The IEEE 802.15.4 has been studied for its possible use to support networked control systems. A careful management of the network resources allows the enhancement of the quality of control (QoC) of the controlled system. This can be achieved by a co-design approach to manage the interaction between the WNCS and the wireless network in order to online adapt the QoC. This approach allows control loops to have access to the communication medium according to the state of the controlled system meanwhile attempting to optimize the overall control performance. When the QoC of the controlled system is not sufficient, the quality of service of the network is adapted online. This adaptation is realized by modifying the macMinBE parameter of the MAC protocol of the IEEE 802.15.4. Moreover, an implementation way of this scheme using the IEEE 802.15.4 protocol is presented. Simulation results show that this approach improves the control performance.

Networked control systems (NCS) [START_REF] Zampieri | Trends in networked control systems[END_REF] have an increasing number of applications in military, industrial, medical and commercial fields. Since wired networks cause significant limitations in terms of mobility, flexibility and extensibility, wireless networks are an effective alternative to overcome these problems. Hence, Wireless Networked Control Systems (WNCS) are getting a strong interest from both academic and industrial communities. The IEEE 802.15.4/ZigBee is an interesting standard for some WNCS requiring low cost and low energy consumption (e.g., the case of the RUNES project [RUN]). Moreover industrial WirelessHART [START_REF] Hart | [END_REF] uses the IEEE 802.15.4-based Physical layer and MAC PDU.

In WNCS, the quality of control (QoC), i.e., the performance [START_REF] Felicioni | Impact of a (m,k)-firm data dropouts policy on the quality of control[END_REF][START_REF] Åström | Computercontrolled systems: theory and design[END_REF] delivered by each closed-loop operation , depends not only on the controller design but also on the quality of service (QoS) offered by the wireless network.

The degradation of the QoC of the controlled process can be caused by the network or by the controlled system. In order to manage this QoC many researchers try to enhance the QoS offered to the WNCS. Thus several network resource allocation techniques for WNCS have been proposed. These techniques are based on static strategies that ensure average control performance at the expenses of permanently occupy the available bandwidth. An adaptive online QoC management protocol is proposed: if the QoC of the controlled process is not sufficient, the network offers more resources to the WNCS. Moreover, since the degradation of the QoC can be due to the control loop, if there is no enhancement of the QoC for a certain amount of time, action must be taken on the control loop ( changing the sampling period for example). This work deals with the degradation of the QoC caused by the lack of network resources.

The adaptation of the QoS is ensured through a priority mechanism which adapts the backoff exponent value in the IEEE 802.15.4 MAC. Two priority mechanisms are studied: a probabilistic one and a deterministic one. Then, an implementation of this protocol using the IEEE 802.15.4 is proposed. To illustrate its benefit, this approach is implemented in TrueTime [START_REF] Ohlin | TrueTime1.5-Reference Manual[END_REF], a Matlab/Simulink simulator, and experimented on a simulated cart. The simulation results reveal that this adaptive online QoC management protocol enhances the QoC of the controlled system.

The rest of the paper is organized as follows. The related work is presented in Section 2. Section 3 deals with the considered WNCS. In Section 4, an overview of IEEE 802.15.4 is presented. In Section 5, the limitations of the CSMA/CA mechanism are shown. Thus, in Section 6 an online adaptive protocol is proposed. Then, in Section 7, an implementation of this protocol over IEEE 802.15.4 is proposed. In Section 8, the simulation results are presented. Section 9 gives the conclusion and the future work.

RELATED WORK

There are several works which deal with the resource allocation for control loops. Marti et al. [START_REF] Marti | Optimal state feedback based resource allocation for resource-constrained control tasks[END_REF] studied the CPU resource management and showed that by using feedback to dynamically allocate resources to controllers as a function of the current state of their controlled systems, control performance can be significantly improved. They present an optimal resource allocation policy that maximizes control performance within the available resources. In this work the management is dependent of the controller since when there is a perturbation, the sampling period is adapted.

Velasco et al. [START_REF] Velasco | A control approach to bandwidth management in networked control systems[END_REF] propose a dynamic approach to bandwidth management in networked control systems that allows control loops to consume bandwidth according to the dynamics of the controlled process meanwhile attempting to optimize overall control performance. This is done by augmenting the original state-space representation of each controlled system with a new state variable that describes the network dynamics.

Ji et al. [START_REF] Ji | Optimal bandwidth allocation and qos-adaptive control co-design for networked control systems[END_REF] assign the network-bandwidth dynamically to each control loop according to the quality of performance of each control loop. This is done by using an adaptive controller.

All these works try to adapt the control loop to its environment. Thus, the parameters of the control loop are changed, especially the sampling period.

Marti et al. [START_REF] Marti | Managing quality-of-control in network-based control systems by controller and message scheduling codesign[END_REF] propose an approach to adaptive controllers for NCS that online adapts the control decisions according to the dynamics of both the application and the executing platform. This approach offers capabilities for dynamic management of QoC through message scheduling. They formulate a scheduling strategy that uses feedback information from the control application in order to schedule messages in such a way that the degrading effects of the message latencies are minimized. Thus, the overall QoC is improved. However, this strategy was not analyzed nor tested.

All above works are designed for wired networks. For the best of our knowledge, there is no QoC online adaptive strategy for WNCS using the IEEE 802.15.4 which adapts the QoS of the network to the control loop requirements. This QoS management can be done through the service differentiation. Koubâa et al. [START_REF] Koubâa | Improving the ieee 802.15.4 slotted csma/ca for time-critical events in wireless sensor networks[END_REF] proposed a simple differentiated service scheme for slotted CSMA/CA in IEEE 802.15.4 to improve the performance of time sensitive message. In [START_REF] Rao | Adaptive backoff exponent algorithm for zigbee[END_REF], the authors have modified the initial value of backoff exponent in IEEE 802.15.4 MAC (slotted CSMA/CA) and proposed an adaptive backoff exponent (ABE) algorithm. These works only focused on the slotted CSMA/CA and they are not linked to networked control systems. In this paper, an online adaptive scheme is proposed for wireless networked control systems.

THE CONSIDERED WIRELESS NETWORKED CONTROL SYSTEM

A system of a cart whose movement is guided along a rail [START_REF] Felicioni | Impact of a (m,k)-firm data dropouts policy on the quality of control[END_REF] is considered as an example. We aim to control the cart's position. The variable characterizing the system's state

( x T = [ d ḋ ]
) are: d, the cart position along the rail measured from a reference point, and, ḋ its velocity. The simplified model of the system is described by the following differential equation where u is the input and k 1 , k 2 two parameters :

d = -k 1 ḋ + k 2 u (1)
where k 1 = 12.6559 and k 2 = 1.9243 according to the system identification. The continuous model of the system based on the state space representation is given by:

{ ẋ = Ax + Bu y = Cx + Du ( 2
)
where

A = [ 0 1 0 -k 1 ] , B = [ 0 k 2 ] .
The output of the system corresponds to its state variable

(y = x). So C = [ 1 0 0 1 ] , D = 0.
The used controller is a State Feedback Controller defined by

u t = L(x ref -x t ) (3)
where

x ref = [ r 0 ]
T , r is the reference position of the cart and L = [ k c k d ]. The parameters k c and k d were evaluated by applying the LQR method. For a sampling period equal to 0.01s, k c = 121 and k d = 6.5 [START_REF] Felicioni | Impact of a (m,k)-firm data dropouts policy on the quality of control[END_REF]. A wireless network containing the sensor (S), the controller (C) and the actuator (A) is introduced. The network adds new delays: τ sc is the delay between the sensor and the controller, and τ ca is the delay between the controller and the actuator as shown in Figure 1. The maximum value of the sampling period is 100ms for keeping the system stable. This paper provides a study of the impact of the network performance on the controlled system in a realistic case. Besides, the QoC is managed online by adapting the QoS offered to the controlled cart.

IEEE 802.15.4 PROTOCOL OVERVIEW

The MAC protocol supports two operational modes that may be selected by the coordinator: beacon-enabled mode and non beacon-enabled mode.

• Non beacon-enabled mode : Medium access control is provided by an unslotted CSMA/CA (Carrier Sense Multiple Access/ Collision Avoidance) mechanism (using a random backoff time based on backoff period and Backoff Exponent (BE). There is no priority mechanism so no way to isolate a particular flow among all traffic.

• Beacon-enabled mode : Beacons are periodically sent by Zigbee coordinator to synchronize nodes that are associated with it, and to identify the Personal Area Network (PAN). Superframe is contained between two consecutive beacon frames. The superframe structure is used to manage communication between these devices. The superframe contains a Contention-Access Period (CAP) and Contention-Free Period (CFP), and it may include an inactive period.

CSMA/CA

In a realistic case, there are other nodes than the control loop nodes using the wireless network. In our example, the communication channel is shared by 2 cyclops (sensors equipped with camera) and a main control unit as shown in Figure 2. Hence, the wireless network is used to transmit image packets from cyclops to the main control unit. The image sensor has CIF resolution (352 × 288). Each cyclops sends, periodically, 133 bytes. In the following, the plant behavior is studied for different perturbation load. The transmission period is modified in order to see the effect of the new additional network load on the WNCS. The QoC of the controlled cart is satisfying if the additional network load is less than 44% of the total bandwidth. However, if this additional network load reaches 44% ( i.e. the transmission period of each cyclops = 0.02s), the cart becomes unstable. Thus, the additional load of 44% of the total bandwidth is the upper limit for the stability of our WNCS. In general, the unslotted CSMA/CA of the non beacon-enabled mode is not convenient for WNCSs since influenced by the total network load. GTSs may be allocated by the network coordinator to applications with real-time and specific data bandwidth requirements. In fact, this scheme offers an alternative choice to GTS one. For hard real-time, GTS is preferable while for soft real-time, prioritized CSMA/CA, that will be described below, could be suitable. In addition, this will overcome the problems of GTS. In fact, the number of the control loop having the same sampling period is limited as shown in [START_REF] Boughanmi | Wireless networked control system using IEEE 802.15.4 with GTS[END_REF] since at most only 7 GTS slots can be used. Moreover, the GTS deallocation is not easy and that makes the GTS mechanism rigid.

