# Deciphering spatiotemporal patterns of rhizodeposition with a functional-structural root model: RhizoDep

Frédéric Rees, Tristan Gérault, Marion Gauthier, Romain Barillot, Céline

Richard-Molard, Alexandra Jullien, Claire Chenu, Christophe Pradal, Bruno

Andrieu

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► To cite this version:

Frédéric Rees, Tristan Gérault, Marion Gauthier, Romain Barillot, Céline Richard-Molard, et al. Deciphering spatiotemporal patterns of rhizodeposition with a functional-structural root model: RhizoDep. Plant and Soil, In press, 10.1007/s11104-025-07766-z. http://hal-05215320v2

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# Deciphering spatiotemporal patterns of rhizodeposition with a functional-structural root model: *RhizoDep*

Frédéric Rees ID · Tristan Gérault ID · Marion Gauthier ID ·

Romain Barillot ID · Céline Richard-Molard ID · Alexandra Jullien ID ·

Claire Chenu ID · Christophe Pradal ID · Bruno Andrieu ID ·

Received: 22 April 2025 / Accepted: 20 July 2025

© The Author(s) 2025

## Abstract

**Background and Aims** Rhizodeposition, i.e. the release of organic matters by roots, constitutes a significant fraction of the plant carbon (C) budget and plays a key role in plant-soil interactions. However, its spatial and temporal dynamics remain poorly understood.

**Methods** We developed *RhizoDep*, a new functional-structural root model that simulates 3D root growth, respiration, and rhizodeposition based on C balance and root morphology at the individual root segment level.

Responsible Editor: Hans Lambers.

**Supplementary Information** The online version contains supplementary material available at https://doi.org/10.1007/s11104-025-07766-z.

F. Rees (✉) · T. Gérault · M. Gauthier ·
C. Richard-Molard · A. Jullien · C. Chenu · B. Andrieu ·
Université Paris-Saclay, INRAE, AgroParisTech, UMR ·
EcoSys, 91120 Palaiseau, France ·
e-mail: frederic.rees@inrae.fr

R. Barillot
INRAE, UR P3F, 86600 Lusignan, France

C. Pradal
CIRAD, UMR AGAP Institut and Inria, Montpellier,
France

C. Pradal
AGAP, Univ Montpellier, CIRAD, INRAE, Institut Agro,
Montpellier, France

**Results** Our model successfully reproduced the dynamics of belowground C flows observed in a previous pulse-labelling field experiment on spring wheat. Our simulations revealed that root C exudation largely dominated over mucilage secretion and cap cells sloughing in terms of C release. The spatial distribution of exudation rate along the roots was driven by the preferential unloading of sugars to support root elongation and emergence, and was modulated by the formation of apoplastic barriers. Furthermore, our results demonstrated that, for a given C allocation flow to roots, variations in root hairs or lateral root number had minimal effects on rhizodeposition, whereas changes in root tissue density had a significant impact.

*Conclusion* *RhizoDep* offers a new opportunity to explore the dynamics of C exchange at the plant-soil interface and to identify traits and environmental conditions that favor rhizodeposition.

**Keywords** FSPM · Root exudation · Mucilage · Cells sloughing · Root hairs · Root architecture · ArchiSimple

## Introduction

Rhizodeposition, i.e. the release of organic carbon (C) by plant roots into the soil over their life, is a major yet poorly quantified component of the plant C cycle. This process accounts for 5–15% of net
photosynthesized C and more than a third of C allocated to roots (Nguyen 2003; Pausch and Kuzyakov 2018). Rhizodeposits encompass various materials including water-soluble, low-molecular weight exudates, polymers (e.g. mucilage), sloughed cells, and volatile organic compounds (Jones et al. 2009). While root exudates have sometimes been considered as an undesired loss of C by the plant (Jones and Darrah 1996), they have been increasingly recognized as fundamental to plant's adaptation to its environment. For instance, plants benefit from rhizodeposition by solubilizing phosphorus via the release of carboxylates (Hinsinger 2001) or mobilizing soil nitrogen (N) through exudate-induced acceleration of soil organic matter (SOM) mineralization (Cheng et al. 2014; Henneron et al. 2020). Additionally, mucilage secretion, and to some extent cap cell release, can favor root penetration, maintain plant water uptake, and protect the root tip against contaminants or pathogens (Morel et al. 1986; Uden 2000; Hawes et al. 2002; Cannesan et al. 2011; Carminati et al. 2016). Certain exudates and volatiles also contribute to plant defense mechanisms (Bertin et al. 2003; Czarnota et al. 2003; Guo et al. 2017) and communication (Dam et al. 2016; Rasmann et al. 2017). Rhizodeposits significantly influence SOM storage, either positively by contributing to the formation of long-lasting, microbial-processed organic compounds (Sokol et al. 2019), or negatively through rhizospheric priming effect (Villarino et al. 2021). In this context, the spatial localization of root C inputs (i.e., rhizodeposits and root necromass) within the soil profile is critical, as the rate of SOM decomposition usually decreases with soil depth while the susceptibility of SOM to priming effect increases (Balesdent et al. 2018; Gaudel et al. 2022). Distinct rhizodeposits have contrasted effects on SOM dynamics (Mary et al. 1993), yet few studies have quantified the individual contribution of root exudates, mucilage, sloughed cells and volatiles to the overall release of C by roots. While mucilage secretion and cells sloughing contribute have been suggested to contribute to rhizodeposition at least 10 times less than root exudates (Nguyen 2003; Rees et al. 2005), high-molecular-weight exudates were shown to constitute 14–52% of total rhizodeposited C in maize (Jones and Darrah 1993).

Despite growing recognition of its importance,
the spatial and temporal evolution of rhizodeposition
over different scales has remained largely unexplored

(Galindo-Castañeda et al. 2024). Root tips are widely
considered the primary site of exudation (Badri and
Vivanco 2009; Jones et al. 2009), though some stud-
ies have suggested alternative “hotspots” such as
the root hair zone, lateral root emergence sites, or
even the root base (Badri and Vivanco 2009; Holz
et al. 2018; Voothuluru et al. 2018). Additionally,
the temporal dynamics of rhizodeposition remain
unclear. Plant labelling experiments have shown that
rhizodeposited C primarily originates from recent
photoassimilates, and therefore follows a diurnal
pattern (Liljeroth et al. 1990a; Badri and Vivanco
2009). However, rhizodeposition rates also evolve
over the course of the growing season. In cereals,
mass rhizodeposition rates (per gram of root bio-
mass) are usually maximal at early growth stages and
then decrease over time, e.g. after tillering (Keith
et al. 1986; Remus and Augustin 2016; Pausch and
Kuzyakov 2018). These temporal patterns have been
attributed to changes in C allocation, as root exuda-
tion is often considered a passive efflux driven by the
gradient of metabolites concentration between roots
and the growing medium (Jones and Darrah 1996;
Henry et al. 2005; Personeni et al. 2007). However,
studies indicate that variations in the exudation of a
given compound do not necessarily follow variations
of its concentration inside root cells (Canarini et al.
2016; Proctor and He 2017). Processes such as the re-
uptake of specific exudates by roots (Jones and Dar-
rah 1993) and root morphological changes such as
the formation of hydrophobic barriers limiting radial
transport may modulate these concentration-driven
loss of exudates by the roots. Eventually, the spati-
otemporal variability of rhizodeposition arises from
complex interactions between genotype, environment,
and growth stage, contributing to the high variability
observed across studies.

Plant models are valuable tools for integrat-
ing these interactions and predicting rhizodeposi-
tion dynamics. However, most crop models do not
explicitly represent rhizodeposition, often treating
it solely as root decay, as in STICS (Beaudoin et al.
2023). An increasing number of models focusing
on soil or rhizosphere include a flow of C input as
rhizodeposits/exudates, but only a few of them pro-
vide an actual mean to estimate it. In such models,
the rate of rhizodeposition is usually calculated using
a predetermined C allometric distribution within
the plant (Zhang et al. 2021), or is allowed to vary

<figure><img src="image_3.png" /></figure>
to match certain patterns (Raynaud 2010). Given the interplay between root architecture and plant metabolism in rhizodeposition, Functional Structural Plant Models (FSPM) offer a promising approach. Despite their potential, only a few FSPM have incorporated rhizodeposition processes until now. Some models consider rhizodeposition as a fixed fraction of root-allocated C (Barillot et al. 2016), while others do not distinguish it from root decay (Louarn and Faverjon 2018). Landl et al. (2021) extended the CPlantBox model that explicitly includes a dynamic root architecture, by considering a constant term of citrate exudation and mucilage secretion along roots. Giraud et al. (2023, 2025) developed the CPlantBox model further and included a unidirectional rate of sucrose exudation restricted to root tips and regulated by the local concentration of sucrose in the phloem, which itself depends on the C dynamics simulated in other parts of the growing plant. This regulation of exudation echoed the pioneer work of Jones and Darrah (1996), who proposed a conceptual model linking sugar exudation to sugars concentration and root cell membrane permeability. This model was later refined to account for a decrease in the permeability with the distance from root tip (Personeni et al. 2007), although it was not tested at the whole root system scale. Giraud et al. (2025) also recently added the simulation of mucilage secretion as a function of starch content in CPlantBox, and linked the two rhizodeposition processes at root tips to a model of soil carbon and water dynamics. Although these recent progresses offer new opportunities to explore the functioning of the rhizosphere as a function of plant development, no models have so far enabled to investigate the spatial and temporal variability of distinct rhizodeposition processes along the roots.

