Root foraging strategies at the whole plant scale: hypothesis of a trade-o between soil exploration and occupation

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Root traits involved in root foraging strategies

A rst, relatively obvious trait that aects both soil exploration and occupation is the allocation of carbon, nutrients and energy to roots, from which depends the overall root system size (biomass) and activity. A given quantity of root biomass can be spread over a wide range of horizontal or vertical distance (Jackson et al., 1996; Hartle et al., 2006; Schenk and Jackson, 2002; Casper et al., 2003). Root lateral spread and maximum rooting depth give the ultimate border of the soil explored by plants (Schenk and Jackson, 2002; Casper et al., 2003). I focused in my work on the horizontal distribution of roots. The relative size of the below- and above-ground zones of inuence are also parameter that plant can adjust depending on the context. (Casper et al., 2003) showed that plants growing in arid soils tend to have a larger belowground ZOI compared to aboveground. The dierence of size of the ZOI is also a parameter involved in the creation of islands of fertility accumulation of carbon and nutrients below the plant canopy (Scholes and Archer, 1997).
The distribution of roots within the explored volume of soil is often heterogeneous. Part of this heterogeneity comes from an architectural development constraints that causes roots to concentrate near the plant stem (Casper et al., 2003). However, plants are also able to locally adjust root density and activities to the heterogeneity of nutrients (Hodge, 2004) and the presence of competitors (Gersani et al., 2001). Plant morphological and physiological plasticity potentially aect the degree of soil occupation. Some soil activities can be directly correlated to root density (e.g. (Lata et al., 2000)) and the geometry of the rhizosphere depends directly on the rates of uptake or exudation (see subsection 1.3.1).
Root system architecture is also subject to a wide range of variations among plant species, with implications for the eciency of the root system functioning (Lynch, 1995). The same is true for the organisation of clonal species, which vary in the organisation of their ramets (Harper, 1977; Oborny et al., 2012). For example rhizomatous and caespitose grass species do not have the same impact on thesoil where they grow (Derner and Briske, 2001).
Life history traits are also important in plant-soil interactions. As an example, annual plants interact with a given portion of soil at shorter temporal scales and generally explore a smaller 1. Integrating plant control of nutrient cycling within root foraging strategies volume of soil than biennials or perennials (Schenk and Jackson, 2002). At a smaller scale, root demography aects the duration of plant-soil interaction.

Relationships between local root density and soil functioning

Here I consider the interaction of a portion of the root system within a xed soil volume. In this context, an ecient root foraging strategy can be dened as the co-occurrence of a root length density, an uptake rate and a level of exudation which together optimize total nutrient uptake rate. An optimal strategy maximises the benets in terms of nutrient uptake with the lowest possible costs in terms of root construction and activity (Lynch and Ho, 2005). Root foraging strategy in the presence of competitors follows a dierent formalism (O’Brien et al., 2007), which is discussed at the end of this thesis (section 5.2.3).
Increasing root densities can lead to more overlap between the rhizospheres (Pagès, 2011; Ge et al., 2000), which may reduces the mean uptake eciency. This possibility is described by applying the concept of competition to the roots of a same individual plant (Ge et al., 2000). Considering nutrient uptake only, the most ecient root systems should be the ones that minimize root overlap. However, the same portion of root aects the surrounding soil through dierent processes, including some that can increase nutrient availability. As the sizes of the rhizospheres depend on the process considered (subsection 1.3.1), there may be situations where exudation rhizospheres overlap, but not the depletion rhizospheres. In such a case, a plant may benet from root proximity: a root may benet from the positive feedback generated by a neighbour root. A hypothesis considered in my thesis is that in cases where roots also increase the availability of nutrients, the overlap of rhizospheres may lead to synergy between roots.

