2.1 Citrus production basins and the experimental set-up
The study was conducted in the humid forest zone of Cameroon, which has two agro-ecological zones:
(i) the monomodal rainforest zone (latitude 2° 6' to 6°12' N, longitude 8°48' to 10°30' E, altitude: 200-800 m). It is a very humid and hot area, with average annual temperatures ranging from 22 to 29 °C and relative humidity between 85 and 95 %. The average annual rainfall ranges from 2500 to 4000 mm and even 11000 mm in some places. It is characterized by a dry season of 3 months (December to February) and a rainy season of 9 months (March to November). The Muyuka site, located in the administrative region of the South West was chosen;
(ii) Bimodal Rainforest Zone (latitude 2°6'-4°54'/5°48' N, longitude 10°30'-16°12' E, altitude 500-1000 m). The climate in this area is hot and humid with temperatures around 25 °C and an average relative humidity of 75 %. Rainfall is divided into two rainy seasons, the first of which extends from March to June; and the second from September to November. The study sites were established in Bokito, Evodoula, Bikok, and Boumnyebel. All of these sites are located in the Centre Region (Aulong et al. 2000; Ndo 2011).
In each site, CBAS with at least 12 citrus trees (all species), a significant number of forest trees, and other fruit trees were preferentially selected. These plots are located in villages that are more or less distant from each other to be representative of the entire site. A network of 33 CBAS was thus established: (i) five in Boumnyebel, (ii) six in Muyuka, (iii) seven in Bikok, (iv) seven in Evodoula, and (v) eight in Bokito.
2.2 CBAS mapping and tree identification and characterization
CBAS mapping consisted of acquiring spatial and structural data on the different trees that make up the plant stand to analyze the interactions that take place within it. However, the mapping of the sampled experimental units requires the acquisition of explicit spatial data, indicating the cartesian coordinates (x, y) of all perennial plants, having a diameter at breast height (DBH) ≥ 10 cm. Mapping was performed using a Leica TCR 703 Total Station following the method explained by (Mvondo et al. 2022).
For each tree, the names of the species and family were identified. Five groups, referred to here as "sub-populations" were previously defined: (i) cocoa trees, (ii) forest trees, (iii) other fruit trees, (iv) citrus trees, and (v) palms. Trees characterization consisted was done, and consisted essentially of taking measurements on trees and characterizing their foliage. Data taken were: the shape of the canopy (which can be ellipsoidal, semi-ellipsoidal, cylindrical, or conical), the trunk circumference (allowing to have the DBH), the trunk height, the canopy width and height, the tree height and finally the foliage density (opacity). This last value was quantified using a scale from 0 to 100: at 0, 100% of the light passing through the tree's foliage reaches the ground, while at 100, 0% of the light passing through the foliage reaches the ground.
2.3 Citrus spatial structure analysis
Analysis of the spatial structure of citrus in each plot was performed by Ripley's method, using the modified Besag L(r) function (Goreaud and Pelissier 2000; Gidoin et al. 2014). Indeed, for the Poisson process (random distribution), which serves as the null hypothesis, the expectation of the number of neighbors E(r) = λπ r², and thus K(r) = πr². For an aggregate process, the points have on average more neighbors than for the null hypothesis, and thus K(r) > πr². Conversely, for a regular process, the points will have on average fewer neighbors than for the null hypothesis, and K(r) < πr² K is the expectation of the number of neighbors around each point. K regular < K random < K aggregate (Goreaud and Pelissier 2000; Gidoin 2013b; Ngo Bieng et al. 2013). The function K(r) (Equation 1) is not easy to interpret because the curve obtained for the null hypothesis is a parabola, so we used L(r) which is derived from it (Equation 2). L(r) = 0 indicates a random distribution, L(r) > 0: aggregated distribution, L(r) < 0: regular distribution.
![](data:image/png;base64,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)
In the second step, a hierarchical cluster analysis based on the Euclidean distance between the L(r) function values of citrus fruits from different plots was performed. These analyses were done using the ade4 and ads packages of the R.4.1.1 software.
2.4 Shade rate quantification and interactions between CBAS parameters and PFRD intensity
The concept of shade rate used in this study refers to the ''number of hours of shade'' received by a point on the sampled area, calculated over the simulation period. This shade rate was calculated for each citrus tree within the sampled CBAS using ShadeMotion 5.1.4.2 software as described by (Mvondo et al. 2022).
Shademotion allows counting the hours of shade stored at each "point" of a plot with trees during a specific period. During the simulation, hours (moments) are the basic time units of the simulation (Somarriba et al.). The amount of shade received by the citrus trees was calculated for 1 year (between 01 January 2022 and 31 December 2022). The frequency of solar movements was set every hour with 10 hours of sunlight per day (07:00 to 17:00). As the study was conducted in the tropics and near the equator, it was assumed that the sunshine duration was equal for all days of the year. In addition, the topographic slope angle was not taken into account because most of the plots studied were located on relatively flat land. Equation 3 below measured the total moments, which allows the total number of moments in a simulation to be calculated. To account only for the shade, cast on the ground by shade trees, citrus and cocoa trees were excluded from the simulation. The shade rate was noted from the location of the tree on the shade map obtained after the simulation.
![](data:image/png;base64,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)
With Mt: total moments; NJS: number of days in the simulation; NMJ: number of moments per day.
Once the shade rate received by each citrus tree was calculated, they were grouped into three categories: (i) citrus trees that received < 30% shade were considered as those not receiving shade; (ii) citrus trees that received 30 < shade rate < 70% were considered those placed under light shade; and finally, (iii) citrus trees that received > 70% shade were considered those placed under dense shade.
2.5 Interactions between CBAS structural characteristics and PFRD intensity
We constituted 9 treatments by considering the possible combinations between spatial structure patterns (aggregated, regular and random) and shade rate levels (dense shade, light shade, and no shade). Thus, the treatments were constituted as follows: Regular-Dense shade, Regular-Light shade, Regular-No shade, Aggregated- Dense shade, Aggregated-Light shade, Aggregated-No shade, Random-Dense shade, Random-light shade, and Random-No shade. Once data normality was verified, Anova was performed between treatments and PFRD intensity. When significant differences were detected, comparisons of means were made using the Tukey test at P=0.005. These analyses were done with the R software 4.1.1.1.
To determine the combined effect of shade rate and spatial structure on PFRD intensity, generalized linear mixed effects models (GLMM), with a binomial error structure, using the glmer function of the lme4 package of R 2.14.0 were performed; with citrus production basins as a random effect. To compare the effect of different trained treatments on the means, Tukey contrasts were used with the glht function of the multicomp package of R 4.1.1.1 When only the main effect of shade was significant in the GLMM, the interaction means argument to compare the mean shade levels on the interaction terms was used. When a significant interaction between treatments in the GLMM, a comparison of all combinations was made.