In order to provide the required QoC to the control loop to maintain the stability of the controlled process, the required QoS must be guaranteed to the WNCS. Thus, a joined design algorithm is proposed: the QoS is adapted depending on the QoC.

A dynamic QoC management is proposed. This is ensured by an additional "network control loop" presented in Figure 8 and will be detailed in Section 7. Here, the principle is stated: depending on the current state of the QoC metric, the given QoS to the WNCS can be adapted online. Thus, the QoC of the plant is improved.

It is supposed that there is no sampling period change because it may cause the plant instability and this paper deals only with the problems caused by the network.

QoC metric

The QoC of the WNCS is evaluated using the controlled process error e. If the WNCS is stable, the error is bounded. Thus, the same criterion, as in [START_REF] Ji | Optimal bandwidth allocation and qos-adaptive control co-design for networked control systems[END_REF], is adopted: the error should be bounded by a threshold to ensure the required QoC to the plant. This threshold depends on the controlled process and on the reference value if there is any. If e > threshold, the WNCS is considered to be in a critical situation and action has to be taken. The trouble is caused either by the controlled system itself or by the network (overloaded network). Action should be taken on the network for a certain period of time through offering more resources to the WNCS. If the situation is not improved (there is a problem in the control loop), action should be taken on the WNCS by changing the sampling period for example. This work deals with the adaptation of the QoS in order to enhance the QoC.

For the systems with architecture presented in Figure 1, the error e is equal to |r -y| where r is the reference and y is the process response. In order to have a good QoC, the condition is

|r -y| < threshold + r ( 4
)
has to be satisfied. The reference value is added in order to take into account the case where there is a change in the reference value that makes |r -y| = r and there is no network problem.

Dynamic management of the QoC

The QoC of the controlled process is dynamically managed through the QoC metric e (the system error). First, the controller checks the error value so that it can decide its priority level because there are two: the maximum priority, and the normal one. If the error e is higher than the threshold, then the WNCS is in critical situation. Thus, the controller priority is set to its maximum value. Else, the controller has a normal priority. This priority data is expressed through the random range of the waiting delay of the CSMA/CA. There are two alternatives :

(1) this range is set to a big one for all the nodes in the network, then when the controller priority is equal to the maximum value, this range is decreased for both the sensor and the controller, (2) this range is set to the default one for all the nodes, then if the controller priority is equal to the maximum value, this range is increased for all the nodes in the network except the sensor and the controller.

The first solution is the most suitable for hard real-time applications considering the robustness aspect. However, it induces the waste of the network resources by the large waiting delay. Thus, the second solution is adopted.

The priority parameter is transferred to the MAC layer which will send it to the WSN coordinator. This coordinator is in charge of informing all the other nodes of the current controller's priority. Once one node gets the controller priority information, it decides if it will apply the CSMA/CA either with the probabilistic priority or without. This decisions is related to the controller priority value. Moreover, the transition between the two mechanisms is done progressively. In fact, if the controller priority is equal to the maximum value, the range of the random delay is increased, else, it decreased until it is equal to the default range.

QoS adaptation: CSMA/CA with priority

The CSMA/CA mechanism for IEEE 802.15.4 uses the random waiting delay for collision avoidance. It uses the backoff exponent (BE) which is related to how many backoff period (BP) a device must wait before attempting to assess the channel activity. The algorithm attempts to avoid collision by waiting during a given delay randomly generated in the range of [0, 2 BE -1] × BP . If batterylife extension is activated then, BE = min(2, macM inBE) else, BE = macM inBE where macMinBE attribute specifies the minimum of backoff exponent, which is set to 3 by default. This aspect is exploited in order to differentiate the services offered by the WSN. We propose to vary the randomly generated waiting delay depending on the priority of the packet. Thus, by choosing a higher macMinBE for the applications different from the control loop, the probability to have a longer delay is increased and the control loop nodes will be able to send their data packets.

The nodes are divided into two classes: the high priority (h) class contains the nodes of the WNCS (sensor, controller, and actuator), and the low priority (l) class is composed of the other nodes present in the WSN. BE CL represents the BE of the control loop nodes macM inBE CL its macM inBE, and it is set to the default value 3. The macM inBE OA and BE OA are the macM inBE and the BE of the other applications sharing the WSN. When the batterylife extension is not activated, the control loop nodes have to wait random[0,

2 BECL -1] × BP ( random[0, 7] × BP ).

Probabilistic priority

The macM inBE OA of the low priority nodes is increased in order to make their data packets wait during a delay randomly generated in a longer range (random[0, 2 macM inBEOA -1] × BP ) than the one for high priority nodes. Figure 3 shows these two ranges .Thus, a probabilistic priority is assigned to the nodes in the WSN by modifying the range for the random delay. Hence, the higher priority nodes (the control loop nodes here) have more chance to send their data packets. Fig. 3. Waiting ranges for high and low priority nodes using the probabilistic priority Figure 4 shows the macM inBE OA , obtained by simulations, which allows the control loop to be stable for different loads. For a small load (less than 35%), there is no need to increase the macM inBE since the default value 3 can afford the stability for the WNCS. When the disturbing load becomes important, the control loop becomes to be unstable because of the long delay and the packets losses. Thus, increasing the macM inBE OA allows the control loop to reach the stability in spite of the perturbing load. For the considered control loop, the value of 7 for macM inBE affords the stability for the control loop for a perturbation load of 90% of the total bandwidth. Deterministic priority This part deals with the minimization of the collisions between nodes of the two classes (control loop and other applications). Thus, the intersection between the waiting ranges of the high and low priority nodes is eliminated as shown in Figure 5. The lowerpriority applications will wait during a delay randomly generated in the range of [variable, 2 BEOA -1] backoff periods. The question is how to choose the variable's value. This variable is set to 2 BECL so that there is no collision between the members of the two classes ( variable = 8).

Figure 6 presents the evolution of the macM inBE OA which allow the WNCS to be stable for different perturbation loads. The macM inBE OA value, obtained using this method, is less than the one found when only the macM inBE is modified. Thus, separating the ranges of random waiting value of the two classes improves the QoS Fig. 5. Waiting ranges for high and low priority nodes using the deterministic priority offered to the WNCS. In the following of this work, the deterministic priority scheme is adopted. Online probabilistic priority adaptation Action will be taken on both the variable and macM inBE OA . Moreover, since a static assignment of these variables can lead to the under-use of the network resources due to the large waiting delay, these variables are adapted online depending on the controller's priority level. Thus, if the control loop is in a critical situation, the variable is set to 8 and the macM inBE OA is increased by 1 in order to enlarge the waiting delay, else the variable is set to 0 and the macM inBE OA is decreased by 1.

How to choose the threshold?

The QoS management depends on the QoC metric which is represented by the controlled system error. Thus, the upper bound of the allowed error ( e ≤ threshold), the threshold, has to be chosen carefully. This threshold is defined, in equation 5, by the control loop threshold (threshold process ) and a security margin. threshold = threshold process -security margin [START_REF] Ji | Optimal bandwidth allocation and qos-adaptive control co-design for networked control systems[END_REF] Then, the delay introduced by the network should be taken into account in order to make the new QoS effective. This delay represents the propagation time of the new priority value to all the nodes. This time is composed of the transmission time of the priority message from the controller to the coordinator and the transmission time of the beacon as shown in Figure 7.

The network delay d net is given by

d net = random backof f + waiting time. (6)
In the beacon-enabled mode, the beacons are sent periodically (else if they are event-triggered this will cause an additional network load). Moreover, the random backof f (RB) value will be set to its maximum to get the worst case value ( RB = random[0, 2 BE -1] * BP ). The needed Fig. 7. The network delay to activate the probabilistic priority mechanism time to send the beacon will vary depending on the current time position in the beacon interval. The waiting time is set to the value of the Beacon Interval BI (the worst case). Thus, the equation 6 is equivalent to

d net = max(RB) + min(BI). ( 7
)
The maximum RB is calculated as max(RB) = 7 * BP where BP is equal to 320µs. The beacon interval is defined as follow

BI = aBaseSuperf rameDuration • 2 BO (8)
where 0 ≤ BO ≤ 14 and BO is the beacon order. The minimum value of BI is calculated with BO equal to 0 and min(BI) is equal to 15.36ms. Thus, the network delay is calculated as

d net = max(RB) + aBaseSuperf rameDuration • 2 BO , (9)
when BO = 0, d net = 17.6ms.

Relation between the d net and T e

The new priority information (or update) has to arrive on time to the network's nodes to be taken into account. Each new priority update has to be effective before a new one arrives. Since the controller is event triggered by the sensor which is periodical with the sampling period T e , the minimum interval between two control message is equal to T e . Thus, the constraint to satisfy, so that the enhancement of the QoS offered to the considered control loop is achieved, is the following: T e ≥ d net .

In order to use the probabilistic priority mechanism, the minimal sampling period T e min of the control loop has to be as the following: T e min = d net so T e min = 17.6ms.

