Improving Hierarchical Ecosystem Structures and Multicriteria Evaluations for Current Land Ecosystem Classification

doi:10.21203/rs.3.rs-2961079/v1

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Improving Hierarchical Ecosystem Structures and Multicriteria Evaluations for Current Land Ecosystem Classification

https://doi.org/10.21203/rs.3.rs-2961079/v1

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Background

Ecosystem classification provides a systematic means to organize landscape resources for the purposes of environmental management and planning. The ecosystem classification attempts to capture earth processes over large geographic areas that produce persistent ecosystem patterns on the landscape. Past studies included the hierarchical ecosystem classification in the 300 Dry Domain of the United States and the 100 Polar Domain of Canada. In this paper, the land ecosystem classification (LEC) was developed and simplified as the structure level of organization with the hierarchical system and global ecoregions examined by using hierarchical theory and Multicriteria Evaluations.

Results

The generalized real-world components model relates the classification and level structure as a function of climate, landform, parent material, hydroregime, soil, ecological site, and fauna. Top Domain verification provided physical links and comparison bases for developing mapping ecosystems at continental and global scales. The focal levels were the main national and regional ecosystem classification components. The bottom level and its component were objectively defined by the related ecological site or vegetation stand.

Conclusions

The real-world component model was used to implement the analysis. Once the dimension of the ecosystem classification was significantly reduced to less than ten levels, the component effect ranks and importance ranks demonstrated the comprehension of the level of organizational structures and the land ecosystem classification. Furthermore, the Real-World Component Model quantitatively assessed the component effect and importance features. The component effect values W_i of the ecosystem hierarchies exhibited a significant relationship with the component importance values V_i (R² = 0.8025, P < 0.01).

Ecosystem Classification

Hierarchy

Multicriteria

Component Effect and Importance

Environment scientists have studied Earth's unique ecosystem for a long time. They have attempted to provide a more explicit theory describing the components such as Geosphere, Biosphere, Hydrosphere, Atmosphere, and Cryosphere (Kolasa and Pickett 1989; Hutchinson et al. 2005; Haeussler 2011; Gunaydin et al. 2022). However, when ecologists observed the observation sites, every species was identical and dependent on each other, making it challenging to draw defined boundaries for gradually changing ecosystems (Müller 1992; Creque et al. 1999; Bourgeron et al. 2001; Bailey 2004). The ecosystem classification for a nation has undergone development in theory, principle, criteria, and implementation practices (Simon 1991; Bailey 1995; West et al. 2005; Wu 2013). Notably, recent development in GIS-based Multicriteria Evaluation ( Dragićević et al. 2015; Montgomery 2016; Walker and Schuurman et al. 2021; Yuan and Wen et al. 2022) and remote sensing technology provide higher accuracy and resolution data that are available in open access (Hornsmann et al. 2008; Prudhomme et al. 2020; Keith et al. 2020). With these tools, ecologists and geographers have obtained better chances to classify land territories into simple ecosystems where plant, animal, and bacteria populations live together (Klijn et al. 1994; Bailey 1995, 1996a, 1996b). At different regional scales, they outlined the ecosystem as systemically organized, nested, and with multiple layers (Bailey 1985, 2004; Bailey and Hogg 1986; O'Neil et al. 1986; Lieberman 2017; Chen et al. 2019; Mu et al. 2020; Zhang et al. 2021).

In the 1970s to 1990s., Bailey R., an Ecologist from the US, defined the regional boundaries and outlined the ecoregions of the United States, North America, and the continents worldwide. Consequently, Federal Geographic Data Committee (FGDC) established the National Hierarchy of Ecological Units (NHEU) in the United States. Additionally, in 1993, ECOMAP created an eight-level hierarchical system for the land ecosystem classification, which includes the Domain, Division, Province, Section, Subsection, Landtype Association, Landtype, and Landtype Phase.

On a global scale, ecologists have recognized the landscape-scale processes when they want to compare them at the top level of the ecosystems or the global scale. Quantitative simplification and structuring of the landscape-scale variation and combination of abiotic and biotic factors can be achieved by categorizing the levels of structure and components (Hutchinson et al. 2005; West et al. 2005; Rietman et al. 2011; Zhang 2021; Zhang et al. 1992, 2021). Therefore, quantitatively, it is necessary to compare the ecosystem components crossing comparable structure levels (Jafary et al. 2018 Fábregas-Tejeda et al. 2018).

