An Evaluation of Plotless Sampling Using Vegetation

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An Evaluation of Plotless Sampling Using Vegetation Simulations and Field Data from a Mangrove ForestRenske H ijbeek1'2*, Nico Koedam1, Md Nabiul Islam Khan1'5, James Gitundu Kairo3, Johan Schoukens4, Farid Dahdouh-G uebas1'51 Laboratory o f P lant Biology and N ature M anagem ent, Vrije Universiteit Brussel, Brussels, Belgium, 2 Plant Production System s, W ageningen University and Research Centre, W ageningen, The N etherlands, 3 M om basa Research Centre, Kenya M arine and Fisheries Research Institute, M om basa, Kenya, 4 D epartm en t o f F undam ental Electricity and Instrum entation , Vrije Universiteit Brussel, Brussels, Belgium, 5 Laboratory o f System s Ecology and Resource M anagem ent, U niversité Libre d e Bruxelles,

Brussels, Belgium

AbstractIn 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 Quarter Method, are often used as an alternative. In this study we investigate the accuracy o f different plotless sampling methods. To this end, tree densities o f a mangrove forest were determ ined and compared w ith estimates provided by several plotless methods. None o f these methods proved accurate across all field sites w ith mean underestimations up to 97% and mean overestimations up to 53% in the field. Applying the methods to different vegetation patterns shows that when random spatial distributions were used the true density was included w ith in the 95% confidence limits o f all the plotless methods tested. It was also found that, besides aggregation and regularity, density trends often found in mangroves contribute to the unreliability. This outcom e raises questions about the use o f plotless sampling in forest m onitoring and management, as well as for estimates o f density- based carbon sequestration. We give recommendations to minimize errors in vegetation surveys and recommendations for further in-depth research.

C ita tio n : Hijbeek R, K oedam N, Khan MNI, Kairo JG, Schoukens J (2013) An Evaluation o f Plotless Sam pling Using V egetation Sim ulations and Field Data from aM angrove Forest. PLoS ONE 8(6): e67201. doi:10.1371/journal.pone.0067201

E d ito r: Bruno Hérault, Cirad, France

R eceived February 20, 2012; A c cep ted May 15, 2013; P u b lish ed Ju n e 27, 2013

C o p y rig h t: © 2013 H ijbeek e t al. This is an open-access article d istribu ted u n d er th e term s o f th e Creative C om m ons A ttribution License, w hich perm itsunrestricted use, distribution , and reproduction in any m edium , provided th e original au th o r and source are credited .

F u n d in g : This s tudy w as financially su p p o rted by th e Vlaam se Interuniversitaire Raad (VLIR-UOS) and Fonds N ationales d e la R echerche Scientifique. The fundershad no role in s tudy design , d a ta collection and analysis, decision to publish, o r p repara tion o f th e m anuscript.

C o m p e tin g In te rests : The au tho rs have declared th a t no com peting in terests exist.

* E-mail: renske.hijbeek@ wur.nl

Introduction

M angrovesM angroves are forests found in tropical and subtropical regions

with their tree roots partly o r completely in the saline substrate or surface w ater. T hey predom inantly grow in intertidal areas o f shorelines, exhibit a m arked degree o f tolerance to high salt concentrations and soil hypoxia and have propagules that a re able to survive and exploit dispersal by seawater [1], Unlike most tropical forests, m angroves have a very low species diversity [2]. Besides the in ternal value and beauty o f m angroves, they provide a num ber o f services [3]: i) Act as an atm ospheric CCD sink; ii) Are an essential source o f oceanic carbon iii) Support fisheries; iv) Buffer for seagrass beds an d coral reefs against the im pacts o f river-borne siltation v) Protect coastal com m unities from sea-level rise, storm surges, and tsunamis; vi) Provide essential food, fibers, tim ber, chemicals, an d medicines for com m unities living close to m angroves.

H igh population pressure in coastal areas has led to the conversion of m any m angrove areas. It has been estim ated that betw een 1980 an d 2000 the w orld m ight have lost 5 m illion ha o f m angroves, o r 25 pe r cent o f the extent found in 1980 [4], N um bers however, have to be taken w ith caution as m onitoring is scarce an d not com prehensive.