IMPLEMENTATION CONSIDERATION

The proposed protocol takes into account the QoC of the control loop in order to regulate the QoS offered by the network to the WNCS. This protocol is divided in three actors: the controller of the considered control loop, the WSN coordinator, and the nodes which do not belong to this control loop. Figure 8 presents the network control loop with the different actors and message changes and details are given in the following parts. Depending on the error value, the priority of the controller will be set. If e > threshold then the priority will be equal to the maximum value max prio, else, the priority will be set to the normal priority value normal priority. The priority information will be transferred to the MAC layer through the payload added to the data part of the message to send to the actuator.

When the MAC layer gets the message to send to the actuator from the upper layer, it takes the priority value contained in the frame payload. This value will be converted to a boolean value and will be sent in a message to the WSN coordinator. Then, the MAC layer will send the first message to the actuator.

The question, now, is: how to indicate that the message is with priority one? There are two possible solutions :

(1) use a MAC command frame and indicate that it is a priority message by setting the command frame identifier to 0 × 00 since this value is not used by the standard. The first bit of the command payload will be set to the prio msg data. (2) use the first bit of the MAC payload to indicate that this message deals with the priority. Thus if this bit is equal to 1 so the message is a priority one, and the following bit is the prio msg data, else it is a normal data message.

The second alternative is chosen such that the standard IEEE 802.15.4 is not modified. In fact, the command frame identifier which is available now (0 × 00) can be used in the future.

Second level: the coordinator

When receiving the message sent by the considered controller :

(1) if the controller uses a command frame to send the priority message, the command frame identifier allows the coordinator to recognize the nature of the information. This coordinator get the priority data from the first bit of the command payload. (2) if the controller uses a command frame to send the priority message, the coordinator checks the first bit of the frame payload to identify the message. If this bit is equal to 1, then the priority data will be set to the second bit of the frame payload.

When the coordinator receives the priority message from the controller, it broadcasts the controller priority information using a beacon frame showed in Figure 9. The first bit of the beacon payload is used to encode the controller priority information and the remaining bits are used for the controller address. The controller address will be used to identify the control loop.

Fig. 9. Beacon frame format

Third level: all nodes

First, each node has to verify if it is the controller or the sensor of the control loop which needs better QoS. Thus the node compares the controller address to its address if they are different it compares the controller address to the destination of its data messages if they are different the node concludes that it does not belong to the considered control loop and that it has to preform the deterministic priority algorithm. The beacon inf o = 1 which means that the control loop needs better QoS, the macM inBE OA is increased by 1 until it reaches its upper bound the aM axBE OA and the variable which is the beginning of the range of the random delay is set to 8 to eliminate the collision with the nodes of the WNCS. Otherwise, if the beacon inf o = 0 the macM inBE OA will be decreased by 1 until it reaches the default value which is set to 3 and the variable will be set to 0.

SIMULATION RESULTS

TrueTime, a Matlab/Simulink simulator, is used because it allows the simulation the temporal aspects of multitasking real-time kernels and wireless networks within Simulink together with the continuous-time dynamics of the controlled plant. The online adaptive protocol with simplified priority and beacon frame is implemented and added to TrueTime package so that this protocol can be chosen as shown in Figure 10. Thus, it is on the simulated WNCS presented in Figure 2. The sensor is time-triggered whereas the controller and the actuator are event-triggered.The load generated by the two cyclops is around 90% of the total bandwidth. When using the CSMA/CA of the IEEE 802.15.4/ZigBee, the QoC of the cart is not satisfactory as shown in Figure 11.

Figure 12 presents the cart behavior when the upper bound of the error which triggers the adaptation mechanism is set to 0.5. The QoC of the control loop is enhanced comparing In this paper, a QoS management scheme using the priority is presented. First, the case with probabilistic priority is studied and the case with deterministic priority are studied. Then, the deterministic priority QoS management scheme is adopted. An online adaptive scheme is proposed in order to manage the QoC through the adaptation of the QoS offered by the wireless network to the control loop. This QoS adaptation is ensured by means of the presented deterministic priority MAC mechanism. An implementation of this proposition is presented. This protocol is implemented and added to the TrueTime package to experience it on a simulated WNCS. The simulation results are encouraging since the QoC was enhanced with this approach. As future work, the case where there are several control loops will be studied. So, this solution must be extended to handle more than two priorities. Moreover, this online adaptive scheme will be implemented on micaz motes.

  * YQ. Song * * E. Rondeau * * * 1. INTRODUCTION

Fig. 1 .

 1 Fig. 1. The networked control system architecture

Fig. 2 .

 2 Fig. 2. IEEE 802.15.4/Zigbee using CSMA/CA: shared network 6. ONLINE ADAPTIVE PROTOCOL A one-hop wireless network with peer-to-peer topology is considered. Moreover, the MAC protocol operational mode is the beacon-enabled one and we are interested in the Contention Access Period of the superframe. To regulate the QoS offered to the WNCS, the prioritized CSMA/CA mechanism ( explained in subsection 6.3) is used instead of the Guaranteed Time Slot (GTS) one.GTSs may be allocated by the network coordinator to applications with real-time and specific data bandwidth requirements. In fact, this scheme offers an alternative choice to GTS one. For hard real-time, GTS is preferable while for soft real-time, prioritized CSMA/CA, that will be described below, could be suitable. In addition, this will overcome the problems of GTS. In fact, the number

Fig. 4 .

 4 Fig. 4. macM inBE OA variation depending on the perturbation load Collisions still exist since the nodes of WSN can choose the same waiting delay.

Fig. 6 .

 6 Fig. 6. macM inBE OA variation depending on the perturbation load

Fig. 8 .

 8 Fig. 8. Control over network (C: controller, A: actuator, and S: sensor) 7.1 First level: the controller i At the application layer, the controller check the error value e. The control loop can tolerate the error if it is less than a threshold which allows to ensure the required QoC.Depending on the error value, the priority of the controller will be set. If e > threshold then the priority will be equal to the maximum value max prio, else, the priority will be set to the normal priority value normal priority. The priority information will be transferred to the MAC layer through the payload added to the data part of the message to send to the actuator.

Fig. 10 .Fig. 11 .

 1011 Fig. 10. TrueTime Network parameter block

Fig. 12 . 5 FigureFig. 13 .Fig. 14 .

 1251314 Fig.[START_REF] Zampieri | Trends in networked control systems[END_REF]. The system response using the online QoC adaptive approach with threshold = 0.5Figure13and Figure14present the cart response for a threshold of 0.6 and respectively 0.7. The threshold

This work is partially supported by Safe-NECS project funded by ANR under ANR-05-SSIA-0015-03.


Samuel E Wuest

Nuno D Pires

Shan Luo

Francois Vasseur

Julie Messier

Ueli Grossniklaus

Pascal A Niklaus

METHODS AND RESOURCES Increasing plant group productivity through latent genetic variation for cooperation

Keywords: G-I, group versus individual, GWAS, genome-wide association study, NIL, nearisogenic line, SNP, single nucleotide polymorphism

AU : Pleaseconfirmthatallheadinglevelsarerepresentedcorrectly: Historic yield advances in the major crops have, to a large extent, been achieved by selection for improved productivity of groups of plant individuals such as high-density stands. Research suggests that such improved group productivity depends on "cooperative" traits (e.g., erect leaves, short stems) that-while beneficial to the group-decrease individual fitness under competition. This poses a problem for some traditional breeding approaches, especially when selection occurs at the level of individuals, because "selfish" traits will be selected for and reduce yield in high-density monocultures. One approach, therefore, has been to select individuals based on ideotypes with traits expected to promote group productivity. However, this approach is limited to architectural and physiological traits whose effects on growth and competition are relatively easy to anticipate. Here, we developed a general and simple method for the discovery of alleles promoting cooperation in plant stands. Our method is based on the game-theoretical premise that alleles increasing cooperation benefit the monoculture group but are disadvantageous to the individual when facing noncooperative neighbors. Testing the approach using the model plant Arabidopsis thaliana, we found a major effect locus where the rarer allele was associated with increased cooperation and productivity in high-density stands. The allele likely affects a pleiotropic gene, since we find that it is also associated with reduced root competition but higher resistance against disease. Thus, even though cooperation is considered evolutionarily unstable except under special circumstances, conflicting selective forces acting on a pleiotropic gene might maintain latent genetic variation for cooperation in nature. Such variation, once identified in a crop, could rapidly be leveraged in modern breeding programs and provide efficient routes to increase yields.

Introduction

Crop breeding is currently undergoing fundamental transformations. Speed breeding and genomic prediction can shorten generation times and increase effective population sizes, leveraging rates of phenotypic change to unprecedented levels [START_REF] Watson | Speed breeding is a powerful tool to accelerate crop research and breeding[END_REF][START_REF] Crossa | Genomic Selection in Plant Breeding: Methods, Models, and Perspectives[END_REF]. At the same time, largescale, high-throughput phenotyping platforms have become available and allow for the simultaneous quantification of multiple traits in ever larger greenhouse and field settings [START_REF] Furbank | Phenomics-technologies to relieve the phenotyping bottleneck[END_REF]. Yet, some studies suggest that current rates of yield increase are insufficient to meet growing demands from increasing human and animal populations under a changing climate [START_REF] Ray | Recent patterns of crop yield growth and stagnation[END_REF][START_REF] Ray | Yield Trends Are Insufficient to Double Global Crop Production by 2050[END_REF].