The IUCN Global Ecosystems Typology is hierarchically structured with three upper levels exhibiting similar ecological functions (Keith et al. 2020, 2022; McGill et al. 2022). These ecoregions belong to the Terrestrial Realm of the GET classification system, which is the highest level and includes a comparable mixture of biomes. The ecosystem function group types also share the same function classifications for upper levels, such as T4.4 Temperate Woodland, T5.1 Semi-desert Steppe, T5.4 Cool Desert and Semi-Desert. Fortunately, the descriptions of ecological traits present and describe the ecological drivers and disturbances for the lower group functions, representing the lower levels of Global Ecosystem Classification (GET). So far, the INCN GET has made signs of progress for a Global Ecosystem Classification in terms of typology, design of principle, levels of classification, reflections of typology development, and descriptive profiles for ecosystem function groups. However, the three lower-level functional groups of GET still needed to be considered and completed as the land ecosystem framework for a deliverable Global Ecosystem Classification. Furthermore, hierarchical ecosystem structures, multicriteria evaluations and real-world models can approve the capacities and tools to generate a deliverable Land Ecosystem Classification.

This paper defines the real-world component model by applying hierarchical theory. Consistently, we sought to identify multi-components of abiotic and biotic factors at multiple levels and create top, focal, and lower levels of the ecosystem classifications for an ecoregion. Furthermore, we evaluated some hierarchical ecosystem theories (Kolasa et al. 1989; Wu and David 2002; Wu 2013; Valérie 2017) using real-world ecosystem components and multicriteria evaluations.

2.1 Conceptual Model

We established a Real-World Component Model by the ecosystem components (Klijn et al. 1994, West et al. 2005) as Eq. (1):

E [I, J] = LS [C, LD, PM, H, S, ES, VS] (1)

where E-Ecosystem, LS-Level Structure, C-Climate, LD-Landform, PM-Parent Material, H-Hydroregime, S-Soil, ES-Ecological Site, VS-Vegetation Stand. E[I, J]-defined in Fig. 1 and Eq. (2).

The structures of the Real-World Component Model were described with three component portions of Top, Focal, and Lower levels (Fig. 1). The Ecosystem Classification matrix E [I, J] is expressed by the roles of the ecosystem functions (Müller 1992).

E [i, j] =$\left(\begin{array}{ccc}E11& \cdots & E1n\\ ⋮& \ddots & ⋮\\ Em1& \cdots & Emn\end{array}\right)$ (2)

where i = 1, 2, 3,….m j = 1,2,3…. n

To form the normalized matrix R[i, j] by Eq. (3) that each $Eij$ took the sum of squares and roots of the criterion values in the decision matrix. (Gunaydin et al. 2022)

${R}_{i j}$ = $\frac{Eij}{\sqrt{{\sum }_{j=1}^{n}{Eij}^{2}}}$ i= 1, 2, 3,….m j = 1,2,3…. n (3)

then R [i, j] =$\left(\begin{array}{ccc}R11& \cdots & R1n\\ ⋮& \ddots & ⋮\\ Rm1& \cdots & Rmn\end{array}\right)$

so that we obtained the columns: $Uia$ =$\left(\begin{array}{c}R1a\\ ⋮\\ Rma\end{array}\right)$ and $Yib$ = $\left(\begin{array}{c}R1b\\ ⋮\\ Rmb\end{array}\right)$ (4)

${U}_{ia }$ and ${Y}_{ib }$are defined as criterion contribution values for Utah and Yukon in the

matrix. a and b are two regional entities, a ≠ b < j.

2.2 The ecosystem component effect and importance features and their weights

Using the minimum value between the ecosystem components, we calculated the component effect in the ecosystem; and using the maximum value between the ecosystem components, we figured the component importance in the ecosystem as Eq. (5)and Eq. (7), respectively. Their weights were expressed as Eq. (6) and Eq. (8).

