# Spatial heterogeneity of nitrification contributes to tree-grass coexistence in West African savannas

Sarah Konaré, Kouamé Fulgence Koffi, Simon Boudsocq, Jacques Gignoux, Jean-christophe Lata, Xavier Raynaud, Sébastien Barot

► To cite this version:

Sarah Konaré, Kouamé Fulgence Koffi, Simon Boudsocq, Jacques Gignoux, Jean-christophe Lata, et al.. Spatial heterogeneity of nitrification contributes to tree-grass coexistence in West African savannas. Journal of Ecology, 2024, 112 (1), pp.86-97. 10.1111/1365-2745.14220. hal-04304285

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1 Spatial heterogeneity of nitrification contributes to tree-grass

2 coexistence in West African savannas

3 Sarah Konaré¹,², Kouamé Fulgence Koffi²,³, Simon Boudsocq⁴, Jacques Gignoux²,

4 Jean-Christophe Lata², Xavier Raynaud² and Sébastien Barot²

5 ¹UFR Sciences biologiques, Département Géosciences, Université Pôle de Recherche

6 Korhogo, Côte d'Ivoire

7 ²Sorbonne Université, Université de Paris-Cité, UPEC, IRD, CNRS, INRAE, Institute of Ecology

8 and Environmental Sciences, iEES Paris, 75005 Paris, France

9 ³UFR des Sciences de la Nature, Station d'Ecologie de Lamto/CRE, Pôle de Recherche

10 Environnement et Développement Durable, Laboratoire d'Ecologie et du Développement Durable,

11 Université Nangui Abrogoua, 02 BP 801 Abidjan 02, Côte d'Ivoire

12 ⁴Eco&Sols, INRAE, CIRAD, IRD, Montpellier SupAgro, Univ Montpellier, Montpellier, France

13 Corresponding author: Sarah Konaré

14 E-mail: ksarahfaike@upgc.edu.cn

15 Adress: UFR Sciences biologiques, Département Géosciences, Université Pôle de Recherche

16 BP 1328 Korhogo, Côte d'Ivoire

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25 Abstract

26 1. In savannas, the coexistence between trees and grasses is determined by complex mechanisms based on water partitioning and disturbances. But little is known about the contribution of other resources such as N. In West African savannas, nitrification inhibition by grasses and nitrification stimulation by trees create spatial heterogeneity in nitrification fluxes and N stocks. Besides, savanna trees can also extend a part of their roots in the surrounding open area to take up N.

32 2. To investigate the role of the spatial heterogeneity of nitrification on tree-grass coexistence, we used a two-patch model simulating N dynamics between an open patch (without trees) and a tree clump patch (trees with grasses under their canopy). The open patch was characterized by a low nitrification rate while the tree clump patch was characterized by a high nitrification rate. Both patches were connected through horizontal fluxes due to soil horizontal exploration by tree roots. We tested coexistence for different spatial tree distributions as they are known to strongly influence savanna dynamics.

39 3. Our results show that the spatial heterogeneity of nitrification induces a spatial partitioning between ammonium (NH₄⁺) and nitrate (NO₃⁻) promoting tree-grass coexistence. As nitrification inhibition by grasses leads to high NH₄⁺ availability in the open, the possibilities of coexistence are optimized when trees have different preferences in the open versus under their canopy. Tree-grass coexistence is thus observed when grasses prefer NH₄⁺, while trees prefer NH₄⁺ in the open and NO₃⁻ under their canopy.

45 4. Contrary to random tree distribution, tree clumping enhances tree-grass coexistence. Intraspecific aggregation strengthens the effect of spatial heterogeneity, which decreases interspecific competition and favors tree-grass coexistence. By contrast, increasing the surface explored by tree roots in the open tends to increase tree-grass competition. This enhances the competitive ability of trees for N acquisition and consequently favors invasion by trees.
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5. **Synthesis.** This study shows that this new coexistence mechanism based on mineral N partitioning into NH<sub>4</sub><sup>+</sup> and NO<sub>3</sub><sup>-</sup> can be determinant in the functioning of West African humid savannas. This mechanism probably interacts with disturbance-based mechanisms, but such interactions should be studied through new models.

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**Keywords:** NH<sub>4</sub><sup>+</sup> versus NO<sub>3</sub><sup>-</sup> preference, nitrogen partitioning, nitrification, savanna, spatial heterogeneity, spatial tree distribution, tree-grass coexistence

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**Introduction**

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Savanna vegetation is characterized by a continuous layer of grasses intermixed with a discontinuous stratum of trees. The coexistence of many plant species has long been debated as it is in apparent contradiction to the principle of competitive exclusion stipulating that two species competing for the same resource cannot coexist over the long term (Hardin, 1960; Barot & Gignoux, 2004). In savannas, tree-grass coexistence has been attributed to two main causes, resource partitioning and disturbances (Sankaran et al., 2004)□. In dry savannas, the scarcity of resources, and especially water, leads to niche partitioning as grasses are more competitive than trees in the topsoil layers while trees can explore the soil vertically and take up water at greater depth (Schenk & Jackson, 2002)□. This niche differentiation through different rooting depths can favor coexistence between trees and grasses (Walter, 1971; Walker & Noy-Meir, 1982). In contrast to dry savannas, wet savannas are not limited by water and could turn into forests, but the presence of disturbances such as fire or herbivory reduces the density of trees (Sankaran et al., 2004; Staver et al., 2011)□. Fire is the main disturbance limiting woody cover by affecting the survival of tree seedlings and saplings (Gignoux et al., 2009)□. In the same way, herbivores such as grazers and browsers can have negative effects on grass and tree growth and therefore contribute to regulate the tree-grass ratio (Sankaran et al., 2008; Van Langevelde et al., 2003)□.

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In West African savannas, the dominant perennial grass species inhibit nitrification, nitrification being the process of transformation of ammonium (NH<sub>4</sub><sup>+</sup>) into nitrate (NO<sub>3</sub><sup>-</sup>) (Lata et al., 2004; Subbarao et al. 2009; Srikanthasamy et al., 2018)□. This biological nitrification inhibition (BNI)
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occurs through the release of grass root exudates impeding the activity of nitrifying microorganisms (Lata et al., 2004; Srikanthasamy et al., 2018). Because $NH_4^+$ is less prone to leaching than $NO_3^-$, keeping nitrogen (N) in the $NH_4^+$ form decreases N losses by $NO_3^-$ leaching and therefore maintains a high primary productivity (Boudsocq et al., 2009)□. By contrast, in the Lamto humid savanna (Côte d'Ivoire), the dominant tree species have been found to stimulate nitrification (Srikanthasamy et al., 2018). The mechanism explaining this stimulation is not known but one hypothesis would be that as for grasses, specific molecules from the tree root system directly impact microbial communities. Another hypothesis is that the observed increase of soil organic matter and soil humidity below tree canopy could also increase soil microorganisms activity and therefore mineralization and nitrification processes (Mordelet et al., 1993; Srikanthasamy et al., 2018)□.

