Comparative efficiency and accuracy of variable areatransects versus square plots for sampling tree diversityand density

Cheryl D. Nath • Raphael Pelissier • Claude Garcia

Received: 7 April 2009 / Accepted: 22 September 2009

� Springer Science+Business Media B.V. 2009

Abstract Agroforestry systems have been recog-

nized as areas with high conservation potential, and

there is a need to quickly assess the biodiversity and

tree stocking density available in these systems.

However, it is not clear if the commonly used fixed

area plot is most efficient for sampling such land-

scapes, or if a different method could provide

equivalent data with less effort. Thus, a field and

simulation-based study was carried out to compare

the efficiency and accuracy of a variable area transect

versus the fixed area square plot. Field efficiency tests

were carried out in three habitat types, robusta coffee

plantations, arabica coffee plantations and a privately

owned forest fragment, in Kodagu, southern India. A

simulation study of bias, precision and accuracy of

the two methods for tree density estimation also was

carried out using various spatial distribution patterns

and densities. The variable area transect was signifi-

cantly more efficient per unit effort in the field than

the fixed area square plot. In the simulation tests both

methods performed equally well under random

spatial distribution. However, under simulated aggre-

gated distribution both methods were positively

biased (square plot up to 12% at low density, variable

area transect 9–12% at all densities), and under

simulated regular distribution the variable area tran-

sect was slightly negatively biased (-5 to -7% at

medium to high density). The variable area transect

thus can be recommended over the square plot for

rapid assessment of tree diversity and density, when

the vegetation is expected to be randomly dispersed.

Keywords Man-hours � Bias � Precision �Spatial dispersion � Coffee agroforestry �India

Introduction

Landscapes dominated by coffee agroforestry have

been identified as potential areas for future biodiver-

sity conservation in the tropics (Perfecto et al. 1996;

McNeeley and Schroth 2006). The small district of

Kodagu (4,104 km2), situated in the Western Ghats

of southern India, is an interesting location for such

non-formal conservation efforts, as its landscape is

dominated by protected forests, community-owned

or private forest patches and shade coffee estates

C. D. Nath (&) � R. Pelissier � C. Garcia

French Institute of Pondicherry, 11 St Louis Street,

PB 33, Pondicherry 605001, India

e-mail: cheryl.nath@ifpindia.org

R. Pelissier

UMR AMAP, TA-A51/PS2, Boulevard de la Lironde,

34398 Montpellier Cedex 5, France

C. Garcia

CIRAD—UPR 36, TA 10/D, Campus de Baillarguet,

34398 Montpellier Cedex 5, France

123

Agroforest Syst

DOI 10.1007/s10457-009-9255-5

(Elouard 2000; Garcia et al. in press). The coffee

agroforestry practiced in this region utilises medium

to high density shade from native and exotic trees

located between coffee bushes. Tree stocking density

varies greatly between estates, depending on factors

such as the original vegetation type, species of coffee

grown and management practices (Elouard et al.

2000; Moppert 2000). The landscape matrix is known

to harbour a high proportion of native biodiversity

(Bhagwat et al. 2005) as the existing bioclimatic

regime and topography support vegetation types

ranging from wet evergreen to dry deciduous forests

(Pascal 1988; Elouard 2000). In order to sample such

a varied landscape for biodiversity, we would have to

ensure wide geographic coverage of the region to

include rare species and habitat types (Gimaret-

Carpentier et al. 1998).

An appropriate sampling method was sought that

would be quick and easy to implement across a wide

range of habitat types. The best sampling technique

should provide accurate and representative informa-

tion about the population studied, while also being

geometrically compact and requiring the least amount

of field effort (Parker 1979; Laycock and Batcheler

1975; Scott and Gove 2002). The fixed area square

quadrat has traditionally been used for vegetation

sampling (Clapham 1932). However, other shapes for

fixed area plots such as rectangular and circular plots

or belt transects also have been used due to their

improved habitat coverage or ease of implementation

(Barbour et al. 1987). Plotless density estimators that

utilise distance measurements from random points to

nearest trees or from trees to their nearest neighbours

have been popularized on the basis of their greater

speed, ease of implementation, and economy of effort

in dense habitats (Cottam and Curtis 1956). More

recently, variable area plots and transects also were

introduced as a means to collect relatively fixed

amounts of field data irrespective of the local habitat

density (Parker 1979; Sheil et al. 2003).

We initially carried out a pilot test to compare

the relative field performances of four different

sampling methods: fixed area square plot, belt

transect, cluster sampling with point-centred quarter

(PCQ), and a new variable area transect method

developed by Sheil et al. (2003). The pilot survey

indicated that the square plot and variable area

transect were most efficient in the field in terms of

total time spent per sample, as well as in terms of

numbers of individuals and species recorded per

unit time (unpublished results). Therefore we

decided to test these two methods further, while

eliminating the belt transect and cluster sampling

with PCQ from further testing. The use of PCQ also

has been discouraged by other studies as it produces

biased results under nonrandom spatial distributions

(Lyon 1968; Risser and Zedler 1968; Mark and

Esler 1970; Good and Good 1971; Laycock and

Batcheler 1975; Bryant et al. 2004). Thus, the

square plot (hereafter referred to as ‘‘QUAD’’) and

the variable area transect (‘‘VAT’’) developed by

Sheil et al. (2003) were selected for further field

tests and computational analyses, which are the

subject of this paper.