This study aims to explore spatial and temporal patterns of rhizodeposition in silico using *RhizoDep*, a new mechanistic functional structural root model. We hypothesize that local C balance along roots represents the main factor explaining rhizodeposition patterns. First, we introduce the principles of *RhizoDep* and then validate its simulation outputs against belowground C flows from a previously published ¹⁴C-labelling field experiment on spring wheat. We then analyze the spatial variability of distinct rhizodeposition processes along wheat roots and finally evaluate the impact of key root traits on rhizodeposition.

# Methods

## Model overview

*RhizoDep* is a process-based FSPM that simulates how roots grow, respire, and emit rhizodeposits into the soil, in interaction with a dynamic 3D root architecture and the distribution of available C (Fig. 1). The model operates at fine spatial and temporal scales, typically simulating root segments of 1-mm with an hourly time step. *RhizoDep* incorporates simplified physiological processes that account for major C transfers within the roots and between roots, soil and atmosphere. Aside from soil temperature, which can affect rates in various ways, the main input variable of the model is the net C transferred from the aerial parts of the plant to the root system. This input is represented as sucrose (C₁₂H₂₂O₁₁) transported through the phloem vessels. A portion of this sucrose is then unloaded and converted into hexose (C₆H₁₂O₆), which serves as the substrate driving key metabolic processes. These include: i) the production of root structural mass, associated with the elongation of roots or root hairs and secondary growth, ii) root maintenance, iii) sugar immobilization in or remobilization from a reserve pool, and iv) rhizodeposition. No priority is assigned to any of these processes in terms of hexose consumption. Additionally, a simple representation of the fate of rhizodeposits outside the roots has been implemented, though such processes are expected to be managed by a dedicated soil model in the future. *RhizoDep* focuses on C dynamics within the root-soil system and does not simulate the aerial parts of the plant, C allocation from shoots to roots, or the dynamics of water and mineral nutrients. Similarly, C costs associated with symbiotic microorganisms (e.g. *Rhizobium*, mycorrhizae) or parasitic organisms (e.g. root-knot nematodes, broomrape) have been excluded but may be incorporated in future versions.

Below, we provide a brief summary of the main features of the model. Additional details, including equations and justifications, are available in the Supplementary file 1. A list of the key variables and parameters of the model can be found in Supplementary file 2.
<figure><img src="image_4.png" /><figcaption>**Fig. 1** Overview of the *RhizoDep* model. Photoassimilated C enters the root system as sucrose (model input), which is then distributed among each root element (1) and can be converted into hexose (2). Hexose may be stored in a reserve pool (3), used for maintenance (4), or consumed for growth, contributing to structural mass production—either through longitudinal growth (for an apex) or radial growth (for a segment), or through the emergence of new lateral roots or root hairs (5).</figcaption></figure>

Once exuded outside the root, sugars can be reabsorbed by the root (6) or lost from the root-soil interface due to microbial degradation, sorption, or diffusion (7). Similarly, other rhizodeposits (e.g., mucilage, sloughed cells) can accumulate at the root-soil interface or be lost. The local C balance within each root element ultimately constrains potential root architecture development, as defined by growth rules adapted from the *ArchiSimple* model (Pagès et al. 2014).

## Representation of the root-soil system

In *RhizoDep*, the root system is discretized into root elements represented as cylindrical segments, each defined by its length and radius. Any given root axis consists of a series of segments of constant length *l*_{segment}, terminating in an apical cylinder. Segments can grow radially but not longitudinally, whereas apices can elongate but cannot expand radially. When an apex exceeds *l*_{segment} in length, it is segmented to form at least one new segment and one apex. Each root element is characterized by its dimensions, 3D coordinates, structural mass, and individual pools of sucrose, hexose, and reserve C (Fig. 1). Structural C is determined based on the element's volume, using a constant root tissue density and C content; it can

only be modified by longitudinal or radial growth. As sucrose is the primary compound transported through the phloem (Lohaus 2022), it represents in the model the only form of C that can be transported between root elements. Hexose, on the other hand, includes all mobile C available within the epidermal, cortical, and non-vascular stele's cells. Reserve C encompasses all starch, fructan, and vacuolar sugars that are not immediately available to support root growth, maintenance, or rhizodeposition. The concentrations of sucrose, hexose, and reserve are assumed homogeneous within each root element and are expressed relative to structural mass (moles per gram). *RhizoDep* does not differentiate between root tissues (e.g. epidermis, cortex, stele) except when calculating the effective exchange surface between the root and the

<figure><img src="image_5.png" /></figure>
surrounding soil solution. Root hairs are treated as a specific extension of this exchange surface and as a contributor to the structural mass of the root element. The “soil” compartment in *RhizoDep* is limited to the root-soil interface associated with each root element, characterized by its exchange surface and the concentration of hexose, mucilage, and sloughed cells. The use of an intermediary root-soil interface, rather than an explicit soil volume, has been introduced to facilitate coupling *RhizoDep* with external model capable of describing rhizodeposits transformation in the soil.

### Distribution of sucrose

The C allocated as sucrose from the aerial parts to the root system is distributed across root elements under the assumption of no resistance to longitudinal transport (see details in SI 1.1). As a result, sucrose concentration remains homogeneous throughout the root system, consistent with the theory of rapid pressure-concentration waves propagating along the phloem (Thompson and Holbrook 2004). Within each root element, sucrose is partly converted into hexose (SI 1.2) based on local concentration gradient between sucrose and hexose (Eq. S1) and the rate of hexose consumption for growth in the element (Eq. S2). Conversely, hexose can be reconverted into sucrose depending on the concentration of mobile hexose (Eq. S3), mimicking the phloem reloading occurring in non-growing parts of the root system.

### Root growth

The potential growth of each root element is defined based on an adaptation of the growth rules implemented in *ArchiSimple* (Pagès et al. 2014). Further details are provided in section SI 1.3. Briefly, lateral root primordia form at the root tip of the “mother” root, maintaining a constant distance between primordia along the same axis. In *ArchiSimple*, most root properties derive from the initial root apical diameter. The diameter of a new lateral root is randomly drawn from a Gaussian distribution centered on a mean diameter proportional to that of the mother root, and the new root lateral emerges following a predetermined dormancy period. The potential elongation rate of a root apex and its lifespan are both proportional to its diameter, while the total elongation duration of a root is proportional to the square of its diameter. The

lifespan of a root also depends on its root tissue density. Finally, root abscission occurs when the apex of the root, along with the apices of all lateral roots on the same axis, have reached the end of their lifespan.

While most of the rules of *ArchiSimple* remain unchanged in *RhizoDep*, a key difference lies in how actual root growth is regulated by available C. In *ArchiSimple*, root elongation is constrained by a single “satisfaction coefficient”, which represents the ratio between biomass input from the shoots and the total cumulative root biomass demand for elongation across all axes. In *RhizoDep*, growth is instead limited by the amount of locally available hexose that can be converted into new structural material. Actual growth rates are further modulated within each root element by the local hexose concentration (Eq. S6). Notably, the mobile hexose available for elongation corresponds to the hexose within the root elongation zone, whose length depends on the apical radius (Eq. S7) and may span multiple root elements (Fig. S1). Additionally, the conversion of hexose into structural mass generates growth respiration (Thornley and Cannell 2000), consuming an additional fraction of the available hexose (Eq. S12).

### Root hairs dynamics

In *RhizoDep*, root hairs on each element are defined by their density (number of hairs per unit root length), as well as their average length, diameter, and age (see SI 1.4). Root hairs are assumed to emerge just above the root elongation zone (Guichard et al. 2019) and to elongate until they reach their maximal length $l_{hair\_max}$ (meter). The elongation of living root hairs follows a potential growth rate, regulated by the concentration of hexose available within the supporting root element (Eq. S15). Once emerged, root hairs remain alive for a predefined duration. Given the lack of evidence suggesting that dead root hairs are sloughed off over time (Fusseder 1987; Nguyen 2003), we assume that dead root hairs remain attached to the supporting root element—and consequently to the root system—until the root element itself dies.

### Root maintenance

In *RhizoDep*, root maintenance is represented by a single function that encompasses all growth-independent processes requiring energy to sustain the functioning of a given root element (see SI 1.5).
Maintenance costs are assumed to be proportional to the dry structural mass and increase with the concentration of mobile hexose within the root element (Eq. S16), as suggested in previous modelling studies (Thornley and Cannell 2000; Barillot et al. 2016).

## Exchange with reserve

RhizoDep simulates a C reserve pool for each element, defined by its concentration in hexose-equivalent (see SI 1.6). Depending on the equilibrium between the reserve concentration and the concentration of mobile hexose, a net immobilization or remobilization of hexose may occur within the root element (Eq. S18-19). The reserve pool is also constrained by a maximal achievable concentration.

