Eduardo Redondo-Iglesias

S Pelissier

P Venet

Efficiency Degradation Model of Lithium-ion Batteries for Electric Vehicles

Eduardo Redondo-Iglesias, Pascal Venet, Serge Pelissier

Abstract-The purpose of this paper is to analyse efficiency degradation of lithium-ion batteries. Two lithiumion cell technologies are considered under calendar ageing. It is well known that ageing mechanisms have an impact in cells' performances. Most of studies focus on capacity fade and impedance rise but efficiency is less frequently studied. However, from the application point of view, battery efficiency degradation directly impacts the system energy efficiency. Results reveal the importance of considering battery ageing in the design phase of electric vehicles, not only for capacity but also for efficiency reasons: efficiency degradation depends of the technology, so when comparing two technologies one must take into account the cells' performances not just when cells are fresh but during the whole lifespan. Another finding reported in this paper is the high correlation between capacity fade and energy efficiency for the tested technologies. Finally, two empirical models for energy efficiency degradation were developed in both technologies: the first one is based on Eyring relationships and the second one lies on the existing correlation between capacity fade and efficiency. Quality of each model is reported for both model types and battery technologies.

Index Terms-Efficiency model; Energy storage systems; Lithium-ion batteries; Accelerated ageing; Modelling

I. INTRODUCTION

Battery Electric Vehicles (EV) are much more efficient than ICE Vehicles (ICEV). EV's and ICEV's powertrain efficiency are about 70% and 20% respectively but this difference can significantly decrease when considering primary energy efficiency [1]. For this reason, every element in the energy conversion chain should be optimised: from power generation and distribution to vehicle energy use.

The battery is probably the most sensitive element in the EV powertrain system because of its cost and lifespan. Lithium-ion is nowadays the main technology for traction batteries because of its higher energy density and energy efficiency compared to previous existing technologies.

Ageing mechanisms are responsible of performance degradation of batteries: decrease of the amount of storable energy (capacity fade) and power availability (impedance increase). Depending on ageing path and battery composition, each ageing mechanism may act in a different magnitude. Hence, there is not always a direct correlation between impedance increase and capacity fade [2][3][4].

Within SIMCAL project a vast campaign of calendar ageing tests of commercial lithium-ion cells was conducted [START_REF] Delaille | ECS Meeting Abstracts[END_REF][START_REF] Kassem | [END_REF][7][8][9][10][11][12]. In [START_REF] Kassem | [END_REF], a study of capacity and impedance degradation of LFP cells from SIMCAL project is done. Some of these cells were analysed in post-mortem studies [8] demonstrating that main ageing mechanism is LLI (loss of lithium inventory) due to Solid Electrolyte Interphase(SEI) formation and growth.

In [13], a similar ageing campaign to SIMCAL was carried out: capacity and impedance were analysed. Postmortem studies confirmed that LLI was again the main ageing mechanism. An empirical capacity fade model with an Eyring relationship was developed. This model was validated with dynamic calendar ageing conditions (periods of different temperatures and states of charge). In [14] a combined cycling/calendar capacity fade model for LFP cells was developed.

On one hand, previous works on lithium-ion ageing dealt with modelling capacity fade [9,12,[15][16][17][18], impedance rise [2,7,19] or both [11,[20][21][22][23]. On the other hand, some authors dealt with efficiency [24][25][26] and its dependence of current rate. But efficiency evolution throughout battery's lifespan was not often considered. Some authors shown interest about efficiency evolution throughout battery's lifespan. For example, [10] made a first analysis of the performance evolution of cells from SIMCAL project. This analysis was made on a subset of SIMCAL ageing tests for each technology. Efficiency degradation was also mentioned in [27], where the authors included some values of energy efficiency for LFP cells for various current rates and states of ageing.

Battery efficiency is often considered in the design In [28], the authors aimed to perform a life cycle analysis of LFP cells for use in second life application. The authors of this paper were interested in efficiency evolution of LFP cells, but a lack of efficiency evolution data led them to make the following assumption: efficiency evolution would follow the same trend that capacity fade. This is a very strong assumption: an efficiency degradation model would be a useful tool to obtain more precise results.

The present paper is an extended and updated version of the conference paper [START_REF] Redondo-Iglesias | Twelfth International Conference on Ecological Vehicles and Renewable Energies (EVER)[END_REF]. In this work, we intent to analyse all ageing tests from SIMCAL for two technologies (LFP and NMC). That includes 27 different combinations of T and SoC for two technologies.

In part II an analysis of efficiency as a function of SoC is provided, this could be used to better assess the best SoC regions to use depending on both ageing and efficiency.

In part III we develop an efficiency degradation model by two approaches: by using an Eyring relationship and by exploiting the existence of the correlation between capacity and efficiency fades.