In nutrient-limited ecosystems such as savannas, plant-soil feedbacks on N cycling can locally alter N availability (Knops et al., 2002) by creating a spatial heterogeneity in soil resources, and thereby influencing primary productivity. Trees and grasses, through their respective stimulation and inhibition strategies, could induce a resource partitioning, if grasses preferentially absorb $NH_4^+$ and trees $NO_3^-$ promoting tree-grass coexistence in the Lamto savanna (Boudsocq et al., 2012; Konaré et al., 2019). Some studies have shown that plant preferences for different chemical N forms (organic and mineral N) can facilitate their coexistence (Ashton et al., 2010; McKane et al., 2002)□. Spatial heterogeneity due to nitrification heterogeneity could further reduce niche overlap, likely decreasing interspecific interactions and promoting coexistence of different species even on a single limiting resource (Barot & Gignoux, 2004; Chesson, 2000; Huston & DeAngelis, 1994)□. This leads to a complex picture requiring a spatially structured model to understand the consequences of plant-soil feedbacks on $NH_4^+$ and $NO_3^-$ availability and tree-grass coexistence.

Many studies highlighted the relevance of spatial patterns in ecological dynamics (Grimm et al., 1996; Grimm & Railsback, 2012). For example, intraspecific aggregation decreases the strength of interspecific competition (Pacala, 1997; Stoll & Prati, 2001), which can slow down competitive exclusion (Armstrong & McGehee, 1980)□. Spatial tree distribution is known to play an important
role in savanna dynamics and is strongly affected by disturbances (Menaut et al., 1990). In addition, tree clumps are generally considered as nutrient-rich patches (Mordelet et al., 1993) and this higher soil fertility under tree canopy is partly due to the horizontal soil exploration by tree roots in the open as it improves nutrient transfers between the open and tree clumps (Konaré et al., 2021). While spatial heterogeneity tends to foster niche partitioning (Amarasekara, 2003), horizontal fluxes can minimize the impact of this heterogeneity by homogenizing $NH_4^+$ and $NO_3^-$ availability between the two patches (Barot et al., 2015; Barot et al., 2014). This could thus be influential for predictions of tree-grass coexistence.

In contrast to the work of Konaré et al. (2019) that does not consider spatial heterogeneity (all plants explore the same N pools) and Konaré et al. (2021) that focused on the effects of spatial heterogeneity of nitrification fluxes on N fluxes and N budget, the goal of this study is to analyze the role of the spatial heterogeneity in tree-grass coexistence. To do so, we used a modified version of the two-patch model previously published (Konaré et al., 2021) considering a patch of open area with a low nitrification rate and a tree clump patch with a high nitrification rate. These two patches are interconnected by horizontal fluxes (due to horizontal exploration of soil in the open area by tree roots). The novelty of this model relies on considering the relation between two model parameters (the proportion of tree roots in the open and the proportion of the savanna surface covered by tree clumps) that depends on spatial tree distribution. Using this general model, we tested the following hypotheses: (i) Compared to the mean-field model (Konaré et al., 2019), accounting for the existence of distinct N pools below and outside tree clumps fosters coexistence. (ii) Spatial heterogeneity in nitrification increases the likelihood of tree-grass coexistence with grasses preferring $NH_4^+$ and trees preferring $NO_3^-$ under tree canopy and $NH_4^+$ in the open. Indeed, this spatial heterogeneity leads to a spatial niche partitioning that reduces exclusion and favors coexistence. (iii) Tree-grass coexistence depends on spatial tree distribution and is facilitated when trees are clumped. More specifically, tree clumping reduces soil exploration by tree roots in the open and thus reduces competition between trees and grasses in the open. (iv) Increasing the surface explored by tree roots in the open increases
128 horizontal fluxes between the open and the tree clump patches, which increases the competition
129 between trees and grasses for N and consequently reduces the chances of coexistence.

130 **Two-patch model**

131 **Model description**

132 The two-patch model explores competitive interactions between trees and grasses through two
133 patches: an open patch occupied by grasses and some tree roots (patch 1), and a tree clump patch
134 occupied by trees with grasses growing below their canopy (patch 2) (Appendix S1). This model is a
135 spatially explicit extension of a previously published mean-field model (Konaré et al., 2019). The
136 model tracks N dynamics between plant compartments: grass biomass (G<sub>l</sub>) in the open and, grass
137 (G<sub>2</sub>) and tree (T) biomass in the tree clump patch, and soil compartments: soil organic matter (O),
138 ammonium (N<sub>A</sub>) and nitrate (N<sub>N</sub>) in both patches (see Fig. 1, Konaré et al., 2021). Spatial
139 heterogeneity due to nitrification inhibition (BNI) by grasses and nitrification stimulation by trees is
140 represented by a low nitrification rate in the open (n<sub>l</sub>) and a high nitrification rate under tree clumps
141 (n<sub>2</sub>). Both patches are interconnected through horizontal fluxes due to the ability of trees to extend
142 horizontally their roots to take up nutrients in the open. In the model, N is supposed to be the limiting
143 factor of primary production and grass and tree growth depend on the acquisition of mineral N forms,
144 that can be acquired under two forms (NH<sub>4</sub><sup>+</sup> and NO<sub>3</sub><sup>-</sup>) with a certain preference (β) for NH<sub>4</sub><sup>+</sup> versus
145 NO<sub>3</sub><sup>-</sup>. This preference ranges between 0 and 1 with high values of β corresponding to a high
146 preference for NH<sub>4</sub><sup>+</sup>. N is absorbed by plants through N uptake rates βu for NH<sub>4</sub><sup>+</sup> uptake and (1-β)u
147 for NO<sub>3</sub><sup>-</sup> uptake. Plants release N into organic N pool at constant mortality rates d<sub>G</sub>, d<sub>l</sub> and d<sub>r</sub>
148 respectively for grasses, tree leaves and tree roots. Organic N mineralized into NH<sub>4</sub><sup>+</sup> at rate m and
149 NH<sub>4</sub><sup>+</sup> can be transformed into NO<sub>3</sub><sup>-</sup> at rate n. Each patch receives N inputs through dry and wet
150 depositions that provide N under organic and mineral forms into O, N<sub>A</sub> and N<sub>N</sub> compartments
151 respectively at rates i<sub>O</sub>, i<sub>NA</sub> and i<sub>NN</sub>. Non-symbiotic fixation contributes to the input of NH<sub>4</sub><sup>+</sup> and is
152 included in i<sub>NA</sub> (Abbadie, 2006). N losses from savannas result from the burning of the plant
153 compartments (l<sub>G</sub> and l<sub>T</sub>), and leaching for other compartments (l<sub>O</sub>, l<sub>NA</sub> and l<sub>NN</sub>). NO<sub>3</sub><sup>-</sup> losses by
denitrification are included in $l_{NN}$. All parameters but nitrification rates are equal between the two patches to keep the model relatively simple and focus on the effects of nitrification heterogeneity (see model parameter Table, Appendix S2). All compartments are N stocks expressed as a quantity of N by surface unit, i.e kilograms of N per hectare of savanna (kg N ha⁻¹). The system of differential equations is the same used in Konaré et al. (2021):