## Dynamics of rhizodeposits

In Rhizodep, rhizodeposition processes are represented as the exudation of sugars, the secretion of mucilage, and the release of root cap cells, while the emission of VOC has been neglected so far. Root exudation is modeled as the transfer of the two mobile C compounds represented in RhizoDep—hexose and sucrose—from the root into the soil solution (see SI 1.7). The net efflux of hexose from non-vascular cells and sucrose from phloem cells (Eq. 1 and 2) is described as the balance between gross exudation, driven by a diffusion gradient of concentration across the root plasma membrane, and active influx from the root-soil interface, modeled using a Michaelis–Menten formalism (Jones and Darrah 1993; Farrar et al. 2003; Personeni et al. 2007). The net losses in the amounts of hexose (Hex, moles of hexose) and sucrose (Suc, moles of sucrose) within a given root element i due to exudation are therefore expressed as:

where [Hex]symplast(i), [Hex]soil(i) and [Suc](i) represent the concentrations of root mobile hexose, hexose at the root-soil interface and sucrose within the root element i (mol gDW⁻¹), Tᵢ is the soil temperature perceived by the root element i (K), Pexudation is a permeability parameter involved in the diffusion of sugars (gDW s⁻¹ m⁻²), Vup.hexose represents the maximal uptake rate of hexose from soil (mol of hexose s⁻¹ m⁻²), and Kup_hexose corresponds to the concentration for which the uptake rate is equal to half of the maximal rate (mol gDW⁻¹). The exchange surface area (m²) for hexose (S symplast-soil(i)) and sucrose (S phloem-soil(i)) depends on the morphology of the root element, particularly the presence of barriers to radial solute transport. When new root elements are formed, the apoplast (i.e. the intercellular space outside root plasma membranes) allows the external soil solution to reach the center of the root (Fig. S2), enabling sugar exchange with all root cells, including the phloem vessels. As the endodermis develops between the stele and cortex, direct access of the external soil solution to the root cells within the stele is lost, thereby restricting the exchange surface to epidermal and cortical cells only (Kamula et al. 1994). Similarly, if an exodermis forms beneath the epidermis, the exchange surface is further reduced, eventually being limited to the membrane of epidermal cells and living root hairs. Events such as the emergence of lateral roots can temporarily disrupt these transport barriers, increasing the exchange surface between root cells and the surrounding soil solution.

Mucilage secretion corresponds to a unidirectional flux from the root epidermis into the soil. The potential secretion rate is maximal at root tip and is assumed to decrease non-linearly with distance from the tip until becoming negligible (Paull and Jones 1975) (see S1.8, Eq. S32). The actual secretion

$$ \left(\frac{dHex}{dt}\right)_{\text{netexudation(i)}} = S_{\text{symplast-soil(i)}}(t) \cdot \left[ P_{\text{exudation}}(T_i) \cdot ([\text{Hex}]_{\text{symplast(i)}}(t) - [\text{Hex}]_{\text{soil(i)}}(t)) - V_{\text{up.hexose}}(T_i) \cdot \frac{[\text{Hex}]_{\text{soil(i)}}(t)}{K_{\text{up.hexose}} + [\text{Hex}]_{\text{soil(i)}}(t)} \right] \quad (1) $$

$$ \left(\frac{dSuc}{dt}\right)_{\text{netexudation(i)}} = S_{\text{phloem-soil(i)}}(t) \cdot \left[ P_{\text{exudation}}(T_i) \cdot ([Suc]_{(i)}(t) - 0.5 \cdot [Hex]_{\text{soil(i)}}(t)) - V_{\text{up.hexose}}(T_i) \cdot \frac{[Hex]_{\text{soil(i)}}(t)}{K_{\text{up.hexose}} + [Hex]_{\text{soil(i)}}(t)} \right] \quad (2) $$
rate depends on the external root surface area, and is constrained by both the hexose concentration in peripheral root cells and the surfacic concentration of mucilage at the root-soil interface (Eq. S32-S33). Consequently, mucilage secretion is inhibited when mucilage accumulates at the root-soil interface, as observed during dry conditions (Morré et al. 1967).

The release of root cap cells also follows a unidirectional flux of matter. The potential release rate decreases linearly with distance from the root tip and drops to zero above the elongation zone (see SI 1.9). The actual rate of cell release depends on the external surface area of the root element but is independent of mobile hexose availability (Curlango-Rivera et al. 2010). However, it is limited by the surfacic concentration of root cap cells accumulated at the external surface, eventually becoming inhibited beyond a certain threshold (Brigham et al. 1998) (Eq. S34-S35). Notably, this description of cell release excludes the contribution of root hairs sloughing, which was not incorporated into RhizoDep due to a lack of evidence that dead root hairs are shed over time (Fusseder 1987; Nguyen 2003).

Once released into the soil, each type of rhizodeposit either accumulates at the root-soil interface or disappears (SI 1.10). We assume that sucrose, once it has been exuded, is instantly cleaved into hexose. Hence, rhizodeposits at the root-soil interface are represented by hexose, mucilage and cap cells only. In the absence of a dedicated soil model able to represent the degradation of rhizodeposits, a Michaelis–Menten kinetics approach was implemented to mimic microbial degradation for each rhizodeposit (Eq. S36-38).

## Carbon balance

At the end of a time step, a local C balance is established by accounting for all relevant processes. This balance determines the changes in the amounts of sucrose (Suc, in moles of sucrose), hexose (Hex, in moles of hexose), mucilage (Muc, in moles of equivalent-hexose) and sloughed cells (Cells, in moles of equivalent-hexose) within the various compartments of each root element i, which are then used to update the system for the next time step: (see details in SI 1.11):

$$ \left(\frac{d\text{Hex}}{dt}\right)_{\text{symplast(i)}} = \left(\frac{d\text{Hex}}{dt}\right)_{\text{production(i)}} - 2 \cdot \left(\frac{d\text{Suc}}{dt}\right)_{\text{production(i)}} - \left(\frac{d\text{Hex}}{dt}\right)_{\text{growth(i)}} - \left(\frac{d\text{Hex}}{dt}\right)_{\text{maintenance(i)}} - \left(\frac{d\text{Hex}}{dt}\right)_{\text{netimmobilization(i)}} - \left(\frac{d\text{Hex}}{dt}\right)_{\text{netexudation(i)}} - \left(\frac{d\text{Hex}}{dt}\right)_{\text{secretion(i)}} - \left(\frac{d\text{Hex}}{dt}\right)_{\text{sloughing(i)}} \quad (4) $$

$$ \left(\frac{d\text{Hex}}{dt}\right)_{\text{reserve(i)}} = \left(\frac{d\text{Hex}}{dt}\right)_{\text{netimmobilization(i)}} \quad (5) $$

$$ \left(\frac{d\text{Hex}}{dt}\right)_{\text{soil(i)}} = \left(\frac{d\text{Hex}}{dt}\right)_{\text{netexudation(i)}} + 2 \cdot \left(\frac{d\text{Suc}}{dt}\right)_{\text{netexudation(i)}} - \left(\frac{d\text{Hex}}{dt}\right)_{\text{degradation(i)}} \quad (6) $$

$$ \left(\frac{d\text{Muc}}{dt}\right)_{\text{soil(i)}} = \left(\frac{d\text{Hex}}{dt}\right)_{\text{secretion(i)}} - \left(\frac{d\text{Muc}}{dt}\right)_{\text{degradation(i)}} \quad (7) $$

$$ \left(\frac{d\text{Cells}}{dt}\right)_{\text{soil(i)}} = \left(\frac{d\text{Hex}}{dt}\right)_{\text{sloughing(i)}} - \left(\frac{d\text{Cells}}{dt}\right)_{\text{degradation(i)}} \quad (8) $$

If the C balance results in a negative amount in any compartment of root element i, the amount is set to zero, and the deficit is accounted for in the next time step (see details in SI 1.11).

## Model organization, implementation and resolution

RhizoDep is implemented in Python 3 (version > 3.6) (Van Rossum and Drake 2009) and integrated within the OpenAlea platform (Pradal et al. 2008). It utilizes the Multiscale Tree Graph structure (Godin and Carglio 1998; Pradal and Godin 2020), which allows for the storage and retrieval of all topological, geometrical, and functional properties of each root element at every time step. The geometry of the root system and the spatial distribution of variables along the roots can be

$$ \left(\frac{d\text{Suc}}{dt}\right)_{\text{phloem(i)}} = \left(\frac{d\text{Suc}}{dt}\right)_{\text{production(i)}} - \frac{1}{2} \cdot \left(\frac{d\text{Hex}}{dt}\right)_{\text{production(i)}} + \left(\frac{d\text{Suc}}{dt}\right)_{\text{allocation(i)}} - \left(\frac{d\text{Suc}}{dt}\right)_{\text{netexudation(i)}} \quad (3) $$
visualized in a 3D graph using PlantGL (Pradal et al. 2009) or Pyvista (Sullivan and Kaszynski 2019). The code is open-source, licensed under CeCILL-C, and available as an OpenAlea package on GitHub (https://github.com/openalea/rhizodep).

*RhizoDep* is structured in several modules, each corresponding to a specific process (Fig. S3). The model operates using a discrete-time numerical integration scheme with a time step of 1 h. At each time step, starting at *t* and ending at *t+Δt*, all modules compute the new state variables defined at *t+Δt* based on the state variables from *t* (i.e., the end of the previous time step). This approach ensures that all processes operate simultaneously without anyone process being prioritized in resource consumption and allocation.

## Simulation plan

### Validating *RhizoDep* for spring wheat

To validate *RhizoDep*, we used the data from the field study conducted by Swinnen et al. (1994a). These authors monitored the entire growth cycle of spring wheat (*Triticum aestivum* var. Minaret) from March to August 1989 in Netherlands. Using repeated ¹⁴CO₂ pulse labelling and belowground respiration measurements over several days, they estimated the temporal distribution of photoassimilated C among root biomass production, root respiration, and rhizodeposition. They also derived belowground C fluxes based on the evolution of shoot biomass and shoot:root biomass ratio, fitted with empirical functions (see details in SI 4). To extend their dataset, we supplemented their calculations to estimate C flows at both germination and harvest stages (see SI 5). The estimated C flow allocated to roots over time served as the sucrose input in *RhizoDep*, allowing us to simulate the experiment in silico. Soil temperature variations over the simulation period were derived from temperature measurements recorded one year later at the same site (SI 4.6).

