Agroforest Syst (2010) 79:223–236 DOI 10.1007/s10457-009-9255-5

Comparative efficiency and accuracy of variable area transects versus square plots for sampling tree diversity and density Cheryl D. Nath • Raphae¨l Pe´lissier • Claude Garcia

Received: 7 April 2009 / Accepted: 22 September 2009 / Published online: 11 October 2009  Springer Science+Business Media B.V. 2009

Abstract Agroforestry systems have been recognized 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 landscapes, 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 significantly 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 aggregated 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 transect 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 C. D. Nath (&)  R. Pe´lissier  C. Garcia French Institute of Pondicherry, 11 St Louis Street, PB 33, Pondicherry 605001, India e-mail: [email protected] R. Pe´lissier 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

Landscapes dominated by coffee agroforestry have been identified as potential areas for future biodiversity 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

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(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 (GimaretCarpentier 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 information 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

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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 documented 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.

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The main objectives of the study were: (1)

(2)

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. 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 characterised by heterogeneous spatial distributions and densities of trees.

Methods

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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.

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

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 (12140 57.800 N to 12190 48.400 N; and 75530 11.700 E to 75560 41.700 E). 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 (12050 55.200 N, 75520 47.800 E). 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

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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

Robusta

Arabica

Forest

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)

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)

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 9

850, 940 690, 730

5.00, 22.75 Not rec.

4 6

111 361

26 48

184 (150, 222) 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

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; however, there was moderate weed occurrence (mainly Strobilanthes kunthianus) in the undergrowth, indicating 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.

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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 (Student’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 confirmation, 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

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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) (ii) (iii)

Total number of man-hours per replicate (mh). Total number of trees sampled per man-hour in the field (trees mh-1). 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) (ii) (iii)

Tree density (trees ha-1). Species richness, or the total number of species per replicate. 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-independence 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 differences between methods after adding the covariate, ‘‘tree density’’, in the models. This parameter was

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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 residual plots for homoscedasticity; standardized residual plots for linearity) and, where necessary, transformations 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 generally 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 significance. 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 significance 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

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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 significance (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 distribution 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 common 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 conditions 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

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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 ‘‘offspring’’ 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 artificial 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 pffiffiffi neighbour distance, Re, was calculated as 1= 2 A , where A is the true population 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).

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Analysis of simulation data The bias, precision and accuracy of density estimation 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)

(2)

(3)

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 as P ðE  AÞ=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. Precision: the dispersion of density estimates obtained with each sampling method was measured by the coefficient of variation (CV),  where E is the mean across calculated as SD/E, replicates and SD its standard deviation; precision increases when CV decreases. 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 ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P and precision, calculated as 1=A ðE  AÞ2 =n, where symbols are as defined above.

Bias, precision and accuracy values were considered 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 relation 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 software (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.

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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 performed 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 differences between the mean values of efficiency parameters (Table 2), but for all three efficiency parameters the habitat effects were non-significant when modelled 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.

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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 VAT

QUAD

Explanatory variable: habitat types F-value

Robusta

Arabica

Forest

F-value

0.49 ns

Efficiency parameters Man-hours

6.17

8.81

17.81***

6.60

6.43

13.27

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

225.49

217.26

0.17 ns

125.13

223.63

536.18

3.88 ns

10.43

10.19

0.10 ns

8.20

8.56

22.00

1.29 ns

0.77

0.74

1.09 ns

0.75

0.71

0.91

0.36 ns

Vegetation parameters Trees ha-1 Species richness Simpson index

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 Parameter

Power (%)

Significance limits

N = 30

N = 50

89

99

Efficiency parameters 1. Man-hours -1

2. Trees mh 3. Species mh-1

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%

Economic -0.11a a

20 93

31 99

4. Density (trees ha-1)

4

5

-0.37, ?0.36b

5. Species richness

4

4

±0.51

13

19

Vegetation parameters

6. Simpson index

Sample size required

0.10 0.11

51 273 341

Biological

-0.05, ?0.06c

801 2,064 586

In all cases power was calculated for the t-test of means a

Natural log transformed values

b

Square-root transformed values

c

Squared values

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).

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For all the efficiency parameters the difference between means was greater than the minimum value required for economic significance (Fig. 1). However, 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

0.8 0.4 −1

Ln (man-hours)

2

2

4

4

Vegetation Parameters

-4

-2

-2

0

0

Biol. significance

−1

Sqrt (trees.ha )

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 impractical 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 significant 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.

−1

Ln (trees.mh )

Species richness

Species.mh

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20

-0.6

-0.2

0.0

0.2

0.0

-0.4

0.2

-0.2

Econ. significance

0.6

0.4

0.0

Efficiency Parameters

0.6

231

-4

Difference between means

Fig. 1 Plots of differences between means of the two sampling methods (filled diamond, VAT–QUAD; see text), with 95% confidence intervals, in relation to minimum economic significance value (‘‘Econ. significance’’, single dashed line) or biological significance limits (‘‘biol. significance’’, two dashed lines’’) for six parameters measured in the field. ln Natural logarithm, mh man-hours, sqrt square root, ha hectare

Difference between means

Agroforest Syst (2010) 79:223–236

Squared Simpson index

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 distributions in the range of 0.98–1.00, aggregated distributions 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

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Agroforest Syst (2010) 79:223–236

Table 4 Results of the simulation study to assess bias, precision 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

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

200 300

0.00 0.00

0.00 0.00

0.02 0.01

0.02 0.02

0.02 0.01

0.02 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

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

Random

Regular

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)

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

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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 distributions 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, precision 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). However, 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.

233

40 20 0

g ic al

sign if

ica n c

e l im it

-40

-20

Bio lo

-60

Difference between means

60

Agroforest Syst (2010) 79:223–236

10

100

200

300

400

500

600

700

Density (trees.ha−1) 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 (open diamond), 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

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 biodiversity inventories. Reduced sampling effort per replicate also could promote greater representation of geographic variation by allowing many small replicates 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 significantly 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 precision as the basis for comparing efficiency across different sampling methods (Clapham 1932; Bormann 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 performance 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 efficiency. 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

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234

appropriate testing environment in which to compare known population parameters against estimates provided 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 recommended using fixed area quadrat methods instead, under such conditions. On the other hand, the degree of bias observed here could be considered unimportant 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 distributions. 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 distribution 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

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Agroforest Syst (2010) 79:223–236

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 agrosilvicultural 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 (GimaretCarpentier 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 population 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 generally 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/2006/114382/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 (2010) 79:223–236 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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