Open patch (patch 1)

$$ \frac{dG_1}{dt} = (1 - \gamma)(\beta_G u_G N_{A1} G_1 + (1 - \beta_G) u_G N_{N1} G_1 - (d_G + l_G) G_1) \quad (1) $$

$$ \frac{dO_1}{dt} = (1 - \gamma)(i_0 + d_G G_1 + d_r \left(\frac{\gamma}{1-\gamma}\right) \alpha r T - (m + l_0) O_1) \quad (2) $$

$$ \frac{dN_{A1}}{dt} = (1 - \gamma)(i_{NA} + m O_1 - (\beta_G u_G G_1 + n_1 + l_{NA} + \beta_{T1} u_r \left(\frac{\gamma}{1-\gamma}\right) \alpha r T) N_{A1}) \quad (3) $$

$$ \frac{dN_{N1}}{dt} = (1 - \gamma)(i_{NN} + n_1 N_{A1} - ((1 - \beta_G) u_G G_1 + l_{NN} + (1 - \beta_{T1}) \left(\frac{\gamma}{1-\gamma}\right) u_r \alpha r T) N_{N1}) \quad (4) $$

Tree clump patch (patch 2)

$$ \frac{dG_2}{dt} = \gamma (\beta_G u_G N_{A2} G_2 + (1 - \beta_G) u_G N_{N2} G_2 - (d_G + l_G) G_2) \quad (5) $$

$$ \frac{dT}{dt} = \gamma (1 - \alpha) (\beta_{T2} u_r N_{A2} r T + (1 - \beta_{T2}) u_r N_{N2} r T) + \alpha (\beta_{T1} u_r N_{A1} r T + (1 - \beta_{T1}) u_r N_{N1} r T) - (d_l (1 - r) + d_r \alpha r + (1 - \alpha) d_r r + l_T) T \quad (6) $$

$$ \frac{dO_2}{dt} = \gamma (i_0 + d_G G_2 + (1 - \alpha) d_r r T + d_l (1 - r) T - (m + l_0) O_2) \quad (7) $$

$$ \frac{dN_{A2}}{dt} = \gamma (i_{NA} + m O_2 - (\beta_G u_G G_2 + (1 - \alpha) \beta_{T2} u_r r T + n_2 + l_{NA}) N_{A2}) \quad (8) $$

$$ \frac{dN_{N2}}{dt} = \gamma (i_{NN} + n_2 N_{A2} - ((1 - \beta_G) u_G G_2 + l_{NN} + (1 - \beta_{T2}) (1 - \alpha) u_r r T) N_{N2}) \quad (9) $$

## Spatial setting of the model

The description of the spatial setting in the model relies on the proportion of tree roots in the open (α) and the proportion of the savanna surface covered by tree clumps (γ) (leaving (1-γ) to the open savanna). Compared to Konaré et al. (2021) in which α and γ had fixed values, in this version of the model, α is a function of γ and γ is a function of tree biomass (T). We assume that α depends on the proportion of tree cover and the spatial patterns of trees: for a given canopy and root system radius,
178 $\alpha$ should decrease with $\gamma$. However, this relation should also depend on tree distribution with lower values of $\alpha$ when trees are clumped and high values of $\alpha$ when they are randomly or regularly distributed. Although tree distribution can vary in different savanna ecosystems, it is often clustered (Barot et al., 1999; Gignoux et al., 2006). Similarly, we assume a positive relationship between $\gamma$ and tree biomass $T$: the more trees, the more surface they occupy in savanna.

183 The shape of the relation between $\alpha$ and $\gamma$ was studied by simulating different distributions of trees (random, clustered and regular). We assumed that trees were represented as two superimposed discs describing the canopy and the root system as the majority of tree roots has been found within a radius 10 m away from tree clump center (Menaut, personal communication). In our simulations, canopy radius was set to 2 m and root system radius to 6 m. The relation between $\alpha$ and $\gamma$ was obtained by calculating the proportion of root system that did not fall under the canopy of other trees for each tree distribution and for different tree densities exploring a wide range of tree cover. We calculated the relation between $\alpha$ and $\gamma$ for random, clumped and regular tree distributions. To simulate random patterns, a Poisson process with a tree density varying from 1 to 100 trees ha⁻¹ by step of 10 and from 100 to 2000 trees ha⁻¹ by step of 200 was used. Clumped patterns were obtained by using a Matérn cluster process (Matérn, 1960) with a tree density varying from 1 to 100 trees ha⁻¹ by step of 10 and from 100 to 1000 trees ha⁻¹ by step of 100 with a mean clump radius of 2 m and a mean number of trees per clump of 10. Finally, regular patterns were modeled using a Matérn hard-core process (Matérn, 1960; 1986) with an inhibition distance of 2 m and the same tree densities as the random patterns. To determine the relation between $\alpha$ and $\gamma$, and between $\gamma$ and $T$, we calculated the quantity of tree roots outside tree canopy at the individual scale and the mean of all individual values to obtain $\alpha$ for a given tree density. We then calculated $\gamma$ for each tree density by determining the total space occupied by trees. Linear regression models were then used to determine the relation between $\alpha$ and $\gamma$. Besides, we used data from Menaut & César (1979) to establish the relation between $\gamma$ and tree biomass ($T$) through a linear regression model. Equations from linear models and parameters were included in the two-patch model to link $\alpha$, $\gamma$ and $T$.
204 **Model analysis and parameterization**

205 The analysis of the model relied on numerical simulations as it could not be analytically solved. All
206 simulations were coded in R (R development Core Team, 2022) using deSolve package for the
207 resolution of differential equations (Soetart et al., 2010). All simulations were run for 3000 years,
208 which was sufficient to reach steady states for all compartments.

209 We used the same parameter sets as in Konaré et al. (2021; see Appendix S2) but run a
210 completely different simulation experiment. These parameters are based on data from the Lamto
211 savanna in Côte d'Ivoire (06°13′N, 05°02′W) (Abbadie et al., 2006) (Appendix S2).

212 Tree-grass coexistence was determined using the mutual invasibility criterion (Chesson & Ellner,
213 1989). This criterion considers a pair of invader and resident species (for example grasses invading a
214 forest, starting with a negligible biomass of 0.01 kg N/ha compared to the tree biomass, with a high
215 biomass of 10 kg N/ha, and then the reverse situation with trees invading a grassland). When the two
216 species are able to invade each other, they are assumed to mutually coexist over the long term
217 (Chesson & Ellner, 1989). Nitrification stimulation under tree clumps suggests a preference of trees
218 for NO3- at least for roots under the tree canopy. Because NH4+ should be the dominant N form in the
219 open due to nitrification inhibition by grasses, a preference of trees for NH4+ in the open is more
220 expected. We thus decided to distinguish the preference of trees for NH4+ versus NO3- in the open
221 patch (βT1) and under tree clumps (βT2) and tree preference under tree clumps was fixed to a constant
222 value (βT2 = 0.25). Simulations of N stocks and fluxes were performed for different combinations of
223 grass and tree preference for NH4+ versus NO3- in the open (βG and βT1) varying between 0 and 1 with
224 an increment of 0.005. We first simulated mutual invasion between trees and grasses for different
225 combinations of grass and tree preference for NH4+ versus NO3- (tree preference was the same in the
226 open and under tree canopy: βT) versus different combinations of grass and tree preferences for NH4+
227 versus NO3- in the open (βT1) to compare the effect of tree preference on tree-grass coexistence.
228 Nitrification rates in the open and under tree clumps were calculated by dividing nitrification fluxes
229 under grasses and under trees by their respective ammonium stocks (Srikanthasamy et al., 2018). We
increased the nitrification rate in the open to compare a spatial homogeneity to a spatial heterogeneous nitrification rate to test the importance of heterogeneity in nitrification flux on tree-grass coexistence. Moreover, because the proportion of tree roots in the open does not depend only on tree density or biomass, but also on the spatial distribution of individual trees, we tested the effects of tree distributions in space (random, regular and clustered) on tree-grass coexistence. We tested the sensitivity of results to the root radius by increasing this radius from 6 to 12 m to assess the relationship between α and γ and then analyze the effect of these new equations on tree-grass coexistence.