A comparison of the results of two approaches of modelling is provided as a brief discussion about suitability of each considered lithium-ion technology depending of temperature for an example of application.

II. MEASURING CAPACITY AND EFFICIENCY FADE

A. Experimental setup

In the SIMCAL project, more than a hundred lithiumion cells from different manufacturers and positive electrode compositions were tested in calendar ageing [START_REF] Delaille | ECS Meeting Abstracts[END_REF]. The calendar ageing tests consisted in a full test matrix with three different temperatures and three different SoC levels i.e. a full factorial design 3 2 (2 factors, 3 levels per factor). Lithium-ion manufacturers recommend not to use this technology over 60°C, thus this is the higher limit of temperature for ageing tests. Higher temperatures may induce thermal runaway even in rest conditions [START_REF] Jousse | dustrial Electronics Society, IECON 2013 -39th Annual Conference of the IEEE[END_REF].

Accelerated ageing tests consisted in storing each cell at a fixed temperature [START_REF] Jousse | dustrial Electronics Society, IECON 2013 -39th Annual Conference of the IEEE[END_REF]45 x during charge x discharge x during discharge cells were tested at each test condition for each lithiumion technology in order to improve the representativeness of results. Two technologies were tested: NMC cells are from Kokam (SLPB 70205130P, 12Ah pouch cells), whereas LFP cells are from A123 (ANR26650M1A, 2.3Ah, cylindrical cells).

The cells' characteristics were periodically measured at 25°C by the means of RPT (Reference Performance Test) using Biologic potentiostats with electrochemical impedance spectroscopy capability. RPT's (figure 1) are composed of 4 phases:

(A) a full discharge to measure the remaining charge in the cell, (B) two full-charge/full-discharge cycles to measure the cell capacity, (C) a partial-discharge/partial-charge cycle with cell impedance measurements at 5 SoC levels, (D) a full charge followed by a partial discharge to restore the SoC to a value in agreement with the ageing test conditions.

B. Methodology to measure efficiency

Efficiency can be measured by several ways. The most common one consists in calculating the whole cycle efficiency of a full-charge/full-discharge cycle. For example, the International Organization for Standardization (ISO) defines a protocol to characterize efficiency in this way [START_REF]Electrically propelled road vehicles -Test specification for lithium-ion traction battery packs and systems -Part 2: High-energy applications[END_REF].

US-DOE (the United States Department of Energy) method [START_REF] Pngv | [END_REF] is based on the performance of 100 charge balanced power profiles at specified SoCs. Any variation in the SoC of the batteries under test enables to estimate the energy efficiency at this specified SoC. The main disadvantages of this method are the test duration and the difficulty to avoid excessive SoC drift during the tests.

Kang et al. [24] proposed a method to measure efficiency of battery cells under constant current (CC) charges or discharges. This method lies on the definition of the net energy of a cell as a function of I, OCV (open circuit voltage) and SoC.

Firstly, OCV must be characterized by a pseudo-OCV or an incremental-OCV approach [START_REF] Petzl | Energy Conversion[END_REF]. Pseudo-OCV is obtained by cycling the battery at very low current rates and averaging U charge and U discharge . Incremental-OCV is obtained by partial charges and discharges followed by rest periods.

Once OCV as a function of SoC is known, net energy is easily obtained by integration :

W net = SoCf SoCi I • OCV • dSoC (1)
. Charge and discharge energy are obtained in the same way with U charge and U discharge respectively:

W charge = SoCf SoCi I • U charge • dSoC (2)
W discharge = SoCf SoCi I • U discharge • dSoC (3)
Finally, charge and discharge energy efficiencies are the relation between charge and discharge energy and net energy [24,25]:

η en,charge = W net W charge (4)
η en,discharge = W discharge W net (5)
Energy efficiency of a battery under charge and discharge can be expressed as:

η en = η en,charge • η en,discharge = W discharge W charge (6)
RPT design in SIMCAL project was originally intended for measuring capacity and impedance, not for efficiency.

In this work, we analyse efficiency in a similar way to [24]. Unlike Kang's method, we do not attempt to separate charge and discharge efficiencies because SIMCAL RPTs do not offer a reliable measure for OCV (absence of pseudo-OCV phase), i.e. we focus on battery efficiency (equation 6).

For each RPT, the efficiency of last discharge-charge cycle (figure 1, t 1 to t 4 ) is calculated. From t 1 to t 2 battery is discharged with CC at 1C, from t 2 to t 3 battery is in rest condition and from t 3 to t 4 battery is charged with CC at 1C (figure 2). Obviously, full charge is not reached during CC charges and a subsequent CV (constant voltage) phase is performed from t 4 to t 5 to ensure full charging of the cell. We will only consider CC phases for efficiency (t 1 to t 4 ).