Field and laboratory-based comparisons of the

efficiency and accuracy associated with different

vegetation sampling techniques have been carried out

before. However, only a few studies have docu-

mented the time required for data acquisition in the

field (Lindsey et al. 1958; Laycock and Batcheler

1975; Batcheler and Craib 1985; Kenkel and Podani

1991), which is an important component of total

sampling effort. Most often studies were focused on

assessing efficiency in terms of the precision of

sample estimates (Clapham 1932; Bormann 1953;

Cottam and Curtis 1956; Lyon 1968; Parker 1979;

Bryant et al. 2004), and on assessing biases with

spatially explicit datasets (Engeman et al. 1994;

White et al. 2008). Thus, in previous studies where a

QUAD was compared with a VAT, the VAT was

expected or assumed to be quicker and more efficient

to implement in the field (Parker 1979; Engeman

et al. 1994; White et al. 2008), but no relevant field

data were presented. With the exception of one study

(Batcheler and Craib 1985), data on comparative field

efficiencies of a fixed area square plot versus a

variable area transect method are lacking.

For the purpose of sampling broad swathes of the

landscape quickly, it is important to establish any

practical advantages gained in the field from the

sampling method to be used. In addition, it is critical

to show that the more efficient method does not suffer

from any major biases in estimating tree density or

diversity. Our study provides a unique comparison of

two methods for sampling trees, by carrying out tests

of efficiency in terms of field effort per replicate as

well as computer simulations to test their accuracy

under diverse habitat conditions.

Agroforest Syst

123

The main objectives of the study were:

(1) To establish which of two sampling methods,

the QUAD or the VAT, is more efficient in

terms of field effort for sampling individuals

and species of trees across a human-modified

landscape.

(2) To characterise the bias, precision and accuracy

of these two methods for estimating density,

under various spatial arrangements and density

distributions of trees.

The results of this study should be applicable to

other human-transformed landscapes that are charac-

terised by heterogeneous spatial distributions and

densities of trees.

Methods

Methods compared

The following two sampling methods were tested in

this study:

• Fixed area square plots or quadrats (‘‘QUAD’’):

QUADs have been recorded in use for vegetation

quantifications for at least 100 years (Clapham

1932). They are popular due to the ease with

which plots can be demarcated and enumerated

by minimally trained field crews, as well as the

generally low bias associated with tree density

estimates (Engeman et al. 1994). In this study we

tested square plots of 40 m length.

• Variable area transect (‘‘VAT’’) of Sheil et al.

(2002, 2003): Variable area plot or transect

methods are generally expected to improve the

sampling efficiency over fixed area plots,

although they are expected to be associated with

biases under nonrandom conditions (Parker 1979;

Engeman et al. 1994). Early VAT methods were

simple and included sampling a small fixed

number of individuals from a point or line up to

a fixed maximum search distance (Parker 1979;

Batcheler and Craib 1985; Engeman et al. 1994).

The number of individuals sampled per transect

generally was small (\5) in order to keep the

method practical and efficient. A more complex,

yet versatile, VAT method has been developed

recently for rapid sampling of landscapes (Sheil

et al. 2002, 2003). This method allows larger

samples to be collected per replicate, while

remaining compact and easy to apply under

different field conditions. According to this

method a baseline transect of 40 m is established

initially, and on either side of the baseline four

consecutive rectangular cells (of 10 m width

along the baseline, and up to 20 m length

perpendicular to the baseline) are searched for

five trees each. The length of each cell is

determined by the position of the fifth-most

distant tree from the baseline. If five trees are

identified within 20 m from the baseline (i.e., the

maximum search distance) the cell length is the

distance to the fifth tree, whereas if less than five

trees are encountered, the cell length is taken as

20 m. Thus, the eight cells together per transect

provide data on up to 40 trees, and the maximum

area sampled is 40 m by 40 m.

Field-based study

Field sampling

The first phase of the study involved collection of

data for field tests of the two sampling methods.

Coffee estates in the Kodagu district of Karnataka

state, southern India, were sampled during October

and November, 2007. Coffee estates in Kodagu grow

robusta (Coffea canephora) and arabica (Coffea

arabica) coffee. These two species usually are grown

in separate blocks because robusta requires less shade

than arabica. Our study included the following three

habitat types to represent an increasing gradient of

tree stocking density in human modified landscapes:

robusta coffee blocks, arabica coffee blocks and a

relatively undisturbed forest fragment.

Seven coffee estates were sampled in eastern

Kodagu (12�14057.800N to 12�19048.400N; and

75�53011.700E to 75�56041.700E). The estates were

2–10 km distant from each other, and presented a

range of different elevations and slopes (Table 1). In

addition, a large privately owned forest fragment on

relatively flat land was sampled, approximately 15 km

from the sampled coffee estates (12�05055.200N,

75�52047.800E). Six of the estates, as well as the forest

fragment, were each associated with only one of the

three habitat categories (corresponding to sites 2–4

Agroforest Syst

123

and 6–9 in Table 1). Only one estate was sampled for

both, robusta and arabica habitats (corresponding to

sites 1 and 5, respectively), as the two kinds of habitat

were well differentiated from each other within the

estate.

Robusta coffee habitat was sampled at sites 1–4,

where average tree densities ranged from 72 to

200 trees ha-1, while arabica coffee habitat was

sampled at sites 5–8, where average tree densities

ranged from 184 to 273 trees ha-1 (Table 1). In the

forest site average tree density was relatively high

(536 trees ha-1) compared to coffee estates; how-

ever, there was moderate weed occurrence (mainly

Strobilanthes kunthianus) in the undergrowth, indi-

cating human disturbance.