## 238 Results

### 239 Links between soil exploration by tree roots and tree cover and between tree biomass and tree cover

For all spatial distributions tested, a negative linear relation was observed between α and γ (p-value < 0.0001 and R² = 0.999 for random and regular; p-value < 0.0001 and R² = 0.996 for cluster tree pattern) (Fig. 1a). As expected, the relation yields lower α values in the case of clustered trees compared to random and regular distribution. The regression lines whereas follow: α = -0.897γ + 0.889, α = -0.872γ + 0.890 and α = -0.698γ + 0.694 respectively for random, regular and clustered tree patterns. We observe a significant difference between cluster and random or regular patterns but the difference between random and regular patterns was not significant. Fig. 1b shows that γ significantly increases with tree biomass (p-value < 0.005, R² = 0.962), which leads to T = 530.56γ - 2.81. Despite the potential nonlinearity between γ and T, we chose to use a linear relationship in our model for simplicity. We used these results to parameterize simulations testing for tree-grass coexistence.

### 252 Tree-grass coexistence is affected by tree preference for NH₄⁺ in the open versus under tree canopy

Model simulation for clustered tree distribution leads to three cases of coexistence: (1) a case where trees and grasses are spatially separated (no grasses under trees, only in the open hereafter called tree-
256 grass mosaic), (2) a case where grasses can only grow under tree clumps (no open area) hereafter
257 called savanna woodland, and (3) a case where grasses grow both under tree canopy and in the open
258 (hereafter called savanna). When tree preference is the same in the open and under tree canopy (Fig.
259 2a), grasses successfully invade and exclude trees for a large range of grass preference for NH₄⁺
260 versus NO₃⁻ and when trees prefer NO₃⁻. Tree-grass mosaic occurs when grasses have a higher
261 preference for NH₄⁺ than trees (0 < βₜ < 0.8). By contrast, when tree preference for NH₄⁺ is higher than
262 grasses, trees completely invade and exclude grasses. We also observe a small portion of the
263 parameter space where tree clumps establish when grasses prefer NO₃⁻ and trees strongly prefer NH₄⁺
264 (βₜ > 0.98). Savanna tree-grass coexistence is possible when grasses have a high preference for NH₄⁺
265 and trees prefer NO₃⁻ and when grasses have a higher preference for NH₄⁺ than trees (0 < βₜ < 0.3).

266 If trees have different preferences in the open (β<sub>T1</sub> ranged between 0 and 1) versus under
267 tree canopy (β<sub>T2</sub> constant) (Fig. 2b), the sizes of the zone of savanna woodland and savanna strongly
268 increases while the zone of tree-grass mosaic decreases. Savanna is favored for a large range of tree
269 preference in the open (β<sub>T1</sub>) and a grass preference for NH<sub>4</sub><sup>+</sup>. Tree clumps establishment becomes
270 possible when grasses and trees in the open prefer NH<sub>4</sub><sup>+</sup>. Taken together, a same tree preference in the
271 open and under tree canopy reduces possibilities of complete coexistence between trees and grasses
272 but favors tree-grass mosaic, while different tree preference in the open and under tree canopy
273 increases possibilities of coexistence between trees and, grasses in the open and under tree canopy.
274 We thus consider different tree preference in the open versus under tree canopy for all other
275 simulations.

276 Tree-grass coexistence depends on spatial tree distribution

277 Because results of regular and random tree distribution are virtually the same (Appendix S5), we only
278 presented clustered and random distribution in the main text. Tree distribution strongly influences the
279 conditions of coexistence between trees and grasses (Fig. 3). For random tree distribution, grasses
280 invade and exclude trees when grasses have a higher preference for NH<sub>4</sub><sup>+</sup> than trees in the open (β<sub>T1</sub>
281 < 0.4). However, when tree roots in the open have a higher preference for NH<sub>4</sub><sup>+</sup> than grasses (β<sub>G</sub> <
0.7), trees successfully invade and exclude grasses. The model also predicts a zone in which savanna establishes when $\beta_G > 0.7$ and $0.4 < \beta_{TI} < 0.73$, a zone where tree clumps invade when grasses and trees in the open prefer $NH_4^+$ and a small zone of tree-grass mosaic.

Compared to random tree distribution, clustered pattern strongly increases the size of the zones of savanna and tree-grass mosaic. Tree-grass mosaic is enhanced when the grass preference for $NH_4^+$ is higher than the tree preference for $NH_4^+$ in the open ($\beta_{TI}$). Savanna zone extends to large range of $\beta_{TI}$ values and a preference of grasses for $NH_4^+$. Switching from random to clustered tree distribution also reduces the size of the zone of invasion by grasses or by trees or by savanna woodland (Appendix S3).

## Comparison between spatial heterogeneity and spatial homogeneity cases

Spatial heterogeneity of nitrification due to its control by plants alters conditions of coexistence between trees and grasses. We compared the case of spatial heterogeneity (Fig. 3) to a case of spatial homogeneity where grasses do not inhibit nitrification (Fig. 4). In the case of a random tree distribution, increasing nitrification rate in the open promotes invasion by tree clumps ($\beta_G > 0.69$ and $\beta_{TI} > 0.35$) or by trees only ($\beta_G < 0.69$ and for all combinations of $\beta_{TI}$). Compared to cases where nitrification is spatially heterogenous (Fig. 3), we observed a zone of tree-grass mosaic for $0.4 < \beta_G < 0.62$ and $\beta_{TI} < 0.13$ and a zone of savanna when grasses prefer $NH_4^+$ ($\beta_G > 0.62$) and trees prefer $NO_3^-$ in the open ($\beta_{TI} < 0.28$) in the spatial homogeneity case. For a clustered tree distribution, the overall pattern is virtually the same, but a second zone of tree-grass mosaic appears when grasses and trees in the open strongly prefer respectively $NO_3^-$ ($\beta_G < 0.2$) and $NH_4^+$ ($\beta_{TI} > 0.95$). Increasing nitrification rate reduces total coexistence between trees and grasses and facilitates zones with only trees or trees with grasses under their canopy. This shows that different nitrification rates in the open and in the tree clump patch improve chances of tree-grass coexistence.

