Is the Concentric Plot Design Reliable for Estimating Structural Parameters of Forest Stands?

Abstract

Monitoring forest stands using sampling techniques offers a valuable alternative to conventional forest condition assessment methods in Central Europe. While these designs are optimized for assessing production parameters, their effectiveness for structural characteristics remains unclear. This study evaluates various plot designs to determine their reliability in estimating structural diversity indices, including the Gini index, Artenprofile index, and Shannon index. We compared ten fixed-radius (FR) sampling designs (plot sizes: 50–1250 m²) and a concentric circle (CC) design (500 m²) employed at the Mendel University Forest Enterprise (Křtiny, Czech Republic). The CC design proved adequate for assessing production parameters and structural diversity indices like Artenprofile and Shannon. However, it showed significant limitations for the Gini index (p < 0.01), due to a smaller number of sampled trees. For the Gini index, fixed-radius plots of at least 150 m², with 200 m² being the most cost-effective size, provided the most reliable estimates. Interestingly, the CC design may also be less suitable for production parameters, where smaller fixed-radius plots (50 m²) were more effective, requiring fewer total samples despite the need for more plots.

1. Introduction

Central European forests have gradually been transformed from deciduous to coniferous due to the demand for rapid timber production [1,2]. Over time, the composition of these forests has shifted, with coniferous species (66% of forests) largely replacing the formerly dominant deciduous woodlands [1]. Current global climate change models [3] predict dramatic impacts on the environment worldwide. Emphasis is placed on the decline and uneven distribution of precipitation during the growing season, as well as on the occurrence of extreme weather events [4,5,6,7]. Additional concerns include an increased risk of forest stands being affected by fungal pathogens or outbreaks of insect pests [8,9] alongside an anticipated rise in forest mortality [10].

The prevailing spruce and pine monocultures are expected to be most vulnerable to these projected changes [11,12]. These stands exhibit sensitivity to rising temperatures and water deficits [13], which elevate the risk of biotic pest outbreaks, particularly bark beetles [14,15]. The consequences extend beyond production losses, including reductions in biodiversity, decreased soil water retention, the disruption of nutrient cycles, and the formation of site-specific extremes that hinder reforestation efforts [16,17].

Numerous strategies have been developed to address the potential adverse effects described above. Beyond assisted migration to promote species diversity, changes in forest ecosystem management are also deemed essential [4,13,18]. In this context, supporting the structural diversification of forest stands appears advantageous. Diameter-, height-, and species-diverse stands exhibit greater stability and biodiversity, improved water retention capacity, and increased resistance to harmful agents [19,20,21,22,23]. Moreover, higher diversity of small mammals and birds has been documented in such stands [24,25,26,27]. Structural diversity in forest stands thus contributes not only to enhanced stability in timber biomass production but also to greater biodiversity within forest ecosystems.

Monitoring the condition of structurally diverse forests using traditional methods, developed primarily for even-aged monocultures, has become increasingly challenging. A solution lies in relying exclusively on sampling-based monitoring methods. These are widely used at national and local levels in many countries, with the collected data employed for assessing forest conditions and predicting timber production. The results are then integrated into forest management planning [28,29,30,31]. Forest monitoring using sampling methods is typically optimized for reliable estimates of production parameters. However, as increasing structural diversity is considered a key adaptation strategy to mitigate the impacts of climate change, there is a growing need to measure and monitor it.

Forest stand structure is usually described across multiple dimensions, including diameter, height, species, and spatial differentiation. Numerous specific indices can be used to quantify these differentiations [27,32]. For indices to be effectively applied in routine forest inventory processes, their sensitivity to the size of inventory plots must remain minimal [33].