Root foraging strategies at the whole plant scale: hypothesis of a trade-o between soil exploration and occupation

The Guerilla vs. Phalanx metaphor was formulated in a context of competition for resources by plants to account for contrasted behaviours of clonal plants (Harper, 1980; Clegg, 1978) (gure 1.2A). A guerilla strategy maximises the discovery of new pools of resources, while the phalanx strategy is a better way to locally outcompete other plants. In this thesis I will propose the use of the exploration vs. occupation distinction as a way to generalize the guerilla vs. phalanx metaphor to other plant-soil interactions than nutrient preemption in a competitive context alone. Figure 1.2 shows how this metaphor can be applied to the exploration of soil by plants. In panel A, the explored area of the army (in light grey) expands when soldiers penetrate in the unexplored area (in black). At a given time, the area actually controlled by individual soldiers is in white. The guerilla strategy (top left) allows the exploration of a wide area with a low control of what happens inside, while the phalanx strategy (bottom right) leads to a smaller but better controlled explored area. Brown and violet lines respectively represent newly grown and dead roots, and the small blue ellipses represent the long-term feedback of previous rhizospheres on soil functioning. If this feedback is positive and dead roots are sources of nutrients, the degree of soil occupation by plants depends not only on the white/grey ratio but also on the proximity between the white and blue areas. Thus, as in the rst panel, the guerilla vs. phalanx metaphor leads to the idea of a trade-o between exploration and occupation.
On the three panels of gure 1.2, the grey area quanties the intensity of soil exploration while the white over grey area ratio is an approximation of soil occupation eciency. From this schematic representation, dierent hypotheses can be made on the relationships between soil occupation and soil exploration. First, soil occupation decreases mechanically when soil 1. Integrating plant control of nutrient cycling within root foraging strategies exploration increases, as root can only directly interact with a limited volume. Second, this eect should increase with the explored area as more and more root length is dedicated to structure and transport, and less to interaction with soil. Third, if the phalanx strategy is associated to slower growth of roots, the temporal dynamics of root development during exploration may further favour this strategy. The distance between old (blue) and new (white) rhizosphere is reduced. This means that if there is a delay between exudation from a portion of root and a resulting benecial eect in terms of nutrient availability, plant would benet more from this eect. Last, as already hypothesized by Abbadie and Lata (2006), the proximity between living and dead roots (in blue) may favour the uptake of nutrients diusing from dead roots. All this can be summarized under the general hypothesis of a trade-o between the extent of soil exploration and the eciency of soil occupation. In the followings, I will use the shorter exploration/occupation trade-o.

Spatial organization of the plant-soil system

For simplicity, we use an implicit representation of space where we divide the soil on the horizontal plane into two distinct areas: the soil that is occupied (O) or unoccupied (U) by roots. This is a discrete approximation of the horizontal distribution of roots, which is generally more continuous in the eld (Hook et al., 1994; Lata et al., 2000). We assume that, below a threshold value of root density, most of the soil nutrients are out of reach of the ne root rhizospheres. Neglecting possible spatial heterogeneities, we assume a constant and homogeneous rate of aboveground litter and other nutrient inputs on to the modelled area. Parameter x quanties soil exploration, dened as the proportion of soil surface occupied by the belowground zone of inuence of plants over the total soil area 0 < x 1 (gures 2.1&2.2).
We consider a population at equilibrium and suppose x to be constant by making the hypothesis that (i) changes in the occupied/unoccupied status of the soil are due to plant demography, and (ii) plant mortality is perfectly compensated by the appearance of new individuals. We can thus consider compartments of the limiting mineral nutrient to be at equilibrium.

Nutrient uxes in the plant-soil system

Inputs of nutrients to the ecosystem are uniform over space and time: rD for detritus and rN for mineral nutrients. Losses of nutrients from the system can be due to mechanisms such as re, volatilization, or harvest. We model them as donor-controlled and proportional to the compartment stocks, with coecients lP , lD and lN (for plants, detritus and mineral nutrient pools, respectively; see equations below). Nutrient cycling includes three processes: (i) uptake of mineral nutrients by plant roots, (ii) plant losses to the detritus pool, and (iii) mineralization of plant detritus into mineral nutrients. Since nutrient uptake depends on both plant root biomass and nutrient availability in the soil, we model it as a donor-receiver controlled ux proportional to PO and NO, with constant coecient uN (Barot et al., 2007). Fluxes of organic nutrients between the PO and DO occur through organ mortality and root exudation, and increase inputs of nutrients to soil detritus. This ux is donor-controlled, with a rate dP . We do not distinguish the recycling of above- and belowground plant biomass that we suppose to occur over the same spatial area, i.e. within the occupied soil. Finally, mineralization describes the ux between detritus (DO, DU) and the mineral nutrient pool (NO, NU). We assume that these uxes are donor-controlled with the same rate mD. For simplicity, we suppose that all the nutrient cycling parameters that do not depend on the plant compartment (rD, rN, mD, lD, lN) are the same between zones O and U.
We developed two models, depending on whether the horizontal dynamics of the two zones are taken into account or not.