## Soil exploration by tree roots affects tree-grass coexistence

Fig. 5 displays the outcome of mutual invasion between trees and grasses when the tree root system radius is increased from 6 m to 12 m. As described above, savanna (grasses grow both under tree
canopy and in the open) in random distribution cases occurs when $\beta_G > 0.7$ and $0.4 < \beta_{TI} < 0.73$ and the size of this zone increases and extends to more combinations of $\beta_{TI}$ when we switch from a random to a clustered tree distribution (root radius = 6 m, Figs 5a and b). We observe the same tendencies when the root radius is increased to 12 m (Appendix S4). Overall, clustered distributions tend to increase the size of the savanna zone. However, increasing the surface explored by tree roots reduces the sizes of the zone of tree-grass coexistence in cases of both random and clustered distributions (Figs 5c and 5d). This is more perceptible for clustered patterns for which the size of the savanna and tree-grass mosaic zones largely decreases while the zone of invasion by grasses increases (Fig. 5d).

## Discussion

In our model, tree-grass coexistence occurs when plants have contrasted preferences for $NH_4^+$ versus $NO_3^-$.
This is in agreement with theories showing that the coexistence of different species is possible when they differ in their use of resources (Armstrong & McGehee, 1980). This is also in agreement with published works on competition for $NH_4^+$ and $NO_3^-$ between plants (Boudsocq et al., 2012; Konaré et al., 2019). These results are also supported by empirical studies on N partitioning indicating that plant having different preferences for different chemical N forms can coexist (Ashton et al., 2010; McKane et al., 2002). Mineral N partitioning appears as a stabilizing mechanism (Chesson, 2000; Barot & Gignoux, 2004) fostering coexistence between savanna trees and grasses. Here, we further analyze the influences of these processes on tree-grass coexistence testing for the effects of spatial heterogeneity in nitrification fluxes (hypothesis 1), mineral N partitioning into $NH_4^+$ and $NO_3^-$ (hypothesis 2), spatial tree patterns (hypothesis 3) and horizontal soil exploration by tree roots (hypothesis 4).

## Comparison between the one-patch and the two-patch model

Compared to the mean-field model (Konaré et al., 2019), the two-patch model allows to simulate distinct pools of mineral N available below tree clumps and in the open. Although the sizes of the zone of savanna in the two-patch model (cluster distribution, Fig. 3) and in the mean-field model (Fig. 2A, Konaré et al. (2019)) are not significantly different, the two-patch model predicts different
possible cases of coexistence that corresponds to different landscape structures. Indeed, while the mean-field model only allows one possible case of tree-grass coexistence, the two-patch model can lead to three types of coexistence: savanna woodland (trees with grasses under their canopy only), tree-grass mosaic (trees with grasses only in the open) or savanna (trees with grasses everywhere). These results are in accordance with theories showing that coexistence in a spatially heterogeneous environment is facilitated (Chesson, 2000; Amasekare, 2003) even with a single resource. In this case, spatial heterogeneity separates the mineral N resource so that this resource is no longer fully shared between the competitors leading to more diverse scenarios of coexistence in the two-patch than in the one-patch model.

### 343 Heterogeneity in nitrification influences tree-grass coexistence in the Lamto savanna

Studies on resource-based mechanisms of tree-grass coexistence in savannas have focused on water competition (Walter, 1971; Walker & Noy-Meir, 1982). Little is known, however, about other resources that are essential for plant growth, such as N (Donzelli et al., 2013) ☐. In our model, when trees have the same preference in the open and under tree canopy, savannas occur when grasses have a high preference for $NH_4^+$ and trees a high preference for $NO_3^-$ (Fig. 2). This confirms that tree-grass coexistence is possible when grasses prefer $NH_4^+$ and trees prefer $NO_3^-$ at least under tree canopy.

Wang and Macko (2011) studied the preference of grasses depending on climatic conditions and found that grasses tend to prefer $NH_4^+$ in humid areas. Moreover, ongoing studies on *Hyparrhenia diplandra* in the Lamto savanna (Barot, personal communication) as well as a study on *Andropogon gayanus* (Rossiter-Rachor et al., 2009) ☐ suggest that these two species that inhibit nitrification, have a preference for $NH_4^+$. Unlike the mean-field model where trees and grasses coexist when grasses prefer $NO_3^-$ and trees prefer $NH_4^+$ (Konaré et al., 2019), in the two-patch model, tree-grass coexistence becomes possible when grasses prefer $NH_4^+$ and trees prefer $NO_3^-$.

This is more in accordance with the Lamto savanna case as grasses are known to inhibit nitrification while trees stimulate it (Lata et al., 2004; Srikanthasamy et al., 2018). The N limitation in the Lamto savanna (Abbadie et al., 2006)
has induced the evolution of different strategies: a conservative strategy for grasses through the BNI capacity and an acquisitive strategy for trees through nitrification stimulation (Barot et al., 2015)□.

Konaré et al. (2021) showed that NH₄⁺ uptake by tree roots outside tree canopy (35.58% of total N uptake by trees) increased tree biomass. Our results confirm this scenario because different tree preference for NH₄⁺ versus NO₃⁻ in the open and under tree canopy (trees prefer NH₄⁺ in the open and NO₃⁻ under their canopy) increases the zone of savanna, i.e. tree-grass coexistence (Fig. 2). Besides, simulations testing different values of tree preference for NH₄⁺ versus NO₃⁻ under their canopy showed that increasing tree preference for NH₄⁺ under tree canopy reduces the establishment of savanna zones but promotes tree invasion (Appendix S6). These results suggest that plasticity of tree root systems in their preferences for NH₄⁺ versus NO₃⁻ should occur depending on the spatial distribution of NH₄⁺ and NO₃⁻ (Britto & Kronzucker, 2013)□. In both cases (same versus different tree preferences), our results show that local interactions between species and their environment can induce a spatial heterogeneity leading to niche partitioning and thus promote their coexistence (Huston & DeAngelis, 1994; Amasekare, 2003). These different impacts of trees and grasses on nitrification create small-scale heterogeneities by increasing the availability of their preferred N form, which induces niche complementarity for N acquisition. In comparison, increasing nitrification rate in the open reduces coexistence and favors the establishment of zones with only trees and savanna woodland (Fig. 4). Indeed, increasing this rate reduces heterogeneity in nitrification which increases niche overlap (Chesson, 2000; Amasekare, 2003) and increases the competitive ability of trees for N. Taken together, these feedbacks based on N recycling tend to stabilize the open and tree clump patches and to favor tree-grass coexistence at a larger scale. Besides, the preference for NH₄⁺ versus NO₃⁻ qualitatively influences savanna dynamics, confirming that this preference can have important consequences at the ecosystem scale on vegetation dynamics (Boudsocq et al., 2012) and quantitatively on plant biomass (Appendix S7). While plasticity in plant preference for NH₄⁺ versus NO₃⁻ has already been described, our results suggest that we should acquire experimental results to
measure this preference on savanna trees and its spatial variability and to analyze the underlying mechanisms along Britto and Kronzucker's arguments (Britto & Kronzucker, 2013).

### Tree spatial distribution alters the conditions of coexistence

Many modeling studies have demonstrated that species coexistence could be facilitated by intraspecific clustered distributions (Inouye, 1999; Hartley & Shorrocks, 2002). Our results confirm that coexistence is easier when trees are clumped than when they are randomly distributed. In a random tree distribution, grass and tree roots growing outside tree canopy easily overlap in the open. This increases competitive interactions between trees and grasses for N acquisition in the open through lateral N exchanges following the horizontal soil exploration by tree roots. The strong competition between trees and grasses in the open prevents the establishment of tree-grass mosaic and savanna zones whereas it facilitates invasions by grasses or by trees depending on their preferences for $NH_4^+$ versus $NO_3^-$.