While standard inventory plots for estimating basal area, timber volume (m³/ha), and biomass quantification typically cover areas of 500–600 m² [34], larger plots may be necessary for reliable assessments of structural diversity. For example, a minimum plot size of 1500 m² is recommended to estimate height diversity [32]. For comprehensive descriptions of stand structure, a minimum inventory plot size of 500 m² is similar to the requirements for remote sensing-based stand structure analyses [34]. However, increasing the size of inventory plots can reduce the spatial variability of production parameters and structural attributes [35]. This effect can be mitigated by reducing the required number of such plots. In forest stands with an old-growth structure and a high proportion of trees exceeding the diameter at breast height (DBH) of 120 cm, the minimum plot size for describing structure and biometric parameters is 0.35–0.5 ha [36,37].

In Central Europe, the standard design to estimate forest production parameters typically involves circular plots, which are preferred due to their ease of establishment in complex forest environments and their ability to minimize edge effects. Concentric plot designs, which feature multiple inventory circles with a shared centre, are also commonly used, with each circle targeting different diameter classes of trees [38,39,40]. Square plot designs, which are less common, are generally employed in remote sensing methods, where individual image pixels are squares with varying sizes [34,41].

The aim of this study is to recommend a sampling design that enables the simultaneous assessment of both production parameters and structural diversity metrics. The primary hypothesis of this article asserts that the currently prevalent concentric plot design, in its existing form, is suitable for sampling the structural diversity of forest stands.

2. Materials and Methods

The research area was situated in the southeastern region of the Czech Republic (49°25′ N, 16°68′ E) within the University Forest Enterprise “Masaryk Forest” Křtiny (a special purpose utility of the Mendel University in Brno), specifically in the Habrůvka forest district. The site experiences a mean annual temperature of 7.5 °C and receives mean annual precipitation ranging from 550 to 650 mm. Throughout the entire area, a gradual transition from clear-cutting to shelterwood management has been taking place over the past 20 years. In 2002, a total of 270 concentric inventory plots were established to enable the monitoring of the production parameters of forest stands, mainly the current volume increment. From these, a pool of 200 plots on nutrient-rich (mesotrophic) sites was taken. From this pool, we randomly selected and remeasured 40 plots (Figure 1) for further analyses in 2021. Plots were chosen randomly, using the local pivotal method (LPM) implemented through the BalancedSampling package in R [42]. The selected set of 40 plots covers the full spectrum of transition phases from clear-cutting to shelterwood management.

Table 1. Basic parameters of inventory plots with concentric circle design (CC).

Plot	Forest Site Complex	Species Composition (% of the Basal Area)	Number of Trees (pcs/ha)	Basal Area (m2/ha)	Growing Stock (m3/ha)
1	3B—Querceto-Fagetum mesotrophicum	EB 68, EL 32	325	54.9	823
2		EB 73, DF 14, EH 1, EL 12	1312	52.5	635
3		EB 45, EL 39, TR 16	2093	18.9	99
4		EB 100	505	28.1	373
5		EB 4, DF 78, EL 19	220	40.2	605
6		EB 92, SO 6, EH 2	1984	52.0	617
7		EB 18, EA 38, FM 8, SM 36	460	31.8	416
8		EB 53, SP 6, SF 10, NS 31	565	39.6	516
9		EB 45, SO 27, SL 17, EL 11	1477	40.9	447
10		EB 46, SO 25, NS 29	145	19.3	291
11		EB 69, DF 17, NS 14	455	57.8	940
12		EB 82, SP 7, NS 11	605	46.8	646
13		EB 88, EL 7, NS 5	345	33.4	517
14		EB 94, EH 1, NS 5	350	33.8	416
15		EB 7, EH 53, SL 3, EL 37	928	29.4	250
16	3H—Querceto-Fagetum illimerosum mesotrophicum	EB 98, NS 2	1013	30.5	310
17		EB 17, EH 1, EL 82	395	38.0	503
18		EB 95, EL 5	620	22.5	239
19	3S—Querceto-Fagetum oligo-mesotrophicum	EB 35, SP 29, EL 15, NS 21	185	19.7	222
20		EB 53, EH 1, EL 36, NS 10	1008	35.8	376
21		EB 35, EL 65	893	16.6	121
22		EB 100	1263	30.3	291
23		EB 100	1331	23.8	269
24		EB 32, EL 33, NS 35	245	26.2	354
25		EB 10, DF 20, EL 7, NS 63	898	54.7	669
26		EB 60, EL 24, NS 16	495	43.3	560
27	4B—Fagetum mesotrophicum	EB 100	275	22.3	306
28		EB 53, EL 19, NS 28	350	44.4	672
29		EB 61, EL 39	315	27.4	376
30		EB 50, SP 20, SO 30	330	28.8	389
31	4H—Fagetum illimerosum mesotrophicum	EB 1, NS 99	620	53.2	670
32	4S—Fagetum oligo-mesotrophicum	EB 12, EL 88	740	47.7	519
33		EB 81, EL 8, NS 11	1322	30.6	310
34		EB 73, EL 1, NS 26	530	26.4	290
35		EB 2, EL 62, NS 36	485	27.3	289
36		EB 7, EH 1, EL 42, NS 50	540	52.2	664
37		EB 53, EL 47	415	32.4	405
38		EB 20, EL 59, NS 21	1003	50.7	578
39		EB 65, SP 16, EL 15, NS 4	590	33.5	552
40		EB 3, EL 51, NS 46	715	42.0	454