Historically, the highest rates of yield increase were achieved in the middle of the 20th century, at the beginning of the "Green Revolution." Combining breeding with improved management, yield potentials of major crops, such as wheat and tropical rice, approximately doubled in only a few plant generations [START_REF] Borlaug | Wheat Breeding and its Impact on World Food Supply[END_REF][START_REF] Khush | Green revolution: the way forward[END_REF][START_REF] Datta | Effect of Plant Type and Nitrogen Level on the Growth Characteristics and Grain Yield of Indica Rice in the Tropics1[END_REF]. In retrospect, these gains in yield potential have been unusually large. In contrast to most classical breeding that operates through selection on polygenic variation, they were largely realized by capitalizing on single genes, notably by the introgression of discrete but pleiotropic dwarfing alleles with major effects on plant form and function [START_REF] Hedden | The genes of the Green Revolution[END_REF][START_REF] Spielmeyer | Semidwarf (sd-1), "green revolution" rice, contains a defective gibberellin 20-oxidase gene[END_REF]. These alleles resulted in smaller and less bushy individuals, which diverted less resources to competition and allocated more into reproduction, i.e., into grain yield. The resulting more "cooperative" genotypes could be cultivated in high-density stands, which resulted in an increased crop yield per unit land area, with little productivity increase at the individual level. In other words, a trade-off between individual fitness and group-level yield was exploited to promote yield in well-fertilized high-density stands [START_REF] Datta | Effect of Plant Type and Nitrogen Level on the Growth Characteristics and Grain Yield of Indica Rice in the Tropics1[END_REF][START_REF] Donald | Competitive plants, communal plants, and yield in wheat crops[END_REF][START_REF] Donald | The breeding of crop ideotypes[END_REF][START_REF] Jennings | Plant Type as a Rice Breeding Objective[END_REF][START_REF] Jennings | Studies on competition in rice I Competition in mixtures of varieties[END_REF][START_REF] Duvick | Long-Term Selection in a Commercial Hybrid Maize Breeding Program[END_REF][START_REF] Tsunoda | A Developmental Analysis of Yielding Ability in Varieties of Field Crops: II. The assimilationsystem of plants as affected by the form, direction and arrangement of single leaves[END_REF][START_REF] Weiner | Looking in the Wrong Direction for Higher-Yielding Crop Genotypes[END_REF]. This trade-off, however, also causes the traits that benefit the group to be selected against in mixed or segregating populations containing larger, more competitive individuals, where cooperative individuals have lower relative fitness [START_REF] Jennings | Studies on competition in rice I Competition in mixtures of varieties[END_REF][START_REF] Jennings | Studies on competition in rice II: Competition in segregating populations[END_REF].

Thus, a key lesson from the "Green Revolution" is that selection for competitive individuals must be avoided to achieve the highest-possible yields. One way to achieve this in breeding is to anticipate "ideotypes" with a suite of phenotypic traits that reduce competition and thereby promote cooperation. Traits desirable for the breeder are, for example, a short stature, erect leaves, and a compact root system [START_REF] Donald | The breeding of crop ideotypes[END_REF][START_REF] Jennings | Plant Type as a Rice Breeding Objective[END_REF][START_REF] Peng | Progress in ideotype breeding to increase rice yield potential[END_REF]. However, a limitation of ideotype breeding is that the specific trait variation relevant for high crop yield in high-density groups often remains elusive to the human observer, especially for belowground traits. In principle, this can be avoided by shifting the focus on selection for quantitative genetic variation for cooperative traits at the group level [START_REF] Wade | Group selection and social evolution in domesticated animals[END_REF][START_REF] Goodnight | The influence of environmental variation on group and individual selection in a cress[END_REF][START_REF] Murphy | Kin recognition, multilevel selection and altruism in crop sustainability[END_REF], but this is often impractical (especially early in the breeding cycle), requiring more land and resources for phenotyping. Further, when genetic variation for the trait of interest does not exist in the breeding population, it first must be discovered in a wider crop population or in wild relatives (e.g., secondary gene pool).

Cooperative strategies in natural plant communities may be selected for under certain circumstances [e.g., spatial clustering of closely related individuals, or in cases where individuals recognized close relatives (kin recognition) and reduce competitive responses] [START_REF] Dudley | Plant cooperation[END_REF][START_REF] File | Fitness consequences of plants growing with siblings: Reconciling kin selection, niche partitioning and competitive ability[END_REF], but when competing individuals are unrelated, the evolutionary stable strategy generally is one that maximizes individual performance (and resource use) to the detriment of the group as a whole [START_REF] Falster | Plant height and evolutionary games[END_REF][START_REF] Anten | Tragedies and Crops: Understanding Natural Selection To Improve Cropping Systems[END_REF][START_REF] Rankin | The tragedy of the commons in evolutionary biology[END_REF][START_REF] Axelrod | The evolution of cooperation[END_REF]. However, if genetic variation for cooperation exists in nature, for whatever reason, it could potentially be leveraged in breeding [START_REF] Denison | Darwinian Agriculture[END_REF]. The difficulty, however, is to discover relevant alleles in a diverse set of plants, in particular if they do not correspond to classical ideotypes. Here, we present a methodological framework for the discovery of such alleles. We aimed for such a framework to be as general and unbiased as possible in order to detect yield or biomass gains (or any other performance measure) that emerge from any type of cooperation, including for unknown resources and through unidentified traits. Specifically, we designed competition experiments and corresponding analytical tools that allow to rank plant genotypes on a scale ranging from "competitive" to "cooperative." We then applied these methods in a proof-of-concept experiment with a population of Arabidopsis thaliana genotypes and produced a genetic map of a group versus individual (G-I) performance trade-off.

Variation at one genomic region was strongly associated with variation along this trade-off, whereby the allele of minor frequency promoted cooperation. However, the identified genetic variants were not associated with individual, or monoculture-level, productivity. They only became evident when mapping the G-I performance trade-off itself. In separate experiments, we then showed that the associated genetic polymorphisms allowed predicting productivity responses of genotypes along plant-density gradients. We argue that the method we present here has a large application potential, not least because of recent advances in technology including genome-wide association studies (GWAS) and large-scale phenotyping that make these methods widely applicable.

Results

Quantifying a plant group-versus-individual (G-I) performance trade-off by growing genotypes in different social contexts

The core principle of our method is to measure the performance of a set of genotypes in different "social contexts" [START_REF] Weiner | Evolutionary agroecology: individual fitness and population yield in wheat (Triticum aestivum)[END_REF], allowing for the quantification and subsequent genetic mapping of variation in a G-I trade-off (Weiner [START_REF] Weiner | Evolutionary agroecology: individual fitness and population yield in wheat (Triticum aestivum)[END_REF] discusses this trade-off in detail). To achieve this, we grew individuals of a set of genotypes (1) in monoculture, i.e., we confronted them with their own social strategy; and (2) in competition with a set of "tester" genotypes that represent the range of social strategies present in the population. According to game theory [START_REF] Axelrod | The evolution of cooperation[END_REF], the most cooperative genotype of the set will perform best with similarly cooperative neighbors (i.e., as a group in monoculture) but will lose when facing selfish, highly competitive neighbors (i.e., as an individual in mixtures). Conversely, the most competitive genotype will perform worst when grown with similarly competitive neighbors but will fare well when facing a cooperative neighbor. Comparing the performance of a genotype in monoculture relative to the performance with the tester set therefore allows to quantify the genotypes' G-I performance trade-off (Fig 1 ) and thereby rank all genotypes on a continuum between cooperative and competitive. In principle, this approach is applicable to any species, but for simplicity we tested it with an association panel of 98 natural A. thaliana genotypes-a subset of the RegMap population [START_REF] Horton | Genome-wide patterns of genetic variation in worldwide Arabidopsis thaliana accessions from the RegMap panel[END_REF]. Aboveground dry matter production (shoot biomass) served as the measure of performance (Materials and methods), but any other target characteristic, such as agricultural yield, could also be used. Each of the 98 focal genotypes was grown in a pot that contained another congenotypic individual (genotype monoculture). We further grew individuals of all genotypes in full factorial combination with an individual of each of ten tester genotypes (genotype mixtures; Figs 1A and 1B and S1). This design was replicated in two blocks.

As expected, competitive interactions among individuals were strong, with large negative effects of average tester shoot biomass (average across all pots) on shoot biomass of the focal genotypes (ANOVA F 1,960 = 88.23; P < 0.001). To evaluate the G-I performance trade-off of genotypes, we related the monoculture shoot biomass of the target genotype to the average individual biomass of the same genotype grown in competition with tester genotypes (average individual performance in mixed stand; Fig 1C). Not surprisingly, across genotypes, group and individual performance were highly positively associated, with more vigorous genotypes producing more biomass both in monoculture groups and as individuals subject to competition by testers. This relationship was also nonlinear (second degree polynomial; F 1,95 = 8.4, P = 0.005 for quadratic term), possibly because space became progressively limited as plant size increased [START_REF] Weiner | Evolutionary agroecology: individual fitness and population yield in wheat (Triticum aestivum)[END_REF][START_REF] Laird | Size inequality and the tragedy of the commons phenomenon in plant competition[END_REF]. However, the exact nature of this deviation from linearity is unimportant since we treated the overall relationship as heuristic. We then used the distance of each genotype's data from this empirical relationship to locate each genotype on an orthogonal axis that quantified the G-I trade-off (Materials and methods and procedure transforms the separate values for group performance in genotype monoculture and mean individual performance in genotype mixtures into two orthogonal metrics: the position along the overall relationship reflects general genotypic vigor (e.g., increased productivity due to better adaptation to the specific growth conditions), and the position perpendicular to the general relationship reflects a G-I trade-off value that characterizes the communal properties of the focal genotype (inset Fig 1C ). Specifically, the G-I value is positive for more cooperative genotypes, which have relatively lower individual performances in mixtures (competitive environment) but a higher performance in monoculture (cooperative environment).

