Mathematical Modeling of Ecological Associations and Spatial Distribution of Nepenthes Tobaica in Ria-Ria Village, North Sumatra: Implications for Conservation and Management

Indonesia is one of the world's richest biodiversity hotspots, with at least 47 distinct natural ecosystems teeming with plant and animal life, including numerous endemic species [1, 2]. Among these, Nepenthes, a genus of carnivorous plants, is particularly notable. Indonesia harbors approximately 15.5% of the world's flora, and its archipelago, especially Kalimantan and Sumatra, represents the global center of Nepenthes diversity [3, 4].

Nepenthes tobaica, an endemic species in Sumatra, is adapted to various ecological niches, often found in nutrient-poor environments where it relies on carnivory for nutrient acquisition [5, 6]. Despite its ecological significance, nepenthes tobaica faces increasing threats due to habitat fragmentation, land-use change, and environmental degradation, which have led to population declines [7]. Conservation efforts for this species are hindered by limited quantitative studies on its ecological interactions and habitat preferences, particularly in terms of its associations with other plant species and how these relationships influence its distribution and survival [8, 9].

While previous studies have primarily focused on the taxonomy, morphology, and habitat characteristics of Nepenthes, there is a lack of research that quantitatively analyzes the ecological relationships of nepenthes tobaica within its plant community. Understanding these associations is crucial for conservation strategies, as plant species interactions can influence habitat stability, species resilience, and potential reintroduction efforts. This study advances the understanding of nepenthes tobaica ecology by integrating mathematical models and ecological indices to quantify species associations and distribution patterns. The application of quantitative methods in studying Nepenthes ecology remains underexplored, making this approach novel in several ways. Unlike traditional qualitative descriptions, this study employs mathematical models to measure species diversity, distribution, and association. The use of the Ochiai index allows for precise determination of association strength between nepenthes tobaica and coexisting species. By identifying key species interactions and environmental conditions supporting nepenthes tobaica, this study provides actionable data for habitat conservation and management [10, 11].

To address these gaps, this study aims to analyze the population structure of nepenthes tobaica in the Ria-Ria Village Forest, Pollung District, Humbang Hasundutan Regency and quantify its ecological associations with other plant species using mathematical models and ecological indices. The study employs a robust quantitative framework, incorporating vegetation analysis metrics such as density, relative density, frequency, relative frequency, dominance, and the Importance Value Index (IVI) [12, 13]. The Ochiai index is used to measure species co-occurrence, while several diversity indices, including the Shannon-Wiener diversity index (H’), Margalef’s species richness index, species evenness index, and Morisita’s index, are applied to assess species diversity and spatial distribution. Additionally, the Basal Field Area (BFA) formula is used to quantify tree stem coverage.

By integrating these mathematical models, this research establishes a reproducible, quantitative foundation for ecological studies on nepenthes tobaica. The findings will not only enhance conservation strategies but also serve as a reference for future ecological research on Nepenthes and other carnivorous plant species.

Identification of Plant Species in the Habitat of Toba Semar Bag (Nepenthes Tobaica) in Ria-Ria Village

Based on the results of the research that has been carried out, 21 species of lower plant level vegetation were found in location 1, 13 species in location 2 and 8 species of lower plant level vegetation in location 3 around the habitat of the toba semar bag (nepenthes tobaica) in Ria-Ria Village, Pollung District, Humbang Hasundutan Regency. The growth of these vegetation in the village in all three locations is very good and is still very much found, indicating that the environment at the research site still supports the sustainability of the species. However, for this level of growth, eradication or burning is often carried out because the local community is dominant in their livelihoods as farmers. The lower plant level vegetation found in the three research locations in detail can be seen in Table 2.

Table 2. Undergrowth plant community around nepenthes tobaica in Ria-Ria Village, Pollung District, Humbang Hasundutan Regency

At the tree growth level, 10 tree species were found in Site 1, 4 tree species in Site 2, and 1 tree species in Site 3 that grew around the habitat of the toba semar bag (nepenthes tobaica) in Ria-Ria Village, Pollung District, Humbang Hasundutan Regency. These species grow well in the research location and coexist with the toba semar bag (nepenthes tobaica). The vegetation at the tree level found in detail can be seen in Table 3.