Forest site complex according to Czech forest ecosystem classification [43]. Tree species: EB—European beech (Fagus sylvatica L.); EA—European ash (Fraxinus excelsior L.); EH—European hornbeam (Carpinus betulus L.); EL—European larch (Larix decidua Mill.); SO—Sessile oak (Quercus petraea (Matt.) Liebl.); SL—Small-leaved lime (Tilia cordata Mill.); FM—field maple (Acer campestre L.); SM—Sycamore maple (Acer pseudoplatanus L.); NS—Norway spruce (Picea abies (L.) H. Karst.); DF—Douglas fir (Pseudotsuga menziesii (Mirb.) Franco); SP—Scotch pine (Pinus sylvestris L.); SF—Silver fir (Abies alba Mill.).

presents the basic parameters of 40 randomly selected plots. The forest site complex is described according to the Czech forest ecosystem classification [43]. Other parameters are species composition, number of trees per hectare, basal area, and growing stock.

The concentric inventory plot consists of three circular subplots with a maximum radius of 12.62 m. The radii of subplots and tree inclusion limits are shown in

Table 2. Inventory plot designs and their parameters.

Plot Design	Design Name	Radius [m]	Area [ha]	Tree Inclusion Limit [mm]
Concentric circles	CC	3	0.0028	70 ≤ dbh < 120
		7	0.0150	120 ≤ dbh < 300
		12,616	0.0500	dbh ≥ 300
Fixed radius	FR50	3989	0.005	dbh ≥ 70
	FR100	5642	0.01
	FR150	6910	0.015
	FR200	7979	0.02
	FR300	9772	0.03
	FR400	11,284	0.04
	FR500	12,616	0.05
	FR750	15,451	0.075
	FR1000	17,841	0.1
	FR1250	19,947	0.125

. For each included tree, the position relative to the plot centre was recorded in polar coordinates (geographical azimuth and distance) using the FieldMap system (www.fieldmap.cz, accessed on 7 November 2024), along with the tree species, diameter at breast height (DBH), and some additional information such as tree damage, indications of deadwood, breakage, or stem forks. The height was measured for approximately 30% of the trees.

Subsequently, a larger circular plot with a radius of 19.95 m (1250 m²) was established around the centre of the original inventory plot. Within this new plot, all trees were recorded, documenting their geographic azimuth, distance from the plot centre, species, and DBH in millimetres. The DBH was determined as the average of two perpendicular measurements, with the first measurement taken with the calliper scale orientated towards the plot centre and the second measurement taken perpendicularly to the first measurement direction. Heights were measured for selected sample trees, and for those not measured, heights were modelled using height curves.

