 2
- 9 7 to - 1 3
- 3 1 to - 3 7
- 2 to - 1 7
- 8 8 to - 3
- 9 7 to - 8 7
- 8 5 to - 7 2
- 3 2 to +49
- 3 7 to - 1 2
Tree d en sity e stim atio n is th e m e an o f 10 e stim atio n s using each m e th o d w ith 30 ran d o m sam p lin g p o ints; half 95 Cl is th e half w id th o f th e 95% co n fid en ce interval for
th e 10 e stim ates; NN is N earest N eighbour; BD is Basic D istance; OD is O rd ered Distance; PCQM is P oint C en tred Q u arter M ethod; VAT is V ariable Area Transect.
doi:10.1371 /journal.pone.0067201 .t004
In the field, vegetation m ost p ro bably displays a m ix o f patterns:
a forest can display b o th aggregation a n d random ness a t different
sites, o r even ra n d o m aggregations o r aggregations o f ra n d o m
clusters.
Varying tree density. W hile varying the tree density u n d e r
ra n d o m a n d sem i-regular p attern s is ra th e r straight forw ard, w ith
aggregated p a tte rn s the question is w hat will h a p p en w ith the size
o f the clusters: W ill the density w ithin tree clusters re m a in the
sam e w ith varying tree density, or will it also vary? F or o u r study
we assum ed th a t the density w ithin the tree clusters rem ains
sim ilar. T his causes a h igher a low er R index; a h igher degree o f
aggregation. C onsequently the e rro r in the density estim ates for
aggregated vegetation p a tte rn s is m u ch higher. T his could be an
effect o f the assum ption m ad e (similar w ithin cluster densities),
ra th e r th a n a n observation w hich could also be m ad e in the field.
T hese results therefore ask for m o re elab o ratio n a n d research a n d
concise conclusions u p o n the effect o f density variations c an n o t be
m ad e for now.
Reflection. N o n e o f the plotless sam pling m ethods gave good
results across all study sites a n d vegetation patterns. T ak in g a
com bination o f m ethods m ight b e a n alternative. W hite et al. [13]
found a co m b in ed estim ator taking the m ea n o f two N earest
N eighbour m ethods a n d one Basic D istance m eth o d to perform
the best. T his com bination how ever is very difficult to apply in the
field. A ccording to th eir study, the 2nd a n d 3rd o rd e r P C Q M
ran k ed highest for the clum ped distribution a n d the V ariable A rea
T ran sec t m eth o d p erfo rm ed m oderately well overall. C o m p a ra ­
tively, o u r analysis does show b e tte r p erfo rm an ce for h igher ord er
m ethods like P C Q M 2 a n d 3 a n d theV ariab le A rea T ran sec t
m ethod. T h e difficulty lies w ith aggregation a n d zonatio n patterns,
as these m ethods still give errors up to 80% in these circum stances.
T his gives very low certain ty using these m ethods w hen vegetation
p attern s are unknow n.
A n alternative to field sam pling is the use o f rem o te sensing.
T o d a y in te rp reta tio n still needs to be g ro u n d e d in field data.
N a g en d ra et al. [29] m ad e a n extensive review a n d stress the
im p o rtan ce o f in situ d a ta for accu rate in te rp reta tio n o f im agery.
Studies in m angroves show th a t d a ta from field surveys a n d
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rem otely sensed d a ta do n o t always correspond (for exam ple due
to overgrow th o f one species by another) [20,30] a n d th a t different
d a ta sources should be com bined. W ith the advance o f tech n o ­
logical developm ents, one day rem o te sensing alone m ight be able
to m o n ito r forest resources. In the m eantim e, errors m ight be
inevitable, b u t ignorance o f u n certain ty is avoidable.
T his study has show n large errors in vegetation survey m ethods
currently used in four field sites. T hese field sites are small a n d do
not represent the large a n d diverse m angrove com m unities w hich
can b e found a ro u n d the w orld. U sing plotless sam pling w ithin
different vegetation p attern s shows th a t especially b a d results are
o b tain e d w ithin n o n -ran d o m ly dispersed vegetation. T h erefo re, it
is im p o rta n t to find out w hat p ro p o rtio n o f m angroves w orldw ide
is c haracterised by a ra n d o m spatial distribution o f trees.
C a u tio n should b e taken w h en applying plotless sam pling
m ethods in the field p articularly w h en used for societal purposes.
C urren tly m ore th a n 90 p e rce n t o f the w o rld ’s m angrove forests
a re located in developing countries [3]. Like elsew here, the local
c om m unity in o u r study site obtains direct benefits from the forest
in term s o f w ood a n d non-w ood products. In d irect benefits m ay
com e in the future w hen carb o n sequestration b y n a tu ra l a n d
re p la n te d forests is v alued a n d p a id for. LTsing g ro und-based forest
inventory approaches, the e rro r gen erated in the tree density
estim ation m ultiplies w ith uncertainties in o th er variables.