The consequences of space exploration on nutrient cycling parameters

The donor-receiver controlled equation describing nutrient uptake in eq. 2.3 simply expresses that the more roots and the more available nutrients, the higher the nutrient uptake. However, the supply of mineral nutrients within the zone of inuence also depends on root activity and feedbacks between these activities and soil (see detailed explanation in the introduction) that may directly increase the availability of mineral nutrients (e.g. through mineralization or solubilization) or decrease nutrient losses (e.g. through the inhibition of nitrication), which increases the long terme nutrient availability (Hinsinger et al., 2009). Given a certain root biomass, the rhizosphere of a plant with a small zone of inuence will more completely ll its zone of inuence than a plant with a larger zone of inuence (Figure 2.1). If nutrient availability depends on exudation (or other root activities whose eect increases with root density), the zone of inuence  is better exploited in the former case and the supply of mineral nutrient will be higher. We thus suppose that the root-soil feedbacks are stronger when soil exploration is spatially limited. This leads to assume a negative relationship between nutrient uptake rate (uN) and soil exploration (x). We test the signicance of this trade-o by comparing a version of the model with a constant uN to a version with a linear trade-o: uN(x) = u1 N(1 + UN (1 􀀀 x)).

Table of contents :

I. Introduction et synthèse bibliographique 
Introduction Générale
1. Integrating plant control of nutrient cycling within root foraging strategies 
1.1. Introduction
1.2. Plants ability to control nutrient cycling
1.2.1. Direct control of nutrient availability
1.2.2. Interaction with soil microbes
1.2.3. Interaction with large herbivores
1.3. The spatial and temporal scales of plant-soil interactions
1.3.1. The rhizosphere
1.3.2. The below-ground zone of inuence
1.3.3. The above-ground zone of inuence
1.3.4. Extended above-ground zone of inuence
1.4. Linking plant control of nutrient cycling to root foraging strategies
1.4.1. Root traits involved in root foraging strategies
1.4.2. Relationships between local root density and soil functioning
1.4.3. Root foraging strategies at the whole plant scale: hypothesis of a trade-o between soil exploration and occupation
1.5. Conclusions
II. Pourquoi et quand les plantes devraient-elles limiter l’exploration du sol par leurs racines ? 
2. Why and when should plant limit the exploration of soil by their roots? 
2.1. Abstract
2.2. Introduction
2.3. Material and Methods
2.3.1. Models descriptions
2.3.1.1. Spatial organization of the plant-soil system
2.3.1.2. Compartments of the nutrient cycle
2.3.1.3. Nutrient uxes in the plant-soil system
2.3.1.4. Model without nutrient uxes between unoccupied and occupied soil
2.3.1.5. Model considering a spatial dynamic of the zones of inuence .
2.3.1.6. The consequences of space exploration on nutrient cycling parameters
2.3.2. Parametrisation
2.3.3. Partial recycling eciencies and system closure
2.4. Results
2.4.1. Equilibrium and stability conditions
2.4.2. Conditions for which a reduced explorations optimizes plant biomass
2.4.3. Consequences of reduced soil exploration on the plant-soil system functioning
2.4.4. Role of the spatial dynamics between occupied and unoccupied soil .
2.5. Discussion
2.5.1. When is it benecial for plants to reduce soil exploration by roots?
2.5.2. Generality of model predictions
2.5.3. Potential applications
Perspectives