Additionally, ten new inventory circles were virtually created at the geographic positions of the 40 original plot centres. Data from the largest inventory circle were divided into ten additional circles based on the distance of the trees from the plot centre (Figure 2). The following table shows parameters of all plot designs and limits for inclusion of trees.

We selected six target inventory parameters to compare the performance of applied designs. Three of these are common target parameters of forest inventories: the number of trees per hectare (n), basal area (ba), and standing timber volume (v). The other three parameters are the Gini index of diameter distribution inequality [44], the Artenprofile index of height structure [45], and the Shannon index of species diversity [46]. All three indices are basal area-based and, at the same time, not spatially explicit. Calculation of all three indices assumes that the diameters of all trees are available. This requirement is met for inventory plots with a fixed radius (FR50–FR1250), but for designs with concentric circles, this requirement is not met. Therefore, we had to develop a procedure that accounts for the different inclusion probabilities of trees with varying DBH. For this purpose, we used the principle of local density published by Mandallaz (1991) [47], to which the Horwitz–Thompson theorem [48] can then be applied.

When this procedure is applied to the CC plot design, the inclusion indicator of a tree in the plot I = 1 is divided by the area of the inventory circle on which it was registered. This relationship is expressed by the equation $n_i={\displaystyle \raisebox{1ex}{$I_i$}\!\left/ \!\raisebox{-1ex}{$\lambda $}\right.}$, where $I_i$ is the inclusion indicator of a tree, taking the value 1 for inclusion and 0 for non-inclusion, and $\lambda$ is the area of the inventory circle on which the tree is registered. In the case of a tree registered on a circle with r = 3 m, the tree’s contribution to the local tree density per hectare is 354. For a circle with a radius of 7 m, it is 65, and for the largest circle with a radius of r = 12.616 m, it is 20. To ensure compatibility with data from fixed-radius plots, the inclusion indicators of individual trees were also recalculated as contributions to the local tree density per hectare by dividing by the corresponding area of the inventory circle (Table 2).

The Gini index was originally designed to describe income inequality [44]. Later, it was introduced for use in describing the diameter structure of a forest [49]. For forestry purposes, Duduman adopted the Gini index as a measure of inequality in a diameter distribution. Its calculation involves several steps that transform distribution data into a Lorenz curve and subsequently calculate the coefficient of inequality. In the first step, data of tree diameter are transformed into cross-sectional areas. The data are then sorted in ascending order to create a cumulative distribution function. Each sorted value is assigned a cumulative share of the total sum of all values. This step normalizes the data to the interval [0, 1]. Then, the Lorenz curve is constructed from the cumulative shares by plotting the cumulative sum of values (Y-axis) against the cumulative number of units (X-axis). In the next step, the area under the Lorenz curve is calculated as the sum of the areas of trapezoids between points of the cumulative distribution. Finally, the Gini index is calculated as the ratio of the area between the diagonal (representing perfect equality) and the Lorenz curve to the total area under the diagonal. The formula for the Gini index is as follows:

$$GI={\displaystyle \frac{1}{2n^2\mu }}{\sum }_i^n{\sum }_j^n\left|g_i-g_j\right|$$

where n is the number of observations, μ is the mean of the values, and g is the sectional area of the i-th or j-th tree.

The Artenprofile index evaluates the distribution of the basal area of represented tree species across three height levels. For an inventory plot, it is calculated using the formula

$$AP={\displaystyle \frac{-\sum _{i=1}^m{\sum }_{j=1}^3\left(g_{ij}\ln \left(g_{ij}\right)\right)}{\mathrm{l}\mathrm{n}\left(3m\right)}},$$

where $g_{ij}$ is the sectional area of the i-th tree species in the j-th canopy layer, i is the species index, j is the canopy layer index, and m is the number of species. The first canopy layer contains trees with heights greater than 80% of the maximum height, the second layer includes trees with heights between 50% and 80% of the maximum height, and the last layer encompasses trees up to 50% of the maximum height. The value of the index ranges from 0 to 1, with a higher value indicating greater height diversity of the stand.