M ethods Available for Quantifying BiomassQ uantifying the am ount o f biomass in the tropics can allow for

be tte r deforestation estimates and w ould allow calculation o f the am ount o f carbon lost. C urrently, for m ost tropical forests, neither the averages no r the spatial distribution o f forest biom ass are know n [5].

M onitoring forest stocks an d forest a rea changes requires reliable m ethods. Despite the necessity, quantifying biomass in forests rem ains a challenge [6], Texts on M onitoring, R eporting and Verification recom m end a com bination o f rem ote sensing and ground-based forest inventory approaches [7]. In ground-based forest inventories one o f the variables often used is tree density.

D eterm ining tree density is relatively straightforw ard w hen large field plots can be laid ou t in w hich trees are counted. Alternatively, plotless sam pling (sometimes spelled plot-less), also called distance m ethods, have been developed [8-11], bu t proven no t to be reliable in all cases [12,13]. Plotless sam pling m ethods calculate the average a rea pe r tree by m easuring distances betw een points and trees o r betw een trees. T hese techniques have the advantage o f not requiring plot boundaries an d are generally fast, since in tertree distances tend to be low in m angrove forests an d therefore rapidly m easured [14],

W hen entering a m angrove forest for research purposes, one has to be aw are o f the tide schedule and progress is particularly

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An Evaluation o f Plotless Sampling

difficult w hen trying to get deeper into the forest as often clim bing over tree roots is required. Laying plots in a m angrove forest can range from being extrem ely tim e consum ing up to unfeasible. M easuring distances betw een trees is com paratively m ore easy and fast. For these reasons one ploüess sam pling m ethod - the Point C en tred Q u arte r M ethod (PCQM ) - has been recom m ended for m angrove research [14] and since then been used for a variety o f purposes [15-19]. Besides P C Q M , a num ber o f o ther plodess sam pling m ethods exist.

Research QuestionsThis research tries to find the accuracy o f P C Q M in relation to

o ther plodess sam pling m ethods. T h e objectives are threefold: i) T o evaluate the accuracy o f P C Q M bo th w ith field and sim ulation data; ii) T o com pare the accuracy o f P C Q M with o ther plodess sam pling m ethods; iii) T o relate results obtained from field da ta to different vegetation patterns.

Set-up of th e StudyThis study consists o f two parts: i) an observation-based study

and ii) a sim ulation-based study. In the first part, the locations o f all trees w ere m apped in four sites in a m angrove forest. In the second p a r t tree patterns were sim ulated using M A TLAB T M (student version 7.7.0 R 2008b T h e M athworks). As such, two different types o f da ta sets were acquired on w hich different plodess m ethods were tested. In each o f the following sections, first the observation-based study and then the sim ulation-based study will be discussed.

M ethods

Ethics S ta tem en tFor this study, fieldwork was conducted in a m angrove forest at

Gazi bay in the C oast Province o f K enya. For this area, the K enyan M inistry o f Science and T echnology issued a research clearance perm it (no. N C S T 5 /0 0 2 /R /1 5 8 ) . C onsequentiy, all necessary perm its were obtained for the described field studies.

O bservation-based StudyT o find the accuracy of a sam pling m ethod, one should first

know the actual (true) density. W e established the true density o f four sites in a m angrove forest in G azi bay, K enya (4°25 S and 39°30E) by counting an d m apping all trees in these four stands. This m eans th a t we could reproduce the forest stands on a com puter to test the plotless sam pling m ethods as if they were applied in the field. In plotless sam pling distances are m easured between trees and therefore the tree location is the relevant variable. W e digitized all tree locations and developed an algorithm for each plotless sam pling m ethod. This allowed num erous repetitions o f the density estim ations and thus the calculation o f the m ean estim ate an d confidence intervals for each sam pling m ethod.

M ap p in g tree lo ca tio n s in the fie ld . In the m angrove forest in G azi bay 10 m angrove species have been reported [20]: Avicennia m arina (Forssk.)Vierh., B ruguiera gym norrhiza (L.) Lam , Ceriops tagal (Perr.) C.B. R obinson, H eritiera littoralis D ryand, L um nitzera racem osa W illd, R hizophora m ucronata Lam , Sonneratia alba Sm, X ylocarpus g ranatum K oen and X ylocarpus m oluccensis (Lamk.) R oem [21]. In this a rea m angrove zonation has been previously described in detail [22].