Model parametrization was conducted independently of the Swinnen et al. (1994a) dataset. The only exception corresponded to the life duration coefficient of a root, which we calculated by assuming the life duration of a seminal root to be equal or higher than the period over which no significant root decay occurs according to the dataset of Swinnen et al. (1994a). A complete list of model parameters, their estimated values, and sources is provided in Supporting Tables

ST. Growth parameters for *RhizoDep* were estimated based on our own unpublished pot and rhizobox experiments (see SI 6.1), while other parameters were sourced from literature data for wheat and, in some cases, other plant species (see SI 6.2). For approximately 25% of the 133 numerical parameters, no direct data were available, so values were inferred based on similar parameters already defined in the model. In only two instances did the initial parameter estimates produce unrealistic results, requiring manual adjustment by trial and error until plausible sucrose unloading patterns in growing roots were achieved (see SI 6.2).

### Testing the influence of specific root traits

To determine which root traits most strongly influence rhizodeposition and its contribution to root C balance, we ran the same baseline simulation for spring wheat (Sc1) and compared it against modified scenarios related to three root traits:

* **Root hair density:** Root hairs were either repressed (Sc2) or their density was doubled along the roots (Sc3).

* **Lateral root formation:** The average distance between lateral root primordia was either doubled (Sc4), reducing lateral root number, or halved (Sc5), increasing lateral root number.

* **Root tissue density:** Tissue density was either halved (Sc6) or increased by 50% (Sc7) to capture a plausible range of variation (Pagès et al. 2014).

We hypothesized that scenarios reducing root exchange surface (Sc2 and Sc4) would lead to lower rhizodeposition, whereas increasing the number of active exudation sites (e.g., root tips in Sc5) or lowering C consumption for structural mass production (Sc6) would increase rhizodeposition.

## Simulation results

### Simulation of belowground C flows during spring wheat growth

We simulated the temporal evolution of belowground C flows throughout the entire growth cycle of spring wheat (scenario Sc1). As shown in Fig. 2a,
<figure><img src="image_6.png" /><figcaption>**Fig. 2** Comparison of belowground C flows of spring wheat, as calculated from the data of Swinnen et al. (1994b) (dashed lines) and simulated by *RhizoDep* (continuous lines) in scenario Sc1, using the same C input to the roots. Flows are</figcaption></figure>

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

shown either cumulatively (a) or on a daily basis (b) over the entire growth period. Note that in Swinnen et al., root mass production corresponds to total biomass, whereas in *RhizoDep*, it represents structural mass only

the cumulative flows of root biomass production, respiration, and rhizodeposition predicted by *RhizoDep* closely matched those calculated by Swinnen et al. (1994b). The final distribution of belowground C among biomass production, root respiration, and rhizodeposition was 0.38, 0.33 and 0.21 gC plant⁻¹, respectively—differing by only 7%, 10% and 3% from the estimation of Swinnen et al. (1994b). The daily production of root structural mass (gC per day per plant) increased rapidly after mid-April, peaking

at the end of May. In contrast, the flows associated with root respiration and rhizodeposition peaked one to two weeks later (Fig. 2b), a period corresponding to the onset of stem elongation, as reported by Swinnen et al. (1994a). The simulated release of C through dead roots became significant in June and surpassed rhizodeposited C from early July onward (Fig. 2b).

As expected, root exudation was the dominant rhizodeposition flow, accounting for 98.4% of the

<table><caption>**Table 1** Comparison of cumulative belowground C allocation in spring wheat over 6 months of growth, as simulated by *RhizoDep* across the scenarios Sc1-Sc7 differing in root hairs density, lateral root density, and/or root tissue density</caption><thead><tr><th></th><th>Sc1</th><th>Sc2</th><th>Sc3</th><th>Sc4</th><th>Sc5</th><th>Sc6</th><th>Sc7</th></tr></thead><tbody><tr><td>Root hairs density (hairs cm<sup>-1</sup> mm<sup>-1</sup>)*</td><td>3750</td><td>0</td><td>7500</td><td>3750</td><td>3750</td><td>3750</td><td>3750</td></tr><tr><td>Lateral root density (laterals m<sup>-1</sup>)</td><td>210</td><td>210</td><td>210</td><td>105</td><td>420</td><td>210</td><td>210</td></tr><tr><td>Root tissue density (gDW cm<sup>-3</sup>)</td><td>0.14</td><td>0.14</td><td>0.14</td><td>0.14</td><td>0.14</td><td>0.07</td><td>0.21</td></tr><tr><td>Biomass production (mgC plant<sup>-1</sup>)</td><td>383</td><td>378</td><td>389</td><td>353</td><td>385</td><td>258</td><td>463</td></tr><tr><td>Respiration (mgC plant<sup>-1</sup>)</td><td>328</td><td>337</td><td>324</td><td>346</td><td>332</td><td>264</td><td>324</td></tr><tr><td>Rhizodeposition (mgC plant<sup>-1</sup>)</td><td>212</td><td>208</td><td>210</td><td>224</td><td>206</td><td>387</td><td>129</td></tr><tr><td>&gt; Net exudation of hexose (mgC plant<sup>-1</sup>)</td><td>203</td><td>199</td><td>201</td><td>216</td><td>195</td><td>374</td><td>123</td></tr><tr><td>&gt; Net exudation of sucrose (mgC plant<sup>-1</sup>)</td><td>5.60</td><td>6.00</td><td>5.41</td><td>5.59</td><td>6.28</td><td>9.17</td><td>3.74</td></tr><tr><td>&gt; Mucilage secretion (mgC plant<sup>-1</sup>)</td><td>0.66</td><td>0.53</td><td>0.79</td><td>0.62</td><td>0.79</td><td>0.79</td><td>0.58</td></tr><tr><td>&gt; Cap cells sloughing (mgC plant<sup>-1</sup>)</td><td>2.68</td><td>2.69</td><td>2.66</td><td>2.30</td><td>3.12</td><td>3.14</td><td>2.38</td></tr></tbody></table>

Sc1: reference scenario. Sc2: no root hairs. Sc3: twice more root hairs. Sc4: 50% less lateral roots. Sc5: twice more lateral roots. Sc6: 50% lower RTD. Sc7: 50% higher RTD. * Root hairs density is expressed as the number of hairs per centimeter of root for a root with a 1-mm diameter.
rhizodeposited C over the entire growth period. In contrast, the total release of root caps cells and the secretion of mucilage contributed to only 1.3% and 0.3% of the rhizodeposited C, respectively (Table 1). The exudation of hexose from the symplast of roots was much higher than the exudation of sucrose from the phloem, which only contributed to 2.7% of the overall C exudation over the simulation (Table 1).

### Spatial distribution of rhizodeposition along the roots

A large spatial variability of rhizodeposition was simulated across the root system. As shown in Fig. 3 and Supplementary file 3, the lineic rate of rhizodeposition (gC per day per cm) peaked near growing root tips. To explore this pattern in detail, we examined the first seminal root and analyzed the distribution of the three rhizodeposition processes alongside potential explanatory variables every

30 days (Fig. 4 and Fig. S6-S13). As long as the seminal root continued elongating ($t \le 104$ days), the lineic rhizodeposition rate was highest at 0.5–1 cm and around 3 cm from root tip. The rate plateaued around 6 cm from the tip (Fig. S6), at a level 20 to 30 times lower than at 1 cm, and remained stable further along the root (data not shown). Once elongation ceased, the rhizodeposition rate became uniform along the seminal root axis (Fig. 3 and Fig. S6). The spatial distribution of exudation closely matched that of total rhizodeposition (Fig. 4a, Fig. S7). Exudation was 15% lower than total rhizodeposition at the root tip but differed by less than 1% beyond 10 mm. In comparison, root cap cell release was highest at the tip and decreased linearly over the first cm until disappearing (Fig. 4a, Fig. S8). Mucilage secretion also peaked at the tip, decreasing sharply over the first 2 cm and more gradually along the rest of the root (Fig. 4a, Fig. S9). Exudation profile appeared to be more strongly linked to root mobile hexose

<figure><img src="image_8.png" /><figcaption>**Fig. 3** Simulated dynamic growth and rhizodeposition of the spring wheat root system from March to August 1989, based on *RhizoDep* scenario Sc1 and the data from Swinnen et al. (1994b). Colors indicate the net rhizodeposition flow (in gC</figcaption></figure>

per cm per day) along each root over time. The volume of living root hairs is represented as a semi-transparent colored cylinder, while dead roots and dead root hairs are shown in black
<figure><img src="image_9.png" /><figcaption>**Fig. 4** Distribution of rhizodeposition rates and mobile hexose concentration (a), as well as exudation rate, sucrose unloading rate, and C consumption rate for sustaining growth (b) along the first seminal root of spring wheat, 60 days after germination.</figcaption></figure>

concentrations (Fig. S10) than to root exchange surface (Fig. S13). When pooling data from all five time points, net rhizodeposition correlated strongly with root mobile hexose concentration along the first seminal root ($r=0.94$), while its correlation with root exchange surface was weaker ($r=0.79$) (Fig. S14). However, when analyzing each time point separately and focusing on mature root segments (> 3 cm from the tip), rhizodeposition varied closely with root exchange surface ($R^2>0.98$), but was negatively correlated with root mobile hexose concentration (Fig. S15-S16).