By contrast, the clumping of trees limits the proportion of tree roots in the open as tree individuals are surrounded by more conspecifics (tree roots tend to be more under the canopy of neighbouring trees). This decreases transfers of N between the open and the tree clump patch through horizontal fluxes and highlights the impact of spatialization: intraspecific aggregation tends to foster intraspecific competition over interspecific competition. Some studies found that intraspecific aggregation is influential for species coexistence as it facilitates the maintenance of weaker competitors (Stoll & Prati, 2001; Monzeglio & Stoll, 2005). Taken together, tree spatial patterns influence the outcomes of competition by impacting the strength of intra relative to interspecific competition (Stoll & Prati, 2001). Besides, in some savannas (Couteron & Kokou, 1997; Skarpe, 1991) and particularly in the Lamto savanna (Barot et al., 1999; Gignoux et al., 2006), trees often show an aggregated spatial distribution. They form clumps leaving an important proportion of the surface covered by grasses. Tree clumps are maintained by fires: reduced grass biomass under tree shading decreases fire intensity and hence increases tree sapling survival (Hochberg et al., 1994; Gignoux et al., 2006). This mechanism somehow increases the likelihood of tree-grass coexistence by impeding fires (promoted by grass biomass) to kill all tree saplings. Our
results suggest that tree clumps may favor tree-grass coexistence and savanna maintenance through another mechanism: a decrease in the competition for mineral N, but empirical studies are needed to support this effect of tree spatial distribution on savanna dynamics.

## The impact of horizontal soil exploration on coexistence

Horizontal soil exploration contributes to nutrient enrichment under tree canopy (Konaré et al., 2021) but little is known about their possible effects on coexistence. Our results show that regardless of tree distribution, savanna and tree-grass mosaic zones are reduced by the increase of the surface explored by tree roots. Indeed, horizontal soil exploration by tree roots leads to spatial transfers of N between the open and the tree clump patches. Increasing the proportion of tree roots in the open increases the competitive ability of trees to take up N and thus the competition between trees and grasses for N in the open. Although, cluster distribution allows a spatial partitioning by increasing intraspecific competition, this proliferation of tree roots in the open increases the strength of interspecific competition relative to intraspecific competition (Stoll & Prati, 2001) and consequently prevents grass establishment. These lateral fluxes between these two patches lowers the spatial heterogeneity by homogenizing the N availability between these two patches (Barot et al., 2015; Barot et al., 2014), which tends to reduce complete coexistence and favors the zones of exclusion by trees and by grasses (Appendix S3). Moreover, when the size of the tree root system relative to the canopy increases, the relation between the proportion of tree roots in the open and tree cover is virtually the same for each distribution (Appendix S4). As a result, increasing the surface explored by tree roots decreases the differences between random and clustered tree distribution.

## Conclusion

Savanna ecosystems can be viewed as small scale meta-ecosystems (Loreau et al., 2003) where the spatial heterogeneity in nitrification between the two patches and the intensity of lateral N fluxes strongly influences the outcomes of competition between trees and grasses. Our findings confirm that spatial heterogeneity in nitrification promotes tree-grass coexistence when trees and grasses have different preference for NH₄⁺ versus NO₃⁻ with grasses preferring NH₄⁺ and trees NO₃⁻ under their
canopy. While increasing the soil exploration by tree roots in the open tends to increase the competitive ability of trees to acquire N, intraspecific aggregation through cluster tree distribution intensifies the effect of spatial heterogeneity, which lowers the competition between trees and grasses favoring their coexistence. Mineral N partitioning into $NH_4^+$ and $NO_3^-$ can play an important role by promoting tree-grass coexistence. Although the ability to inhibit nitrification seems to be common in African perennial grasses and some crops (Lata et al., 2004; Subbarao et al., 2009; Rossiter-Rachor et al., 2009, O'Sullivan et al., 2016; Lata et al., 2022), little is known about environmental conditions that have selected for this behavior (but see Lata et al. (2022)). Even if this inhibition has not been assessed in other savanna types, mineral N partitioning could be involved in the tree-grass coexistence of all West African humid savannas that have virtually the same dominant grass and tree species as Lamto savanna. The high performance of African grasses and their effects on N cycling in northern Australian and South American savannas (D'Antonio & Vitousek, 1992; Rossiter-Rachor et al., 2009) also seem to be linked to their BNI ability. Though the frequency of this ability in other African grasses is not fully known (Lata et al., 2022), many African grasses seem to be able to inhibit nitrification so that the new coexistence mechanism we emphasize should be studied at a large geographical scale and particularly in Eastern and Southern African savannas. Besides, N fixing trees and large herbivores, that are absent in the Lamto savanna, are known to be influential in the functioning of other savannas such as East African savannas (Sankaran et al., 2008). These mechanisms, that provide important N inputs through symbiotic fixation, animal dungs and urine and impact N cycling differently, should be included in new models to assess the robustness of our results.

Clearly, our new mechanism of coexistence based on the partition of the mineral N resource, probably interacts with formerly identified mechanisms based on the impact of disturbances on tree demography to explain tree-grass coexistence (Higgins et al., 2000). Although fire is determinant for the maintenance of savanna structure by reducing woody cover (Gignoux et al., 2006), mineral N partitioning likely acts in interaction with fire as the intensity of fire depends on the biomass of flammable grasses, this grass biomass depending in turn on their N acquisition, essential
462 nutriment for their growth. For instance, nitrification inhibition by grasses has been shown to increase grass biomass, which should increase fire intensity and its capacity to impede tree encroachment.
463
464 This would ultimately favor tree-grass coexistence. However, new models should be built to take into account mechanisms based on both resource competition and demography.
465

466 Acknowledgments

467 This research work was funded by the GainGrass Project (Global Assessment of Nitrification
468 Inhibition by tropical Grasses Project, ANR-19-CE02-0009) funded by the French National Research
469 Agency (ANR). We thank the Ministry of Higher Education and Scientific Research of Côte d'Ivoire
470 for the PhD grant of SK. We also thank Prof. Yéo Kolo, the Director of the Lamto station for the
471 access to the station.

472 Conflict of interest statement

473 The authors declare no conflict of interest.

474 Author contributions

475 SK, KFK, S Bo, JG, JCL, XR and S Ba conceived the ideas and designed methodology. SK analyzed
476 the model and wrote the manuscript with the contribution of all co-authors. All authors gave final
477 approval for publication.

