Influence of Spatial Distribution on the Regeneration of Piptadeniastrum africanum and Ocotea usambaernsis in Kalikuku, Lubero, North Kivu, Democratic Republic of Congo

The aim of our study is to highlight the spatial structure of the trees and to determine its influence on the natural regeneration of the Kalikuku dense forest, with a view of its optimal conservation and enhancement. Data collection was done by measuring diameter at breast height along 10 plots of 0.5 ha in size. In analyzing these data, the Dajoz test was used to determine the horizontal spatial distribution pattern of the two most abundant tree species in the forest (Piptadeniastrum africanum and Ocotea usambarensis). The χ2 test was used to compare the frequency distribution of diameter classes for the two species tested. To estimate the difference between the number of seedlings in aggregate versus non-aggregate areas, the Wilcoxon signed-rank test was used. In addition, the equability index was used to test the preponderance of proportions between diameter classes. Finally, the natural regeneration index was evaluated.


Introduction
In a forest, the spatial structure of the trees depends on their density and hori-zontal distribution, which can be random, aggregated or uniform [1] [2]. Natural regeneration is achieved by vegetative propagation through offshoots from existing stumps and by germination of seeds from mature trees [3]. [4] shows that spatial structure and natural regeneration of trees are intimately linked and play an important role in forest dynamics. In addition, human disturbances affect the spatial structure and natural regeneration of trees.
Regeneration is therefore the basis of the dynamic and demographic balance of plant populations, ensuring the renewal of individuals and the sustainability of species [5].
These are the uncontrolled removal of forest resources, extensive agriculture and forest fires that [6] and [7] consider being the most harmful given the frequency and extent that they affect in a short period of period.
The present study focuses on the dense forest of Kalikuku Reserve, which has enjoyed "protected area" (Nature Reserve) status since 1952 [8].
As this forest is surrounded by the villages of Vwandanze, Kimbulu and the agglomeration of Lubero, the local populations cannot help but illegally harvest the various forest resources they need. Its conservation is thus compromised. In development and sustainable management of natural forest ecosystems and the Kalikuku dense forest in particular, this study is therefore necessary.
The central hypothesis to be tested in this research is that the spatial distribution pattern of the trees influences the natural regeneration of Kalikuku dense forest.
The aim of this study is multiple. The main purpose is to determine the density of trees in the Kalikuku dense forest, to analyze their horizontal spatial distribution, to show the effect of the spatial pattern found on the number of seedlings and to evaluate the state of natural regeneration of the main tree species, in this case the first two most abundant tree species in this forest.

Study Site
Geographically, the Kalikuku Forest Reserve is located 7 km from the chief town Like Lubero and its surroundings, this reserve is between 29˚30' Longitude East, 00˚30' Latitude South, with an altitude varying between 1830 m and 2000 m, thus forming part of the highlands of Lubero territory [12].
The dense forest of Kalikuku enjoys a tropical climate of Af type [13]. It covers an area of approximately 89 ha spread over a hilly terrain whose highest peak reaches 2000 m. The soils of the Beni-Lubero region are derived from the bedrock that is mostly clayey. It appears from this work that the soils of the highlands in the extreme of North Kivu are essentially clayey and weakly ferritic, crystalline terrains of the Lower Cambrian [14].

Sampling Method
To establish the list of tree species and their density in Kalikuku dense forest, data collection was carried out by measuring diameter at breast height (dhp). However, only data with dhp ≥ 10 cm [16] were kept for further analysis under [17]. These measurements were made along 10 plots spread over a 2000 m long layon through the forest in agreement with [18]. The width of a plot is 20 m while the length was 250 m. For each plot, counts of seedlings (dhp < 10 cm) of each of the more abundant tree species were also made in aggregate (A) and non-aggregate (B) areas. Next, we counted the number of tree seedlings in all plots for the respective species.
Thus, the seedling count was conducted in these two plots to have paired or matched samples. The identification of tree species was based on the nomenclature of [19].

Data Analysis Method
In terms of the horizontal spatial distribution of trees, [1] [2] distinguish three horizontal spatial models: the random horizontal spatial model when, given the location of an individual, the probability that another individual will be found in its vicinity is unaffected; the aggregated horizontal spatial model when this probability is increased; and the uniform horizontal spatial model when this probability is reduced. In this study, the horizontal spatial distribution model of the trees was tested and confirmed by the method of [20] (Da) adapted to small samples. This test was applied based on the number of trees counted on an equal inventory area for all 10 plots (10 = pn). Further analysis was given by the values of λ = 2 σ/m; 2 σ being the variance and m the arithmetic mean. With a uniform distribution, λ < 1; in a random distribution λ ≈ 1; and in an aggregated distribution, λ > 1.
The value of λ varies, for a probability rate, between confidence limits that are a function of the number of samples np. The deviation from unity of λ is significant for α = 0.05 where Da > β (in this case, Da = λ − 1 and The effect of aggregates on the number of seedlings was determined using the Wilcoxon signed-rank test (W) [21]. This test is most appropriate for comparing paired or paired numbers in this case, the numbers of tree seedlings counted in aggregate and non-aggregate areas of the same transect. Finally, the value of the natural regeneration index (Rn) was determined by the ratio of the proportion of seedlings (dhp < 10 cm) to other three individuals (dhp ≥ 10 cm). According to [24], if the value of this index is less than unity, the population is in deficit; if it is greater than or equal to unity; the population is balanced, i.e., in terms of the distribution of tree individuals in diameter classes, the numbers continue to decrease as one moves from the lower to the higher diameter class.