${W}_{ia }$= │($Uia$ - $Yib$)│ (5)

$${W}_{i }= \frac{{W}_{ia}}{ {\sum }_{i=1}^{m}{W}_{ia}}$$

where${W}_{i }$- each weight of the component effect is divided by the sum of weights

$Via$= │($Uia$ + $Yib$)│ (7)

$${V}_{i }= \frac{{V}_{ia}}{ {\sum }_{i=1}^{m}{V}_{ia}}$$

where${V}_{i }$- each weight of the component importance is divided by the sum of weights

2.3 Definition of a group and a subgroup

A group and a subgroup were given as follows (Rietman et al. 2011):

A) A group is a set G, a binary operation *: G² → G, and an element e = e_G ∈ G such that satisfied.

B) subgroup of a group G is a subset H ∈ G, which is also a group using the same operation as in G.

We have pseudocodes in the available data sources. For example, the Group-Verify-Test 1 in Pseudocode 1 was to terminate the area or ecoregion within the study area or defined boundary. The Subgroup-Verify- Test 2 in Pseudocode 2 was to verify the subregions were nested under the levels.

2.4 Two study sites and Data Sources

First study site: Western Utah State and Nevada's eastern border combined a total area of 45,065.79 Km² (4.5-million-hectare), centered in a Desert Ecosystem within the 300 Dry Domain. The ecological sites were surveyed in the Summer of 1996 in a buffered DOD/BLM fenceline (West et al. 2005). And 30 m DEM data was used.

Second Study site: Yukon Territory is approximately 483,450 km² and intersects with Southern Arctic, Taiga Plain, Taiga Cordillera, and Boreal Cordillera within the 100 Polar Domain and a non-Polar Domain area of Pacific Maritime Ecozone. Ecological sites were surveyed in the Summer of 2021 in the central region of the Yukon Territory, Keno town within Ecodistric 898 (Environment Yukon 2016; Zhang et al. 2021). And 20 m DEM data was used as the data source.

2.5 Procedures of ECL's validations and formations

Based on Bailey's top-level Domain of a global framework, we only verified the top-level Domain of the 100 Polar Domain for Yukon Territory, Canada, by the Group-Verify-Test 1. The lower levels of ECLs were established in the previous study. The examples of full ECLs were retrieved from the ELC model (West et al. 2005) and are presented in Table 1.

The SubGroup Test 2 was used to verify the next level of Ecoprovince, Ecoregions, and Ecodistricts separately within the boundaries of Yukon Territory. In Keno town, the central Yukon Territory of Canada, the focal and lower levels of ECLs were conducted to implement the bioclimatic ecosystem classification in terms of the slopes and aspects, and the buffered areas of ridges and lakes. In the meantime, a two-dimensional (2D) diagram initialized the multiple ecosystem distributions by integrating the soil moisture and the nutrient regimes as the attribute data. The examples of full ECLs were retrieved from the ECL model (Zhang et al. 2021) and are presented in Table 2.

2.6 Ecosystem components and their comparable values

Bailey's top-level Domain was based on a global framework of Köppen's climate classification (Bailey 1995; Belda et al. 2014). The component value of U1 was selected as Thot- the Hot Month Mean Temperature for 300 Dry Domain. In the Polar Domain, Polar Thot ≤ 10^oC, and Tundra Thot ≥ 0^oC, we used an average of 5^oC for Y1. Cold Month Mean Temp is ≤ 0^oC for Division U2, and we retrieved − 18^oC for Boreal Cordillera Ecozone Y2 from the online data source in Table 2. The Average Annual Temp Ranging was 3-10^oC, and we used the average 6.5^oC for U3 component value and retrieved − 3.8 ^oC for the Northern Boreal Cordillera Ecoprovince of Y3 from the online data source.

Bailey (1995) depicted Section U4 with the Annual Average Precipitation climate feature. We used the average PPT of 465 mm for the Section U4 component value and the average PPT of 975 mm for the Y4 Ecoregion component value. Erosional Landtype Subsection U5 was classified by slope degree over 30^o with common area elevation at 2600. The slope ratio divided by height was used as the Landscape component value. Thus 30/2600 and 30/1600 were utilized for Landtype U5 and Eodistrict Y5, respectively. Landtype Association was classified by topographic position, and Hard Sedimentary Erosional Landtype Association U6 was associated with the dry regime 0.2 over 1.0 scale. The Broad Ecosystem of Y6 was associated with a wet regime (Wetland), given a 0.9 over 1.0 scale (Zhang et al. 2021).