Shannon’s index is calculated based on the equation

$$SH={\displaystyle \frac{-\sum _{i=1}^m{g}_i\mathrm{l}\mathrm{n}\left(g_i\right)}{\mathrm{l}\mathrm{n}\left(10\right)}}$$

where g_i is the sectional area of the i-th tree species, whereas a standard of ten tree species was chosen for a species-rich stand. The indices range from 0 to 1, where 0 indicates minimal biodiversity and 1 indicates maximum biodiversity.

Differences between parameters quantified by the individual designs of inventory plots were tested using ANOVA and post hoc Tukey HSD test.

For each combination of inventory design and target inventory parameter, the necessary number of plots to achieve a 10% relative confidence interval at an alpha level of 0.05 was calculated. The resulting number was then multiplied by the average number of trees per inventory plot for the given design (fixed radius of various sizes and concentric circles). The result was the minimum required number of measured trees to achieve the target confidence interval. The result was 66 values (11 types of design x 6 target parameters) of the minimum required number of measured individuals (

Table 3. Effect of inventory designs on target parameters.

Inventory Parameter		Design
		CC	FR50	FR100	FR150	FR200	FR300	FR400	FR500	FR750	FR1000	FR1250
N [pcs/ha]	Mean ±SE	709 ±10%	735 ±11%	698 ±9%	683 ±8%	671 ±8%	660 ±8%	655 ±9%	652 ±8%	633 ±8%	629 ±8%	622 ±8%
	ANOVA	p = 0.962
	Tukey HSD
BA [m2/ha]	Mean ±SE	36.0 ±5%	36.5 ±11%	34.3 ±8%	34.7 ±7%	35.5 ±6%	35.1 ±6%	35.4 ±5%	34.6 ±5%	34.5 ±4%	34.7 ±4%	35.10 ±5%
	ANOVA	p = 0.999
	Tukey HSD
V [m3/ha]	Mean ±SE	450 ±6%	423 ±11%	453 ±9%	420 ±8%	432 ±7%	451 ±7%	442 ±7%	446 ±6%	432 ±6%	426 ±6%	437 ±6%
	ANOVA	p = 0.999
	Tukey HSD
Gini index	Mean ±SE	0.32 ±3%	0.30 ±11%	0.37 ±7%	0.42 ±4%	0.44 ±3%	0.46 ±3%	0.46 ±3%	0.46 ±2%	0.47 ±2%	0.47 ±2%	0.48 ±2%
	ANOVA	p < 0.001
	Tukey HSD
Artenprofile index	Mean ±SE	0.31 ±8%	0.29 ±13%	0.40 ±8%	0.46 ±6%	0.27 ±9%	0.30 ±8%	0.31 ±8%	0.33 ±7%	0.35 ±6%	0.35 ±6%	0.36 ±6%
	ANOVA	p < 0.001
	Tukey HSD
Shannon index	Mean ±SE	0.30 ±9%	0.12 ±18%	0.19 ±13%	0.23 ±11%	0.26 ±10%	0.29 ±9%	0.31 ±8%	0.33 ±7%	0.36 ±6%	0.38 ±6%	0.40 ±6%
	ANOVA	p < 0.001
	Tukey HSD

Mean—arithmetic mean; SE—standard error of the mean; ANOVA—p value of the analysis of variance, with value < 0.05 indicating one or more statistically significant influences of inventory design on target parameter; Tukey HSD—homogeneous groups of inventory designs (indicated with coloured bars) resulting from the Tukey HSD post hoc test.