In a cc u rate estim ates, as can easily b e gen erated b y in ap p ro p riate
m ethods, can m ake society p a y too m u ch o r the com m unity
receive too little.
Conclusions
Using plotless sampling in the field. T h e m ost im p o rtan t
reason w hy plotless sam pling techniques are bein g used is the
relative ease c o m p a red w ith plot-based m ethods. T his reflects the
trad e-o ff b etw een m ax im u m accuracy a n d m in im u m tim e
required. Because plotless m ethods give the largest bias w hen
vegetation has a high degree o f non-random ness, we w ould like to
reco m m e n d not using these m ethods w hen this is a know n
vegetation feature beforehand.
6
June 2013 | V olum e 8 | Issue 6 | e67201
An Evaluation o f Plotless Sam pling
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June 2013 | V olum e 8 | Issue 6 | e67201
An Evaluation o f Plotless Sam pling
S ite 1: A vicennia m arin a
S ite 3: A vicennia m arin a
S ite 2: C e rio p s ta g a l
0,6
0.1 5
CM
I
CM
E
'S
0.1
(D
CD
CD
Q>
ë . 0,3
>,
»
0 .05
I
0,2
0.5
æ
T3
o
■o
NN
BD
01
VY
NN
S ite 1: C e rio p s tag al
BD
01
NN
VY
S ite 2: R h iz o p h o ra m u c ro n a ta
BD
Ol
P1
VX
VY
S ite 4: A vicennia m arin a
0 .25
ÍN
E
i/t
S
CD
CD
0 .15
ë . 0.4
s
S'
»
a>
■o
0.6
™
0.2
CD
CD
cn
0.1
I
0.2
S
0.2
0 .05
NN
BD
01
VY
NN
BD
01
VY
NN
BD
Ol
P1
VX
VY
Figure 3. Tree d en sity estim ations b y app lying plotless sam pling m ethods to field d ata. The density estim ations found by applying
plotless sam pling m eth o d to th e field d ata. The field d a ta consisted of m angrove tree locations in four sites. In each graph th e horizontal lines are th e
real tree densities in th e sites. The closed squares are th e m ean o f 10 estim ations with 30 random sam pling points. The verticals crossing th e m eans
are th e 95% confidence intervals. NN = Nearest Neighbour; BD = Basic Distance; 01 = O rdered distance 1; VY = Variable Area T ransect in th e y-direction
w ith 3 trees; VX = Variable Area T ransect in th e x-direction w ith 3 trees; P1 = Point C entred Q uarter M ethod with th e nearest tree in each q u ad ran t.
doi:10.1371/journal.pone.0067201 ,g003
W h en the spatial p a tte rn is unknow n, it could b e a rational
a p p ro ac h to use a m ix o f two m ethods - for exam ple plot-based
a n d plotless - o r two plotless m ethods w ith know n contrasting
R andom
biases - like N earest N eig h b o u r a n d Basic D istance. In all cases we
recom m end: i) T o check results w herever possible w ith a second
m ethod; ii) T o use a h igher o rd e r o f m eth o d (so O rd e re d D istance
S e m i- re g u la r
A g g r e g a te d
0.4
0.4
<n
CN
0.3
E
0
0
0.2
0.2
Ui
£
c0
0
T3
0,5
T3
0.2
NN BD 01 0 2 0 3 P1 P2 P3 VX VY
R a n d o m w ith t r e n d
0.4
£
NN BD 0 1 0 2 0 3 P1 P2 P3 VX VY
S e m i- r e g u la r w ith t re n d
A g g r e g a te d w ith tre n d
0.4
0.3
<n
V
)
0
0
N N BD 01 0 2 0 3 P 1 P2 P3VXVY
0.3
CM
E
w
0
10/5
0
0
0.2
~
0.2
>>
’</>
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£
c
"O
N N B D 01 0 2 0 3 P1 P2 P3VXVY
~0o
NN BD 01 0 2 0 3 P1 P2 P3 VX VY
0,5
NN BD 0 1 0 2 0 3 P1 P2 P3 VX VY
Figure 4. Tree density estim ations by applying plotless sam pling m ethods to 6 vegetation patterns. In each grap h , th e horizontal lines
are th e real d ensities (0.2 p o in ts p e r m 2 for all patterns). The d o s e d sq u a res are th e m ean o f 10 estim atio n s w ith 30 random sam pling p oints. The
verticals crossing th e m ean s are th e 95% confidence intervals. NN = N earest N eighbour, BD= Basic Distance, 01 = O rd ere d distance 1, 0 2 = O rdered
distan ce 2 , 0 3 = O rdered d istan ce 3, P1 = PCQM 1, P2 = PCQM 2, P3 = PCQM3, VX = Variable Area T ransect in th e x-direction w ith 3 trees, VY= Variable
Area T ransect in th e y-direction w ith 3 trees.