Soil conditions classified Landtype U7 and soil nutrition level was used for component value, 0.2 over 1.0 scale. Broad ecosystem phase Y7 was identified as having a high nutrition level, given 0.8 over 1.0 scale. Geological groups identified Landtype Phase U8, and we have no component value for comparison. Ecological Site U9 and Ecosite Y8 were objectively defined and classified at the lower level. We used an average pH value of 7.8 for sandy loam for the U9 ES component value. We retrieved Turbic Cryosol pH 7.53 for the ES component value of Y8 from the data source presented in Table 1 and Table 2.

2.7 Comparison of the component values between two regional ecosystems

We compared two different ecosystems using the same environmental factor for the same structure level. Based on the environmental criteria used for the multilevel ECLs. In Table 3, the component effect and importance weight values and ranks were calculated using Eq. (3) to Eq. (8). And the correlation was tested at P < 0.01 level.

3.1 The Validation of Top-Level Ecosystem Classification between the United States and Canada

The Group -Verify-Test 1 program was used to confirm the presence of Ecozones within the Polar Domain. It examined the Yukon Territory within the Polar Domain and eliminated the southwestern corner of the M241 Pacific Forest Province. Additionally, we employed the Subgroup-Verify-Test 2 to validate the alignment of the next level of Ecoprovince, Ecoregions, and Ecodistricts within the study boundaries of the Yukon Territory, as specified in the Pseudocodes. The Canada Ecological Stratification Working Group (1996) provided data resources and a comprehensive Ecological Framework, including the Ecozone, Ecoprovince, Ecoregion, and Ecodistrict, that accurately characterized the Yukon Territory. This framework reflected abiotic and biotic factors on a subcontinental scale (Zhang et al., 2021) and was encompassed by the 100 Polar Domain (Fig. 2) except for Pacific Maritime Ecozone.

Figure 2 Verified Focal Level of the Yukon Ecosystem Structures Framework under 100 Polar Domain

3.2 The Formation of Ecosystem Classification in Western Utah of the United States

Eq (1) is a general Real-World Component Model expressed by the ecosystem components. Based on Bailey's ecoregion framework, we derived the climate features C1, C2, and C3 for Domain, Division, and Province. The hydrology H was identified for the Section. And the Subsection referred to as "Bolson" of Landform for LD1.To classify Macroterrain units, we created an algorithm based on elevation and apparent slope. Polygons were categorized as upslope of an equal or higher slope position as LD2. Mesoterrain Units were delineated using geologic soil data (West et al. 2005) to identify attributes associated with metamorphic rock, moderately hard sedimentary rock, basalt alluvium, glacial sediment, and eolian sediments as S1. Microterrain units were further defined as subdivisions based mainly on landforms for erosion surfaces and landforms plus soils for deposition-dominated landscapes as S2. The protocols added two additional levels below the 8th level. Ecological Site (ES) is the 9th level, and Vegetation Stand (VS) is the 10th and finest-grain level (Table 1).

The summarized description of Eq. (9)

E [I, J] = LS [C1, C2, C3, H, LD1, LD2, S1, S2, ES, VS] (9)

where Eq. (9) was derived from Eq. (1), with all components defined in Table 1. The climate features were extended to encompass the top three levels of ECLs, namely C1, C2, and C3. The sequence of the components in Eq. (9) depended on ecosystem structures and the levels of the ecological organization. However, the component matrix was populated with equivalent values.

Table 1

Western Utah's ECL component values in 300 Dry Domain
Levels	Utah's Nested ECL	Example Classification	Component Criteria	Values
U1	Domain	300 Dry Domain	C1 – Thot = 25 ^oC	Average 25 ^oC
U2	Division	340 Dry Temperate	C2 – Cold Month Mean Temp ≤ 0 ^oC (bwk)	0 ^oC
U3	Province	341 Intermountain Semi-Desert	C3 - Average Annual Temp Ranging 3–10 ^oC	Average 6.5 ^oC
U4	Section	Central Great Basin	H- PPT high = 765 mm PPT low = 165 mm	Average 465 mm
U5	Subsection	Erosional Landtype	LD1-Mountain-Erosion 30^o to Elevation 2600 m	30/2600 m
U6	Landtype Association	Hard Sedimentary Erosional Landtype Asso.	LD2- Dry 0.2 over 1.0	0.2
U7	Landtype	Eolian Sediments	S1- Soil Nutrition Level, Lower 0.2 over 1.0	0.2
U8	Landtype Phase	Moderately Hard Sedimentary	S2- Soil	N/A
U9	Ecological Site	Desert Flat	ES - Sandy loam, 0–20 cm pH 7.6 20–40 cm pH 8.0	Average 7.8
U10	Vegetation Stand	Black Greasewood	VS	N/A
Notes: U- Utah, with levels of 1,2, 3,...10. C1- Thot Hot Month Mean Temp; C2- Cold Month Mean Temp - p82, C3- Average Annual Temp- p 87 to 88, H – Annual Average Precipitation PPT- p 87 Referring to Bailey 1995; LD1- Mountain Erosion Slope to Elevation Referring to West et al. 2005; LD2-Dry Slope and S1- Soil Nutrition Level Referring to Zhang et al. 2021; ES- Sandy loam pH value Referring to online.