Table 3. Tree community around nepenthes tobaica in Ria-Ria Village, Pollung District, Humbang Hasundutan Regency

Vegetation found around nepenthes tobaica habitat, both at the understorey and tree level, plays an important role in supporting the survival of this species. Understory plants such as Arsam (Pteridium aquilinum) and Appapaga (Centella asiatica) can help maintain soil moisture in nepenthes tobaica habitats. This is important considering that the pouch plant needs a moist environment to grow optimally. On the other hand, trees such as Pinus (Pinus merkusii) and Simartolu (Schima wallichii) provide shade that protects the pouch semar from direct sunlight, while creating a microclimate that supports its growth [18-20].

Environmental factors are factors that greatly affect the growth of toba semar bags (nepenthes tobaica) in a habitat. In this study, toba semar pouches (nepenthes tobaica) were found in 3 locations with altitude variations between 1443.6 to 1528 meters above sea level. The temperature at the research site ranged from 20.98℃ to 22.16℃ with humidity ranging from 50% to 86%. Temperature and humidity conditions in this location are within the normal range of Nepenthes growth. Nainggolan et al. [6] stated that this plant can survive in air temperature and air humidity of 20-32℃ and 67-93% respectively. Light intensity at the sites ranged from 188 to 197 lux, the soil type at the three sites had a clay texture, which could affect drainage. Nepenthes generally grows on nutrient-poor soils but with high moisture [16]. The extreme slope level (46.63-62.15%) indicates that this habitat is located in a steep area, which is in accordance with the ecological characteristics of Nepenthes in the wild, especially on cliffs and mountains. All sites were in agroforestry areas, which provided partial shading benefits while minimizing habitat disturbance. The environmental factors in which the toba antlered pouch (nepenthes tobaica) was found can be seen in detail in Table 4.

Table 4. Environmental factors of the Toba Semar Pockets Habitat (nepenthes tobaica)

Vegetation Analysis and Association of Nepenthes Tobaica at Understory, Seedling, Sapling, Pole, and tree Levels

The results of vegetation analysis show that the vegetation composition at the research site consists of 36 species. The many types of species found at the research site indicate that the research site still has a balanced ecosystem, so it still has quite abundant diversity. The results of vegetation analysis and associations with the highest IVI value in the plant community around the habitat in Ria-Ria Village in detail can be seen in Table 5.

Table 5. IVI and association of nepenthes tobaica in plant communities surrounding habitat in Ria-Ria Village, Humbang Hasundutan Regency, North Sumatra, Indonesia

Note: S: Significant, NS: Not Significant

Table 5 presents the IVI and Association of nepenthes tobaica in Plant Communities Surrounding Habitat in Ria-Ria Village, Humbang Hasundutan Regency, North Sumatra, Indonesia. The table is divided into multiple locations and vegetation types (undergrowth, pole, and tree).

Nepenthes tobaica, the focus species, is present in all three locations within the undergrowth category, with its Importance Index varying across locations and being highest in Location-3. While most species exhibit a positive association with N. tobaica, the majority of these relationships are not statistically significant. However, there are a few significant associations, both positive and negative. The dominant species differ among locations, with Pteridium aquilinum, Dicranopteris sp., and Struthiopteris spicant having the highest IVI in Location-1, Location-2, and Location-3 undergrowth, respectively. The comprehensive data provided in the table includes vegetation layers (undergrowth, pole, and tree), showcasing the rich plant community structure and biodiversity in the study area, with the varying associations and importance indices suggesting a complex ecological relationship between N. tobaica and other plant species within its habitat.

A Pareto diagram at Figure 2, visually represents the IVI and association of nepenthes tobaica with other plant species. The bars represent IVI values for different species in descending order, while the line shows the cumulative percentage of IVI values. This helps identify the most important species and demonstrates the potential application of the Pareto principle (80/20 rule).

Figure 3 displays the relationship between the Importance Value Index and the Ochiai Index for plant species associated with nepenthes tobaica. It shows how a species' ecological importance correlates with its association strength with N. tobaica, reveals species distribution patterns, identifies key species with high IVI and OI values, highlights unusual species (outliers), and may indicate groups of species with similar ecological roles. The range of IVI and OI values shown reflects the diversity of ecological importance and association strengths within the community. 

Pareto diagram in Figure 4 showing the IVI and association of nepenthes tobaica. The diagram visually represents the relative importance and association of different factors related to nepenthes tobaica, a species of pitcher plant. These frequencies are compared across the three study locations and broken down by the plants' growth stages (understory, seedling, sapling, pole, and tree).