478 Data availability statement

479 All data regarding the model is included in the paper.

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639

640

641

642
643

644

645 **List of figures**

646 **Figure 1:** (a) Proportion of tree roots in the open ($\alpha$) as a function of tree cover ($\gamma$) according to cluster, random and regular tree distribution, (b) Tree biomass as a function of tree cover ($\gamma$) for a root radius equals to 6 m.
647
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649

650 **Figure 2:** Mutual invasibility plots between trees and grasses according to grass ($\beta_G$) and tree preference for $NH_4^+$. (a): trees have identical preferences for $NH_4^+$ in the open and the tree patches ($\beta_T$). (b): trees have different preferences for $NH_4^+$ in the open ($\beta_T$) and the tree patch ($\beta_{T2}$). In these simulations, $\beta_{T2}$ was set constant to 0.25. Simulations correspond to clustered tree distributions. 651
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654 Invasion zones: G1+G2: grasses invade and exclude trees, T: Trees invade and exclude grasses, G1+T: tree-grass mosaic (coexistence between trees and grasses in the open), G2+T: savanna woodland 655
656 (coexistence between trees and grasses under their canopy), G1+G2+T: savanna (coexistence 657 between trees and grasses under their canopy and in the open). 658

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659 **Figure 3:** Mutual invasibility plots between trees and grasses according to random (a) and clustered (b) tree distributions at the savanna scale. Invasion zones: G1+G2: grasses invade and exclude trees, T: Trees invade and exclude grasses, G1+T: tree-grass mosaic (coexistence between trees and grasses in the open), G2+T: savanna woodland (coexistence between trees and grasses under their canopy), G1+G2+T: savanna (coexistence between trees and grasses under their canopy and in the open). 660
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666 **Figure 4:** Mutual invasibility plots between trees and grasses according to random (a) and clustered (b) tree distributions at the savanna scale. These figures correspond to cases where grasses do not inhibit nitrification (spatial homogeneity: $n_1 = n_2 = 4.16 \text{ yr}^{-1}$). Invasion zones: G1+G2: grasses invade and exclude trees, T: Trees invade and exclude grasses, G1+T: tree-grass mosaic (coexistence 667
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669 between trees and grasses in the open), G2+T: savanna woodland (coexistence between trees and grasses under their canopy), G1+G2+T: savanna (coexistence between trees and grasses under their canopy and in the open)

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673 **Figure 5:** Mutual invasibility plots between trees and grasses according to random (a and c) and clustered (b and d) tree distributions at the savanna scale. The first (a and b) and second (c and d) rows of graphs respectively corresponds to simulations of tree distributions with a root system radius of 6 and 12 m when determining the relation between α and γ. Invasion zones: G1+G2: grasses invade and exclude trees, T: Trees invade and exclude grasses, G1+T: tree-grass mosaic (coexistence between trees and grasses in the open), G2+T: savanna woodland (coexistence between trees and grasses under their canopy), G1+G2+T: savanna (coexistence between trees and grasses under their canopy and in the open).

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<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 1</figcaption></figure>

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<figure><img src="image_4.png" /><figcaption>Fig. 2</figcaption></figure>

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<figure><img src="image_5.png" /><figcaption>Fig. 3</figcaption></figure>

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<figure><img src="image_6.png" /><figcaption>Fig. 4</figcaption></figure>

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<figure><img src="image_7.png" /></figure>

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Fig. 5
1 Supporting information

2 Appendix S1: Schematic representation of the two-patch model

3 Appendix S2: Model parameters

4 Appendix S3: Graphical representation of scenarios of invasion by trees versus invasion by grasses

5 Appendix S4: Relation between soil exploration by tree roots and tree cover

6 Appendix S5: Regular distribution

7 Appendix S6: Effect of tree preference under their canopy depending on spatial tree distributions

8 Appendix S7: Plant biomass depending on tree distributions

9

10 Figure S1: Schematic representation of the two-patch model showing the patchy vegetation of the Lamto savanna with the open patch only occupied by grasses and the tree clump patch with trees and grasses beneath their canopy.

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12 Table 1: Model parameters

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14 Figure S3-a: Two-patch model representing N dynamics between the open patch and the tree clump patch. This figure displays a scenario of invasion by trees resulting from the two-patch model simulation for cluster tree distribution. Red lines correspond to fluxes strongly influenced by the invasion by trees while black lines the fluxes less influenced by the invasion by trees.

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16 Figure S3-b: Two-patch model representing N dynamics between the open patch and the tree clump patch. This figure displays a scenario of invasion by grasses resulting from the two-patch model simulation for cluster tree distribution. Red lines correspond to fluxes strongly influenced by the invasion by grasses while black lines the fluxes less influenced by the invasion by grasses.

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**Figure S4:** Proportion of tree roots in the open ($\alpha$) as a function of tree cover ($\gamma$) according to cluster, random and regular tree distribution for a root radius equals to 12 m.

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**Figure S5-a:** Mutual invasibility plots between trees and grasses according to grass ($\beta_G$) and tree ($\beta_{T1}$) preference for $NH_4^+$ in the open patch at the savanna scale. Simulations correspond to regular tree distribution with cases of spatial homogeneity ($n_1 = n_2 = 4.16 \text{ yr}^{-1}$) (left) and cases of spatial heterogeneity ($n_1 \neq n_2$) (right). Invasion zones: G1+G2: grasses invade and exclude trees, T: Trees invade and exclude grasses, G1+T: tree-grass mosaic (coexistence between trees and grasses in the open), G2+T: savanna woodland (coexistence between trees and grasses under their canopy), G1+G2+T: savanna (coexistence between trees and grasses under their canopy and in the open).

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**Figure S5-b:** Mutual invasibility plots between trees and grasses according to grass ($\beta_G$) and tree ($\beta_{T1}$) preference for $NH_4^+$ in the open patch at the savanna scale. The graph corresponds to simulations of regular tree distributions with a root system radius of 6 m (left) and 12 m (right) when determining the relation between $\alpha$ and $\gamma$. Invasion zones: G1+G2: grasses invade and exclude trees, T: Trees invade and exclude grasses, G1+T: tree-grass mosaic (coexistence between trees and grasses in the open), G2+T: savanna woodland (coexistence between trees and grasses under their canopy), G1+G2+T: savanna (coexistence between trees and grasses under their canopy and in the open).

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**Figure S6:** Mutual invasibility plots between trees and grasses according to random (left) and clustered (right) tree distributions at the savanna scale. The preference of trees under tree canopy increases from the top to the bottom and corresponds respectively to $\beta_{T2}=0.25$; $\beta_{T2}=0.35$ and $\beta_{T2}=0.5$. Invasion zones: G1+G2: grasses invade and exclude trees, T: Trees invade and exclude grasses, G1+T: tree-grass mosaic (coexistence between trees and grasses in the open), G2+T: savanna woodland (coexistence between trees and grasses under their canopy), G1+G2+T: savanna (coexistence between trees and grasses under their canopy and in the open).

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**Figure S7-a:** Grass (patterns a and b) and tree (patterns c and d) biomass as a function of grass ($\beta_G$) and tree ($\beta_{TI}$) preference for $NH_4^+$ in the open according to random tree distributions at the savanna scale.

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**Figure S7-b:** Grass (patterns a and b) and tree (patterns c and d) as a function of grass ($\beta_G$) and tree ($\beta_{TI}$) preference for $NH_4^+$ in the open patch according to clustered tree distributions at the savanna scale.