3.3 The Formation of Ecosystem Classification in the Yukon Territory of Canada

The 100 Polar Domain's was characterized as climate feature C. The upper focal levels were specified as the bioclimates of Bc1, Bc2, and Bc3 in Eq. (10). The Ecodistrict, as its landform, was classified as LD. The relative moisture regime as a classification criterion classified the broad ecosystem types at the lower focal levels (as shown in Table 2). It facilitates the functional retrieval of ecological relationships using the generalized Edatopic Grid (Grods et al. 2012; Zhang et al. 2021). Therefore, the lower layers had three components: SL for Slope position, M for Moisture, and ES for Ecological Site, as indicated in Eq. (10).

The summarized description of Eq. (10)

E [I, J] = LS [C, Bc1, Bc2, Bc3, LD, SL, M, ES] (10)

where Eq. (10) was derived from Eq. (1), with all components meticulously specified. The bioclimate characteristics were established as the upper focal levels of ECLs, specifically Bc1, Bc2, and Bc3. The arrangement of the components in Eq. (10) was determined by the ecosystem structures and the levels of the organization. Nonetheless, the component matrix was populated with identical values.

Table 2

Yukon's ECL component values in 100 Polar Domain
Levels	Yukon's Nested ECL	Example Classification	Component Criteria	Values
Y1	Domain	100 Polar Domain	C - Polar Thot ≤ 10^oC, Tundra Thot ≥ 0 ^oC	Average 5 ^oC
Y2	Ecozone	12 Boreal Cordillera Ecozone	Bc1 - Cold Month Mean Temp	-18 ^oC
Y3	Ecoprovince	12.2 Northern Boreal Cordillera Ecoprovince	Bc2 - Average Annual Temp	-3.8 ^oC
Y4	Ecoregion	12.2.176 Yukon Plateau-North Ecoregion	Bc3 - PPT high 1500 mm PPT low 450 mm	Average 975 mm
Y5	Ecodistrict	12.2.176.0898 Elsa Ecodistrict	LD- Mountain-Erosion Slope 30^o to Elevation 1600 m	30/1600 m
Y6	Broad Ecosystem	Wetland	SP - Wet 0.9 over 1.0	0.9
Y7	Broad Ecosystem Phase	Shrub and Carex Grasses	M - Nutrition Level High 0.8 over 1.0	0.8
Y8	Ecological Site/Ecosite	Lodgepole Pine Spruce-Grass-Lichen	ES - Turbic Cryosol pH	7.53
Notes: Yukon-Y, with levels of 1,2, 3,...8. C- defined by Beck 2018; Bc1- Cold Month Mean Temp Referring online; Bc2- Average Annual Temp Referring online; Bc3-Average Precipitation Referring online; LD-Mountain Erosion Slope to Elevation Referring to West et al. 2005; SP- Slope Position and M- Nutrition Level Referring to Zhang et al. 2021; ES- Turbic Cryosol pH Referring to Alexco 2009 and Lavkulich 2021.

3.4 ECL's comparison by the component values between two regional ecosystems

Based on the different level component values in Table 1 and Table 2, we used Eq. (3) to (8) to obtain the component effect and importance ranks in Table 3. The effect difference of the same component on the different ecosystems was represented by ${W}_{ia }$. Each weight ($Wi$) was assigned to provide the component effect ranks for the ecosystems. For instance, the average annual temperature was the primary climate factor affecting the difference between the two regional ecosystems. On the other hand, $Via$ indicated the importance range of the components in the ecosystems. Each weight ($Vi$) provided the component importance ranks at a certain level. For example, pH value was identified as the most crucial factor for the ecological sites of the two regional ecosystems. Even though both ecological sites had alkaline soils, the sandy loam soil in western Utah resulted from the ground water leaching into the soil. In contrast, the Turbic Cryosol soil was caused by soil parent material abundant in CaCo3 (Lavkulich 2021).