In February an d M arch of 2009, x- and y- coordinates o f single trees were recorded in four sites a t G azi Bay. T his was done by m aking field grids o f l O m by 10 m, 5 m by 5 m, and 2 m by 2 m and m easuring the distances from the trees to the grid borders. Site 1 an d 2 w ere located in an a rea w ith m ultiple m angrove species,

while site 3 and 4 were in a monospecific Avicennia marina stand. T ogether, site 1 and 2 stretched from the shore to land, form ing a com plete section o f the m angrove zonation. Site 3 was chosen in an a rea with closed canopy and site 4 in an a rea w ith open canopy. In site 1 an d 2 all trees higher th an 1.30 m were recorded, while in site 3 and 4 all trees h igher th an 0.50 m were recorded. Both heights represent phases o f survival and target trees th a t are m ost likely to be recruited into the adult tree layer. Figure 1 shows all the coordinates o f the trees in the four sites.

Simulation-based StudyFrom previous studies it is know n th a t errors in plotless

sam pling can be (partly) ascribed to the degree of non-random ness o f a vegetation pattern . [23]. In vegetation analysis, two basic types o f spatial patterns a re know n besides random ness: regular and aggregated dispersion, w here dispersion refers to the a rrangem ent o f points in a p lane [24]. In m angrove forests an additional spatial pa tte rn exists: species show a differential distribution perpendicular to the coastline (parallel to elevation). This p a tte rn is probably due to the different physiological adaptations and different tolerance levels to, for exam ple, salinity, resulting in different optim al grow th conditions and hence position (Saenger 2002). T he pa tte rn has been referred to as zonation, w hich can be discrete or gradual.

T o gain m ore insight into how the accuracy of the m ethods varies w ith the vegetation patterns, six spatial patterns were created in M ATLAB: a regular, random and aggregated pa tte rn and each o f these three w ith o r w ithout a distributional gradient (zonation).

First, random , aggregated an d sem i-regular p a tte rn were generated: for the random p a tte rn the M A TLAB function randQ was used. This function draws pseudorandom values from the standard uniform distribution. T h e aggregated p a tte rn was generated by clustering trees a round uniform random spots. O n average these clusters contained 10 trees. T he trees w ithin the aggregates had a uniform random distribution. T h e semi- regular pa tte rn was generated by placing points a t regular distances along the x- and y-direction in the plane. Second, a gradient (density trend) was applied to all three patterns in the y-direction with a na tura l logarithm , creating three new spatial patterns with zonation.

T ree d en s ity o f the veg eta tio n p a ttern s . In our 4 field sites, densities were found betw een 0.08 and 1.22 tre e s /m 2. T o test the effect o f different vegetation patterns 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 acquired data sets were used to test a num ber o f plotless sam pling m ethods. These large plo t sizes allowed us to also com pare higher order m ethods (for w hich the field sites were too small). A visualisation of the resulting six patterns with 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 on the accuracy o f the density estim ations we m ade an additional analysis in w hich we varied the density o f each vegetation patterns betw een 0.05 and 1 tre e s /m 2.

Testing Plotless Sampling M ethods on the Acquired Data Sets

As far as we know, P C Q M is the only plotless sam pling m ethod used in m angrove research. T o investigate possible alternative techniques, this evaluation is extended 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 ered D istance m ethods, the V ariable A rea T ransec t m ethods and the Angle




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Figure 1. Spatial distribution of mangrove trees in 4 field sites at Gazi Bay. The do ts show the location of each tree. The d iam eter o f the do ts is proportional to the d iam eter of the stem above the root. The colour of the do ts represents the tree species: Dark blue is Avicennia marina, light blue is Bruguiera gymnorrhiza, g reen is Ceriops tagal, o range is Rhizophora mucronata and brow n is Xylocarpus granatum. Together site 1 and 2 form a com plete section of th e forest; from low tide shore to terrestrial vegetation (supralittoral level). The y-axis o f site 1 starts a t th e terrestrial vegetation and ends a t th e beginning o f site 2. The y-axis of site 2 ends a t the last tree a t th e creek side. Site 3 had closed canopy, while site 4 had open canopy.doi:10.1371/journal.pone.0067201 ,g001

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Figure 2. Vegetation patterns. Spatial point patterns representing 6 possible vegetation distributions (from left to right and from to p to bottom ): Random, semi-regular, aggregated , random with a density trend, sem i-regular with a density trend and aggregated with a density trend. doi:10.1371/journal.pone.0067201 ,g002