In total 21 replicates each of QUAD and VAT

were obtained, of which 20 replicates occurred in

robusta, 16 replicates in arabica and 6 replicates in

the forest. Each site had 2–6 replicates with equal

numbers of QUAD and VAT replicates per site

(Table 1). Replicates were situated at least 100 m

apart. The starting point of each replicate was

randomly located by utilizing random numbers to

select an estate management block, as well as the

number of steps and direction to follow within each

block. Whenever possible a replicate each of QUAD

and VAT were randomly located within the same

large block, to reduce variability due to management

effects.

Field crews consisted of 4–6 people at the estate

sites and 6–7 people at the forest site. These small

differences in crew size were due to day-to-day

variations in the availability of temporarily hired field

assistants, and only when sampling forest habitat a

slightly larger crew size was required for clearing

undergrowth. However, daily variations in field crew

size did not bias the efficiency of data collection for

either sampling method, as approximately two

QUADs and two VATs were completed per day

and we always sampled a QUAD followed by a VAT,

and vice versa. There was no significant difference in

crew size between the two sampling methods (Stu-

dent’s two-tailed t-test, N = 21, t = 0.33, P = 0.74),

and the same team leader and botanical specialist

were present during all field collection trips for this

study. Data collected per replicate included the

number of people involved with plot set up and data

collection, the starting and ending time, and any

breaks taken by workers before completing the data

collection.

Tree species identities were recorded whenever

possible in the field. For most species at least one

botanical sample was obtained for identity confirma-

tion, and all samples were deposited at the herbarium

of the French Institute of Pondicherry (HIFP). Only

trees whose main stems were C30 cm gbh (girth

at breast height, 1.3 m above the ground) were

recorded. In total, 1,284 trees belonging to 98 species

Table 1 Main features of the nine sites (eight coffee agroforests and a natural forest fragment) sampled in Kodagu district, Western

Ghats of Karnataka, India

Habitat Site

number

Elevation range

(m asl)

Minimum,

maximum

Slope range (�)

Minimum,

maximum

Number

of replicates

Number

of trees

Number

of species

Avg. density

(trees ha-1),

(minimum,

maximum)

Robusta 1 775, 825 2.75, 7.00 6 69 16 72 (56, 94)

2 775, 825 0.63, 15.00 6 144 29 151 (125, 200)

3 790, 867 2.00, 5.33 4 58 12 91 (56, 138)

4 820, 845 2.75, 5.75 4 115 27 200 (106, 282)

Arabica 5 845, 855 1.25, 3.18 2 88 12 273 (176, 369)

6 835, 910 3.40, 12.00 6 204 9 241 (88, 475)

7 820, 860 Not rec., 5.50 4 134 27 214 (198, 232)

8 850, 940 5.00, 22.75 4 111 26 184 (150, 222)

Forest 9 690, 730 Not rec. 6 361 48 536 (463, 653)

The range of values obtained across all replicates per site is shown, and includes trees more than 30 cm in girth at breast height. Slope

value for each replicate is the average of readings recorded in different directions (‘‘Not rec.’’ = flat areas where slope measurements

were not recorded). The number of replicates includes equal numbers of QUAD and VAT samples at each site

Agroforest Syst

123

were sampled during this study across all sites. The

robusta and arabica habitats together contained 67

species, while the forest habitat contained 48 species,

of which 17 species were common to both (see

Table 1 for details per site).

Analysis of field data

From the field datasets, three parameters were

calculated to represent efficiency in sampling trees

and species. These ‘Efficiency’ parameters were:

(i) Total number of man-hours per replicate (mh).

(ii) Total number of trees sampled per man-hour in

the field (trees mh-1).

(iii) Total number of species sampled per man-hour

in the field (species mh-1).

Man-hours was used as the standard unit of time or

effort as this took into account the variations in field

crew sizes across different replicates. The calculation

of total man-hours per replicate was achieved by

totalling the time spent (in hours) by each worker on

that replicate.

Three additional parameters were calculated to

evaluate differences, if any, between the two methods

for estimating tree density and diversity. These

‘Vegetation’ parameters were:

(i) Tree density (trees ha-1).

(ii) Species richness, or the total number of species

per replicate.

(iii) Simpson Index of diversity.

In order to assess differences between sampling

methods or habitats on each of the 6 parameters

above, linear mixed-effects models (LME models,

Pinheiro and Bates 2000) were used. In these models

the main fixed effects were ‘methods’ and ‘habitats’.

In order to address the possibility of non-indepen-

dence of replicates per site or of sites per habitat, the

additional random factor, ‘sites’, was nested in

‘habitats’. This has the effect of correctly partitioning

the variance and leading to more powerful tests for

the main effects. Interactions between methods and

habitats were included in the initial models, but were

non- significant for all parameters, and thus the

interaction term was excluded from the final models.

For efficiency parameters we also tested for differ-

ences between methods after adding the covariate,

‘‘tree density’’, in the models. This parameter was

correlated with species richness (Spearman rank

correlation coefficient = 0.72) and was expected to

account for some of the unexplained variation in the

models as it was highly variable across sites. LME

was implemented using the package ‘‘nlme’’ (Pinheiro

et al 2008) with R statistical software (R Development

Core Team 2008).