Table 3

ECL's component comparisons between two regional ecosystems
Levels	U1/Y1	U2/Y2	U3/Y3	U4/Y4	U5/Y5	U6/Y6	U7/Y7	U9/Y8
U$ia$	0.982	0.055	0.852	0.427	0.524	0.217	0.243	0.728
Y$ib$	0.189	-0.998	-0.505	0.904	0.852	0.976	0.970	0.685
${W}_{ia }$ Eq. (4)	0.793	1.054	1.368	0.478	0.328	0.759	0.728	0.043
${W}_{i }$Eq (5)	14.30	19.00	24.60	8.60	5.90	13.70	13.10	0.80
Effect Ranks	3	2	1	6	7	4	5	8
$Via$ Eq. (6)	1.171	0.943	0.359	1.331	1.376	1.193	1.213	1.414
$Vi$ Eq. (7)	13.10	10.50	4.00	14.80	15.30	13.30	13.50	15.70
Importance Ranks	6	7	8	3	2	5	4	1
Note: R² = 0.8025, P < 0.01 for the weights of ${W}_{i }$and${V}_{i }$

4.1 Top-level Domain and its verification

Bailey (1985, 1986, 1995) developed the national, continental, and global ecosystem classification and outlined the ecosystem classification framework and regimes. However, Bailey and Zoltai et al. (1985) made compelling recommendations to address potential issues when mapping ecological regionalization in Canada and the United States. Group Verify Test 1 was used to examine the top Domain in this study and enhance the accuracy of classifications. The top Domain verification established physical connections and comparison bases for developing ecosystem mapping at the continental and global scales. Thus, these tests were essential and fundamental (Zhang 2021).

4.2 Focal-level components and ecological features for two global continental ecoregions

The diagram in Fig. 1 displays the focal level, including components (1 < i < m) between the bottom and top levels. Lieberman (2017) stated that these components represented major national ecosystem classifications. The comparison between the Dry Domain's and Polar Domain's ecosystems reveals clear differences and dissimilarities that indicate distinct regional characteristics. Unique ecosystems can be identified based on climate, landform, hydrology, and bioclimatic features. Habitats found in the Dry Domain are not interchangeable with those in the Polar Domain (Zhang et al. 2022). This finding has significant implications for understanding how ecosystems respond to global warming impacts. It emphasizes that species adapted to specific ecosystems cannot survive in drastically different environments, and invading species must come from similar ecosystems or habitats (Zhang et al. 2022).

ECOMAP is a top-down regionalization approach explicitly designed for geographic areas, which is used to create the focal levels. The ecosystem classification units, used from national to local levels, are nested structures that integrate the outer polygons created at lower levels with those at upper levels. The hierarchical design of ECOMAP is strictly top-down, with progressively smaller polygons for each level. A terrestrial ecosystem represents a volume of organic material within the environmental earth system, which is separated from neighboring ecosystems with reasonable divisions based on climates, landform, hydrology, biota, soil, and physiography, as illustrated in Fig. 1 and Eq. (1). This real-world model can theoretically be precisely modeled using E [I, J] matrix method (Gunaydin et al. 2022).

Interpretation of ecological phenomena requires consideration of scales and their consequences. To establish comprehensible connections between small-scale site-specific measurements and regional-scale phenomena, parallel implementation of both bottom-up and top-down approaches is necessary (Wessman 1992). Direct investigations at both small and large scales are required to understand complex scale interactions, and knowledge of small-scale dynamics alone is insufficient to predict large-scale processes. An important symmetry matrix E [I, J] directs the hierarchical system in terms of prediction or relation, which posits that components of an ecological entity existing at lower levels always operate at a higher frequency or change at a higher rate than components above them (Waltho et al. 1994). The identification or definition of hierarchical levels can be made in terms of tangible boundaries that are spatial hierarchies and related, as explained by Wu and Davis (2002), and Wu (2013). Thus, hierarchical theory can be used to identify and order hierarchical levels to simplify a complex system, and the dimension of the system is significantly reduced, as expressed by Eq. (9) and Eq. (10). Consequently, understanding the level of organizational structure is essential for comprehensively understanding the system (Waltho et al. 1994; Miller 2008; Mueller et al. 2014).