T a b le 1. An o v e rv ie w o f th e p lo tle ss sa 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 scrip tio n o f d is tance(s ) m easu red E q u atio n L ite ra tu re source

N earest n e ighbou r The d is tance be tw een a tre e and th e n earest tre e is m easured .b =

2 . 7 7 S * ( E i W A T

[8], [12], [13]

Basic d istance The d is tance be tw een a po in t and th e nearest tre e is m easured .1 ,

4 * ( E R w / n y

[8]

O rdered d istance 1 The d is tance be tw een a po in t and th e nearest tre e is m easured . f )> E * -

[9], [28]

O rdered d istance 2 The d is tance be tw een a po in t and th e second nea re st tre e is m easured .

h 2” ~ ' [9], [28]

O rdered d istance 3 The d is tance be tw een a po in t and th e third nea re st tree is m easured .

- 377 — 1 [9], [28]

PCQM 1 T he d istances b e tw e en a p o in t and th e nea re st tre e in ^ _ 4 (4 « —1) [9], [11]each q u ad ran t a round th e p o in t a re m easured . ~ n 4

* £ £ Vi = ly = l

PCQM 2 T he d istances b e tw e en a p o in t and th e second n ea re st ^ _ 4 (8 « —1) [9]tre e in each q u ad ran t a round th e p o in t a re m easured . ~ n 4

* £ £ % 2)2 U l j = l

PCQM 3 T he d istances b e tw e en a p o in t and th e third nea re st tre e in ^ _ 4 (12«—1) [9]each q u ad ran t a round th e p o in t a re m easured . « 4

n £ £ Rmi = i j = i

Variable Area T ransect T he d is tance from a p o in t to th e g th individual in a given ^ _ g n — 1 [10]direction w ith a certain w idth (a transect) is m easured . u 'E -L s ii

D = estim ated density , R = d istance m easured in th e field, ¡ = n um ber o f sam pling point, j = num ber o f quad ran t, g = th e g th individual, L is length o f tran sec t and W is w idth o f transect, N or n = num ber 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 part. In each m ethod distances are m easured betw een trees o r betw een points and trees to estim ate tree density. For each category a description, equation and reference can be found in table 1.

For each m ethod an algorithm was developed using M ATLAB. T h e algorithm s were used to test the plotless sam pling m ethods on the da ta sets acquired th rough b o th the field-based and the sim ulation study.

T h e algorithm s can be found in File SI and on the website o f the Lhiiversité L ibre de Bruxelles [25].

Preventing edge effects. T h e data sets acquired (both from the field-based and sim ulation-based study) are enclosed and thus contain borders. W hen a sam pling po in t is located close to the border o f a da ta set, the nearest tree m easured m ight be farther away then w ould be m easured in the field (for exam ple, in the field there m ight be a tree right a t the o ther side o f the border, causing a smaller distance m easured). This effect has been described by Peter Flaase [26] an d called edge effects. T o prevent edge effects in this study, three actions were taken:

1. T h e sam pling points were located at a m inim al distance from the site boundaries (0.05*surface a rea " for sites with m ore th an 128 trees and 0.1*surface a rea0'5 for sites with 32 to 127 trees, corresponding to at least the average distance betw een two trees).

2. W hen a m ethod m andated that a tree across the site boundaryshould be used for com putation, the relevant sam pling pointwas om itted (this applied only for P C Q M and the V ariableA rea T ransect method).

3. Fligher o rder m ethods were no t analysed for the field data, bu t only for the sim ulation-based study, w hich h ad large areas o f 100 m. by 100 m.

Replications. E ach m ethod was used to estim ate tree density using 5, 10, 15, 20, 25 an d 30 random sam pling points. These calculations were repeated ten times for each field site and pa tte rn to allow for the m ean an d standard deviation calculation. T he standard deviation was calculated with the following equation:

sd = ^ ( . \ y — .v)2^ , w here the m ean is given by

.\'= — N Xi. Both the estim ated m ean an d standard deviationfi ldid no t change m uch above 15 sam pling points. T herefore in this article only the results for estim ations with 30 random sam pling points are presented. T h e variation in m ean estim ation and standard deviation w hen using 5 to 30 sam pling points can be found in File S2.