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Figure 2. Pareto diagram of the IVI and association of nepenthes tobaica

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Figure 3. Scatter plot to visualize the relationship between IVI and OI values for different species

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Figure 4. Diagram of count of association

Vegetation and Association Analysis of N. Tobaica at the Undergrowth Level

In the population at Site 1, 5 species of understory plants were found with the highest IVI values, namely Pteridium aquilinum (63.95), Cyperus rotundus (43.90), Themeda gigantea (22.26), Nepenthes tobaica (18.93), and Gaultheria leucocarpa (15.25). At the understory level, Pteridium aquilinum species from the Dennstaedtiaceaae family had the highest association value with a value of 0.96, which was positive and real. The lowest association value was found in Cyperus rotundus species with an association value of 0.86, negative and not real.

The highest Index of Importance (IVI) in the understory population at Site 2 was found in Dicranopteris sp. (74.65), Nepenthes tobaica (22.00), Pteridium aquilinum (20.60), Imperata cylindrica (17.07) and Melastoma melabathricum (11.85). Based on the calculation results, the highest association value was found in the Pteridium aquilinum species with a value of 0.78, which was positive and not real.

The highest IVI value in the population at Site 3 for the lower plant level was found in the species Struthiopteris spicant (216.84), Nepenthes tobaica (162.65), Imperata cylindrica (134.84), Melastoma melabathricum (35.78) and Pagit-pagit (17.89). At the lower plant level, species with the highest association value were found in Struthiopteris spicant with a value of 0.84, positive and not significant.

Vegetation and Association of N. Tobaica at Seedling Level

The highest IVI value at the seedling level in location 1 was found in Avicennia germinans (58.23), Saurauia blumeana Spreng (46.04), Macaranga gigantea (33.04), Basillicum polystachyon (20.42) and sp1 (18.50). Based on the calculation results, it was found that the species with the highest association value was Avicennia germinans with an association value of 0.67, positive and not real. The lowest association value was found in 3 species, one of which was Macaranga gigantea with a value of 0.15, was negative and not real.

The highest IVI value at the seedling level in the population at Site 2 was found in the species Macadamia integrifolia (151.03), Pinus merkusii (98.10), Calliandra calothyrsus (30.20) and Persea americana (20.67). At the seedling level, 2 species were found to be associated and 2 species were not associated with N. tobaica. The species with the highest association value was found in Pinus merkusii species with a value of 0.29, positive and not significant, while the species with the lowest value was found in Macadamia integrifolia species with a value of 0.12, negative and not significant.

The highest IVI value at the seedling level in the population at Site 3 was found in the species Saurauia blumeana Spreng (128.28), Silum (49.60) and Schima wallichii (36.67). At the seedling level population in location 3, the highest association value was found in Silum species with a value of 0.62, negative and not real. The lowest association value was found in Saurauia blumeana Spreng species with a value of 0.35, positive and not significant.

Vegetation and Association Analysis of N. Tobaica at Stake level

In the population at location 1, the highest IVI value at the sapling level was found in the species Avicennia germinans (61.24), Morinda tinctoria Roxb (22.01), Celtis tetrandra (20.69), Syzygium myrtifolium (19.69) and Leptospermum javanicum (19.63). Based on the calculation results, the highest association value was found in Avicennia germinans species with a value of 0.75, negative and not real. The lowest association value was found in Syzygium myrtifolium species with a value of 0.37, positive and not significant.

The highest IVI values at the sapling level in the population at Site 2 were found in the species Leptospermum javanicum (103.17), Macadamia integrifolia (37.57), Neonauclea calycina (15.08), sp2 (14.02) and Homalanthus populneus (8.47). In the sapling level population at Site 2, the highest association value was found in the species Leptospermum javanicum with a value of 0.82, positive and not significant. The lowest association value was found in 3 species, one of which was Macadamia integrifolia with a value of 0.08, negative and not significant.

The highest IVI value at the sapling level in the population at location 3 was found in Pinus merkusii species (65.61), sugar medicine (60.32), Helicteres hirsute (15.08), Antiapi (15.08) and Erythrina variegata (14.02). In the sapling level population at Site 3, the highest association value was found in Pinus merkusii species with a value of 0.71, which was negative and not significant.

Vegetation and Association Analysis of N. Tobaica at Pole level

In the population at location 1, the highest IVI value at the pole level was found in Laplacean sp. (84.04), Morinda tinctoria Roxb (32.04), Pinus merkusii (29.53), Quersus salicina (28.45) and sp3 (25.72). Based on the calculation of the highest association value found in Laplacean sp. with a value of 0.84, is negative and not real. The highest IVI value at the pole level in the population at location 2 was found in the species Coffea canephora pierre (109.79), Macadamia integrifolia (52.96), sp4 (28.85), Calliandra calothyrsus (28.22), and Pinus merkusii (27.67). At the pole level population in location 2, the highest association value was found in Pinus merkusii and Leptospermum javanicum species with a value of 0.50, positive and not significant. The lowest association value was found in Macadamia integrifolia species with a value of 0.16, negative and not significant.