doi:10.1371/journal.pone.0067201 .g004
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An Evaluation o f Plotless Sam pling
2 instead o f O rd e re d D istance 1 a n d P C Q M 2 instead o f P C Q M
1) w henever possible; iii) T o choose m ethods know n to have a
relative h igher accuracy u n d e r varying conditions like the V ariable
A rea T ra n se c t (VAT) m ethod.
Supporting Information
F ile S I M A TLA B c o d e s o f t h e s a m p li n g m e t h o d s . F or
each plotless sam pling m eth o d a n algorithm was developed in
M A T L A B w hich could applied to a n y d a ta m atrix presenting
eith er a forest o r a vegetation p a tte rn . In this d a ta m a trix each tree
should b e rep resen ted by a n x-coordinate a n d a n y-coordinate
w ith the x-coordinate in the first colum n a n d the y-coordinate in
the second colum n o f the sam e row.
(D O C)
Ideas for Further Research
T his study has given som e unexpected results a n d therefore
th ere are several possibilities for fu rth er research. Preferably, we
w ould like to find a sam pling m eth o d th a t is easy a n d fast to use
while giving reliable results. As this is n o t w ithin reach a t the
m om ent, reconsidering plot-based m ethods, by m aking a largescale com parison b o th o n accuracy o b tain e d a n d feasibility is a
first recom m endation.
G iven the p ractical advantages in the field, a re-exam ination o f
the theoretical basis o f plodess sam pling m ight be helpful in
red u cin g in h ere n t calculation biases. B ouldin [31] m akes a start
w ith this a n d hopefully this can be extended. H e n ce o u r second
reco m m en d atio n is to m ake a d eep er investigation into the
relation betw een the com binations o f spatial p attern s a n d the
accuracy for each m ethod.
A n ad ditional factor m ight be th a t the tree density itself can also
influence the accuracy o f the sam pling m ethods, as suggested by
E n g em an et al. [12] a n d W hite et al. [13], d ep en d in g on spatial
dispersion a n d estim ator type. In o u r study, w e have m ad e a
p relim inary assessm ent o f the possible effect o f varying densities on
the accuracy o f o u r density estim ations, as can b e found in File S3.
W e hope th a t o th er researchers can extend these p relim inary
insights to a m ore detailed investigation.
B ecause the accuracy o f plotless sam pling depends on the
random ness o f the vegetation dispersion, th ere is a need for future
assessments w ith spatial m ap p in g o f trees in m angrove forests. O u r
final reco m m en d atio n is th a t m o re research can be executed
w hich investigates the degree o f random ness o f m angrove trees in
different environm ents a n d for different species a ro u n d the w orld.
C orrelations w ith biophysical factors could allow for linkages w ith
m ore fu n d am en tal research.
F ile S2 M e a n d e n s it y e s t i m a t e s w it h d if f e r e n t n u m b e r
o f s a m p li n g p o i n t s . T o test the influence o f the n u m b e r o f
sam pling points on the accuracy o f each m eth o d tested, this
n u m b e r was varied b etw een 5 a n d 30 ra n d o m sam pling points.
B oth the m ea n estim ation a n d sta n d ard v a riation for the different
values are are show n in 12 figures, one for each site a n d p a tte rn .
(D O C)
F ile S3 E ffe c t o f d e n s it y i t s e l f o n m e a n d e n s it y e s t i m a ­
t i o n s . T h e vegetation p attern s used in this study h a d a density o f
0.2 tr e e s /m 2. T o test the influence o f the choice o f this density on
the results, we also varied the density betw een 0.05 a n d 1 tre e s /
m 2. T h e results found are presen ted in 6 tables, one for each
vegetation p attern .
(D O C)
A ck n ow led gm en ts
W e would like to thank Oege Dijk and N ibedita M ukherjee for their
constructive comments, O nno Giller for reading the draft docum ent,
A b u d h ab ijam b ia for his contribution to the fieldwork and two anonym ous
reviewers for their valuable remarks.
Author C ontributions
Conceived and designed the experiments: R H N K FD JS JG K . Perform ed
the experiments: R H . Analyzed the data: R H N K FD M N IK . C ontributed
reagents/m aterials/analysis tools: R H M N IK . W rote the paper: R H N K
FD.
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