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# Appendix S1: Schematic representation of the two-patch model

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<figure><img src="image_9.png" /></figure>

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<caption>Figure S1</caption>

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92 **Appendix S2: Model parameters**

93 Table 1: Model parameters

<table><thead><tr><th>Parameters</th><th>Definition</th><th>Unit</th><th>Values</th></tr></thead><tbody><tr><td colspan="4"><strong>Grass parameters</strong></td></tr><tr><td>d<sub>G</sub></td><td>Turnover rate of grass</td><td>yr<sup>-1</sup></td><td>0.6</td></tr><tr><td>l<sub>G</sub></td><td>Rate of N losses from grass compartment</td><td>yr<sup>-1</sup></td><td>0.4</td></tr><tr><td>u<sub>G</sub></td><td>N uptake rate</td><td>ha kg<sup>-1</sup> N yr<sup>-1</sup></td><td>0.14186</td></tr><tr><td>β<sub>G</sub></td><td>Preference for NH<sub>4</sub><sup>+</sup></td><td>No unit</td><td>-</td></tr><tr><td colspan="4"><strong>Tree parameters</strong></td></tr><tr><td>d<sub>r</sub></td><td>Turnover rate of tree roots</td><td>yr<sup>-1</sup></td><td>0.08</td></tr><tr><td>d<sub>l</sub></td><td>Turnover rate of tree leaves</td><td>yr<sup>-1</sup></td><td>0.073</td></tr><tr><td>l<sub>T</sub></td><td>Rate of N losses from tree compartment</td><td>yr<sup>-1</sup></td><td>0.11</td></tr><tr><td>u<sub>r</sub></td><td>N uptake rate by tree roots</td><td>ha kg<sup>-1</sup> N yr<sup>-1</sup></td><td>0.08</td></tr><tr><td>β<sub>TI</sub></td><td>Preference for NH<sub>4</sub><sup>+</sup> in the open patch</td><td>No unit</td><td>-</td></tr><tr><td>β<sub>T2</sub></td><td>Preference for NH<sub>4</sub><sup>+</sup> in the tree clump patch</td><td>No unit</td><td>0.25</td></tr><tr><td>α</td><td>Fraction of roots in the open</td><td>No unit</td><td>-</td></tr><tr><td>γ</td><td>Tree clumps proportion</td><td>No unit</td><td>-</td></tr><tr><td>r</td><td>Root shoot ratio</td><td>No unit</td><td>0.5</td></tr><tr><td colspan="4"><strong>Soil parameters</strong></td></tr><tr><td>i<sub>O</sub></td><td>N organic input to the savanna</td><td>kg N ha<sup>-1</sup> yr<sup>-1</sup></td><td>16.5</td></tr><tr><td>m</td><td>N mineralization rate</td><td>yr<sup>-1</sup></td><td>0.025</td></tr><tr><td>l<sub>O</sub></td><td>N loss from the N organic compartment in surface soil layer</td><td>yr<sup>-1</sup></td><td>0.0027</td></tr><tr><td>i<sub>NA</sub></td><td>NH<sub>4</sub><sup>+</sup> inputs to the savanna</td><td>kg N ha<sup>-1</sup> yr<sup>-1</sup></td><td>23</td></tr><tr><td>n<sub>1</sub></td><td>Nitrification rate in the open patch</td><td>yr<sup>-1</sup></td><td>0.09</td></tr><tr><td>n<sub>2</sub></td><td>Nitrification rate in the tree clump patch</td><td>yr<sup>-1</sup></td><td>4.16</td></tr><tr><td>l<sub>NA</sub></td><td>NH<sub>4</sub><sup>+</sup> loss rate</td><td>yr<sup>-1</sup></td><td>0.0133</td></tr><tr><td>i<sub>NN</sub></td><td>NO<sub>3</sub><sup>-</sup> inputs to the savanna</td><td>kg N ha<sup>-1</sup> yr<sup>-1</sup></td><td>4.1</td></tr><tr><td>l<sub>NN</sub></td><td>NO<sub>3</sub><sup>-</sup> loss rate</td><td>yr<sup>-1</sup></td><td>2.7</td></tr></tbody></table>

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<figure><img src="image_10.png" /><figcaption>Figure S3-a</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure S3-b</figcaption></figure>
## 107 Appendix S4: Relation between soil exploration by tree roots and tree cover

We performed simulations for different tree distributions to determine the relation between the proportion of tree roots in the open ($α$) and tree cover ($γ$) to analyze the effect of spatial patterns on tree-grass coexistence. This relation has been tested for random, cluster and regular tree distributions.

We considered trees with 2 m crown radius and 12 m root radius for each distribution in 1ha plot.

For all spatial distributions tested, a negative linear relation was observed between $α$ and $γ$ (p-value < 0.0001 and $R^2$=0.998 for random; p-value < 0.0001 and $R^2$=0.999 for cluster; p-value < 0.0001 and $R^2$=0.999 for regular tree pattern). $α$ significantly decreases while $γ$ increases regardless of tree distributions. In contrast to the results of the main text where cluster distribution was different to random and regular distributions (Figure 1a), we observe here that the relation between $α$ and $γ$ is virtually the same for all patterns. This leads to these linear equations: $α$ = -0.984$γ$ +0.971, $α$= -0.977$γ$ +0.973 and $α$ = -0.932$γ$ +0.924 respectively for random, regular and clustered tree distributions.

<caption>Figure S4</caption>

<figure><img src="image_12.png" /></figure>
Appendix S5: Regular distribution

<figure><img src="image_13.png" /><figcaption>Figure S5-a</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Figure S5-b</figcaption></figure>
## 156 Appendix S6: Effect of tree preference under their canopy depending on spatial tree distributions
157

158 We did simulations for different combinations of grass and tree preference for NH₄⁺ in the open.
159 Here, we tested different tree preference for NH₄⁺ under tree canopy by gradually increasing tree
160 preference for NH₄⁺ under their canopy (βₜ₂ = 0.35; βₜ₂ = 0.5) knowing that the value by default used
161 in the main text is βₜ₂ = 0.25. Regarding random pattern, when tree preference under tree canopy for
162 NH₄⁺ increases (βₜ₂ = 0.35), trees tend to exclude grasses, which reduces the zone of savanna. This
163 also increases conditions of coexistence between trees and grasses in the open. When tree preference
164 under tree canopy for NH₄⁺ increases further (βₜ₂ = 0.5), the zone of savanna becomes very small
165 while the zone of tree-grass mosaic increases. The overall pattern is similar for cluster pattern but the
166 region of coexistence between trees and grasses in the open is much larger than in the random tree
167 pattern case.

168 Increasing tree preference for NH₄⁺ under tree canopy favors the establishment of trees and the
169 exclusion of grasses in random and cluster patterns. This also leads to an increase of the zone of tree-
170 grass mosaic (trees and grasses in the open) but strongly reduces the zone of savanna (grasses grow
171 both under tree canopy and in the open) in both tree patterns.

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Random

<figure><img src="image_15.png" /></figure>

Clustered

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

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<caption>188 Figure S6</caption>
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191 Appendix S7: Plant biomass depending on tree distributions

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<figure><img src="image_21.png" /></figure>

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<caption>194 Figure S7-a</caption>

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Grass invader; Tree resident

Grass resident; Tree invader

<figure><img src="image_22.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>(c)</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>(d)</figcaption></figure>

<figure><img src="image_25.png" /></figure>

Grass biomass

Tree biomass

Figure S7-b

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