Results

C lark and Evans [27] developed an aggregation index as a crude m easure o f clustering or ordering of a poin t pattern . A value R > 1 suggest regularity, R < 1 suggests clustering and R equals 1 suggests random ness. T he standard range is 0 < R < 2 .1 4 9 1 .T o com pare the degree o f clustering betw een the field sites and the vegetation patterns, the R index was calculated for each o f these.

T able 2 and 3 show the aggregation indices for bo th the field sites and the patterns: T h e patterns o f the field sites vary betw een clustered and close to random . Sites 3 and 4 have patterns most closely approach ing random ness with aggregation indices o f 0.85




and 0.92 respectively. T h e trees in site 1 and 2 show a m ore diverse p a tte rn w ith aggregation indices betw een 0.56 and 0.67. T h e sim ulated vegetation patterns show a w ider range, which provides the opportunity to test the perform ance of plotless sam pling in cases o f m ore extrem e regularity o r aggregation.

T able 4 an d 5 give an overview o f the results for each m ethod, field site an d pa tte rn . T h e results from the observation-based study show the erro 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.

Observation-based StudyIn figure 3, the results for the observation-based study are

shown in a graph. U sing the plotless sam pling m ethods, large underestim ations were found for the density o f the sites, especially in site 1 and 2. T h e largest underestim ation (97%) was found in the estim ation with the O rd ered D istance M ethod (O l) in site 2 with the tree Ceriops tagal. Overall, the V ariable A rea T ransect in the y-direction (VY) and the N earest N eighbour (NN) m ethod perform slightly better in the field data, bu t still generate errors as large as 80% in some sites.

D ue to the size o f the plots (see previous section about preventing edge effects), P C Q M (denoted P I in figure 3) was only tested in sites 3 and 4. In these sites, it has an underestim ation of 31% and 24% respectively. T hese errors are larger than the errors o f the o ther m ethods for these two sites.

Simulation-based StudyIn figure 4, the results for the sim ulation-based study w ith tree

densities o f 0.2 trees/m ~ are shown in a graph. In the random patterns, all m ethods score relatively well: T h e true density was included w ithin the 95% confidence limits o f all plotless m ethods tested.

In the aggregated patterns, all m ethods perform worse w ith no m ean erro r smaller than 45 %. T h e sign o f the erro r in aggregated patterns is negative: the estim ated density is m uch lower than the exact value. For random sam pling points, the chance is h igher to fall outside a cluster than within: the distance m easured, w hich will also be squared, becom es larger w hen the sam pling po in t falls betw een clusters and the estim ated density will be lower than the exact density. For the N earest N eighbour m ethod the exact opposite m echanism operates: in an aggregated pa tte rn the chance o f a random tree falling w ithin a cluster becom es larger while the distances w ithin a cluster betw een trees a re m uch smaller: the estim ated density will be h igher th an the exact density.

In regular patterns, the N earest N eighbour m ethod gives an underestim ation while the others overestim ate the density. In regular patterns the variation in errors is m ixed: the h igher order m ethods (O rdered D istance 2, O rd ered D istance 3, P C Q M 2, P C Q M 3 and V A T X and Y) perform relatively well w ith m ean errors lower than 20% . O n average, the gradient increases the erro r for all three patterns and m ethods selected.

Varying the tree density. T h e effect o f varying the tree densities can be seen in chap ter three o f the supplem entary m aterial. T h e tables presented show that the erro r in the density estim ate becom es (on average) smaller with increasing density. O nly w hen a tren d is present, the accuracy becom es less with h igher densities, p robably because the appearance o f the trend also becom es stronger. U nder clustered patterns, a lower density seems to result in a larger error, p robably because the degree of aggregation also increases. O verall the V ariable A rea T ransect M ethod (VAT) seems to perform best under varying tree density.

T a b le 2 . The aggregation Indices (R) for the field sites.

Site A g g re 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 mucronata) 0.64



doi:10.1371 /journal.pone.0067201 .t002

Discussion

Observation-based StudyIn the field, m ean underestim ations and overestim ations up to

97% an d 53% respectively were found. T hese errors can result in estim ated densities up to 30 times below the real value. O u r findings confirm and extend results from o ther authors [12,13,28], E rrors as large as found here, based on actual field data, were however no t yet reported. This is p robably due to the species zonation present in the m angrove forest. O n e should rem em ber though, that density gradients do occur outside m angroves. O ften these gradients depend on changes in the environm ent like altitude. T herefore, these results apply to m ore types o f vegetation.