To investigate further the contribution of different parts of the root system, we aggregated segments according to root order and/or to their position within the root axis. Over the 6 months of spring wheat growth, seminal roots and adventitious roots contributed more to rhizodeposition than lateral roots (Fig. S17). The apical parts of seminal and adventitious roots, defined here as the first 4 cm of each axis, contributed more to rhizodeposition than the basal parts above 4 cm from root tip, even though their contribution to total root length was much lower (Fig. S17). However, the contribution of roots' basal parts to rhizodeposition gradually increased over time until becoming dominant after 4 months (Fig. S18).

<figure><img src="image_10.png" /></figure>

Simulation were performed using *RhizoDep* in scenario Sc1. Values represent averages over a 7-h period, during which root elongation was less than 2 mm

## Influence of root hairs, lateral roots and root tissue density on wheat's rhizodeposition

To identify the root traits most influential on rhizodeposition and its contribution to the root C balance, we simulated spring wheat growth and conducted a sensitivity analysis focusing on three root traits. Surprisingly, root hairs had minimal impact on overall C flows: their removal (scenario Sc2) or a twofold increase in their density (Sc3) altered total root structural C production and rhizodeposition by no more than 2% (Table 1). Halving lateral root density (Sc4) led to an 8% decrease in root mass production, while root respiration and rhizodeposition increased by 6% each. Doubling lateral root density (Sc5) resulted in only minor changes, e.g. a 3% reduction in root exudation (Table 1). The most pronounced effects were observed when modifying root tissue density: halving it (Sc6) nearly doubled the allocation of belowground C to rhizodeposition (0.39 gC plant⁻¹), while root biomass production and respiration declined by 33% and 19%, respectively (Table 1). Conversely, increasing root tissue density by 50% (Sc7) promoted root biomass production (+21%) at the expense of rhizodeposition, which decreased by 39%.
Discussion

We developed a mechanistic root functional-struc-
tural model, *RhizoDep*, to elucidate the drivers of
rhizodeposition dynamics over time and space. The
model successfully reproduced belowground C flows
similar to those observed in a previous field experi-
ment with spring wheat. Our simulations demon-
strated that root exudation was the primary contribu-
tor to rhizodeposited C, while mucilage secretion
or cells sloughing played only minor roles. When
exploring the spatial distribution of rhizodeposition
along roots, we found that rhizodeposition peaked
at two distinct locations near the growing root tip.
This pattern was primarily driven by the preferential
unloading of sugars to sustain growth near the root tip
and further modulated by changes in root exchange
surface. Additionally, our results indicated that, given
the same total C allocation to the root system, the
presence of root hairs and the number of lateral roots
had minimal impact on the root C balance, whereas a
reduction in root tissue density significantly increased
rhizodeposition at the expense of root biomass
production.

Predicting root-derived carbon emission in soil
throughout plant growth

RhizoDep successfully simulated realistic below-
ground C flow dynamics in spring wheat. Using the
same C input to roots and an independently para-
metrized model based primarily on literature data,
we reproduced the temporal evolution of C allocation
to root production, root respiration, and rhizodepo-
sition, as calculated from field experimental data
by Swinnen et al. (1994b). All three belowground
C flows increased until tillering, then declined from
stem elongation to harvest, following the same trend
as total C allocation to the root system. A similar
decrease in plant rhizodeposition rate at the end of
the vegetative period has been documented for wheat
(Liljeroth et al. 1990b), rice (Aulakh et al. 2001),
and maize (Santangeli et al. 2024). Our simulations
on spring wheat also revealed that, when expressed
per gram of root biomass—as commonly reported in
experimental studies—rhizodeposition rate peaked
at germination and followed three distinct phases: a
continuous decrease in March, an increase in April

with the emergence of adventitious roots, and a sub-
sequent decrease from May to August (Fig. S5). A
comparable 3-phase pattern in sugar exudation per
gram of roots was observed in maize by Matsumoto
et al. (1979), with an intermediate peak before stem
elongation. Similarly, Aulakh et al. (2001) found that
the exudation rate in rice seedlings was 1 to 10 times
higher in early growth stages than at later develop-
ment stages when expressed per gram of roots.

Root mortality, conceptually distinct from
rhizodeposition, was the only belowground C flow
that significantly deviated between our simula-
tions and Swinnen's calculations. According to
*RhizoDep*, root mortality became significant only
in early June, approximately one month later than
expected by Swinnen et al. (1994b) (Fig. 2b). How-
ever, the precise timing of root mortality remained
uncertain in both cases (see section S8). Our results
indicate that rhizodeposits were primarily released
from May to July, whereas dead roots became the
dominant source of root-derived C in the final two
months, ultimately accounting for 64% of the total
root-derived C input to the soil. Estimates of total
root-derived C often rely on allometric relation-
ships, such as the one described by Bolinder et al.
(2007), which assumes that cumulative rhizodepos-
ited C represents 65% of root biomass C at harvest.
*RhizoDep* simulations suggest that, while this 65%
proportion remains plausible at harvest, it does not
apply consistently across earlier growth stages and
is subject to large uncertainty. The accuracy of this
estimate depends on how much of the actual dead
root mass is included in the standing root biomass
measured at harvest (Fig. S22).

Our simulations also provided the first assess-
ment of the relative contributions of distinct
rhizodeposition processes throughout the entire
growth cycle of a crop. We found that the exudation
of soluble compounds accounted for more than 98%
of the total C rhizodeposited by spring wheat, while
the release of cap cells was a minor contributor, and
mucilage secretion remained negligible. This esti-
mation was based on independent parametrization
of each rhizodeposition process using data from
separate studies, sometimes involving plant species
other than wheat. Since no study to date has simul-
taneously measured all three processes under the
same growth conditions, our simulations represent
to the best of our knowledge, the first estimation
of the relative importance of cap cell release and mucilage secretion compared to root exudation. These results align with previous literature-based conclusions that C release through mucilage secretion and cell sloughing is at least 10 times lower than that from root exudation (Nguyen 2003; Rees et al. 2005).

## Deciphering the spatiotemporal patterns of rhizodeposition

A key strength of *RhizoDep* is its ability to simulate spatial variations of rhizodeposition along the roots. In our model, exudation rate varies only due to i) changes in the gradient of sugar concentration between the root symplast and the surrounding soil solution and ii) changes in the exchange surface area between root cells and soil. Our simulations on spring wheat revealed that exudation—and consequently, rhizodeposition—typically peaked at two distinct locations near the growing root tip (Fig. 4). This spatial distribution of exudation near the apex followed the distribution of root mobile hexose rather than variations in root-soil exchange surface area (Fig. S14). However, the decline in exudation rate beyond 4 cm from the growing root tip correlated well with the decrease in root-soil exchange surface area, which offset the small increase in root mobile hexose observed in the region (Fig. S15). In the first seminal axis observed 60 days after germination, the second exudation peak, located 3 cm from the root tip, also coincided with peaks in sucrose unloading and hexose consumption for growth (Fig. 4b), corresponding to the emergence of the first lateral root (Video 2). In *RhizoDep*, the emergence of a lateral root temporarily generates a higher consumption of hexose in the root segment from which it emerges, triggering a higher sucrose unloading rate within the supporting root element (Eq. S2). The higher unloading rate leads in turn to the accumulation of hexose in that zone, resulting in a higher exudation rate. In contrast, the first exudation peak, located around 1 cm from the root tip—just beyond the 7-mm long root elongation zone—did not match with the maxima of sucrose unloading and hexose consumption by growth, which were situated closer to the root tip (Fig. 4b). This suggests that spatial variations in rhizodeposition along a growing root are directly or indirectly linked to preferential C unloading, to sustain either lateral

root emergence or root elongation. In the latter case, the delay likely reflects the period required for the root segment to mature out of the elongation zone. Experimental studies on pea (Egeraat 1975; Nielsen et al. 1994) and maize (Mariano and Keltjens 2003) previously identified two “hot spots” of exudation corresponding to the root extremity and the zone of lateral root emergence. In addition, studies on rape-seed demonstrated that exudation is not maximal at the root tip itself but rather a few mm away from it (Hoffland et al. 1989, 1992). These spatial exudation patterns naturally emerged in *RhizoDep* from spatial variations in mobile hexose concentration associated with root growth. The disruption of apoplastic barriers such as endodermis and exodermis during lateral root emergence could also contribute to increased exudation at the second peak. However, our analysis of root-soil exchange surface area suggests that this effect is transient—lasting only a few hours—and of limited amplitude (see Supplementary file 4). Thus, higher phloem unloading, required to sustain lateral root emergence, appears to be the primary driver of increased exudation at this site.

Unlike exudation, mucilage secretion and cap cell release were maximal at the root tip. Few studies have investigated the spatial distribution of mucilage secretion, but previous finding indicate that it peaks within the first millimeter of the primary root of maize (Paull and Jones 1975). Pankievicz et al. (2022) similarly reported that mucilage secretion by the aerial roots of a high-secreting maize genotype was highest at the root tip and decreased basipetally, becoming nearly undetectable 4 mm from the tip. Due to the lack of precise data, we modeled the decline in mucilage secretion as a gamma function of distance from the root tip, as previously suggested for exudation by Personeni et al. (2007). Additionally, since no evidence supports mucilage secretion by root hairs (Peterson and Farquhar 1996; Nguyen 2003), we excluded them from the surface contributing to mucilage secretion. Cap cell release was concentrated at the root tip and ceased beyond the elongation zone. Due to the distinct spatial distributions of the three rhizodeposition processes, their relative contribution to total rhizodeposited C varied along the root. For example, in the first mm of the primary root 60 days after germination, cap cell sloughing and mucilage secretion contributed 10% and 4% of total C rhizodeposition,
respectively, but these values dropped to just 1.2% and 0.4% when considering the entire root (Fig. 4a).