Efficiency obtained by equation 6 is the average efficiency over a charge/discharge cycle. But in many applications such as electrical vehicles (EV) and hybrid electrical vehicles (HEV), batteries are often used in a partial SoC zone. As SoC is an important factor of battery ageing, efficiency characterisation as a function of SoC is necessary. This would help to determine the best SoC zone to operate in optimal conditions of energy efficiency and minimal ageing. Equation ( 7) expresses efficiency as a function of SoC:

η(SoC) = | Ẇdischarge (SoC)| | Ẇcharge (SoC)| (7)
As in each RPT charge and discharge current rates are equal (1C), equation ( 7) can be simplified [START_REF] Redondo-Iglesias | Twelfth International Conference on Ecological Vehicles and Renewable Energies (EVER)[END_REF]:

η(SoC) = U discharge (SoC) U charge (SoC) (8)
Equation ( 8) is an approximation to power efficiency as the ratio between U discharge and U charge . This equation is valid for applications such as battery pack dimensioning or battery technology benchmarking. For a fine estimation of energy losses, other models are more suitable like, for example, equivalent circuit models.

C. Experimental results

Figure 3 shows charge and discharge curves of these two cells and efficiency calculated by eq. ( 8), obtained from the first RPT (fresh cells). Efficiency of NMC cells is monotonically increasing with SoC. In contrary, LFP cells' efficiency decreases rapidly in the extremities (0 and 100% SoC). LFP efficiency has also a local minimum at 30% SoC.

Figure 4(a) shows the efficiency versus SoC for a NMC cell during ageing at 60°C and 100% SoC. At the beginning of ageing tests mean efficiency was 96%, but after 190 days the mean efficiency went down 87% and the capacity fade reached 37%.

Ageing tests were carried on LFP cells during 378 days (figure 4(b)). Despite of capacity fade, efficiency was almost constant during the ageing tests: initial efficiency was 95% and decreased only 1% (to 94%) at end of life.

D. Discussion on experimental results

In higher energy density (125 and 106 kWh/kg respectively for the considered cells in this paper). However, LFP batteries are good candidates for long life and high current rate applications. Power efficiency (η(SoC)) was calculated for both technologies at different states of degradation. The res-ults reveal that the shape and degradation rate of η(SoC) are very different depending of technology. Efficiency appears to degrade much faster in NMC cells than in LFP cells. For example, for 60°C and 100% SoC (figure 4), we can see that NMC efficiency decreases under 90% after 120 days while LFP efficiency stays much less significant even after 300 days.

Concerning the shape of η(SoC) (figure 3), in NMC cells it is monotonically increasing with SoC. In LFP we can discern three regions: at lower SoC levels efficiency decreases rapidly; at medium SoCs efficiency is mainly flat with a local minimum at approximately SoC = 30%; finally, at higher SoCs efficiency decreases again.

The main reason behind the existing difference in shape of η(SoC) is the difference in shape of positive electrode equilibrium potentials (both negative electrodes are graphite based).

On one hand, NMC electrode's potential is monotonically decreasing with the proportion of lithium, i.e. it is monotonically increasing with SoC. As charge and discharge voltage curves of NMC cells are increasing with SoC and the distance between them is quite constant (see figure 3), η(SoC) increases with SoC (equation 8).

On the other hand, LFP electrode's potential is constant at approximately 3.43 V vs. Li + except in very low SoC (<5%) and very high SoC (>95%) [34]. Graphite electrode's potential decreases rapidly in the first stages of lithiation (low proportion of lithium, lower SoCs) and it decreases slowly from 0.13 to 0.08 V vs. Li + in the last stages of lithiation (from 20 to 100% SoC) [35,36]. LFP-graphite cell's OCV is the difference between LFP's and graphite's potentials, so in the medium SoCs OCV increases slowly from 3.3 to 3.35 V. As charge and discharge voltages follow the same trends, η(SoC) is mainly flat from SoC = 10 to 90% (figure 3).

The local minimum of η(SoC) found at SoC = 30% in LFP cells is probably due to a graphite phase transition (from LiC 12 to LiC 6 ) [35,36]. This phase transition also occurs in NMC cells because they have also a graphite negative electrode, but it is not reflected in η(SoC) by a local minimum because the NMC positive electrode potential is not constant with SoC.

III. MODELLING CAPACITY AND EFFICIENCY FADE

Energy and power capabilities of lithium-ion batteries degrade over time in calendar ageing as a function of SoC and T . Energy and power degradation can be assimilated respectively to capacity and efficiency fade (Q F and η F ). In previous works [12,37] capacity fade of lithium-ion cells in calendar ageing has been modelled by using the Eyring relationship.