Model residuals were subjected to several tests

(Shapiro–Wilk, Kolmogorov–Smirnov, histograms

and normal quantile plots for normality; Bartlett,

Fligner-Killeen, variance test and standardized resid-

ual plots for homoscedasticity; standardized residual

plots for linearity) and, where necessary, transforma-

tions were carried out in incremental steps until all the

required assumptions were met (Sokal and Rohlf

1995; Grafen and Hails 2002). Based on these tests

the parameters ‘man-hours’ and ‘trees mh-1’ required

log-transformation, ‘trees ha-1’ required square-root

transformation and ‘Simpson Index’ required square

transformation in order to conform to the assumptions.

For non-significant results, we used power analysis

to judge if statistical significance could be achieved

by increasing the sample size. Power analysis gen-

erally is recommended for use prior to data collection

for determining the minimum sample size required to

obtain a significant effect (Thomas and Juanes 1996;

Steidl et al. 1997). However, it also can be used

retrospectively to determine the power associated

with a given effect and sample size (Thomas 1997).

An 80% power level is conventionally considered

adequate. Thus, we used a two sample t-test of means

and tested if increased sample sizes of 30 or 50 per

method would be sufficient to obtain 80% power to

detect the existing effect sizes with statistical signifi-

cance. The variance value used was as observed in

the field. Power calculations were carried out using

the statistical package ‘‘pwr’’ (Champely 2007) with

R statistical software (R Development Core Team

2008).

The above analyses relate to the statistical signifi-

cance of differences between methods; however, in

order to evaluate differences in terms of the potential

savings produced by a faster method (in the case of

efficiency parameters) or conservation losses incurred

by a biased method (in the case of vegetation

parameters) it is important to consider their economic

or biological significance also (Steidl et al. 1997).

Thus, 95% confidence intervals for the difference

between means, obtained from the t-test of the

Agroforest Syst

123

QUAD and VAT methods, were interpreted in

relation to predetermined values (Steidl et al. 1997;

Gerard et al. 1998; Di Stefano 2004). The value used

for minimum economic significance (or importance)

in the case of efficiency parameters was 10% of the

QUAD mean (i.e., the two methods should differ by

more than 10% of the QUAD mean in order for the

benefit to be considered as economically significant);

while the value used for minimum biological signifi-

cance (or importance) in the case of vegetation

parameters was a conservative 5% of the QUAD

mean (i.e., the two methods should not differ by more

than 5% of the QUAD mean in order to be assured of

unbiased vegetation assessment). We also calculated

the sample size required for 80% power to detect

these minimal economic or biological significance

values. Variables were transformed as in the previous

tests.

Simulation-based study

Creation of artificial datasets

Intensive testing of the accuracy of sampling methods

was carried out with a computer-based simulation

study. Our methodology, described below, is largely

based on that used by Engeman et al. (1994) and

White et al. (2008). Three types of common spatial

distributions, random (also known as Poisson distri-

bution or complete spatial randomness), aggregated

(also known as clumped, clustered or contagious) and

regular (also known as uniform, even or dispersed),

were artificially generated for estimation of tree

density. These three types of distribution may be

observed in natural populations at different scales.

While random distribution of trees may be considered

fairly common at the community level (Sheil et al.

2003), aggregated distributions may be more com-

mon at the species level in tropical and temperate

forests (Condit et al. 2000; Armesto et al. 1986).

Regular distributions may occur less frequently

(Hubbell 1979) and are more likely under condi-

tions of low density or high inter-tree competition

(Armesto et al. 1986). Human manipulations of trees

for silviculture also could result in regular spatial

distributions.

The random distribution was generated for our

study by randomly and independently selecting from

within the range of available x and y coordinate

values. The aggregated distribution was generated by

randomly selecting ‘‘parents’’ to signify the centre of

each cluster and then randomly selecting 30 ‘‘off-

spring’’ from a bivariate normal distribution around

each parent. Thus offspring were located with

increasing probability closer to parents. The number

of parents and cluster sizes were determined by the

predetermined density (see below). For the regular

distribution the entire area was gridded into equal

squares (according to the required density), and in

each of these a single individual was randomly

located.

The total simulated area was a square of length

2,000 m and the minimum inter-tree distance was

0.5 m. For each type of spatial distribution the

following 15 different tree densities were generated:

10 trees ha-1, and 50–700 trees ha-1 at intervals of

50 (densities of coffee agroforestry systems visited

during this study generally were between 50 and 400

trees ha-1). Thus, in total 45 different combinations

of tree distribution and density were tested. For each

distribution-density combination, 1,000 tree datasets

were artificially generated, within each of which two

sample sizes, 30 and 100, were used to estimate the

known population density by both sampling methods.

Starting points for QUADs or VATs were randomly

located with 0.1 m precision at least 60 m from the

edges of the simulated area, and the direction of

replicates was randomly selected. QUAD and VAT

replicates were paired for each starting point and

sampling direction.

Spatial contagion or nonrandomness of the arti-

ficial datasets was tested with the R index, as described

by Clark and Evans (1954) and White et al. (2008).

For this test each spatial pattern was generated 1,000

times for each of the following densities: 10, 50, 100,

300, 500, and 600 trees ha-1. From each simulated

population the average of all observed nearest

neighbour distances, Ro, was calculated after deleting

the values of individuals that were closer to the edge

than to their nearest neighbours (Crawley 2007). The

expected average nearest neighbour distance, Re, was

calculated as 1= 2ffiffiffi

Ap

� �

, where A is the true popula-

tion density. The ratio R was then calculated as

Ro/Re, which is equal to 1 for random distributions,

\1 for aggregated distributions and [1 for regular

distributions. Significance of R also was tested with a

z-test (Clark and Evans 1954; White et al. 2008).