Although the first 4 cm of the primary root corre-
sponded to the main rhizodeposition zone along this
axis, the rest of the root also contributed significantly.
As the primary root elongated, then stopped, the pro-
portion of total rhizodeposited C within the first 4 cm
decreased from 86% at 30 days to just 8% at 150 days
(Table S2). Similarly, at the scale of the root system,
the contribution of apical parts of roots to the overall
rhizodeposition of the plant decreased over time, from
100% at germination stage to less than 15% at harvest
(Fig. S18). This highlights the limitations of simpli-
fied approaches that assume a uniform rhizodeposi-
tion rate along roots or that restrict rhizodeposition to
root tips alone, and fail to capture the complexity of
spatial and temporal rhizodeposition patterns.

Quantifying the impact of specific root traits

Beyond its contribution to understanding rhizodepo-
sition patterns, *RhizoDep* serves as a valuable tool for
in silico experimentation, allowing us to assess how
specific root traits affect rhizodeposition. While a full
sensitivity analysis was beyond our scope, we exam-
ined the relative importance of three root traits that
we expected to play a key role for rhizodeposition.

Contrary to our hypothesis, altering root hair
density had virtually no impact on rhizodeposition
(Table 1). Holz et al. (2018) compared a hairless bar-
ley mutant to a wild genotype and found that zones
with root hairs contributed up to 75% of the total
rhizodeposited C, yet the presence of root hairs only
marginally increased the mass flux of rhizodeposi-
tion per gram of root (by 1% to 7%). More recently,
Santangeli et al. (2024) investigated a maize root
hair defective mutant and observed a slight increase
in rhizodeposition per plant at specific growth stages
in the presence of root hairs, though the rate of
rhizodeposition per unit of root external surface area
actually decreased. Our simulations provide insight
into these seemingly contradictory findings: while
growing root hairs consume additional C, their contri-
bution to the total root-soil exchange surface remains
minimal. This total surface area includes not only the
external surface but also the accessible symplast sur-
face within the root. Over the entire root system, liv-
ing root hairs accounted for less than 4% of the total
exchange surface area during the first week of growth,

less than 2% over the first three months, and even less
at later stages. Even within the first 4 cm of the pri-
mary root, where rhizodeposition was highest, root
hairs contributed at most 8% to the total exchange sur-
face area (Fig. S13). Notably, we assumed that dead
root hairs do not contribute to exudate release, though
they likely contribute to water uptake (McElgunn and
Harrison 1969). In our simulations, root hairs had a
short lifespan, equivalent to 2 days at 20 °C (McEl-
gunn and Harrison 1969; Fusseder 1987; Nguyen
2003). If we had considered that dead root hairs
continued to released exudates, their contribution to
rhizodeposition might have been slightly higher.

Since rhizodeposition is maximal at root tips,
we expected that reducing the number of lateral
roots would significantly decrease the amount of
rhizodeposited C. However, halving the number
of lateral roots actually resulted in a 5% increase in
rhizodeposited C, while doubling their number led to
a slight 3% decrease (Table 1). This outcome under-
scores the complex relationship between root biomass
production and rhizodeposition, particularly when
accounting for root C balance within distinct root
orders (Galindo-Castañeda et al. 2024). Reducing lat-
eral root density limited potential growth, leading to
an accumulation of mobile C within the root, which
in turn stimulated root exudation despite the decrease
in the number of root tips. Furthermore, the short
growth duration of most lateral roots may have con-
strained their contribution to rhizodeposition, as they
received considerably less C once they ceased elon-
gating. Experimental studies on this relationship are
limited. Henry et al. (2005) observed that increasing
N availability in *Lolium multiflorum* grown in sand
reduced root biomass but increased the number of
root apices, which coincided with higher rhizodeposi-
tion per plant. Aoki et al. (2012) also reported a posi-
tive correlation between organic acid exudation rate
per gram of root biomass and the number of root api-
ces in tropical trees. Conversely, Meier et al. (2013)
found a negative correlation between C exudation rate
per gram of root biomass and the number of root api-
ces in loblolly pine, possibly due to pathogenic fungal
infection.

Among the three investigated traits, root tis-
sue density (RTD) had the most significant impact,
highlighting a potential trade-off between root bio-
mass production and rhizodeposition. When RTD
was halved, the C cost of root production decreased

<figure><img src="image_11.png" /></figure>
accordingly, which led an accumulation of mobile
C that was not used for growth, resulting in an 83%
increase in rhizodeposited C. This finding aligns with
the “root economic spectrum” theory, which associ-
ates low RTD with an “acquisitive” strategy and high
RTD with a “conservative” strategy (Roumet et al.
2016). When considering root exudation within this
framework, Wen et al. (2022) identified a low RTD as
one of the best predictors of high-exuding plant spe-
cies. A negative correlation between RTD and exuda-
tion has also been documented within a single plant
species, as demonstrated in two maize genotypes
grown in different soils (Santangeli et al. 2024).

*RhizoDep* provides a mechanistic foundation for interpreting the effects of such root traits on rhizodeposited C, considering the interaction between root C balance and the evolution of root structure. However, it is important to note that our conclusions here are specific to wheat and do not account for possible feedback mechanisms, such as changes in root architecture influencing C supply from the shoots via enhanced soil nutrient uptake.

Limitations and possible improvements

While our study successfully simulated the expected
belowground C flows of spring wheat, several limi-
tations of our approach should be mentioned. First,
the simulation time—approximately 16 h on a single
computer to simulate 6 months in the reference sce-
nario (Sc1)—could pose challenges when numerous
simulations are needed, e.g. for exploring environ-
mental effects or conducting extensive sensitivity
analyses. Since simulation time correlates directly
with the number of root elements in *RhizoDep*, effi-
ciency could be improved by optimizing root seg-
ment sizes (e.g., using variable sizes along the roots)
or parallelizing computation across different root
groups. Alternatively, rewriting *RhizoDep* into a com-
piled language and/or developing metamodeling strat-
egies allowing fast simulations of a few key variables
could increase its usability.

Another limitation arises from the large number
of parameters in this mechanistic model. Of the 31
parameters related to root architecture, most can be
measured from experimental observations of root sys-
tems. However, approximately 100 parameters asso-
ciated with root metabolism are not readily measur-
able without specific experiments. In this study, we

primarily relied on literature data, noting that 25% of
parameter values were unavailable and thus were esti-
mated based on their expected similarities with other
parameters. This parametrization highlights several
research gaps, e.g. the need for better quantification
of phloem unloading, root mortality, mucilage secre-
tion, and cell sloughing. Although our study focused
on spring wheat, *RhizoDep* was designed as a generic
root model, compatible with any terrestrial plant
species. We hypothesize that most root metabolism
parameters are conserved across plant species, elimi-
nating the need for extensive re-parametrization in
future applications. Validating the model with other
species will test this assumption, though experimental
datasets comparable to Swinnen et al. (1994b) remain
scarce.

In its current form, *RhizoDep* models only the
dynamics of sugars and their effects on root growth
and rhizodeposition, simplifying sucrose transport
and assuming that mobile hexose represent all solu-
ble compounds available for exudation. Integrating
carboxylates—a key component of exudates—would
enable the model to account for additional soil-plant
interactions, such as the solubilization of soil mineral
phosphate or the destabilization of mineral-associated
organic matter. Furthermore, integrating N metabo-
lism (e.g. N uptake, transformation, and transport)
and symbiotic associations in the model will allow
exploration of diverse plant strategies along the root
economic spectrum.

Conclusions

*RhizoDep* offers a novel tool for investigating the
spatial and temporal dynamics of belowground C
flows in detail, enabling the identification of condi-
tions that favor rhizodeposition and/or root biomass
production. Using spring wheat as a case study, we
demonstrated that root exudation is the predominant
rhizodeposition process, with its spatial distribution
primarily governed by the preferential unloading of
sugars to support root growth. Root traits influencing
root architecture had a lesser effect on rhizodeposi-
tion compared to traits affecting the consumption of
C for growth. Our findings also revealed that sim-
pler modelling approach—such as prescribing a uni-
form rhizodeposition rate along roots or restricting
it to root tips—will fail to capture realistic root C
spatial dynamics. Moving forward, we plan to couple *RhizoDep* with a shoot model and a soil model to incorporate additional feedbacks between root architecture and metabolism, such as increased C allocation to roots triggered by an enhance soil nutrient uptake, and their consequences on soil organic matter dynamics. We anticipate that *RhizoDep*, along with its future refinements, will shed new light on the complex interactions within the soil-plant-atmosphere continuum.

**Acknowledgements** We thank Loïc Pagès for his advice regarding *ArchiSimple*, Elisa Clerjeault and Soukeye Gadiaga for helping to determine root architecture parameters, and Raia Silvia-Massad for hosting a delightful writing retreat. We also thank Laurène Perthame for providing an internal review of our manuscript. In addition, we thank the two anonymous reviewers who provided helpful comments and suggestions to improve this work.

**Authors contribution** FR designed and performed the research, and wrote the manuscript with the help of all authors. FR, BA and TG conceptualized the model, and FR, CP, and MG implemented the model.