Simulation-based StudyFor alm ost all m ethods the sign o f the erro r - over or

underestim ation - depends on the p a tte rn (aggregation or regular pattern). This m echanism will increase the erro r w hen tree densities o f two forests w ith differing vegetation patterns are com pared. T he unreliability range then corresponds with the entire erro r range.

T h e patterns o f our field sites vary betw een clustered an d close to random . Sites 3 an d 4 have patterns m ost closely approaching random ness. All m ethods give the highest accuracy for these sites (figure 3), ju st like for the random dispersion patterns in figure 4. T h e trees in site 1 an d 2 show a m ore diverse pa tte rn with also less accurate density estimations. Interestingly, the N earest N eighbour m ethod gives relatively good results in the field study, especially in site 1, while it gives worse results for the vegetation patterns. A possible explanation could be that bo th Avicennia marina and Ceriops tagal have a m ix o f vegetation patterns (both aggregation and regularity) in w hich the N earest N eighbour m ethod happens to perform well.

T a b le 3. The aggregation indices (R) for the vegetation patterns.

S p atia l p a tte rn A g g re g a tio n in d e x (R)

Random 1.03

Random w ith g rad ien t 0.90

Sem i-regular 1.89

Sem i-regular w ith g rad ien t 1.46

A ggregated 0.45

A ggregated w ith g rad ien t 0.42

doi:10.1371 /journal.pone.0067201 .t003




T a b le 4 . Tree density estimations using plotless sampling in four field sites (30 sampling points, 10 replicates).

Exactd e n s ity O D 1 PC Q M 1 V A T X 3 V A T Y 3 R ange o f m ean

S ite (n /m 2) N N (n /m 2) BD (n /m 2) (n /m 2) (n /m 2) (n /m 2) (n /m 2) e rro r (% )

Site 1 (Avicennia m arina) 0.08 0.08 0.02 0.01 - - 0.06 - 8 7 to +5

95% Cl 0.02 0.01 0.01 - - 0.01

Site 1 (Ceriops tagal) 0.20 0.20 0.02 0.01 0.09 - 9 4 to +1

95% Cl 0.07 0.01 0.01 - - 0.03

Site 2 (Ceriops tagal) 1.22 0.16 0.05 0.04 0.14 - 9 7 to - 8 7

95% Cl 0.10 0.02 0.02 - - 0.07

Site 2 (Rhizophora m ucronata) 0.49 0.11 0.11 0.07 0.14 - 8 5 to - 7 2

95% Cl 0.07 0.08 0.07 - - 0.05

Site 3 (Avicennia m arina) 0.22 0.33 0.18 0.19 0.15 0.21 0.21 - 3 2 to +49

95% Cl 0.24 0.03 0.07 0.05 0.06 0.04

Site 4 (Avicennia m arina) 0.57 0.50 0.50 0.43 0.36 0.47 0.46 - 3 7 to - 1 2

95% Cl 0.20 0.21 0.19 0.11 0.15 0.14

R ange o f m ean e rro r (% ) - 8 7 to +53 —96 to -1 2 - 9 7 to -1 3 -3 1 to -3 7 - 2 to - 1 7 - 8 8 to - 3

Tree density estim ation is th e m ean o f 10 estim ations using each m e thod with 30 random sam pling points; half 95 Cl is th e half w idth o f th e 95% confidence interval for th e 10 estim ates; NN is N earest N eighbour; BD is Basic Distance; OD is O rdered Distance; PCQM is Point Centred Q uarter M ethod; VAT is Variable Area Transect. doi:10.1371 /journal.pone.0067201 .t004

In the field, vegetation m ost probably displays a m ix o f patterns: a forest can display bo th aggregation and random ness a t different sites, o r even random aggregations o r aggregations o f random clusters.

Varying tree density. W hile varying the tree density under random and sem i-regular patterns is ra ther straight forward, with aggregated patterns the question is w hat will happen with the size o f the clusters: Will the density w ithin tree clusters rem ain the same w ith varying tree density, or will it also vary? For our study we assum ed that the density w ithin the tree clusters rem ains similar. This causes a h igher a lower R index; a h igher degree of aggregation. C onsequently the e rro r in the density estimates for aggregated vegetation patterns is m uch higher. This could be an effect o f the assum ption m ade (similar w ithin cluster densities), ra th e r than an observation w hich could also be m ade in the field. T hese results therefore ask for m ore elaboration an d research and concise conclusions upon the effect o f density variations cannot be m ade for now.