Analysis of Tree Species Density in Kalikuku Dense Forest
In Kalikuku Dense Forest, 2169 individual trees of 30 species were identified. Table 1 and Figure 3 present the list and density of these identified species. The average density of trees in Kalikuku dense forest is 541 feet/ha. The two most represented species are Piptadeniastrum africanum and Ocotea usambarensis, whose relative abundance is 20.3% and 17% respectively, with a density of 439 and 311 trees/ha, respectively.    shows the test of the horizontal spatial distribution model according to [25] (Da). Individuals of the main tree species in Kalikuku dense forest are spatially distributed according to the aggregated model. Indeed, λ > 1 for all three species tested. For α = 0.05, this deviation from unity is significant given that Da values are well above β, i.e. Da > 0.9 (Table 2 and Figure 4).

Analysis of Natural Regeneration in Kalikuku Dense Forest
The values of the equitability index confirm that for both species, the seedling class (dhp < 10 cm) contains more individuals than the other diameter classes. Indeed, this index is equivalent to R = 0.14 for Piptadeniastrum africana and R = 0.12 for Ocotea usambarensis. Thus, the diameter class does not share equally the pro- Indeed, for Piptadeniastrum africana, Rn = 2.6 and for Ocotea usambarensis, Rn = 1.1 (Table 4 and Figure 6).   Figure 6. Regeneration index values for the two most abundant two species in Kalikuku dense forest.

Discussion
In the Kalikuku dense forest, the analysis of tree density confirms the observations of [26] on the preponderance of Piptadeniastrum, Carapa and Ocotea species in Afromontane forests. Furthermore, the density recorded (541 plants/ha) is lower than the average of 600 plants/ha observed in other dense forests of the Guineo-Congolese domain, notably by Lebrun [19]. This indicates that the Kalikuku forest is at a less advanced stage of evolution than those described by [27] [28]. In fact, the younger the dense forest, the more it presents numerous shrubs that are not widely spaced, which is the opposite for an old stand with large, widely spaced trees. This density obtained remains, however, in the same order of magnitude generally obtained in tropical Africa where the density of trees in the various inventories varies between 368 and 645 feet/ha [29].
The distribution of trees in diameter classes follows a regularly decreasing trend, with a maximum in the first diameter classes. A similar conclusion was reached in the Dja Faunal Reserve in Cameroon by [29]. In nature, such a diametric distribution reflects a state of equilibrium [30], which is itself synonymous with good natural regeneration [5]. This shows that, thanks to the growth of numerous seedlings and via their recruitment into the higher diameter classes [31], the Kalikuku forest will be maintained.
The analysis of the horizontal spatial distribution by the test [20] shows that the individuals of the trees in Kalikuku dense forest are distributed in an aggregated way. This aggregated spatial structure in turn influences the state of natural regeneration in this forest. The state of balanced regeneration is confirmed by Rn values that are all above unity [24]. Ecologically, the observed aggregation of trees can be explained either by the variation or heterogeneity of environmental characteristics, or by the genetic characteristics and behavior of living beings of the same species that often tend to group together [1] [2] [25]. In Kalikuku, the aggregated pattern of spatial distribution of trees is explained by variation in soil characteristics. The soil is silty in structure on the hilltops, whereas it is relatively deep and fine on the slopes and towards the lowlands. In addition, the spatial structure determines the local environment around each tree (in particular the number of neighbors) and thus its growth conditions. This local environment modifies the expression of natural processes such as growth, mortality and regeneration of the stand; this can lead to a local monospecific composition [32]. This trend is confirmed for the Kalikuku dense forest in which all the two most abundant tree species are of different genera.
These authors point out that density is a particularly important concept in forest management because it provides information on the degree of occupation of space by the stand. In the case of the Kalikuku dense forest, the fact that there is a balance in natural regeneration means that it is not necessary to introduce other species for restocking. Furthermore, the density of 541 trees/ha is within the range known in tropical Africa [29]. However, this density of trees observed in the Kalikuku dense forest shows that there is intense competition between these trees for resources.
The behavior of the juvenile stage of the Kalikuku rainforest provides more information about the future of this ecosystem. Indeed, the regeneration of a tree species is subject to the density and spatial distribution of individuals [33]. Thus, the preponderant proportion of seedlings found in the Kalikuku dense forest is a sign of a balanced regeneration. This conclusion corroborates the observations of [34]- [40].

Conclusion
We note that the aggregated horizontal spatial structure of the trees in the Kalikuku dense forest favors natural regeneration in a balanced state despite the many factors of disturbance of anthropic origin that are exerted on this ecosystem. The present analysis constitutes an important argument in favor of taking integral protection measures to maintain the good natural regeneration of this forest. It is therefore not possible to introduce species by reforestation in the Kalikuku dense forest. These protection measures would focus on maintaining the integrity of the forest, in particular by preserving it from any action that could disturb the spatial structure of the trees, such as logging and clearing.