Genome-wide association mapping identifies allelic variation associated with G-I trade-off

Next, we performed genome-wide association tests for the genotypic G-I trade-off value. Genome-wide polymorphism data of our population were available through the RegMap panel, and single nucleotide polymorphism (SNP) information was available for 214,000 sites. The G-I trade-off value was significantly associated with a major effect locus on chromosome three (Fig 2A and2B). The rarer allele (C-allele) was found in 18% of the RegMap population and was associated with lower individual but higher group performance, i.e., with increased cooperation (Fig 1C). The SNP with the strongest association resides in the center of a transposon-rich region and explained approximately 25% of the variation in the genotypic G-I trade-off values (Fig 2C). Direct mapping of untransformed data, i.e., of variation in either individual or monoculture group biomass alone, did not reveal any significant association with this locus (S2A and S2B Fig). This was expected, because such an analysis fails to separate general vigor from the G-I trade-off value that we used here to quantify cooperative properties. We did not find any other associations, likely because monoculture productivity is a complex polygenic trait and depends on a broad range of underlying processes. A more detailed genomic analysis based on a subset of 68 genotypes for which genome-wide resequencing data are available [START_REF] Alonso-Blanco | 1,135 genomes reveal the global pattern of polymorphism in Arabidopsis thaliana[END_REF] revealed association signals across many polymorphisms in a region of approximately 150 kb around the identified RegMap SNP, all in high linkage disequilibrium (Fig 2B).

Cooperative allele improves monoculture productivity at high density

To experimentally validate our finding of enhanced cooperation (i.e., of improved group performance in lines carrying the minor allele at SNP 15'294'955), we performed a stratified sampling of genotypes for plants of different sizes carrying either allele and grew these in monoculture stands of increasing planting density. Cooperative plant traits typically improve group performance especially at high planting densities [START_REF] Duvick | Long-Term Selection in a Commercial Hybrid Maize Breeding Program[END_REF][START_REF] York | Evolution of US maize (Zea mays L.) root architectural and anatomical phenes over the past 100 years corresponds to increased tolerance of nitrogen stress[END_REF][START_REF] Zhu | Evolutionary agroecology: Trends in root architecture during wheat breeding[END_REF]. Genotypes carrying the cooperation-associated allele at SNP 15'294'955 indeed exhibited superior productivity at the highest sowing density (+15% biomass, average across all genotypes; Fig 3A and3B; ANOVA F 1,10.6 = 7.5, P = 0.02), despite slightly lower individual performance across mixtures in the competition experiment (-4% biomass in mixtures; Fig 3B). As anticipated, group performance gains were more pronounced at higher densities where plants experienced more severe space limitations relative to those at lower densities (Fig 3A; ANOVA F 1,14.9 = 7.0, P = 0.019 for allele × ground area per individual). These results demonstrate that the molecular method presented here is able to predict group-level features that cannot be deduced from individuallevel properties and that these allow improving monoculture stand productivity.

Reduced root allocation is associated with enhanced cooperation

We next explored the relationship between the allele for cooperation and phenotypic traits to identify potential mechanism underlying enhanced cooperation. We measured two traits that characterize growth and resource-acquisition strategies of the genotypes in our panel. Specifically, we measured rosette diameter, because rosette lateral size affects light harvesting, and monoculture root-to-shoot ratio as an indicator of relative investment into belowground nutrient acquisition (Materials and methods). We further included two publicly available phenotypic traits into our analysis [START_REF] Atwell | Genome-wide association study of 107 phenotypes in Arabidopsis thaliana inbred lines[END_REF], namely flowering time in the field and vegetative growth rate. Genotypes carrying the allele for cooperation had significantly lower root-to-shoot ratios (ANOVA F 1,95 = 5.13, P = 0.026; effect size: 19% lower root-to-shoot ratio), and these were significantly negatively associated with their G-I trade-off value (ANOVA F 1,95 = 18.4, P < 0.001; Fig 4A and4B). None of the other traits examined showed such an association (Figs 4A andS3). We confirmed that this pattern of lower root-to-shoot ratios in cooperative genotypes holds across environments by conducting an independent experiment, where we explored this effect in both monocultures and in isolated individual plants, and in a different soil type (Figs 4C and S3). Overall, our findings indicate that relative root growth is associated with the identified genetic variation and that reduced root allocation may be part of a strategy associated with enhanced cooperation [START_REF] Biedrzycki | Root exudates mediate kin recognition in plants[END_REF].

The cooperative allele is geographically widespread and associated with pathogen resistance

Evolutionary game theory predicts that an allele that promotes cooperation will be selected against in a natural plant population, except under special circumstances [START_REF] Nowak | Five rules for the evolution of cooperation[END_REF]. We were thus surprised that the allele for cooperation that we identified is found over a wide geographic range and at remarkably high frequency (Fig 5A; minor allele frequency 18%). Genes often have multiple functions and we therefore expected that, in natural populations, conflicting selective forces acting on such pleiotropic genes (or on genes in tight linkage) might underpin the persistence of alleles for cooperation [START_REF] Todesco | Natural allelic variation underlying a major fitness trade-off in Arabidopsis thaliana[END_REF]. Examining genes in the identified genomic region, we found AtMIN7, a documented regulator of both growth and defense. The AtMIN7 protein targets pathogen effectors that suppress the plant immune response [START_REF] Nomura | A bacterial virulence protein suppresses host innate immunity to cause plant disease[END_REF]. Importantly, variation at the AtMIN7 gene is associated with resistance against Hyalonperonospora arabidopsidis, an obligate pathogen of A. thaliana causing downy mildew [START_REF] Nemri | Genome-wide survey of Arabidopsis natural variation in downy mildew resistance using combined association and linkage mapping[END_REF]. Analyzing this published data on resistance against different strains of H. arabidopsidis (incl. Noco2 and Emoy2), we found that the cooperation-associated allele indeed was highly significantly associated with partial or full resistance against strain Noco2 (Fig 5B, Fisher's exact test; P < 0.001). The resistance level against Noco2 also explained significant amounts of variation in the G-I trade-off value of our genotypes (ANOVA F 2,79 = 3.57, P = 0.03; Fig 5C). We therefore refer to this naturally occurring genetic variation as latentAU : PerPLOSstyle; italicsshouldnotbeusedforemphasisofwords:Hence; pleasenotethatth variation for cooperation, since contributions to pathogen resistance rather than cooperation has likely maintained the minor allele in A. thaliana populations.

Lines carrying the cooperator allele have a competitive advantage in conditions of high disease pressure

Further evidence for the idea that the allele for cooperation is advantageous in environments with pathogens emerged from an additional experiment in which we quantified benefits of individual alleles (payoffs) in well-defined competitive interactions modeled according to the classic prisoner's dilemma. For the experiment, we isolated four different pairs of near-isogenic lines (NILs) from Shahdara Bayreuth recombinant inbred lines [START_REF] Loudet | Bay-0 x Shahdara recombinant inbred line population: A powerful tool for the genetic dissection of complex traits in Arabidopsis[END_REF], i.e., pairs of nearly identical genotypes, in which allelic variation was restricted to the region around the focal SNP (see Materials and methods for details). It is predicted that NILs homozygous for the Shahdara (Sha) allele exhibit a more selfish and competitive, and lines homozygous for the Bayreuth (Bay) allele a more cooperative strategy. To separate effects of the Sha and Bay alleles from the general genetic background of the respective NILs, we replicated this design with four different pairs of NILs, i.e., in four different genetic backgrounds. In accordance with classic social dilemmas in evolutionary game theory (e.g., prisoner's dilemma) [START_REF] Axelrod | The evolution of cooperation[END_REF], we assumed the competitive genotypes would receive the highest payoff when growing with a cooperative neighbor (Fig 6A). However, such payoffs are difficult to quantify directly, and, therefore, we refer to payoffs as the reduction in aboveground biomass of plants competing relative to plants grown individually (e.g., a small reduction in biomass under competition = high payoff). We thus ran replicated experiments matching focal plants with neighbors so that all four possible combinations of Sha and Bay alleles were realized. All genotypes were also grown individually without neighbor, and the relative reduction of individual performance in competition was used to quantify the cost of growing with a specific neighbor.

Unexpectedly, the experiment was invaded by a parasite that affected genotypes and allele carriers differently and influenced competitive outcomes. Over the course of the experiment, some plants showed early leaf blotching, and, at harvest, many showed senesced and wilted leaves (Figs 6B andS5). This is a phenotype typical of soil-borne diseases. The symptoms were dependent on genotype and were mainly seen in NIL-background 33RV113 and individuals carrying the competitor (Sha) allele (Fig 6C). At the same time, we detected abundant spores of the obligate plant parasite Olpidium brassicaea in roots of all sampled pots (n = 18; S5 Fig).