The Eyring relationship extends the Arrhenius law (temperature dependence) to other stress factors (e.g. pressure, current, voltage, etc.). Equation ( 9) is a general form for a performance (y(t)) degrading over time under two type of stresses (T and S i ):

y(t, T, S i ) = A • T n • e (Ea/kT +BiSi+CiSi/kT ) • f (t) (9)
In the Eyring relationship, the influence of each additional stress (S i ) is added to the exponential function beside the thermal stress term (E a /kT ). The direct influence of a stress is B i S i while C i S i /kT represents an interaction term between T and S i . The model parameters are: A, n, E a , B i and C i , with k the Boltzmann constant and f (t) the time degradation function of y(t).

In battery ageing, f (t) is typically a power of time (e.g. t, √ t) or a linear combination of both functions (at + b √ t). In calendar ageing of batteries, S i can be SoC or DoD. Both quantities can be calculated relative to initial or current capacity (Q 0 or Q). For comparability and simplicity reasons, in this work as for [37] we chosen S i = DoD, with DoD relative to Q 0 .

As shown in figure 5, we can imagine two approaches to model efficiency and capacity fades: the first one consists in considering separate models (figure 5(a)). The inputs of both sub-models are T and DoD.

The second approach is to model capacity fade and then to model efficiency evolution as a function of capacity fade (figure 5(b)). In this approach, the ageing model is composed of two sub-models: a capacity fade model and a efficiency fade model. The inputs for the capacity fade model are T and DoD. The input for the efficiency model is the estimated capacity fade ( QF ).

A. Eyring capacity fade model

Here, the main assumption is the linear evolution of Q F with the time (t) when the stress factors (T , DoD) are constant. This is equivalent to consider

Q F = C A (T, DoD) • t ( 10
)
where C A is the acceleration coefficient depending of the stress levels [37].

In this work, we will consider a modified Eyring relationship to model C A (from [37]):

QF = A • e ( -Ea k•T +B•DoD+ C•DoD k•T ) -D • t (11)
Finally, the capacity evolution is obtained by subtracting the estimated capacity fade ( QF ) from the initial value of the capacity (Q 0 ):

Q(t, DoD, T ) = Q 0 -QF (t, DoD, T ) (12)

B. Eyring efficiency fade model

The efficiency ageing model can be formulated in the same way as the capacity ageing model:

ηen,F = A η • e -Eaη k•T +Bη•DoD+ Cη •DoD k•T -D η • t (13)
ηen (t, DoD, T ) = η en,0 -ηen,F (t, DoD, T )

C. Polynomial efficiency model

Figure 6 shows the cycle efficiency versus capacity fade for both technologies (NMC and LFP) and for all the storage conditions. We can see that efficiency mainly depends of capacity fade and the type of cell (NMC or LFP): a strong correlation between capacity fade and efficiency degradation exists.

In this approach, efficiency is formulated as a polynomial of the capacity fade:

ηen ( QF ) = n i=0 a i • Q i F (15)
where capacity fade is estimated from eq. (11).

In this work we have chosen second degree polynomials for LFP cells and first degree polynomials for NMC cells.

The obtained model parameters for each model are in table I. For each model, the parameter set has been identified with a least square minimisation of the difference between model estimations and measurements.

D. Modelling results

Figure 7 illustrates some simulations compared to measurements of capacity and efficiency. In this example, three simulations where performed at three SoC levels: 30, 60 and 100% at 45°C for both cell types.

For NMC (figure 7(a)) some cells seem to regenerate their capacity (i.e. negative capacity fade) at the beginning of the tests (e.g. SoC = 65 or 30% for T = 45°C). As explained in [37], this phenomenon is probably due to an initial decrease of impedance in the firsts stages of SEI formation. Capacity measurements are strongly dependent of impedance when they are performed at medium/high rates as in SIMCAL project (1C). By performing capacity measurements at low rates, for example C/5 or lower, distortion due to this initial decrease of impedance is minimised [START_REF] Broussely | Proceedings of the 10th International Meeting on Lithium Batteries[END_REF][START_REF] Dubarry | [END_REF]. In this example (T = 45°C), the model overestimates capacity fade at SoC = 100% for LFP cells (figure 7(c)). Notice that this couple of ageing conditions represent the worst case for this model in terms of precision. As shown in table II, overall quality of LFP's Q F model is good (mean absolute error of 1.3%, R 2 > 0.9).

Results shown in figure 7(b) and 7(d) reveal that the different approaches of efficiency modelling (Eyring relationship versus polynomial of capacity fade) have different behaviours.