Agroforest Syst

123

Analysis of simulation data

The bias, precision and accuracy of density estima-

tion by each sampling method were assessed for each

spatial distribution-density combination and both

sample sizes. We used scaled performance measures

to facilitate easy interpretation and comparisons

(Walther and Moore 2005). These were similar to

the measures used by Engeman et al. (1994) and

White et al. (2008). Calculations were as follows:

(1) Bias: a measure of relative bias was used to

assess positive or negative departures from the

true value of density (similar to RBIAS of

Engeman et al. 1994 and White et al. 2008,

SME in Walther and Moore 2005), calculated asP

E � Að Þ=An, where the summation is over the

n = 100 randomized tree distributions; E and A

are the sample estimates (based on 30 or 100

replicates) and the true (simulated) population

densities, respectively.

(2) Precision: the dispersion of density estimates

obtained with each sampling method was mea-

sured by the coefficient of variation (CV),

calculated as SD/ �E, where �E is the mean across

replicates and SD its standard deviation; preci-

sion increases when CV decreases.

(3) Accuracy: the relative root mean squared error

(RRMSE in Engeman et al. 1994; White et al.

2008, SRMSE in Walther and Moore 2005) was

used to assess overall accuracy associated with

the two methods, as it combines aspects of bias

and precision, calculated as 1=A

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

P

E � Að Þ2=n

q

,

where symbols are as defined above.

Bias, precision and accuracy values were consid-

ered to be good if they were within ±5% (i.e., from

-0.05 to 0.05). In addition, the mean difference

between QUAD and VAT estimations of density for

different sample sizes also was calculated, with 95%

confidence intervals. These were interpreted in rela-

tion to the minimum biological significance limits, as

described for the field efficiency tests. For all analyses

an alpha level of 0.05 was considered as statistically

significant. Analyses were carried out using R soft-

ware (ver. 2.9.1, R Development Core Team 2008).

Differences between the two sampling methods in

assessing tree species richness and diversity also

could be assessed by a similar simulation study.

However, given the large number of variations to be

considered by such a study we did not attempt to do

so in this paper.

Results

Field test results

Differences based on efficiency parameters

For all three efficiency parameters the VAT per-

formed better on average than the QUAD, as it

required fewer man-hours to complete (6.17 mh vs.

8.81 for QUAD), and produced higher numbers of

trees mh-1 (4.29 vs. 3.88) and species mh-1 (1.61 vs.

1.14). These differences were statistically highly

significant (P \\ 0.01) in the case of man-hours and

species mh-1, when tested with LME (Table 2).

Addition of the covariate, tree density, further

improved the F-value and significance of results for

the efficiency parameter man-hours. In the case of the

efficiency parameter, trees mh-1, the addition of

square root-transformed tree density as a covariate

resulted in the difference between sampling methods

becoming significant at the level of P \ 0.10 only

(i.e., new P = 0.098, as compared to P = 0.15

without the covariate in the model).

Across habitat categories also there were differ-

ences between the mean values of efficiency param-

eters (Table 2), but for all three efficiency parameters

the habitat effects were non-significant when mod-

elled with LME (P C 0.18), as the habitat effect was

considerably reduced by the significant random site

effects. Addition of the covariate, tree density, did not

alter the significance of habitat effects for all three

efficiency parameters.

Differences based on vegetation parameters

There were no significant differences between the

QUAD and VAT sampling methods for any of the

three vegetation parameters estimated (P C 0.31;

Table 2). Differences between habitat categories for

the three vegetation parameters were non-significant

when modelled with LME (P C 0.08), meaning that

the habitat effect again included a significant random

site effect.

Agroforest Syst

123

Power of tests and economic or biological

significance

For parameters with non-significant differences

between the QUAD and VAT sampling methods

(all but man-hours and species mh-1), the power to

detect statistical significance appeared to be low even

if sampling effort was increased to 30 or 50 replicates

(Table 3).

For all the efficiency parameters the difference

between means was greater than the minimum value

required for economic significance (Fig. 1). How-

ever, only in the case of species mh-1 the 95%

confidence interval of this difference also completely

excluded the minimum economic significance value.

This was nearly achieved for man-hours also (Fig. 1).

It follows that the VAT is statistically as well

as economically more efficient than the QUAD

Table 2 Mean values obtained in the field for six parameters, using two sampling techniques (QUAD and VAT; see text) in three

habitats (robusta, arabica and forest)