). Within each inventory design, the parameter requiring the highest number of samples to achieve a 10% relative confidence interval was selected. This number of samples would then automatically ensure achieving the desired confidence interval for all other target parameters. This value also serves as a simple measure of time and cost consumption for the inventory if the corresponding design were chosen.

3. Results

3.1. Production Parameters

For all three production target parameters of the inventory (N, BA, and V), ANOVA did not detect a significant effect of the inventory design on the value of the target parameter (Table 3). The highest number of trees per hectare was recorded with the FR50 inventory design (735), while the lowest was with the FR1250 design. However, the differences in mean values are not statistically significant. The standard error (and thus the confidence interval too) decreases with increasing inventory plot radius. The CC design performs well here, representing roughly an average of all inventory designs with fixed radii.

For the basal area (BA), the highest mean value was found with the FR50 design (36.5 m²/ha), while the lowest mean value was observed with the FR100 design (34.3 m²/ha). Here, a trend of decreasing standard error with increasing inventory plot size can also be observed.

In the case of the target parameter V (standing volume), the differences in mean values across the inventory designs are also not statistically significant. The highest average volume per hectare was recorded with the FR100 design (453 m³/ha), while the lowest was observed with the FR150 design (420 m³/ha).

3.2. Structural Parameters

Unlike the production parameters, the analysis of variance found a significant effect of the inventory design on the values of all three structural indices. Using the post hoc Tukey HSD test, it was possible to identify differences between the designs and define homogeneous groups of designs (see Table 3).

In the case of the diameter structure index (Gini), the analysis of variance indicated a significant effect of the inventory design. The Tukey HSD test identified three homogeneous groups of inventory designs with overlapping values. The first group (indicated with green colour in Table 3), with the lowest average Gini index values, includes the CC, FR50, and FR100 designs. The FR50 design achieved the lowest Gini index value overall (0.30).

The second homogeneous group (yellow) includes the FR100, FR150, and FR200 designs, with Gini index values of 0.37, 0.42, and 0.44, respectively. The third homogeneous group (pink) includes the FR150 to FR1250 designs, with the latter achieving the highest Gini index value of 0.48.

In the case of the Artenprofile index, three homogeneous groups of designs were also identified. The first group includes all the designs used, except for FR150, which provided the highest species diversity index value overall (0.46). Within the first group, the lowest value provided the FR200 design (0.27), and the FR100 design provided the highest index value (0.40). The second homogeneous group includes designs FR100, FR150, and FR300 to FR1250. The third group includes only three designs (FR150, FR1000, and FR1250).

In the case of the Shannon index, analysis of variance also detected a significant effect of the inventory plot design on the mean index value (p < 0.001) (see Table 3). The Tukey HSD test identified six homogeneous groups of designs. The lowest Shannon index value was provided by the FR50 design (0.12) and the highest by the FR1250 design (0.40). The first homogeneous group of designs included all designs except FR50 and FR100. This group also included the CC design, which had a relatively high mean Shannon index value (0.30). The second homogeneous group consisted of the FR50, FR100, and FR150 designs. The next group comprised the FR100, FR150, FR200, and FR300 designs. The fourth group consisted of the FR150 to FR500 designs. In the fifth homogeneous group, the FR200 to FR750 designs were grouped together, and the final group included the FR300 to FR1250 designs.

Due to the high variability in estimating the number of trees per hectare, there are no statistically significant differences among the different designs (ANOVA p = 0.962), even though, visually, plots with smaller radii (50, 100 and 150) exhibit a broader dispersion of results (see Table 3 and Figure 3). Thus, CC design does not make a difference in this regard.

The results of basal area estimates across all designs are very similar, and statistically there is no significant difference among them (ANOVA p = 0.999). The advantage of the CC design lies in its low data variability that is comparable with fixed radius designs from 400 square metres and bigger.

There were no statistically significant differences in standing volume estimates per hectare among different designs (ANOVA p = 0.999). The CC design has also very low data variability that is comparable with fixed radius designs from 500 square metres and bigger.