We took advantage of this to test the hypothesis that the allele increasing cooperation also (https://cran.r-project.org/web/packages/maps/readme/README.html) (B) Association of Chr 3 SNP 15'294'955 with resistance or susceptibility against strains of Hyalonperonospora arabidopsidis (Emoy2 and Noco2), based on published data [START_REF] Nemri | Genome-wide survey of Arabidopsis natural variation in downy mildew resistance using combined association and linkage mapping[END_REF]. Numbers indicate genotype counts. n.s. = no significant difference. (C) Association of Noco2 resistance levels with the G-I trade-off. s = susceptible, i+r = intermediately and fully resistant. Data available in Supplementary File of Nemri and colleagues [START_REF] Nemri | Genome-wide survey of Arabidopsis natural variation in downy mildew resistance using combined association and linkage mapping[END_REF]. https://doi.org/10.1371/journal.pbio.3001842.g005 conferred pathogen resistance. As a proxy for root disease expression, we visually scored root yellowing/browning, a phenotype caused by O. brassicae [START_REF] Van Der Meer | The rhizoctonia-and olpidium disease of cauliflower seedlings[END_REF]. We found that this score significantly depended on genetic background (ordinal logistic regression p-value < 0.001 for NIL pair) and was always lower in genotypes carrying the cooperative (Bay) allele (ordinal logistic regression p-value = 0.001;

Fig 6C).
As predicted, plants carrying the allele promoting cooperation were competitively inferior when matched with a competitive neighbor, but only in the two genetic backgrounds that showed low disease expression (Fig 6D). In the two genetic backgrounds with high disease expression, the competitive relationship was very different: It was most pronounced in the most susceptible genetic background, the genotype carrying the allele promoting cooperation was competitively superior.

Together, our results suggest that the cooperative allele is associated with increased resistance against several diseases, which may confer a competitive advantage under high disease pressure. This effect may be caused by antagonistic pleiotropy or by different alleles at closely linked genes. Whether or not such a trade-off between competition and disease resistance affects selection in nature will have to be tested. However, it could explain why a cooperative allele is maintained in a natural population and over such a wide geographic range.

Discussion

Here we used specifically designed competition experiments, combined with genetic association mapping, to identify (1) plant genotypes that perform well when grown in high-density stands; and (2) potential genes and alleles that underlie these cooperative growth strategies. Interestingly, in A. thaliana, we detected a specific allele that is associated with increased growth in high-density stands, representing a strategy we here refer to as "cooperation." The importance of cooperation among individuals for agronomic production has long been recognized. Animal breeding has focused more explicitly on cooperation and social strategies [START_REF] Wade | Group selection and social evolution in domesticated animals[END_REF][START_REF] Muir | Group selection for adaptation to multiple-hen cages: Selection program and direct responses[END_REF]. Domesticated animals are often kept at relatively high densities, which can trigger aggressive behavior among individuals, resulting in high levels of stress, injuries, and increased mortality, all of which are detrimental to animal welfare and productivity. A breeding objective thus has been to obtain relatively docile, cooperative animals that limit adverse interactions when kept at high densities [START_REF] Friedrich | Genetics of cattle temperament and its impact on livestock production and breeding-a review[END_REF]. Conceptually similar considerations apply to plant communities. However, in plants, the traits that underlie cooperation are less easily recognized. In general, such traits may be related to resource sharing in the sense that resources remain accessible to the individuals that most efficiently convert these into biomass or yield. In other words, any excessive investment into competition in the presence of neighbors undermines what is, from an agronomic perspective, an efficient use of resources at the group level [START_REF] Falster | Plant height and evolutionary games[END_REF][START_REF] Anten | Tragedies and Crops: Understanding Natural Selection To Improve Cropping Systems[END_REF][START_REF] Gersani | Tragedy of the commons as a result of root competition[END_REF][START_REF] Cabal | The exploitative segregation of plant roots[END_REF][START_REF] Zhang | Donald's ideotype and growth redundancy: A game theoretical analysis[END_REF][START_REF] Zhu | Donald's Ideotype and Growth Redundancy: A Pot Experimental Test Using an Old and a Modern Spring Wheat Cultivar[END_REF][START_REF] Zhu | Root proliferation in response to neighbouring roots in wheat (Triticum aestivum)[END_REF]. In plants, cooperative growth strategies thus may be characterized by a relative insensitivity to the presence of neighbors, or even a reduction in the development of competitive structures. Indeed, improved group functioning was observed in crop experiments where genotypes exhibited more vertical leaf angles [START_REF] Tian | Teosinte ligule allele narrows plant architecture and enhances high-density maize yields[END_REF], where leaf area [START_REF] Srinivasan | Decreasing, not increasing, leaf area will raise crop yields under global atmospheric change[END_REF] or branch number were reduced [START_REF] Kokubun | Design and examination of soybean ideotypes[END_REF], or where belowground competition was experimentally prevented [START_REF] Gersani | Tragedy of the commons as a result of root competition[END_REF][START_REF] Zhu | Root proliferation in response to neighbouring roots in wheat (Triticum aestivum)[END_REF]. Cooperative responses may also be plastic and expressed predominantly in monocultures; for example, kin recognition studies have shown that plants competing with close relatives reduced root allocation relative to when they competed with strangers [START_REF] Dudley | Kin recognition in an annual plant[END_REF]. Common to all these experiments is the finding that restricting competitive interference between neighbors, either experimentally or by using genotypes with corresponding traits, is beneficial for group yield, especially at high planting densities. In our study, we observed a lower relative investment into root growth in cooperative genotypes, which is in line with this consideration.

Cooperation, although beneficial for group yield, is typically also associated with individual fitness costs in noncooperative environments, i.e., under strong competition [START_REF] Axelrod | The evolution of cooperation[END_REF][START_REF] Denison | Darwinian Agriculture[END_REF][START_REF] Weiner | Evolutionary agroecology: individual fitness and population yield in wheat (Triticum aestivum)[END_REF]. Thus, addressing this G-I trade-off is key to identifying and using cooperative genotypes. In breeding, different strategies have been developed that achieve this goal. First, cooperation can be selected for by anticipating corresponding ideotypes possessing traits expected to foster cooperative strategies. This has been very successfully accomplished during the Green Revolution [START_REF] Borlaug | Wheat Breeding and its Impact on World Food Supply[END_REF][START_REF] Donald | The breeding of crop ideotypes[END_REF][START_REF] Jennings | Plant Type as a Rice Breeding Objective[END_REF][START_REF] Vogel | Semidwarf Growth Habit in Winter Wheat Improvement for the Pacific Northwest1[END_REF] and led to the recognition of the relevance of a G-I trade-off in crop improvement [START_REF] Jennings | Studies on competition in rice I Competition in mixtures of varieties[END_REF][START_REF] Jennings | Studies on competition in rice II: Competition in segregating populations[END_REF]. Second, cooperative strategies can be directly selected for at the group level [START_REF] Weiner | Looking in the Wrong Direction for Higher-Yielding Crop Genotypes[END_REF][START_REF] Murphy | Kin recognition, multilevel selection and altruism in crop sustainability[END_REF][START_REF] Biernaskie | Kin selection theory and the design of cooperative crops[END_REF]. For example, this is often done in field trials with maize, whereby identical hybrid genotypes are planted and evaluated in high-density rows and subsequently in larger field plots. Such a selection at the group level also promotes traits that benefit group yield, for example, reduced tassel size, more vertical leaves, and reduced tillering [START_REF] Weiner | Looking in the Wrong Direction for Higher-Yielding Crop Genotypes[END_REF][START_REF] Denison | Darwinian Agriculture[END_REF][START_REF] Denison | Evolutionary tradeoffs as opportunities to improve yield potential[END_REF]. Another idea is to incorporate kin selection schemes into the breeding process (e.g., in the early cycles of breeding programs where individual genotypes compete with cosegregants), which could also select for crops that exhibit cooperative traits [START_REF] File | Fitness consequences of plants growing with siblings: Reconciling kin selection, niche partitioning and competitive ability[END_REF][START_REF] Biernaskie | Kin selection theory and the design of cooperative crops[END_REF][START_REF] Montazeaud | Farming plant cooperation in crops[END_REF]. Though it is currently unclear how widespread kin recognition is in plants [START_REF] Milla | Growing with siblings: A common ground for cooperation or for fiercer competition among plants?[END_REF], kin recognition studies in wild populations are another avenue that could promote the identification of cooperative traits in plants [START_REF] Murphy | Kin recognition, multilevel selection and altruism in crop sustainability[END_REF]. Finally, genomic predictions are increasingly adopted to predict a genotype's merit purely based on its genome, whereby prediction models are trained on yield variation of high-density stands of pure varieties. These approaches have arguably contributed to historical and contemporary yield advances and implicitly or explicitly include elements that selected to some extent for cooperative traits [START_REF] Murphy | Kin recognition, multilevel selection and altruism in crop sustainability[END_REF]. However, they also rely on genetic variation in the relevant traits to be present in the breeding populations. The method we present here-while motivated by the same broader topic-differs in important respects. First, it directly assesses the G-I trade-off rather than group yield. By exposing genotypes to two "social environments" that represent different ends of the cooperation-competition continuum, genotypes expressing cooperative traits can more easily be distinguished. This contrasts with other methods that either focus only on groups (e.g., row or plot-level selection) or use an environment with mixed neighborhoods (e.g., typical setting in quantitative genetic analyses of indirect genetic effects; [START_REF] Wade | Group selection and social evolution in domesticated animals[END_REF][START_REF] Silva | Genetic-based interactions among tree neighbors: Identification of the most influential neighbors, and estimation of correlations among direct and indirect genetic effects for leaf disease and growth in Eucalyptus globulus[END_REF][START_REF] Camerlink | Indirect Genetic Effects for Growth Rate in Domestic Pigs Alter Aggressive and Manipulative Biting Behaviour[END_REF]). Second, our method systematically decomposes group yield into two effects: general vigor and cooperation. This separation is critical because alleles promoting cooperation may be found at low frequency and in genotypes with low vigor. A prominent example is the recessive semidwarf allele sd1 in rice. It was originally found in the Taiwanese Dee-Geo-Woo-Gen variety, which showed only average yields in the tropics, but was instrumental for boosting tropical rice yields [START_REF] Hedden | The genes of the Green Revolution[END_REF][START_REF] Spielmeyer | Semidwarf (sd-1), "green revolution" rice, contains a defective gibberellin 20-oxidase gene[END_REF][START_REF] Jennings | Studies on competition in rice II: Competition in segregating populations[END_REF]. Third, the fact that we use an empirical, heuristic relationship to correct for general vigor implicitly accounts for nonlinear relationships between genetics and productivity, which is typically difficult to address with other methods.