Parameter Explanatory variable: methods Explanatory variable: habitat types

VAT QUAD F-value Robusta Arabica Forest F-value

Efficiency parameters

Man-hours 6.17 8.81 17.81*** 6.60 6.43 13.27 0.49 ns

Trees mh-1 4.29 3.88 2.18 ns 2.95 5.30 4.65 2.35 ns

Species mh-1 1.61 1.14 23.25*** 1.28 1.32 1.83 0.17 ns

Vegetation parameters

Trees ha-1 225.49 217.26 0.17 ns 125.13 223.63 536.18 3.88 ns

Species richness 10.43 10.19 0.10 ns 8.20 8.56 22.00 1.29 ns

Simpson index 0.77 0.74 1.09 ns 0.75 0.71 0.91 0.36 ns

The F-value and statistical significance of parameters obtained with linear mixed effects models are also provided. Interactions

between methods and habitats were not significant in any of the models. ‘‘Efficiency’’ parameters are related to data collection

efficiency in the field; ‘‘vegetation’’ parameters are related to the estimation of tree density and diversity

ns non-significant

*** P \ 0.001

Table 3 Details of the power to detect significant observed

effects (i.e., differences between means of the two sampling

methods, QUAD and VAT; see text) that was associated with

higher sampling efforts (N = 30 and N = 50). Also shown are

predefined economic (10% of QUAD mean) or biological (5%

of QUAD mean) significance limits (transformed as detailed

below), and sample sizes required to detect the predefined

significance values with a power of 80%

Parameter Power (%) Significance limits Sample size required

N = 30 N = 50

Efficiency parameters Economic

1. Man-hours 89 99 -0.11a 51

2. Trees mh-1 20 31 0.10a 273

3. Species mh-1 93 99 0.11 341

Vegetation parameters Biological

4. Density (trees ha-1) 4 5 -0.37, ?0.36b 801

5. Species richness 4 4 ±0.51 2,064

6. Simpson index 13 19 -0.05, ?0.06c 586

In all cases power was calculated for the t-test of meansa Natural log transformed valuesb Square-root transformed valuesc Squared values

Agroforest Syst

123

regarding species mh-1. In the case of man-hours and

trees mh-1, and although for the former the VAT was

statistically more efficient than the QUAD, the

current results are inconclusive regarding economic

significance and greater sampling effort would be

required to resolve the issue.

In the case of vegetation parameters the difference

between means obtained by the QUAD and VAT

sampling methods was within the limits of minimum

biological significance for all three parameters.

However, for all three vegetation parameters the

95% confidence intervals were wide and clearly

exceeded the biological significance limits (Fig. 1).

Thus it is not clear if there is a biologically important

difference between these two sampling methods with

regard to vegetation parameters.

Additional field sampling appeared to be imprac-

tical for resolving the inconclusive results above, as

the sample size required for 80% power to detect

minimum economically or biologically significant

effects was prohibitively large for all parameters

except man-hours (Table 3). Increasing the sample

size would improve the chance of detecting signifi-

cant economic or biological effects by reducing the

width of confidence intervals. This is attempted in the

next section by using simulations to greatly increase

the sample sizes for tree density estimation.

Simulation results

Spatial contagion of artificial datasets

The artificially generated datasets conformed to

expectations regarding spatial contagion, as they

had the following R index values: random distri-

butions in the range of 0.98–1.00, aggregated distri-

butions in the range of 0.60–0.63 and regular

distributions in the range of 1.23–1.25. These values

were similar to the published values of other studies

(Clark and Evans 1954; White et al. 2008). In

addition, 95% confidence limits obtained from 1,000

randomisations were within 5% of the average value

for random and regular distributions, and within 10%

for aggregated distributions. Z-tests confirmed that

these values were significant only for the non-random

distributions.

Bias, precision and accuracy under different

spatial distributions

Random distribution Both sampling methods showed

very little bias (\2%) when estimating the densities of

random distributions (Table 4). This was true for both

sample sizes tested (30 and 100). The precision of

estimates (CV) also was very similar for both methods

-0.6

-0.4

-0.2

0.0

Ln (man-hours)

Diff

eren

ce b

etw

een

mea

ns

Efficiency Parameters

Econ. significance

-0.2

0.0

0.2

0.4

0.6

Ln (trees.mh−1

)

0.0

0.2

0.4

0.6

0.8

Species.mh−1

-4-2

02

4

Sqrt (trees.ha−1

)

Diff

eren

ce b

etw

een

mea

nsVegetation Parameters

Biol. significance

-4-2

02

4

Species richness -0.1

0-0

.05

0.00

0.05

0.10

0.15

0.20

Squared Simpson index

Fig. 1 Plots of differences

between means of the two

sampling methods (filleddiamond, VAT–QUAD; see

text), with 95% confidence

intervals, in relation to

minimum economic

significance value (‘‘Econ.

significance’’, single dashedline) or biological

significance limits (‘‘biol.

significance’’, two dashedlines’’) for six parameters

measured in the field.

ln Natural logarithm,

mh man-hours, sqrt square

root, ha hectare

Agroforest Syst

123

and decreased as density increased (Table 4). At higher

densities QUAD estimates were more precise (lower

CV) than VAT estimates, although this may not be

important as both methods had precision\5% for most

densities (except the lowest) with both sample sizes.

Thus, the overall accuracy of estimation by both

methods was within 5% for almost the entire density

range, except for density of 10 trees ha-1 for which

neither method produced accuracy within 5%, even

with a sample size of 100 (Table 4).

Aggregated distribution For aggregated distri-

butions both methods had positive biases up to 12%

for tree densities from 10 to 100 trees ha-1. However, at

higher densities the QUAD had consistently low bias

that was\5% and progressively reducing with density

for both sample sizes. However, the VAT continued to

have relatively unchanged bias levels of 10–11%, even

with a sample size of 100 (Table 4). Precision was poor

for both methods, at [5% for all densities, thus

resulting in generally poor accuracy (Table 4).

However, due to the lack of much bias at high

densities by the QUAD, this method was generally

more accurate than the VAT at high densities.

Regular distribution The QUAD showed almost no

bias (\\1%) at all densities with both sample sizes.