The Gini index values increase with the radius of the inventory plot. This is logical because as the number of trees increases, the variability in thicknesses also grows. Statistically, the CD design differs significantly only from the 50 m² and 100 m² plots. It differs significantly from the other designs. However, the low variability of Gini index values is interesting. SPI exhibits roughly the same variability as plots with the largest radius.

Unlike the Gini index, the CD-based estimates of Artenprofile index values do not show statistically significant differences compared to those of most other designs. The only significant difference is observed for design with a plot size of 150 m² (FR150).

For the Shannon index, the CD values exhibit statistically significant differences only compared to those of designs with plot sizes of 50 m² (FR50) and 100 m² (FR100). There were no significant differences observed with all other designs. The CD-based estimates for the Shannon index show relatively high variability, but on average, their values are similar to those of plots with larger radii. This is because the index is influenced by species diversity as determined by their basal area, not by their count.

3.3. Labour Intensity of Individual Designs

Table 4. The required number of sample trees to satisfy the threshold 10% confidence interval for individual designs and target parameters.

	Target Parameter
Design	N	BA	V	Gini	Artenprofile	Shannon	All
CC	7255	1743	2829	735	4213	4988	7255
FR50	1955	1939	2241	2012	2757	5364	5364
FR100	2601	2077	2813	1378	1872	5133	5133
FR150	3118	2175	3047	866	1691	5684	5684
FR200	3994	2386	3434	654	5350	6689	6689
FR300	5838	2900	4587	711	5838	7461	7461
FR400	9187	3350	5283	972	6883	8309	9187
FR500	10,362	3478	5892	955	6562	7802	10,362
FR750	13,379	4172	6672	1147	7293	9209	13,379
FR1000	16,901	5308	9051	1496	9755	11,723	16,901
FR1250	20,967	8076	12,614	1662	11,240	12,448	20,967

Green fields indicate best designs within a target parameter; red fields indicate worst designs within a target parameter. Column assigned with “all” shows number of trees that would satisfy the condition of relCI ≤ 10% for all target parameters.

presents theoretical numbers of trees that would need to be measured within the investigated inventory designs to achieve a relative confidence interval of 10%, given the constant sampling variability. If we were to rank the individual inventory designs according to the “all” column, the result would be that the FR100 design requires the lowest number of inventoried samples to achieve the threshold confidence interval for all target inventory parameters. The FR50 design would be second, and the FR150 design would be third. Next is the CC design. From this order, increasing the radius of the inventory circle leads to an increase in the required number of inventoried samples and thus increases the cost of the inventory.

4. Discussion

Efforts to incorporate structural diversity sampling into existing forest condition monitoring are not new [50,51]. A common element of these efforts is the use of existing designs employed in national and local forest inventories to reduce costs associated with specialized structural diversity assessments. Our findings partially confirm the results of the authors, particularly regarding the use of concentric plot designs for sampling structural diversity. This design is widely used not only in the Czech Republic but also internationally [38,39,40]. To adapt this design for structural diversity sampling, we addressed the inclusion of variable sampling intensities for different diameter cohorts. The method we applied for calculating structural diversity indices aligns precisely with the study published by [52], who utilized the dineq package in R software v. 4.4.1. for computing income inequality [53].

Our study demonstrated that the concentric plot design, as specified in Table 2, is suitable only for sampling alpha diversity of the tree layer using the Shannon index and height diversity using the Artenprofile index. The mean estimates of the Shannon’s species diversity index and the Artenprofile height diversity index derived from the existing concentric design (CC) were not statistically significantly different from those obtained using larger fixed-radius plots. For the Shannon index, the CC design was even the most cost-effective option, requiring the fewest samples for reliable mean estimation.