III. Patrons d’exploration racinaire, eet îlot de fertilité et cycle de l’azote chez trois espèces de Poacées pérennes de savane. 
3. Root exploration pattern and nutrient cycling in the plants-soil system of three savanna grasses 
3.1. Abstract
3.2. Introduction
3.3. Material and Methods
3.3.1. Study site
3.3.2. Experimental design
3.3.3. Sampling procedure
3.3.3.1. Quadrat selection
3.3.3.2. Roots and soil sampling
3.3.4. Analyses performed
3.3.5. Statistics
3.4. Results
3.4.1. Aboveground biomass pattern
3.4.2. Belowground exploration pattern
3.4.3. Soil content in C, N and P
3.4.4. Nitrogen cycling (plant and soil N stock and 15N)
3.5. Discussion
3.5.1. Plant soil exploration strategies
3.5.2. Absence of island of fertility eect ?
3.5.3. Species eects on nitrogen cycling
3.5.4. Conclusion
3.6. Acknowledgement
Perspectives
IV. Modélisation de l’impact de la distribution racinaire sur le contrôle du recyclage des nutriments à l’échelle de la rhizosphère et de la zone d’inuence souterraine 
4. Modelling the impact of root distribution on the control of nutrient availability at the rhizosphere scale 
4.1. Abstract
4.2. Introduction
4.3. Material & Methods
4.3.1. Model Description
4.3.2. Numerical analysis
4.3.3. Upscaling rhizospheres to the below-ground zone of inuence
4.4. Results
4.4.1. Root density eects on nutrient uptake at the centimetre scale
4.4.2. Rhizosphere sizes as predictors of root interactions
4.4.3. Root foraging at the scale of the below-ground zone of inuence
4.5. Discussion
4.5.1. Inter-root competition and facilitation
4.5.2. Inferring optimal root strategies
4.5.3. The exploration/occupation trade-o
4.5.4. Conclusion
4.6. Acknowledgement
5. Discussion Générale 
5.1. Stratégies d’exploration racinaire et cycles des nutriments
5.1.1. Compétition et facilitation racinaire
5.1.2. Intégration des interactions racinaires à l’échelle de la zone d’inuence racinaire
5.1.3. Confrontation aux plantes réelles
5.1.4. Le compromis exploration/occupation : un outil heuristique pertinent ? .
5.2. Généralisation : stratégies d’acquisition des ressources et rétroactions plante-sol .
5.2.1. Un autre mode d’acquisition des ressources : les associations
5.2.2. Spécicité des interactions entre les plantes et les microorganismes du sol
5.2.3. Les rétroactions plantes-sol à l’échelle de la communauté de plantes
5.2.4. Application aux agro-écosystèmes ?
5.3. Conclusion
Bibliography 
V. Annexes 
6. Appendix to Chapter 2 
6.1. Equations and stability conditions for model 2
6.1.1. Model description
6.1.2. Stability of the equilibrium
6.2. Trade-os equations and parameterization of the model
6.2.1. Trade-o equations
6.2.2. Parameterization
6.2.3. trade-o calibration
6.3. Detailed analysis of model 1 with a functional trade-o between exploration and uptake
6.3.1. Stability conditions
6.3.2. Calculation of optimal soil exploration xP
6.3.3. Variation of soil nutrient stocks D and N with soil exploration x
6.3.4. Variation of total nutrient stocks T with soil exploration x
6.4. Generalization of the results of model 1 for other trade-os
6.4.1. Functional trade-o between soil exploration and mineralization
6.4.2. Functional trade-o between soil exploration and lixiviation
6.4.3. Coupled trade-os
7. Appendix to Chapter 3 
7.1. Root scan analysis
7.2. Patterns of root exploration
7.3. Soil content in C and nutrients
7.4. plant and soil C:N
7.5. N isotopic data
8. Appendix to chapter 4 
8.1. Relationships between root length density and uxes of phosphorus whithin the soil
8.2. Relationship between root length density nroot and rhizP =rhizS
8.3. Upscaling to the whole plant
Résumé 

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