Reflection. N one o f the plotless sam pling m ethods gave good results across all study sites and vegetation patterns. Taking a com bination of m ethods m ight be an alternative. W hite et al. [13] found a com bined estim ator taking the m ean o f two N earest N eighbour m ethods and one Basic D istance m ethod to perform the best. This com bination how ever is very difficult to apply in the field. A ccording to their study, the 2nd and 3rd o rder P C Q M ranked highest for the clum ped distribution an d the V ariable A rea T ransect m ethod perform ed m oderately well overall. C o m p ara tively, our analysis does show bette r perform ance for h igher order m ethods like P C Q M 2 and 3 an d theV ariable A rea T ransect m ethod. T he difficulty lies with aggregation an d zonation patterns, as these m ethods still give errors up to 80% in these circumstances. This gives very low certain ty using these m ethods w hen vegetation patterns are unknown.

A n alternative to field sam pling is the use o f rem ote sensing. T oday in terpreta tion still needs to be g rounded in field data. N agendra et al. [29] m ade an extensive review an d stress the im portance o f in situ da ta for accurate in terpreta tion o f imagery. Studies in m angroves show th a t da ta from field surveys and

rem otely sensed da ta do no t always correspond (for exam ple due to overgrow th o f one species by another) [20,30] an d th a t different da ta sources should be com bined. W ith the advance o f technological developm ents, one day rem ote sensing alone m ight be able to m onitor forest resources. In the m eantim e, errors m ight be inevitable, bu t ignorance o f uncertain ty is avoidable.

This study has shown large errors in vegetation survey m ethods currently used in four field sites. T hese field sites are small an d do not represent the large an d diverse m angrove com m unities which can be found a round the world. U sing plotless sam pling within different vegetation patterns shows th a t especially b ad results are obtained w ithin non-random ly dispersed vegetation. Therefore, it is im portan t to find out w hat p roportion o f m angroves worldwide is characterised by a random spatial distribution o f trees.

C aution should be taken w hen applying plotless sam pling m ethods in the field particularly w hen used for societal purposes. C urrently m ore than 90 percent o f the w orld’s m angrove forests are located in developing countries [3]. Like elsewhere, the local com m unity in ou r study site obtains direct benefits from the forest in term s o f w ood and non-w ood products. Indirect benefits m ay com e in the future w hen carbon sequestration by natural and rep lan ted forests is valued and paid for. LTsing ground-based forest inventory approaches, the erro r generated in the tree density estim ation multiplies w ith uncertainties in o ther variables. Inaccurate estimates, as can easily be generated by inappropriate m ethods, can m ake society pay too m uch or the com m unity receive too little.

ConclusionsUsing plotless sampling in the field. T h e m ost im portant

reason why plotless sam pling techniques are being used is the relative ease com pared with plot-based m ethods. This reflects the trade-off betw een m axim um accuracy an d m inim um time required. Because plotless m ethods give the largest bias when vegetation has a high degree o f non-random ness, we w ould like to recom m end not using these m ethods w hen this is a known vegetation feature beforehand.







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Figure 3. Tree density estimations by applying plotless sampling methods to field data. The density estim ations found by applying plotless sam pling m ethod to the field data. The field data consisted of m angrove tree locations in four sites. In each graph the horizontal lines are the real tree densities in the sites. The closed squares are the m ean of 10 estim ations with 30 random sam pling points. The verticals crossing the m eans are the 95% confidence intervals. NN = Nearest Neighbour; BD = Basic Distance; 01 = Ordered distance 1; VY = Variable Area Transect in th e y-direction with 3 trees; VX = Variable Area Transect in th e x-direction with 3 trees; P1 = Point Centred Q uarter M ethod with th e nearest tree in each quadrant. doi:10.1371/journal.pone.0067201 ,g003

W hen the spatial p a tte rn is unknow n, it could be a rational approach to use a m ix o f two m ethods - for exam ple plot-based and plotless - o r two plotless m ethods w ith know n contrasting

biases - like N earest N eighbour an 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 rder o f m ethod (so O rd ered D istance