For example, for NMC cells (figure 7(b)), the efficiency fade (and also the capacity fade) is quite similar at lower levels of SoC (30, 65%) being much faster at 100% SoC. In this example, the model based on a polynomial of Q F is better compared to the Eyring based one. The reason is that the polynomial based efficiency model fits in the same manner that capacity fade: that is degradation at 100% SoC is much faster than at other SoC levels. On the other hand, when performing simulations with the Eyring based efficiency model, the differences between SoC 100% and the lower SoC levels (30, 65%) are less significant than for the polynomial one.

For LFP cells (figure 7(d)), the errors of efficiency simulations are comparable for both approaches (Eyring versus polynomial). However, while the polynomial model leads to parabolic evolutions, the Eyring efficiency model leads to linear evolutions that can diverge from measurements with time.

Figure 8 shows the cumulative distribution of errors P r(|ε|) for all simulations at the nine possible combinations of T (30, 45, 60°C) and SoC (30, 65, 100%) for both technologies (NMC, figure 8(a) and LFP, figure 8(b)). This figure confirms that both approaches to efficiency fade modelling have a similar precision.

More detailed results about the quality of these models can be found in table II. The mean absolute errors |ε| of the capacity fade model simulations are 1.48% and 1.28% for the NMC and the LFP cells respectively and R 2 , the coefficients of determination, are 0.895 (NMC) and 0.925 (LFP). These two quantities confirm that the precision of the capacity fade model is satisfactory.

For NMC cells the polynomial model of efficiency is more satisfactory than the Eyring based one. At higher values of P r (probability), the lowest absolute error corresponds to the polynomial model. The value of R 2 is also substantially higher for this model compared to the Eyring based model (table II.a).

For LFP cells the polynomial and the Eyring based models have both similar values of errors for each value of P r and similar values of R 2 (table II.b). Notice that R 2 is very low (about 0.34) which indicates a bad quality of modelling for both types of models. In fact, as shown in figure 6(b), the efficiency fade is very low in LFP cells. The range of variation of the efficiency over the lifespan in LFP cells is of the same magnitude that the variability between different cells, which explains a lower value of R 2 compared to NMC cells.

E. Discussion on modelling results

In this part, two approaches for modelling capacity and efficiency degradation were presented.

The first approach is based on two independent Eyring relationships: capacity and efficiency are modelled separately as functions of time and ageing factors (T and SoC). Each Eyring relationship has 5 parameters, so for this approach 10 parameters are needed.

The second approach consist in taking advantage of the existing correlation between efficiency and capacity fades. In this approach, two models are cascaded: the output of the capacity fade model is used as input for the efficiency model. A polynomial relation η(Q F ) has been identified from experimental data with 2 or 3 parameters depending of the technology. So for this model 7 to 8 parameters are needed.

The first approach is a priori supposed to be a better solution in terms of accuracy. Firstly, because of the higher number of parameters (higher degrees of freedom). Secondly, in the second approach capacity fade estimation errors are propagated to efficiency.

The quality of results where analysed for both approaches in both technologies. Figure 8 and table II show that there is no great difference in terms of quality between both approaches: mean errors of efficiency and their distributions are similar for NMC and LFP. Nevertheless, there is a difference in R 2 for NMC: 0.701 for the first approach, 0.774 in the second, indicating that second approach would have some benefit over the first one.

IV. CONCLUSIONS

In one hand, efficiency of batteries is usually considered in the design phase, for example, of electric vehicles. On the other hand, capacity fade (sometimes also impedance rise) throughout the lifetime is often evaluated by the means of accelerated ageing tests.

efficiency evolution over lifespan is not often considered.

In this work, we intended to evaluate efficiency degradation in accelerated calendar ageing for two lithiumion technologies: NMC and LFP.

Constant current phases of full charge/discharge cycles allowed us to build the characteristic curves of efficiency over SoC at each state of ageing. Characteristic curves reveal the best SoC regions to operate in terms of efficiency. LFP showed a particular behaviour with a local minimum of efficiency at 30% SoC.

We also provide two approaches to efficiency degradation modelling: first one is based on the Eyring relationship and second one is based on a polynomial expression of capacity fade. The results of two approaches show that second approach can be more convenient for two reasons: simplicity (fewer number of parameters) and precision (similar or higher R 2 ).

Energy efficiency analysis within battery ageing offers a simple but effective way to assess the adequacy of batteries to an application during the whole lifespan. These type of models can be used as decisional tools in the design phase or in life cycle assessments of electric vehicles.