**Funding** Open access funding provided by Université Paris-Saclay. This work benefited from the discussions hold within the IMPULSE project (2019–2022) funded by INRAE and the project MIXROOT-C (2021–2024) funded by the European Union’s Horizon 2020 research and innovation program under grant agreement No. 862695 EJP SOIL.

**Data Availability** The code of *RhizoDep* is available on GitHub (https://github.com/openalea/rhizodep). Additional information and data is provided in the Supporting Materials available in the online version of this article. Other specific data will be made available on request

## Declarations

**Competing interests** The authors have no relevant financial or non-financial interests to disclose.

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## References

Aoki M, Fujii K, Kitayama K (2012) Environmental control of root exudation of low-molecular weight organic acids in tropical rainforests. Ecosystems 15:1194–1203. https://doi.org/10.1007/s10021-012-9575-6

Aulakh MS, Wassmann R, Bueno C et al (2001) Characterization of root exudates at different growth stages of ten rice (Oryza sativa L.) cultivars. Plant Biol 3:139–148. https://doi.org/10.1055/s-2001-12905

Badri DV, Vivanco JM (2009) Regulation and function of root exudates. Plant, Cell Environ 32:666–681

Balesdent J, Basile-Doelsch I, Chadoeuf J et al (2018) Atmosphere-soil carbon transfer as a function of soil depth. Nature 559:599–602. https://doi.org/10.1038/s41586-018-0328-3

Barillot R, Chambon C, Andrieu B (2016) CN-Wheat, a functional-structural model of carbon and nitrogen metabolism in wheat culms after anthesis. I. model description. Ann Botany 118:997–1013. https://doi.org/10.1093/aob/mcw143

Beaudoin N, Lecharpentier P, Ripoche-Wachter D et al (2023) STICS soil-crop model: conceptual framework, equations and uses. Ed. Quae, Versailles

Bertin C, Yang X, Weston LA (2003) The role of root exudates and allelochemicals in the rhizosphere. Plant Soil 256:67–83. https://doi.org/10.1023/A:1026290508166

Bolinder MA, Janzen HH, Gregorich EG et al (2007) An approach for estimating net primary productivity and annual carbon inputs to soil for common agricultural crops in Canada. Agr Ecosyst Environ 118:29–42. https://doi.org/10.1016/j.agee.2006.05.013

Brigham LA, Woo H-H, Wen F, Hawes MC (1998) Meristem-specific suppression of mitosis and a global switch in gene expression in the root cap of pea by endogenous signals. Plant Physiol 118:1223–1231. https://doi.org/10.1104/pp.118.4.1223

Canarini A, Merchant A, Dijkstra FA (2016) Drought effects on Helianthus annuus and Glycine max metabolites: from phloem to root exudates. Rhizosphere 2:85–97. https://doi.org/10.1016/j.rhisph.2016.06.003

Cannesan MA, Gangneux C, Lanoue A et al (2011) Association between border cell responses and localized root infection by pathogenic Aphanomyces euteiches. Ann Bot 108:459–469. https://doi.org/10.1093/aob/mcr177

Carminati A, Zarebanadkouki M, Kroener E et al (2016) Biophysical rhizosphere processes affecting root water uptake. Ann Bot 118:561–571. https://doi.org/10.1093/aob/mcw113

Cheng W, Parton WJ, Gonzalez-Meler MA et al (2014) Synthesis and modeling perspectives of rhizosphere priming. New Phytol 201:31–44. https://doi.org/10.1111/nph.12440

Curlango-Rivera G, Duclos DV, Ebolo JJ, Hawes MC (2010) Transient exposure of root tips to primary and secondary metabolites: Impact on root growth and production of
border cells. Plant Soil 332:267-275. https://doi.org/10.1007/s11104-010-0291-8

Czarnota MA, Rimando AM, Weston LA (2003) Evaluation of root exudates of seven sorghum accessions. J Chem Ecol 29:2073-2083. https://doi.org/10.1023/A:1025634402071

Egeraat AWSMV (1975) Exudation of ninhydrin-positive compounds by pea-seedling roots: a study of the sites of exudation and of the composition of the exudate. Plant Soil 42:37-47. https://doi.org/10.1007/BF02186972

Farrar J, Hawes M, Jones D, Lindow S (2003) How roots control the flux of carbon to the rhizosphere. Ecology 84:827-837. https://doi.org/10.1890/0012-9658(2003)084[0827:HRCTFO]2.0.CO;2

Fusseder A (1987) The longevity and activity of the primary root of maize. Plant Soil 101:257-265. https://doi.org/10.1007/BF02370653

Galindo-Castañeda T, Hartmann M, Lynch JP (2024) Location: root architecture structures rhizosphere microbial associations. J Exp Bot 75:594-604. https://doi.org/10.1093/jxb/erad421

Gaudel G, Poudel M, Mosongo PS et al (2022) Meta-analysis of the priming effect on native soil organic carbon in response to glucose amendment across soil depths. Plant Soil 479:107-124. https://doi.org/10.1007/s11104-021-05168-5

Giraud M, Gall SL, Harings M et al (2023) CPlantBox: a fully coupled modelling platform for the water and carbon fluxes in the soil–plant–atmosphere continuum. In silico Plants 5:diad009. https://doi.org/10.1093/insilicoplants/ diad009

Giraud M, Sırcan AK, Streck T et al (2025) In silico analysis of carbon stabilisation by plant and soil microbes for different weather scenarios. EGUSphere 1-76. https://doi.org/10.5194/egusphere-2025-572

Godin C, Caraglio Y (1998) A multiscale model of plant topological structures. J Theor Biol 191:1-46. https://doi.org/10.1006/jtbi.1997.0561

Guichard M, Allain J-M, Bianchi MW, Frachisse J-M (2019) Root Hair Sizer: an algorithm for high throughput recovery of different root hair and root developmental parameters. Plant Methods 15:104. https://doi.org/10.1186/s13007-019-0483-z

Guo H, Feng X, Hong C et al (2017) Malate secretion from the root system is an important reason for higher resistance of Miscanthus sacchariflorus to cadmium. Physiol Plant 159:340-353. https://doi.org/10.1111/ppl.12526

Hawes MC, Bengough G, Cassab G, Ponce G (2002) Root caps and rhizosphere. J Plant Growth Regul 21:352-367. https://doi.org/10.1007/s00344-002-0035-y

Henneron L, Cros C, Picon-Cochard C et al (2020) Plant economic strategies of grassland species control soil carbon dynamics through rhizodeposition. J Ecol 108:528-545. https://doi.org/10.1111/1365-2745.13276

Henry F, Nguyen C, Paterson E et al (2005) How does nitrogen availability alter rhizodeposition in Lolium multiflorum Lam. during vegetative growth? Plant Soil 269:181-191. https://doi.org/10.1007/s11104-004-0490-2

Hinsinger P (2001) Bioavailability of soil inorganic P in the rhizosphere as affected by root-induced chemical changes:

a review. Plant Soil 237:173-195. https://doi.org/10.1023/A:1013351617532

Hoffland E, Findenegg GR, Nelemans JA (1989) Solubilization of rock phosphate by rape. Plant Soil 113:161-165. https://doi.org/10.1007/BF02280176

Hoffland E, Boogaard RVD, Nelemans J, Findenegg G (1992) Biosynthesis and root exudation of citric and malic acids in phosphate-starved rape plants. New Phytol 122:675-680. https://doi.org/10.1111/j.1469-8137.1992.tb00096.x

Holz M, Zarebanadkouki M, Kuzyakov Y et al (2018) Root hairs increase rhizosphere extension and carbon input to soil. Ann Bot 121:61-69. https://doi.org/10.1093/aob/mcx127

Jones DL, Darrah PR (1993) Re-sorption of organic compounds by roots of Zea mays L. and its consequences in the rhizosphere. II. Experimental and model evidence for simultaneous exudation and re-sorption of soluble C compounds. Plant Soil 153:47-59. https://doi.org/10.1007/BF00010543

Jones DL, Darrah PR (1996) Re-sorption of organic compounds by roots of Zea mays L. and its consequences in the rhizosphere. Plant Soil 178:153-160. https://doi.org/10.1007/BF00011173

Jones DL, Nguyen C, Finlay RD (2009) Carbon flow in the rhizosphere: carbon trading at the soil-root interface. Plant Soil 321:5-33. https://doi.org/10.1007/s11104-009-9925-0

Kamula SA, Peterson CA, Mayfield CI (1994) The plasma-lemma surface area exposed to the soil solution is markedly reduced by maturation of the exodermis and death of the epidermis in onion roots. Plant, Cell Environ 17:1183-1193. https://doi.org/10.1111/j.1365-3040.1994.tb02016.x

Keith H, Oades JM, Martin JK (1986) Input of carbon to soil from wheat plants. Soil Biol Biochem 18:445-449. https://doi.org/10.1016/0038-0717(86)90051-9

Landl M, Haupenthal A, Leitner D, Kroener E, Vetterlein D, Bol R, Vereecken H, Vanderborght J, Schnepf A (2021) Simulating rhizodeposition patterns around growing and exuding root systems. Silico Plants 3(2):diab028. https://doi.org/10.1093/insilicoplants/diab028

Liljeroth E, Bååth E, Mathiasson I, Lundborg T (1990) Root exudation and rhizoplane bacterial abundance of barley (Hordeum vulgare L.) in relation to nitrogen fertilization and root growth. Plant Soil 127:81. https://doi.org/10.1007/BF00010839