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Figure 4. Tree density estimations by applying plotless sampling methods to 6 vegetation patterns. In each graph, th e horizontal lines are th e real densities (0.2 poin ts per m 2 for all patterns). The d o se d squares are th e m ean of 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, 0 2 = Ordered distance 2 ,0 3 = O rdered d istance 3, P1 = PCQM 1, P2 = PCQM 2, P3 = PCQM3, VX = Variable Area Transect in th e x-direction with 3 trees, VY= Variable Area Transect in th e y-direction w ith 3 trees. doi:10.1371/journal.pone.0067201 .g004

PLOS ONE I www.plosone.org June 2013 | Volum e 8 | Issue 6 | e67201



2 instead of O rd ered D istance 1 and P C Q M 2 instead of P C Q M 1) w henever possible; iii) T o choose m ethods know n to have a relative h igher accuracy under varying conditions like the V ariable A rea T ransec t (VAT) m ethod.

Ideas for Further ResearchThis study has given some unexpected results an d therefore

there are several possibilities for fu rther research. Preferably, we w ould like to find a sam pling m ethod th a t is easy and fast to use while giving reliable results. As this is no t w ithin reach a t the m om ent, reconsidering plot-based m ethods, by m aking a large- scale com parison bo th on accuracy obtained an d feasibility is a first recom m endation.

G iven the practical advantages in the field, a re-exam ination o f the theoretical basis o f plodess sam pling m ight be helpful in reducing inheren t calculation biases. Bouldin [31] makes a start w ith this an d hopefully this can be extended. H ence our second recom m endation is to m ake a deeper investigation into the relation betw een the com binations o f spatial patterns and the accuracy for each m ethod.

A n additional 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 ngem an et al. [12] an d W hite et al. [13], depending on spatial dispersion and estim ator type. In our study, we have m ade a prelim inary assessment o f the possible effect o f varying densities on the accuracy o f our density estimations, as can be found in File S3. W e hope th a t o ther researchers can extend these prelim inary insights to a m ore detailed investigation.

Because the accuracy of plotless sam pling depends on the random ness o f the vegetation dispersion, there is a need for future assessments w ith spatial m apping o f trees in m angrove forests. O u r final recom m endation is th a t m ore research can be executed w hich investigates the degree o f random ness o f m angrove trees in different environm ents and for different species a round the world. Correlations with biophysical factors could allow for linkages with m ore fundam ental research.

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(2010) T h e ‘M an g ro v e R efe ren ce D a ta b ase a n d H e rb a r iu m ’.3. D u k e N G , M ey n eck e J - O , D it tm a n n S, E llison A M , A n g er K , e t al. (2007) A

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Supporting InformationFile SI M ATLAB c o d e s o f th e s a m p lin g m e th o d s . Foreach plotless sam pling m ethod an algorithm was developed in M A TLAB w hich could applied to any da ta m atrix presenting either a forest o r a vegetation pattern . In this datam atrix each tree should be represented by an x-coordinate and an y-coordinate with the x-coordinate in the first colum n and the y-coordinate in the second colum n o f the same row.(DOC)

File S2 M e a n d e n s ity e s t im a te s w ith d if fe r e n t n u m b e r o f s a m p lin g p o in ts . T o test the influence o f the num ber o f sam pling points on the accuracy o f each m ethod tested, this num ber was varied betw een 5 and 30 random sam pling points. Both the m ean estim ation and standard variation for the different values are are shown in 12 figures, one for each site an d pattern . (DOC)

File S3 E ffe c t o f d e n s ity i t s e l f o n m e a n d e n s ity e s t im a t io n s . T h e vegetation patterns used in this study had a density o f 0.2 tre 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 and 1 tree s / m 2. T h e results found are presented in 6 tables, one for each vegetation pattern .(DOC)

A cknow ledgm entsWe would like to thank Oege Dijk and Nibedita Mukherjee for their constructive comments, O nno Giller for reading the draft document, A budhabijam bia for his contribution to the fieldwork and two anonymous reviewers for their valuable remarks.

Author ContributionsConceived and designed the experiments: R H N K FD JS JG K . Performed the experiments: R H . Analyzed the data: R H N K FD M N IK. Contributed reagents/m aterials/analysis tools: R H M N IK. W rote the paper: R H N K FD.

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An Evaluation of Plotless Sampling Using Vegetation