The VAT, however, showed a weak negative bias

between -5 and -7% at medium to high densities.

Thus, although both methods had similarly low

values for precision (except at 10 trees ha-1), the

accuracy of QUAD estimates was generally\5% for

most densities whereas that of the VAT was more

often [5%, especially at medium to high densities

([250 trees ha-1).

Overall, the QUAD estimated tree densities fairly

accurately for regular and random distributions,

whereas the VAT had generally good accuracy only

under random distribution. For both methods, preci-

sion improved with increasing sample size and density.

However, the bias associated with the VAT under

regular distribution was magnified at higher densities.

Difference between QUAD and VAT

The mean and 95% confidence intervals of the

difference between QUAD and VAT means were

within biologically significant limits for all densities

simulated under random distribution (Fig. 2). How-

ever, largely due to biases associated with the VAT

the difference between these two methods exceeded

biologically significant limits at medium to high

densities for aggregated and regular distributions.

Table 4 Results of the simulation study to assess bias, preci-

sion and accuracy of the two sampling methods, QUAD and

VAT (see text), in estimating tree density (trees ha-1) under

three different spatial distributions (aggregated, random and

regular)

Pattern,

density

Bias Precision Accuracy

QUAD VAT QUAD VAT QUAD VAT

Aggregated

10 0.12 0.12 0.17 0.17 0.22 0.22

50 0.08 0.09 0.12 0.13 0.16 0.17

100 0.06 0.09 0.10 0.11 0.12 0.16

200 0.04 0.10 0.08 0.10 0.09 0.15

300 0.03 0.11 0.07 0.09 0.08 0.15

500 0.03 0.11 0.05 0.08 0.06 0.14

700 0.02 0.10 0.05 0.15 0.05 0.19

Random

10 0.00 0.00 0.08 0.08 0.08 0.08

50 0.00 0.00 0.04 0.04 0.04 0.04

100 0.00 0.00 0.03 0.03 0.03 0.03

200 0.00 0.00 0.02 0.02 0.02 0.02

300 0.00 0.00 0.01 0.02 0.01 0.02

500 0.00 0.00 0.01 0.02 0.01 0.02

700 0.00 0.00 0.01 0.02 0.01 0.02

Regular

10 0.00 0.00 0.05 0.05 0.05 0.05

50 0.00 0.00 0.02 0.02 0.02 0.02

100 0.00 0.00 0.01 0.01 0.01 0.01

200 0.00 -0.04 0.01 0.01 0.01 0.04

300 0.00 -0.07 0.00 0.01 0.00 0.07

500 0.00 -0.07 0.00 0.01 0.00 0.07

700 0.00 -0.06 0.00 0.01 0.00 0.06

Spatial distributions were generated 1,000 times each, and

sampled with 100 randomly located QUADs and VATs.

‘‘Bias’’ measures the systematic departures of density

estimates from expected values. ‘‘Precision’’ measures the

dispersion of estimates around their mean in terms of the

coefficient of variation. ‘‘Accuracy’’ incorporates aspects of

bias and precision in terms of the relative root mean square

error (RRMSE, see text)

Agroforest Syst

123

Discussion

Efficiency and accuracy of VAT under random

tree distribution

For two of the three efficiency parameters the VAT

was significantly more efficient than the QUAD in

terms of sampling effort in the field. The VAT required

significantly less effort to complete each replicate (in

terms of man-hours) while simultaneously increasing

the species information collected per unit effort (in

terms of species mh-1). This advantage could result in

significant economic savings during large-scale bio-

diversity inventories. Reduced sampling effort per

replicate also could promote greater representation of

geographic variation by allowing many small repli-

cates to be widely distributed across a region rather

than being limited to a few large replicates (Batcheler

and Craib 1985; Gimaret-Carpentier et al. 1998). This

is of relevance in tropical areas, where environmental

gradients, dispersal limitation and other ecological

processes often produce spatial sorting of species

(Condit et al. 2000). Although the QUAD recorded

higher numbers of trees per replicate than the VAT (35

trees on average for QUAD, vs. 26 for VAT), it had

lower numbers of species per tree (per replicate, 0.35

for QUAD vs. 0.41 for VAT) suggesting that QUADs

(at the scale used and the conditions prevailing in this

study) may be more vulnerable to species clumping,

perhaps as a result of their relatively compact,

as opposed to elongated, shape (Clapham 1932;

Bormann 1953). Thus, based on our findings the

VAT presents clear advantages over the QUAD in

terms of optimizing the field sampling effort.

The two sampling methods did not differ signifi-

cantly in their estimation of vegetation parameters,

such as species density, richness and diversity, in the

field, although there was considerable variation

across the sites sampled. The simulation study also

showed no significant difference between the two

sampling methods for estimating tree density under

random spatial distribution, indicating that the VAT

provides accurate assessments of tree density and

diversity when trees are located randomly in the

habitat.

Many previous studies have used statistical preci-

sion as the basis for comparing efficiency across

different sampling methods (Clapham 1932; Bor-

mann 1953; Lindsey et al. 1958; Batcheler and Craib

1985; Kenkel and Podani 1991), with the implicit

assumption that differences in field effort between

different methods would be negligible. However, our

detailed recording of field efficiency data shows that

this assumption is not true in the case of the QUAD

and the VAT. In the current study we are in a position

to use statistical precision as well as field perfor-

mance for comparing efficiencies. Based on these two

kinds of efficiency evaluations, we conclude that the

VAT compares favourably with and even exceeds the

performance of the QUAD in terms of field effi-

ciency. Thus the VAT can be considered a reliable

alternative to the QUAD for efficient sampling of

tree density and diversity across varied habitats and

topographic conditions, subject to the condition of

random spatial distribution.