In combination with genetic mapping, our method provides an "agnostic" approach to discover latent genetic variation for cooperation. In our proof-of-concept study, we identified a genetic variant of large effect. This was surprising, since traits underlying individual growth and yield or environmental adaptations, such as drought tolerance, are often highly polygenic [START_REF] Lynch | Genetics and Analysis of Quantitative Traits[END_REF][START_REF] Boyle | An Expanded View of Complex Traits: From Polygenic to Omnigenic[END_REF][START_REF] Wieters | Polygenic adaptation of rosette growth in Arabidopsis thaliana[END_REF]. On the other hand, there is now increasing evidence that different plant-plant interactions can be affected by few genetic variants of large effects ( [START_REF] Wuest | A plant biodiversity effect resolved to a single chromosomal region[END_REF][START_REF] Montazeaud | From cultivar mixtures to allelic mixtures: opposite effects of allelic richness between genotypes and genotype richness in wheat[END_REF]; this study), maybe resembling the pattern more generally found in plant-parasite interactions [START_REF] Wilfert | The genetic architecture of susceptibility to parasites[END_REF]. Regardless of the reason, the existence of such alleles is important given that many biotechnological methods, including genome editing, typically rely on the availability of traits that are influenced by a single or few genes. Therefore, we propose that biotechnological and breeding research should extend their focus beyond the performance of individuals, often grown as single plants in pots on "conveyor belt systems," towards the performance of groups and the relevant competitive interactions that drive it.

In this work, we focused-primarily for the sake of simplicity-on a model population of A. thaliana and on aboveground biomass (which is a target trait for some crops, such as forage grasses). This is a first case study using the proposed methodology, and a larger-scale systematic search may reveal alleles with comparable effects in crops or their wild relatives. Here, we found that the allele for cooperation among plants remained relatively frequent (18%) in natural populations, likely because it conferred resistance to diseases to the individuals carrying this allele, and thereby higher fitness under high disease pressure. This finding raises hopes that crops and wild plants may also hold hidden cooperative traits that have persisted despite their disadvantages in competitive situations. Once identified, such latent variation in cooperation could rapidly be co-opted in marker-assisted breeding programs or through biotechnology. At a more fundamental level, the finding that large-effect genetic variants for cooperation are maintained in natural populations leads to the intriguing thought that social traits could arise as evolutionary exaptations, i.e., by co-option of an existing trait unrelated to cooperation [START_REF] Gould | Exaptation-a Missing Term in the Science of Form[END_REF].

Materials and methods

Plant material

The natural A. thaliana genotypes used (S1 Data) are a subset of the RegMap population [START_REF] Horton | Genome-wide patterns of genetic variation in worldwide Arabidopsis thaliana accessions from the RegMap panel[END_REF] for which a comprehensive list of traits has been collected [START_REF] Atwell | Genome-wide association study of 107 phenotypes in Arabidopsis thaliana inbred lines[END_REF]. For pairs of NILs isolated from four Bay-Sha RILs, we confirmed homozygosity for a genetic polymorphism upstream of the focal SNP (primer F: 5 0 -TGAGAGAGAGCTGATGATGGATG-3 0 ; primer R: 5 0 -CGCCTTGA TTGACACAGATTC-3 0 ; approx. 100 bp deletion in Sha sequence at position 15'333'951) and a genetic polymorphism downstream of the focal SNP by the use of PCR markers (markers primer F: 5 0 -GCAAGAGGGAGCTAAAGAAACAG-3 0 ; primer R: 5 0 -GCCCTTATCGCCAT GAACTG-3 0 ; approx. 50 bp deletion in Sha sequence at position 14'914'025). These deletions in the Sha sequence were predicted by the Polymorph tool (http://polymorph.weigelworld.org). All eight genomes were also resequenced on the DNBseq plattform (BGI, Hongkong) with a minimum of three Gb sequences per genome. The reads were aligned to the Arabidopsis Col-0 reference sequence with the use of the bwa software (version 0.7.16a) [START_REF] Li | Fast and accurate short read alignment with Burrows-Wheeler transform[END_REF]; read sorting and variant calling was performed using samtools (version 1.5) [START_REF] Li | The Sequence Alignment/Map format and SAMtools[END_REF]. Whole-genome reconstruction was performed as described previously [START_REF] Wuest | A plant biodiversity effect resolved to a single chromosomal region[END_REF], following the approach developed by Xie and colleagues [START_REF] Xie | Parent-independent genotyping for constructing an ultrahigh-density linkage map based on population sequencing[END_REF]. Genome reconstructions were in agreement with the published marker maps of the corresponding RILs ( [START_REF] Loudet | Bay-0 x Shahdara recombinant inbred line population: A powerful tool for the genetic dissection of complex traits in Arabidopsis[END_REF]; S5A Fig) . We confirmed genetic differentiation of each of the four NIL pairs at the locus of interest. Two pairs were otherwise completely isogenic; the two other pairs showed some residual genetic differences on other chromosomes (S5B Fig).

Experimental design

Competition experiment: Pairs of individual plants were grown in small pots (6 × 6 × 5.5 cm) in a factorial design in which the 97 genotypes of the panel were each grown together with one of ten tester genotypes (Bay-0, C24, Col-0, Cvi-0, Ler-1, Sav-0, Sf-2, Shahdara, St-0, Uk-1). These tester genotypes were chosen because they constitute the parents of different publicly available recombinant inbred line populations, i.e., a genetic resource that allows for certain genetic experiments (for example, isolating NILs from heterogeneous inbred families; see Fig 6). The tester genotypes were a subset of the panel, but tester genotypes not part of the original panel would have worked equally well. Each genotype was further grown in a monoculture of two individuals. Each genotype composition was replicated twice, in separate blocks. In the second block, not enough seeds were available for line LP-2-6; in the second block, we therefore replaced this genotype by Kn-0. We thus effectively had 98 genotypes grown with the ten tester genotypes. Overall, the experiment consisted of 2,134 pots with two plants each. Each tester line was also grown as individual plant, once per block. Pots containing single plants, and pots in which one plant died at the seedling stage, were excluded from data analyses.

Density gradient: To test for decreased self-inhibition in plants carrying the cooperationassociated allele, genotype monocultures with different individual densities (3 × 3, 4 × 4, or 5 × 5 plants on 8 × 8 cm area) were constructed. Six genotypes that carried the cooperationassociated allele (Bor-4, Est-1, Mt-0, Ra-0, Sav-0, Wa-1) but varied in average individual performances were paired with seven genotypes (An-1, Br-0, Can-0, Kondara, Nfa-10, Shahdara, St-0) that carried the alternative allele but had similar average individual performances. By matching genotypes by size, we were able to separate the size dependence of self-inhibition from the allele effect.

Preparation of plant material and growth conditions

Competition experiment: Seeds of all genotypes were sown directly onto soil (four parts Einheitserde ED73, Gebru ¨der Patzer, Germany; one-part quartz sand) in February 2016. For germination, the pots of size 6 × 6 × 5.5 cm from a given block were randomly placed into trays covered with plastic lids. The two plants per pot were established 3 to 4 cm apart by sowing 5 to 20 seeds per position and, once seeds had germinated, removing surplus seedlings. Blocks 1 and 2 were sown on February 17 and 18, 2016, respectively. Plants were grown with a photoperiod of 14 hours, providing additional light when necessary. Daytime and nighttime temperatures were maintained around 20 to 25˚C and 16 to 20˚C, respectively. Trays were randomly rearranged within the greenhouse every 3 to 5 days. After 5 to 5.5 weeks, pots were transferred from trays onto three tables with automated watering and randomly rearranged every week. Flowering shoots of individual plants were tied to wooden sticks when they grew taller than approx. 10 cm. All plants were harvested on April 14 (Block 1) and April 15 (Block 2), 2016, i.e., approx. 8 weeks after sowing. Each plant was cut below the rosette and individually dried at 65˚C for 4 to 5 days and then stored at room temperature until weighing. Roots from a pot were washed on a metal sieve, and total root mass determined after drying at 65˚C for 4 days. Flowering time was determined by checking every 2 to 3 days whether flowering bolts were present that exceeded 0.5 cm height.

Density gradient: Monocultures were sown in pots of 9 × 9 × 10 cm (inner pot diameter approximately 8 × 8 cm) at densities of either 9, 16, or 25 plants per pot. Soil and growth conditions were as described above for the competition experiment. Because we observed some seedling mortality early in the experiment, realized planting density was determined from photographs taken 27 days after sowing, i.e., at a time when competition still was very limited. Aboveground biomass was harvested, dried, and weighed 54 days after sowing.

Independent biomass allocation measurements: For an independent assessment of root-toshoot biomass ratios in the studied natural genotypes, 80 genotypes that were used in the main competition experiment were grown for 43 days either as single plants or as monoculture (consisting of four plants per pot) and in pots of 7 × 7 × 8 cm size on a mixture of one-part ED73 and four-parts quartz sand. The measurements were performed as described above.