Components can be defined and selected at the level of the organization. The weights of effect and importance demonstrated a significant relationship between the two regional ecosystems. The ranks of the effect and importance (Table 3) illustrated the environmental factors' fundamental influences and produced similar or dissimilar ecosystems on the regional and global scales. Moreover, the hierarchical ecosystem has comprehensive structures that can be systematically organized (Rietman et al. 2011; Kheybari et al. 2020).

4.3 Bottom-level components and objectively defined ecological sites or vegetation stands

The bottom level of the ecological hierarchy is utilized to evaluate the condition and trends of rangelands (Creque et al. 1999; West et al. 2005; Zhang et al. 2021), providing crucial information for natural resource planning and management. Ecological site mapping is a constructive approach for assessing resources, conducting environmental analyses, and monitoring natural resources (Cleland et al. 1997). In the study cases mentioned, the bottom level of ecological sites and vegetation stands served different purposes. In Utah, ecological sites were determined based on soil types for land use and resource management, while vegetation stands were identified by homogenous vegetation (Table 1). Yukon's ecological sites were identified as the climax community Lodgepole Pine Spruce-Grass-Lichen. (Table 2). To differentiate between regional ecosystems at bottome level, there is a lack of plant species that are commonly shared. As a result, a comparison was made between the ecological sites of the two regions, and the pH values were chosen as a component factor in the E[I, J] matrix.

4.4 Assessments of the component effect and importance values and ranks

The component effect values ${W}_{i }$of the ecosystem hierarchies exhibited a significant relationship with the component importance values${V}_{i }$ (R² = 0.8025, P < 0.01). At the Domain level, the hot month mean temperature was defined as the Dry Domain's climate factor, and the cold month mean temperature was defined as the Polar Domain's climate factor. Their effects ranked third across the multiple levels of the two regional ecosystems. The second-ranked effect component was associated with cold month mean temperature, which significantly affected the upper focal level of the two regional ecosystems, resulting in significant differences and dissimilarities between the two regional ecosystems. Average Annual Temperature at level three (U3/Y3) ranked first as the component effect to the two regional ecosystems.

We found that the pH value's importance rank is first component to Ecological Site U8 or Ecosite Y9. This indicated in these bottom levels that soil condition played similar function. The importance ranked second was the ratio of erosion 30^o divided by height for the fifth layers (U5/Y5). The importance ranks are varied because the same environmental factor may have both positive or negative effects on the two ecosystems, or they produce positive on one ecosystem and negative effects on another (Table 3).

To summarize, applying hierarchy theory in the ecosystem classification of two Domains (Bailey's 100, 300) presents significant challenges and constructive opportunities in the land ecosystem classification. Our research yielded the following findings:

When applied to different global ecoregions, the Köppen climate classification system helps verify and examine the Domains as the top-level ecosystem land classification. Focal level components and ecological features should focus on regional climate features, landforms, hydroregimes, soil, and parent materials. The ecological site and vegetation stand can objectively define the bottom level.

The hierarchy of spatial resolution measurements should be addressed to account for mesoscale heterogeneity because it captures variability within the landscape. In addition, landscapes on the regional scale are crucial in scaling properties when using a top-down approach.

The classification of ecosystems into different levels depends on the complexity of the process being studied and its characteristics, which poses a challenge when quantitatively comparing diverse ecosystems. To overcome this challenge, it is essential to thoroughly understand an ecosystem's components associated with different scales and levels.

The lower level of ecosystem classification can be built-in using a computer algorithm and affordable application in ArcGIS software.

Theoretically, a top-down hierarchical approach or bottom-up reconstruction can be decomposed. Then, the component matrix and quantitative properties from Eq. (3) to Eq. (8) can be used to examine the component effect and importance features.

Once the system's dimension is reduced to less than ten levels, a typical result is quantitatively understandable and comparable between different ecosystem classifications. The Real-World Component Model quantitatively assessed the component effect and importance features.

The component is the general concept of environmental factors. Therefore, the component value used for the comparison could be one of the environmental features.