Figure 1 :

 1 Figure 1: Voltage during first RPT for LFP (up) and NMC (bottom) cells.

Figure 2 :

 2 Figure 2: Zoom in last cycle (LFP cell).

Figure 5 :

 5 Figure 5: Two approaches to modelling: (a) separate models (b) efficiency as a polynomial of capacity fade.

Figure 6 :

 6 Figure 6: Efficiency versus capacity fade (a) NMC cells, (b) LFP cells. Points are measurements at different ageing conditions: red, green and blue for 60, 45 and 30°C respectively, colour shades indicate SoC (30, 65 and 100% from light to dark). The polynomial approximation is represented by a black continuous line.

Figure 7 :

 7 Figure 7: Results of ageing at 45°C. (a) Capacity fade and (b) efficiency versus time of NMC cells. (c) Capacity fade and (d) efficiency versus time of LFP cells. Points are measurements, continuous lines are simulations of Q F and η en Eyring models, dashed lines are simulations of η en polynomial model. Colour shade indicates SoC (30, 65, 100%) from light to dark.

Figure 8 :

 8 Figure 8: Cumulative distribution of errors.

  of vehicles, for example for battery sizing. This characteristic is age dependent: it will degrade over time like other characteristics (capacity, impedance, etc.). Efficiency varies over state-of-charge (SoC), thus the battery use should be optimized to operate in the highest efficient SoC levels. Consequently, for a better consideration, efficiency degradation over time must be taken into account.

This paper is a postprint of a paper submitted to IEEE Transactions on Industry Applications 2019, and is subject to IEEE copyright. The paper is available through IEEE Xplore. DOI: 10.1109/TIA.2018.2877166. phase

  this work we have considered two different lithiumion technologies: NMC and LFP. NMC batteries have several advantages compared to LFP, mainly they have a

	4.2					0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98
	4
	3.8
	3.6
	3.4
	3.2
	3
	2.8
	2.6
	0	0.2	0.4	0.6	0.8	1
	Figure 3: Charge and discharge voltages (left y-axis) and
	efficiency (right y-axis) of fresh cells.
	1
	0.95
	0.9
	0.85
	0.8				0 days 63 days
					126 days
	0.75				160 days 190 days
	0.7
	0	0.2	0.4	0.6	0.8	1
			(a) NMC
	1
	0.95
		0 days
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	0.9	151 days 226 days
		259 days
		294 days
		337 days
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	0.85
	0	0.2	0.4	0.6	0.8	1
			(b) LFP
	Figure 4: Efficiency degradation of cells under calendar ageing
	conditions (60°C, 100% SoC).

Table I :

 I Model parameters.

			a. Eyring capacity fade model
	Parameter NMC cells	LFP cells	units
		A	2.233 • 10 10 2.563 • 10 05 (p.u./day)
		Ea	0.8690	0.5531	(eV)
		B	37.19	12.34	(n.u.)
		C	-1.162	-0.3672	(eV)
		D	1.5 • 10 -05	0	(p.u./day)
			b. Eyring efficiency fade
	Parameter NMC cells	LFP cells	units
		Aη	1.419 • 10 10 1.428 • 10 08 (p.u./day)
		Eaη	0.9021	0.8412	(eV)
		Bη	-8.371	-11.78	(n.u.)
		Cη	0.1813	0.3585	(eV)
		Dη	4.0 • 10 -06	5.5 • 10 -06	(p.u./day)
			c. Polynomial efficiency model
	NMC: ηen(QF ) = -0.2303 • QF + 0.9582
	LFP:	ηen(QF ) = -0.1532 • Q 2 F + 0.003923 • QF + 0.9530
	Table II: Modelling results: mean absolute error (|ε|), error
	for some probabilities of the cumulative distribution of errors
	(|ε|(P r)) and coefficient of determination (R 2 ). The quantities
	are expressed in p.u.
			a. NMC cells
	Model	QF (Eyring) ηen (Eyring) ηen(polynomial)
	|ε|		0.0148	0.00541	0.00551
	|ε|(P r = 0.50)	0.0102	0.00329	0.00385
	|ε|(P r = 0.90)	0.0294	0.0130	0.0142
	|ε|(P r = 0.95)	0.0455	0.0150	0.0175
	|ε|(P r = 0.99)	0.0791	0.0393	0.0219
	R 2		0.895	0.701	0.774
			b. LFP cells
	Model	QF (Eyring) ηen (Eyring) ηen(polynomial)
	|ε|		0.0128	0.00211	0.00215
	|ε|(P r = 0.50)	0.00878	0.00151	0.00148
	|ε|(P r = 0.90)	0.0329	0.00475	0.00503
	|ε|(P r = 0.95)	0.0413	0.00548	0.0062
	|ε|(P r = 0.99)	0.0580	0.00808	0.00743
	R 2		0.925	0.345	0.344

ACKNOWLEDGEMENT

This work uses data from SIMCAL project (2009)(2010)(2011)(2012). SIMCAL project was funded by the French National Research Agency (ANR). SIMCAL partners are CEA, EDF, EIGSI, IFPEN, IFSTTAR, IMS, LEC, LMS-Imagine, LRCS, PSA, RENAULT, SAFT and VALEO.