Competition experiments with NIL pairs: We used four NIL pairs derived from 33RV085, 33RV113, 33RV142, and 33RV192. Each pair consisted of one line carrying the Bay allele and one line carrying the Sha allele. For each pair, we grew 16 monocultures per line and 32 mixtures of the two lines, all consisting of two plants per pot. We additionally grew each line as single plants per pot, also replicated 16 times. Seeds were directly sown into 6 × 6 × 5.5 cm pots filled with a 4:1 parts ED73 soil:quartz sand. Leaf blotching and excessive senescence were noticed midway through the experiment and scored 31 and 50 days after sowing. Scoring was done blindly, i.e., without information about pot or genotype identity. Shoot and root biomass were harvested 57 days after sowing, roots washed, and all biomass dried and weighed as described above. Root browning scores were determined visually by categorizing root browning into three ordinary levels (S5 Fig) . Roots were stained using a 1% cotton blue in 80% lactic acid solution and examined using a Leica microscope for a visual inspection of potential root pathogens.

Statistical analyses

All statistical analyses were performed using the statistical software R version 3.4.1 (http://rproject.org). The block-adjusted individual performance of genotypes across mixtures were estimated using least square means from a model including just block and genotype. Monoculture biomass per individual (i.e., total average monoculture biomass divided by two) was then fitted as function of linear and quadratic forms of individual biomass, using the R-function "lm." The G-I trade-off value was determined as orthogonal distance by determining the point in the quadratic heuristic that was closest to the respective point by nonlinear minimization using the R-function "nlm." The GWAS analyses were performed with easyGWAS (https:// easygwas.ethz.ch) [START_REF] Grimm | easyGWAS: A Cloud-Based Platform for Comparing the Results of Genome-Wide Association Studies[END_REF], using the EMMAX algorithm [START_REF] Kang | Variance component model to account for sample structure in genome-wide association studies[END_REF] and using SNPs from the 250k SNP chip (http://bergelson.uchicago.edu/) or the 1001 genomes project (http://1001genomes.org/) [START_REF] Alonso-Blanco | 1,135 genomes reveal the global pattern of polymorphism in Arabidopsis thaliana[END_REF]. SNPs with a minor allele frequency below 5% were removed.

To test for the dependency of the G-I trade-off value on relative root allocation, we linearly regressed the trade-off value against root-to-shoot ratio and tested for significance the slope term. We did not transform the axes because the relationship was sufficiently linear. Note that analysis on a log-log scale, as frequently used in allometric analyses, was not appropriate here because the G-I trade-off value was centered around zero (i.e., not systematically positive).

For the density gradient experiment, productivity was modeled in dependence of the fixed terms area per individual, allele, plus their interaction (we chose area per individual (available space) instead of density (the inverse of available space) because the relationship with density was nonlinear). The corresponding random terms were genotype, and the interaction between genotype and area per individual. Individual performance in mixture of the previous experiment was included as a covariate in the model, because it was used in the design of the experiment for stratified sampling of genotypes according to size. The realized densities deviated from sown densities because of a relatively high initial mortality. Therefore, we instead used densities determined from photographs of each pot that were made midway through the experiment. Two pots were removed from the analysis because realized densities were much higher than planted densities, probably because they accidentally had not been thinned to the intended densities.

In the NIL pair competition experiment, the payoff for a given combination of strategies was determined as shoot mass of a line grown as individual plant minus its shoot mass under competition, i.e., the payoff quantified the shot biomass reduction induced by to the presence of particular neighbors. The standard error of the payoff σ payoff was calculated by error propagation as p (σ 2 single plant + σ 2 individual | neighbour ). Root browning scores were analyzed using an ordinal logit regression as implemented in the polr-function of the R package MASS, with ordinal root scores as independent variable and community type (single plant or monoculture), genetic background (NIL pair), and allele (Sha or Bay) as explanatory variables. Mixtures were excluded from the analysis of root browning scores.

  Fig 1C). In other words, this

Fig 1 .

 1 Fig 1. A general method for the genetic dissection of the group-vs-individual performance (G-I) trade-off. (A) Experimental design of the competition experiment. G1, G2, . . . G98: focal genotypes sampled from the RegMap panel of natural A. thaliana genotypes. T1, T2, . . . T10: tester genotypes representing a range in plant size to reflect a large portion of the genetic variation present within A. thaliana. (B) Experimental setup. (C) Relationship between a genotype's mean performance as an individual across all mixtures with tester genotypes (average individual shoot biomass) and its group performance in monoculture (average combined shoot biomass of the two individuals in a pot). Black line: second degree polynomial with 99% confidence intervals. The inset outlines three of many possible genetic effects a hypothetical allele could have on a genotype's strategy: variation along the mixture-vs-monoculture regression describes variation in vigor, and variation perpendicular to the regression describes the G-I performance trade-off. Red and blue dots show genotypes carrying different alleles at position 15'294'955 on chromosome 3 (see below), whereby red alleles confer a more cooperative strategy. Data available at https://zenodo.org/record/6983283, file competition. csv. https://doi.org/10.1371/journal.pbio.3001842.g001

Fig 2 .

 2 Fig 2. Allelic variation at a major effect locus affects the group-vs.-individual performance (G-I) trade-off in A. thaliana. (A) Manhattan plots of genomewide association tests for variation in the G-I trade-off, based on the 250k SNP chip data. The genotypic G-I trade-off value is the distance from the overall trend between group and individual performance in monoculture and mixtures, respectively (inset). (B) Zoom in on a segment of chromosome 3, showing Manhattan plots of either an association analysis using SNP chip polymorphisms (top), or, for a subset of 68 genotypes, genome-wide resequencing polymorphisms (bottom). Models of protein-coding genes are drawn as boxes below, on either + (upper) or-(lower) strand. (C) Association of variation at SNP 15'294'955 and the G-I trade-off. Error bars denote means ± SEM. Data available at https://zenodo.org/record/6983283, file competition.csv. https://doi.org/10.1371/journal.pbio.3001842.g002

Fig 3 .

 3 Fig 3. Genotypes carrying the allele for cooperation exhibit superior monoculture performances at high density. (A) Changes in monoculture biomass of genotypes carrying either the cooperation-associated allele (C-allele, red) or the alternative allele (A-allele, blue) across a realized planting density gradient. Lines show linear regression estimates ± SEM. Arrowheads show per plant areas at the sown target densities, which were not always realized due to seedling mortality. (B) Comparison of genotype's mean individual shoot biomass in mixtures versus monoculture biomass at densities of 25 plants per pot (2.56 cm 2 per plant). Horizontal lines: mean values across all genotypes carrying either allele. Red and blue: cooperation-associated allele (C-allele) and alternative allele (A-allele) at SNP Chr 3 15'294'955, respectively. Note the different scales of the left and the right y-axes. Data available at https://zenodo.org/record/ 6983283, file densitygrad.csv. https://doi.org/10.1371/journal.pbio.3001842.g003

Fig 4 .Fig 5 .

 45 Fig 4. Altered allocation to roots but not growth or life history is associated with increased levels of cooperation. (A) Association of allelic variation at SNP Chr3:15'294'955 with variation in traits related to different plant strategies. (B and C) Relationship between the G-I performance trade-off and plant root-toshoot ratio in monocultures of the competition experiment shown in Fig 1 (B) or monocultures of an independent experiment (C; see also Materials and Methods and S3 Fig). Bars and regression lines show means ± SEM; � ANOVA P < 0.05; n.s.: not significant. Data available at https://zenodo.org/record/ 6983283, files competition.csv and sand.csv. https://doi.org/10.1371/journal.pbio.3001842.g004

Fig 6 .

 6 Fig 6. A trade-off between competitive dominance and disease resistance expressed in different near-isogenic lines. (A) Expected payoff matrix of interactions between plants ("cooperate" vs. "compete," as determined by carrying Bay vs. Sha alleles), with Temptation (T) > Reward (R) > Punishment (P) > Sucker's Payoff (S) (color coded). (B) Experimental outline: benefits refer to the cost reduction as measured by the average aboveground biomass of genotypes in competition compared to the biomass of the plant grown alone. A strong reduction refers to a high costs and therefore low benefit, a weak reduction to a high benefit. (C) Pot containing a pair of near-isogenic plants isolated from the RIL parent 33RV113. The plant carrying the competitive Sha allele exhibits strong signs of leaf wilting (arrows). (D) Summary of the competition experiment, separated by genetic background (33RV085, 33RV142, 33RV192, 33RV192), showing disease symptoms (number of plants exhibiting leaf blotching; root browning score) and payoff matrices for all genetic backgrounds and allele combinations. The values in payoff matrix are the average biomass reduction ± SEM in brackets. Data available at https://zenodo.org/record/6983283, file Payoff_longFormat.csv. https://doi.org/10.1371/journal.pbio.3001842.g006

PLOS Biology | https://doi.org/10.1371/journal.pbio.3001842November 29, 2022

Acknowledgments

We thank Bernhard Schmid (UZH) and Andrea Patocchi (Agroscope) for support and helpful discussions, Matthias Lutz (Agroscope) for help in identifying Olpidium brassicae in root samples, Cyrille Violle (CEFE) for helpful comments on the manuscript, Matthias Philipp, Daniel Trujillo, and Mariela Soto Araya for help with sowing and harvesting the competition experiment, and Matthias Furler for technical support in the greenhouse.

This work was supported by the University of Zurich, Agroscope and an Ambizione Fellowship (PZ00P3_148223) of the Swiss National Science Foundation (to SEW), and an Advanced Grant of the European Research Council (to UG). FV acknowledges funding from the French Agency for Research (ANR grant ANR-17-CE02-0018-01, 'AraBreed'), and the Agreenskills fellowship programme (grant agreement n˚3215), which has received funding from the EU's Seventh Framework Programme under the agreement NF P7-609398. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

The datasets described and a basic analysis script are available through the Zenodo data repository (DOI:10.5281/ zenodo.6983283).

Supporting information