Conversely, for diameter diversity quantified by the Gini index, the low number of trees within CC design plots revealed limitations. The mean Gini index was significantly lower in CC design plots than in fixed-radius plots, increasing with plot size. Using a fixed-radius plot of 0.05 ha as a reference, our findings suggest that the CC design is unsuitable for Gini index sampling without additional correction. Similar reference plot sizes applied are also documented [54]. Based on our findings, a fixed-radius design with a minimum plot area of 150 m² is ideal for estimating the Gini index, with a 200 m² plot being the most cost-efficient, as it requires fewer samples for reliable estimation. Should CC plots be used for Gini index sampling, additional corrections would be necessary. Future research could focus on developing a compensation factor to mitigate the influence of small sample sizes in CC plots. For example, a correction term multiplying the Gini index by n/(n − 1), where n is the sample size, could be considered [55]. Further studies could also explore the inclusion of spatially explicit structural indices for point sampling designs [51].

An intriguing finding of our work is that the existing CC design may not always be suitable for sampling production parameters. For instance, for the parameters N (number of trees per hectare) and V (growing stock), a fixed-radius plot with an area of 50 m² proved more appropriate.

While more such plots would need to be established and inventoried, the total number of samples required would be lower. A minimum plot size of 1500 m² is recommended for estimating height diversity [32]. In our opinion, such a size is unnecessarily large. Our results suggest that for fixed-radius plots with areas of 200 m² or more, there is no statistically significant change in the mean estimate of height diversity using the Artenprofile index. Interestingly, our data reveal a noticeable increase in index values between plot sizes of 150 and 200 m², likely due to the inclusion of previously unregistered species cohorts or height classes.

The necessity of the low sensitivity of structural indices to plot size is emphasized [33]. Based on our findings, this requirement is particularly challenging for small plots. All three indices used in our study for describing stand structure showed increasing values with larger plot radii, especially for the smallest plots analysed. Beyond 300 m², further increases in plot size did not result in statistically significant changes in mean values. This contradicts the assertion that areas larger than 500–600 m² are required to describe forest structure adequately [34].

It is logically hypothesized [35] that increasing plot size reduces spatial variability in production parameters and structure per unit area, potentially reducing the number of required plots and associated costs. Our analysis, summarized in Table 4, suggests that the most cost-effective plot sizes were 200 m² for the Gini index, 150 m² for the Arteprofile index, and the concentric design for the Shannon index. For all three indices, the labour effort, expressed as the minimum number of samples required, increased with larger plot sizes.

Interestingly, for comprehensive forest monitoring, encompassing both production and structural diversity parameters, a fixed-radius plot with an area of 100 m² appears most suitable. However, this conclusion needs further validation through targeted studies that encompass a broader range of ecological conditions and management approaches. Although our 40 sites were randomly selected, they represent managed forests on nutrient-rich sites dominated by European beech.

5. Conclusions

The results of this study demonstrate that the concentric plot design is effective for monitoring production parameters as well as species and height diversity in forest stands. There are no statistically significant differences in estimates of production parameters (number of trees per hectare, basal area, and standing timber volume) across different plot designs, indicating that concentric plots can reliably assess these metrics.

For structural diversity indices, the following points are noted:

-

The Gini index values indicate that the concentric design might need additional corrections for diameter diversity assessment, as lower values were recorded compared to those of larger fixed-radius plots.

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The concentric plot design effectively captures height diversity, as measured by the Artenprofile index, performing similarly to larger fixed-radius plots.

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The Shannon index results show that the concentric design is comparable to or better than that of large-radius plots in capturing species diversity.

These findings suggest that the concentric plot design is a versatile and efficient method for forest inventory, balancing the need for detailed structural diversity metrics with traditional production parameter assessments. However, for specific metrics like the Gini index, additional methodological adjustments may be necessary to enhance accuracy.

Future research should focus on verifying these findings across different forest types and environmental conditions to enhance the generalizability of the results. Furthermore, developing correction factors for diameter diversity in concentric plots would improve their utility in comprehensive forest monitoring programs.