Nieves Martín-Robles

Javier Morente-López

Grégoire T Freschet

Hendrik Poorter

Catherine Roumet

Rubén Milla

Nieves Martín
email: nievesmartin@msn.com

Root traits of herbaceous crops: pre-adaptation to cultivation or evolution under domestication?

Keywords: Crop progenitors, domestication, functional traits, origins of agriculture, plant resource economics, root economics spectrum, root tissue density, specific root length

Agricultural fields are commonly characterized by high nutrient and water availabilities, which are favorable for plant growth. Such conditions might promote the evolution of resource acquisitive strategies. We asked whether crop plants show root traits typical of resource acquisitive strategies and whether this strategy is primarily a result of their evolution under domestication or of the early selection of successful candidates for domestication.

2.

We studied a set of 30 crop species and their wild progenitors. We set up a greenhouse experiment to measure five root traits: root thickness, root tissue density, specific root length (SRL), root mass fraction (RMF) and root length ratio. In addition, we compiled data from other wild herbaceous species, growth in similar conditions to this experiment, to place the root traits of our crops in the context of wider botanical variation.

3.

Wild progenitors had thicker and less dense roots, with higher RMF and lower SRL, than other wild herbs. Thicker and less dense roots are indicative of fertile soils, which suggests that wild progenitors could have been adapted for success in agricultural conditions. Additionally, we found that domestication generally increased total plant dry mass, but none of the root traits evolved consistently towards a more resource-acquisitive strategy after domestication across all species. Root trait values differed between progenitors and crop species for most pairs surveyed, but this occurred in diverse directions depending on crop species. Such differences were independent of phylogeny, functional group or variability in the domestication processes, such as timing of the domestication event or organ under focal artificial selection.

INTRODUCTION

Plant domestication involves selection for and modification as well as long-term use of traits regarded as favorable by humans in wild species (Evans, 1996;Gepts, 2004).

Major changes commonly associated with artificial selection include yield increase of the organs of interest (e.g. seeds or fruits), strong apical dominance, and loss of seed dispersal and seed dormancy mechanisms (Evans, 1996;Gepts, 2004;[START_REF] Abbo | Plant domestication versus crop evolution: A conceptual framework for cereals andgrain legumes[END_REF]. The consequences of crop domestication on plant traits also include the decline in herbivore defense (Turcotte, Turley & Johnson, 2014;Whitehead, Turcotte & Poveda, 2016), higher stomatal densities at the upper side of leaves [START_REF] Milla | Shifts in stomatal traits following the domestication of plant species[END_REF] or the nitrogen and phosphorus concentration increase in leaves [START_REF] Delgado-Baquerizo | phenome[END_REF]. Some consequences of crop domestication, such as higher leaf nitrogen contents [START_REF] Delgado-Baquerizo | phenome[END_REF] and higher relative growth rates

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This article is protected by copyright. All rights reserved. [START_REF] Preece | How did the domestication of Fertile Crescent grain crops increase their yields[END_REF], would be typical of fast-growing resource-acquisitive strategies (Lambers & Poorter, 1992;[START_REF] Craine | Resource strategies of wild plants[END_REF]Reich, 2014). Thus, domestication might have led to the evolution towards fast-growing plants with resource-acquisitive strategies in response to agricultural conditions [START_REF] Chapin | The mineral nutrition of wild plants[END_REF][START_REF] Craine | Resource strategies of wild plants[END_REF][START_REF] Milla | Plant domestication through an ecological lens[END_REF].

One obvious cause of these domestication effects is recurrent natural selection by the farmers (Denison Kiers & West, 2003;Zohary, 2004;[START_REF] Milla | Plant domestication through an ecological lens[END_REF]. Such selection in agricultural fields might have led to adaptations in above and belowground traits, because croplands differ from wild habitats in the availability of resources (nutrients and water), or in the intensity and frequency of disturbances [START_REF] Mckey | Ecological Approaches to Crop Domestication[END_REF][START_REF] Milla | Plant domestication through an ecological lens[END_REF]. Nevertheless, an alternative would be that wild progenitors may also have shown acquisitive strategies before domestication started. Human society has been shaping the ecosystems around their settlements before agriculture started changing the environment (Smith, 2007). The new environmental conditions would be characterized by high fertility and increase in the frequency of disturbances (fires, selective plant culling) and would therefore have led to the modification of diversity, enhancing the short-term productivity of herbaceous plants (Smith, 2011). The 'Dump Heap' hypothesis suggests that early domestication started with species growing near human settlements (Sauer, 1952;Zeven, 1973;Hawkes, 1983). If so, successful candidates of domesticated species would be pre-adapted to cultivation conditions (Hawkes, 1983) with ruderal, generalist and fast-growing characteristics [START_REF] Mercuri | Plant behaviour from human imprints and the cultivation of wild cereals in Holocene Sahara[END_REF]. In support of this idea, a few studies have shown greater seed mass, faster growth rates, greater specific leaf areas, and greater nitrogen