In the population at location 3 at the pole level, 1 species was found, namely Pinus merkusii with an IVI value of 13099.68. At location 3 for the pole level, 1 species was found to be associated with N. tobaica with a value of 0.58, which is positive and not real.

Vegetation and Association Analysis of N. Tobaica at Tree Level

In the population at location 1, the highest IVI value at the tree level was found in Laplacean sp. (91.23), sp5 (21.05), Exbulandia populnea (17.54), Schima wallichii (17.54) and Pinus merkusii (14.04). Based on the calculation results, the highest association value was found in Laplacean sp. species with a value of 1.34, positive and real.

The highest IVI values at the tree level in the population at Site 2 were found in the species Macadamia integrifolia (151.03), Pinus merkusii (98.10), Calliandra calothyrsus (30.20) and Persea americana (20.67). In the tree-level population at Site 2, 2 species were found to be associated with N. tobaica and 2 species were not associated with N. tobaica. The highest association value was found in Pinus merkusii species with a value of 0.29, positive and not significant. The lowest association value was found in Macadamia integrifolia with a value of 0.12, negative and not significant.

In the population at location 3 at the tree level, 1 species was found, namely Pinus merkusii with an IVI value of 96.33. At location 3 for the tree level, 1 species was found to be associated with N. tobaica with a value of 0.58, which is positive and not significant.

Index of Diversity, Richness, Evenness of Species, and Morisita Index in Ria-Ria Village

Based on the calculation results, the values of the Diversity Index, Richness, Evenness of Species, and Morisita Index were found in the three research locations. The values obtained in the three locations are different, this shows that the three locations have different environmental conditions such as lighting, humidity, and soil structure that support the growth of diverse species. The values of Diversity Index, Richness, Evenness of Species, and Morisita Index in Ria-Ria Village in detail can be seen in Table 6.

Table 6. Values of diversity index, richness, evenness of species, and Morisita index in Ria-Ria Village

In the population of location 1, all growth stages have moderate diversity, namely understorey (2.00), seedling (1.60), sapling (1.52), pole (1.33), and tree (1.81) (Table 6). The species richness value in the Site 1 population at the understory (2.45) and pole (2.35) levels was low. At the tree level (4.04) is medium and at other levels, namely seedlings and saplings, is high. The species evenness index at the lower plant level (2.56) is high. At the seedling level (1.95) is categorized as low and at other levels, namely saplings, poles and trees are categorized as low. In the location 1 population, almost all growth levels have a clump growth pattern, namely at the seedling level (0.23), sapling (0.37), pole (0.42) and tree (0.20), only at the lower plant level (0.00) including random.

In the population of location 2, all growth stages have moderate diversity, namely understorey (1.66), seedling (1.03), sapling (1.34), pole (1.73), and tree (1.15). The value of species richness in the population of location 1 at all growth stages is in the low category. The species evenness index at almost all levels is in the low category, namely understory (0.61), seedling (0.74), sapling (0.75) and pole (0.83). At the tree level (1.04) is medium. Growth pattern of all growth stages including clumps.

In the population of location 3, the diversity value at the lower plant level (1.08) and saplings (1.15) is medium. The other levels were low, namely seedlings, poles and trees. Species richness at all growth stages is low. The species evenness index at almost all levels is low, namely at the lower plant level (0.52), saplings (0.72), poles (0.00) and trees (0.00). Growth pattern at all growth levels including clumps.

Based on Table 6, it can be concluded that location 1 has the highest H' value at the lower plant level (2.00) which indicates higher diversity than other locations. Similarly, species richness (Margalef Index) shows the highest species richness at Site 1, especially at the seedling level (5.15), while the lowest species richness is at Site 3 with a value of 1.19 at the tree level. This may be due to environmental pressure or human disturbance. Mansur et al. [20] stated that changes in land functions into agricultural land, settlements and other functions besides reducing the habitat area of a species can also affect changes in surrounding environmental factors so that many vegetation species are unable to survive. The highest species evenness index was also found at the lower plant level in location 1 (2.56), which indicates a more even distribution of species than other locations.