Biases under non-random tree distributions

As we were unable to spatially map our field study

sites for assessing the accuracy of the two sampling

methods in the field, the simulation study provided an

-60

-40

-20

020

4060

Diff

eren

ce b

etw

een

mea

ns

10 100 200 300 400 500 600 700

Density (trees.ha−1)

Biological significance limit

Fig. 2 Differences between the mean estimations of tree

density (i.e., ‘‘difference between means’’) by the two sampling

methods (VAT–QUAD; see text) with 95% confidence limits,

when sampling trees distributed spatially in a random (opendiamond), aggregated (open triangle) or regular (open square)

manner, under different densities (‘‘trees ha-1’’). Density

estimations were obtained using 100 sampling replicates per

spatial distribution-density combination, each of which was

simulated 1,000 times. The divergent (dashed) lines delineate

the biologically significant limits of 5% deviation from the

mean QUAD estimate

Agroforest Syst

123

appropriate testing environment in which to compare

known population parameters against estimates pro-

vided by the two sampling methods. Thus, under the

simulated aggregated and regular distributions, biases

were found to be associated with tree density

estimation by the VAT. Parker (1979) had previously

noted the possibility of bias when sampling with a

VAT under aggregated distributions and recom-

mended using fixed area quadrat methods instead,

under such conditions. On the other hand, the degree

of bias observed here could be considered unimpor-

tant in a different context, such as if the variability

observed in the field (i.e., precision) is also relatively

high (Sheil et al. 2003). Also, it may be noted that the

economical and biological significance limits used in

this study are conservative in comparison with those

used by other studies, where bias and precision values

up to 10% or 20% were considered acceptable

(Cottam and Curtis 1956; Lindsey et al. 1958;

Laycock and Batcheler 1975).

The QUAD was less biased, more precise and thus

more accurate than the VAT for estimating tree

densities under simulated nonrandom spatial distri-

butions. This is similar to the findings of other

simulation-based studies (Engeman et al. 1994;

White et al. 2008). Comparison of our simulation

results with those of other studies showed that the

RRMSE values obtained by us were better (lower)

than those reported by Engeman et al. (1994), and

White et al. (2008), especially under random and

regular spatial distributions. White et al. (2008)

reported a negative bias similar to ours, when

sampling regular distributions with a VAT; however,

the corresponding value reported by Engeman et al.

(1994) was positive. Both of those studies reported

negative biases for the VAT under aggregated

distributions. It is possible that the difference in

direction of bias detected by the different simulation

studies is related to differences in the VAT methods

used (the VAT tested by us is larger and more

complex than in the other studies). Further analysis is

required to understand these differences and find

ways to reduce the biases.

Engeman et al. (1994) found no bias associated

with the QUAD under any simulated spatial distri-

bution or density, whereas in our study the QUAD

was positively biased at low densities. Also, both

methods generally performed poorly in terms of

precision at very low densities, which affected the

accuracy. Thus, neither the QUAD nor the VAT

appear to be appropriate for estimating very low tree

densities.

Applications of the study

Landscapes with moderate to high tree stocking

density and variable densities of undergrowth, as in

this study, are likely to be common across agro-

silvicultural landscapes of the tropics. It should be

kept in mind that the optimal strategy for assessing

tree diversity would involve choice of a sampling

method as well as an appropriate estimator (Gimaret-

Carpentier et al. 1998), and that the optimal strategy

for efficient estimation of diversity may differ from

that for density. Nevertheless, in the interest of

inventorying human-modified landscapes quickly, the

variable area transect method developed by Sheil

et al. (2003) appears more suitable than the fixed area

square plot if the trees are distributed randomly. Our

recommendation is based on the greater efficacy of

the VAT with regard to utilization of time, as

demonstrated in the field, plus the absence of bias

in estimating tree density, as demonstrated under

controlled simulation conditions where the popula-

tion density was known. On the other hand, under

non-random spatial distributions the time advantage

gained by using the VAT is to be traded off against the

disadvantage of obtaining slightly biased estimations

of tree density. Given that both types of sampling

methods examined in this study showed biases under

nonrandom tree distributions, bias corrections gener-

ally should be applied if exact density values are

required under these conditions.

Finally, there are situations under which the

traditional QUAD would be preferred regardless of

its field efficiency. For example, if large numbers of

trees are to be censused per replicate without regard

for time, or if repeated long-term sampling of a fixed

location is called for, a single or few large square

plots may be most appropriate.

Acknowledgements Funding was provided by the CAFNET

project of the EuropAid program of the European Union

(Connecting, enhancing and sustaining environmental services

and market values of coffee agroforestry in Central America,

East Africa and India, CAFNET—Europaid/ENV/2006/114-

382/TPS). We are grateful to the farmers and estate managers

who permitted us to use their properties for data collection. We

thank N. Barathan for his assistance with species identification

Agroforest Syst

123

and specimen collection, S. Aravajy for species confirmation,

and the technicians, students and field assistants of the French

Institute of Pondicherry and Forestry College, Ponnampet,

Kodagu, for assistance in the field. We also thank Douglas

Sheil for helpful discussions during fieldwork and critical

comments on the manuscript, and two anonymous reviewers

for their valuable comments.

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