Liljeroth E, Van Veen JA, Miller HJ (1990b) Assimilate translocation to the rhizosphere of two wheat lines and subsequent utilization by rhizosphere microorganisms at two soil nitrogen concentrations. Soil Biol Biochem 22:1015-1021. https://doi.org/10.1016/0038-0717(90)90026-V

Lohaus G (2022) Review primary and secondary metabolites in phloem sap collected with aphid stylectomy. J Plant Physiol 271:153645. https://doi.org/10.1016/j.jplph.2022.153645

Louarn G, Faverjon L (2018) A generic individual-based model to simulate morphogenesis, C-N acquisition and population dynamics in contrasting forage legumes. Ann Bot 121:875-896. https://doi.org/10.1093/aob/mcx154

Mariano ED, Keltjens WG (2003) Evaluating the role of root citrate exudation as a mechanism of aluminium resistance
in maize genotypes. Plant Soil 256:469-479. https://doi.org/10.1023/A:1026106714644

Mary B, Fresneau C, Morel JL, Mariotti A (1993) C and N cycling during decomposition of root mucilage, roots and glucose in soil. Soil Biol Biochem 25:1005-1014. https://doi.org/10.1016/0038-0717(93)90147-4

Matsumoto H, Okada K, Takahashi E (1979) Excretion products of maize roots from seedling to seed development stage. Plant Soil 53:17-26. https://doi.org/10.1007/BF02181875

McElgunn JD, Harrison CM (1969) Formation, elongation, and longevity of barley root hairs1. Agron J 61:79-81. https://doi.org/10.2134/agronj1969.00021962006100010027x

Meier IC, Avis PG, Phillips RP (2013) Fungal communities influence root exudation rates in pine seedlings. FEMS Microbiol Ecol 83:585-595. https://doi.org/10.1111/1574-6941.12016

Morel JL, Mench M, Guckert A (1986) Measurement of Pb2+, Cu2+ and Cd2+ binding with mucilage exudates from maize (Zea mays L.) roots. Biol Fert Soils 2:29-34. https://doi.org/10.1007/BF00638958

Morré DJ, Jones DD, Mollenhauer HH (1967) Golgi apparatus mediated polysaccharide secretion by outer root cap cells of Zea mays. Planta 74:286-301. https://doi.org/10.1007/BF00384849

Nguyen C (2003) Rhizodeposition of organic C by plants: mechanisms and controls. Agronomie 23:375-396. https://doi.org/10.1051/agro:2003011

Nielsen KL, Lynch JP, Jablokow AG, Curtis PS (1994) Carbon cost of root systems: an architectural approach. Plant Soil 165:161-169. https://doi.org/10.1007/BF00009972

Pagès L, Bécel C, Boukcim H et al (2014) Calibration and evaluation of ArchiSimple, a simple model of root system architecture. Ecol Model 290:76-84. https://doi.org/10.1016/j.ecolmodel.2013.11.014

Pankievicz VCS, Delaux P-M, Infante V, Hirsch HH, Rajasekar S, Zamora P, Jayaraman D, Calderon CI, Bennett A and Ané JM (2022) Nitrogen fixation and mucilage production on maize aerial roots is controlled by aerial root development and border cell functions. Front Plant Sci 13:977056. https://doi.org/10.3389/fpls.2022.977056

Paull RE, Jones RL (1975) Studies on the secretion of maize root cap slime: II. Localization of slime production. Plant Physiol 56:307-312. https://doi.org/10.1104/pp.56.2.307

Pausch J, Kuzyakov Y (2018) Carbon input by roots into the soil: quantification of rhizodeposition from root to ecosystem scale. Glob Change Biol 24:1-12. https://doi.org/10.1111/gcb.13850

Personeni E, Nguyen C, Marchal P, Pagès L (2007) Experimental evaluation of an efflux-influx model of C exudation by individual apical root segments. J Exp Bot 58:2091-2099. https://doi.org/10.1093/jxb/erm065

Peterson RL, Farquhar ML (1996) Root hairs: specialized tubular cells extending root surfaces. Bot Rev 62:1-40. https://doi.org/10.1007/BF02868919

Pradal C, Dufour-Kowalski S, Boudon F et al (2008) OpenAlea: a visual programming and component-based software platform for plant modelling. Functional Plant Biol 35:751-760. https://doi.org/10.1071/FP08084

Pradal C, Boudon F, Nouguier C et al (2009) PlantGL: A Python-based geometric library for 3D plant modelling at different scales. Graph Models 71:1-21. https://doi.org/10.1016/j.gmod.2008.10.001

Pradal C, Godin C (2020) MTG as a standard representation of plants in FSPMs. In: Kahlen K, Chen T-W, Fricke A, Stützel H (eds) Book of abstracts of the 9th International Conference on Functional-Structural Plant Models: FSPM2020. Institute of Horticultural Production Systems, Hanovre, pp 86-87

Proctor C, He Y (2017) Quantifying root extracts and exudates of sedge and shrub in relation to root morphology. Soil Biol Biochem 114:168-180. https://doi.org/10.1016/j.soilbio.2017.07.006

Rasmann S, Bennett A, Biere A et al (2017) Root symbionts: Powerful drivers of plant above- and belowground indirect defenses. Insect Sci 24:947-960. https://doi.org/10.1111/1744-7917.12464

Raynaud X (2010) Soil properties are key determinants for the development of exudate gradients in a rhizosphere simulation model. Soil Biol Biochem 42:210-219. https://doi.org/10.1016/j.soilbio.2009.10.019

Rees RM, Bingham IJ, Baddeley JA, Watson CA (2005) The role of plants and land management in sequestering soil carbon in temperate arable and grassland ecosystems. Geoderma 128:130-154. https://doi.org/10.1016/j.geoderma.2004.12.020

Remus R, Augustin J (2016) Dynamic linking of 14C partitioning with shoot growth allows a precise determination of plant-derived C input to soil. Plant Soil 408:493-513. https://doi.org/10.1007/s11104-016-3006-y

Van Rossum G, Drake FL (2009) Python 3 Reference Manual, CreateSpace. Scotts Valley, CA

Roumet C, Birouste M, Picon-Cochard C et al (2016) Root structure-function relationships in 74 species: evidence of a root economics spectrum related to carbon economy. New Phytol 210:815-826. https://doi.org/10.1111/nph.13828

Santangeli M, Steininger-Mairinger T, Vetterlein D et al (2024) Maize (Zea mays L.) root exudation profiles change in quality and quantity during plant development – a field study. Plant Science 338:111896. https://doi.org/10.1016/j.plantsci.2023.111896

Sokol NW, Sanderman J, Bradford MA (2019) Pathways of mineral-associated soil organic matter formation: Integrating the role of plant carbon source, chemistry, and point of entry. Glob Change Biol 25:12-24. https://doi.org/10.1111/gcb.14482

Sullivan CB, Kaszynski AA (2019) PyVista: 3D plotting and mesh analysis through a streamlined interface for the visualization Toolkit (VTK). J Open Source Softw 4:1450. https://doi.org/10.21105/joss.01450

Swinnen J, Van Veen JA, Merckx R (1994a) 14C pulse-labeling of field-grown spring wheat: an evaluation of its use in rhizosphere carbon budget estimations. Soil Biol Biochem 26:161-170. https://doi.org/10.1016/0038-0717(94)90159-7

Swinnen J, Van Veen JA, Merckx R (1994b) Rhizosphere carbon fluxes in field-grown spring wheat: Model calculations based on 14C partitioning after pulse-labelling. Soil

<figure><img src="image_12.png" /></figure>
Biol Biochem 26:171-182. https://doi.org/10.1016/0038-0717(94)90160-0

Thompson MV, Holbrook NM (2004) Scaling phloem transport: information transmission. Plant, Cell Environ 27:509-519. https://doi.org/10.1111/j.1365-3040.2003.01148.x

Thornley JHM, Cannell MGR (2000) Modelling the components of plant respiration: representation and realism. Ann Bot 85:55-67. https://doi.org/10.1006/anbo.1999.0997

Uden NC (2000) Types, amounts, and possible functions of compounds released into the rhizosphere by soil-grown plants. In: The Rhizosphere: Biochemistry and Organic Substance at the Soil-Plant Interface: Biochemistry and Organic Substance at the Soil-Plant Interface. CRC Press

van Dam NM, Weinhold A, Garbeva P (2016) Calling in the Dark: The Role of Volatiles for Communication in the Rhizosphere. Deciphering Chemical Language of Plant Communication. Springer, Cham, pp 175-210

Villarino SH, Pinto P, Jackson RB, Piñeiro G (2021) Plant rhizodeposition: a key factor for soil organic matter formation in stable fractions. Sci Adv 7:eabd3176. https://doi.org/10.1126/sciadv.abd3176

Voothuluru P, Braun DM, Boyer JS (2018) An in vivo imaging assay detects spatial variability in glucose release from plant roots. Plant Physiol 178:1002-1010. https://doi.org/10.1104/pp.18.00614

Wen Z, White PJ, Shen J, Lambers H (2022) Linking root exudation to belowground economic traits for resource acquisition. New Phytol 233:1620-1635. https://doi.org/10.1111/nph.17854

Zhang Y, Lavallee JM, Robertson AD et al (2021) Simulating measurable ecosystem carbon and nitrogen dynamics with the mechanistically defined MEMS 2.0 model. Biogeosciences 18:3147-3171. https://doi.org/10.5194/bg-18-3147-2021

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