Acknowledgments

Correspondence author participated in all research and studies. Thanks to Simon Fraser University Library Open Access Funds for eligible journal support, Dr. Shivanand Balram from the Department of Geography provided GIS online source and reviewed the manuscript.

Funding

Western Utah ECL Project Fund from Utah State University (D910-0210). Haibei Alpine Ecosystem Study Project (Finding 90-0318). Assessment of Ecosystem Classification of Land in Different Continents, research funding (ICSA-funding-2322a) was supported by Instant Calling Spatial Arch Lab, Burnaby, Canada.

Author's contributions

Authors have contributed to this manuscript and approved the final manuscript.

Conflict of Interest

The authors declare no conflict of interest.

Ethics approval and consent to participate

Authors confirmed that there is no ethical conflict.

Consent for publication

Authors have read the manuscript carefully and agreed to submit it for publication.

Competing interests

Authors declare that there are no competing interests.

Availability of data sources

Study sites: Western Utah State of the United States, Click on the site 1 weblink:

Yukon Territory of Canada, click on the site 2 weblink:

ArcGIS Software Version: 3.1 available via ESRI partner http://icomlink.com/

DEM data for Yukon Territory download site: https://maps.canada.ca/czs/index-en.html

GET online protocol: https://global-ecosystems.org/, ( Accessed December 16, 2022)

Standard Ecoregions of North America: https://digital.library.unt.edu/ark:/67531/metadc100519/m1/1/

Pseudocodes

1. Group-Verify-Test 1

TestTopLevelGroup = function(f,n)

local i, G;

for i in [1,NrGroups(n)] do

Print(n, ":", i, "/", NrGroups(n), "\r");

G = Group( n, i );

if f(G) then

Print("\n");

return [n,i];

//in Polar Domain

Print("\n");

return fail;

end;

2. Subgroup-Verify-Test 2

[This size belongs to next level of the SmallGroups library]

NextLevelGroupsInformation(15);

G:=NextLevelGroup(i,2);

//Set group of size 15

AllSmallGroups(Size,15,NilpotencyClassOfGroup,p);

// print [ [ i, p ], [ i, p ], [ i, p ] ]

List(last, IdGroup);

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Improving Hierarchical Ecosystem Structures and Multicriteria Evaluations for Current Land Ecosystem Classification

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Version 1

Abstract

Figures

1 Introduction

2 Methodology

2.1 Conceptual Model

2.2 The ecosystem component effect and importance features and their weights

2.3 Definition of a group and a subgroup

2.4 Two study sites and Data Sources

2.5 Procedures of ECL's validations and formations

2.6 Ecosystem components and their comparable values

2.7 Comparison of the component values between two regional ecosystems

3 Results

3.1 The Validation of Top-Level Ecosystem Classification between the United States and Canada

3.2 The Formation of Ecosystem Classification in Western Utah of the United States

3.3 The Formation of Ecosystem Classification in the Yukon Territory of Canada

3.4 ECL's comparison by the component values between two regional ecosystems

4 Discussion

4.1 Top-level Domain and its verification

4.2 Focal-level components and ecological features for two global continental ecoregions

4.3 Bottom-level components and objectively defined ecological sites or vegetation stands

4.4 Assessments of the component effect and importance values and ranks

5 Conclusion

Declarations

Availability of data sources

References

Status:

Version 1

Levels	U1/Y1	U2/Y2	U3/Y3	U4/Y4	U5/Y5	U6/Y6	U7/Y7	U9/Y8
U\(ia\)	0.982	0.055	0.852	0.427	0.524	0.217	0.243	0.728
Y\(ib\)	0.189	-0.998	-0.505	0.904	0.852	0.976	0.970	0.685
\({W}_{ia }\) Eq. (4)	0.793	1.054	1.368	0.478	0.328	0.759	0.728	0.043
\({W}_{i }\)Eq (5)	14.30	19.00	24.60	8.60	5.90	13.70	13.10	0.80
Effect Ranks	3	2	1	6	7	4	5	8
\(Via\) Eq. (6)	1.171	0.943	0.359	1.331	1.376	1.193	1.213	1.414
\(Vi\) Eq. (7)	13.10	10.50	4.00	14.80	15.30	13.30	13.50	15.70
Importance Ranks	6	7	8	3	2	5	4	1
Note: R² = 0.8025, P < 0.01 for the weights of \({W}_{i }\)and\({V}_{i }\)