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concentrations in wild progenitors in comparison with other wild species, which fits with fast-growing strategies for crops´ ancestry [START_REF] Cunniff | Functional traits differ between cereal crop progenitors and other wild grasses gathered in the neolithic fertile crescent[END_REF][START_REF] Milla | Plant domestication through an ecological lens[END_REF]Preece et al., 2015). Thus, theoretical and empirical evidences based on aboveground traits suggest that domesticated species have fast acquisitive strategies, either as a consequence of pre-adaptions to the agricultural environment and/or as evolution under cultivation. While our knowledge is pretty substantial when it comes to how domestication affected above-ground plant traits, we have only very limited insight into what happened below-ground. [START_REF] Bishopp | The hidden half of crop yields[END_REF]Lynch & Brown, 2012).

A diversity of physiological and morphological root traits has been put forward as indicative of root resource acquisitive strategies (see Freschet & Roumet, 2017 for a review). The root length ratio (RLR; see Table 1 for abbreviations and definitions) and its determinantsroot mass fraction (RMF), specific root length (SRL), mean root diameter (MRD) and root tissue density (RTD)are among the most important morphological and allocational traits determining root nutrient acquisition capacity (Ryser & Lambers, 1995). Fast acquisitive strategies are generally characterized by low structural investment in roots: low RMF, MRD and RTD (Ryser 1996). [START_REF] Poorter | The limits to leaf and root plasticity: What is so special about specific root length?[END_REF] suggested a general model of root trait coordination (Fig. 1a) where increasing soil fertility would result in larger plants, with thicker and less dense roots, with contrasting effects on SRL (see also Freschet, Swart, & Cornelissen, 2015a).

Overall, as fertility would decrease the proportion of biomass allocated belowground (RMF), the model predicts that, via indirect effects, RLR would generally decrease with fertility. Since agricultural and pre-agricultural environments are mostly fertile ecosystems (Denison, Kiers & West, 2003;[START_REF] Mckey | Ecological Approaches to Crop Domestication[END_REF], one

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could therefore expect that crop evolution should have followed the pathway of phenotypic adjustments proposed by [START_REF] Poorter | The limits to leaf and root plasticity: What is so special about specific root length?[END_REF]. If correct, novel agricultural conditions would trigger larger plants with higher MRD and lower RTD, implying contrasting impacts on SRL and, together with the lower RMF would determine the RLR.

In this study we investigated whether domesticated plants show root trait values typical of resource acquisitive strategies and whether this strategy is primarily a result of their evolution under domestication or of the early selection of successful candidates (or wild progenitors) for domestication. These questions will be tested by: i) comparing root traits of 30 domesticated species and their wild progenitors with root traits of other wild herbaceous species taken in global data bases, ii) examining the domestication effect on plant biomass and root traits and iii) testing whether the response of root traits to domestication is consistent with the causal model of [START_REF] Poorter | The limits to leaf and root plasticity: What is so special about specific root length?[END_REF]. We hypothesized that i) wild progenitors already show trait values typical of plants adapted to fertile habitats, ii) domestication has a similar effect on root traits as fertility. Domestication would thus have selected larger plants with higher MRD, but lower RTD, lower SRL, and RMF values as compared to their progenitors which are expected to show more acquisitive root traits than other wild species.

MATERIALS AND METHODS

Study system

To maximize the generality of our results, we worked with a phylogenetically diverse set of 30 herbaceous crop species and their most likely wild progenitors (Table 2). Our set of crops includes eight grasses, 11 legumes and 11 non-leguminous forbs, with different domestication geographies and histories. We obtained seed lots for each of these 30 crops: one belonging to an accession of a common domesticated cultivar and another from the most likely wild progenitor (Table 2). More information about the species and accessions (references of domesticated cultivar and wild progenitor assignment, seed donor banks accession identifier, time under domestication and organ under selection) can be found in Table S1. In addition, to place the root traits of wild progenitors and domesticated plants in the context of global herbaceous variation, we compiled root data from taxonomically diverse wild herbaceous species.

Growth conditions

For logistical reasons, the 30 crop pairs were grown staggered from January to June 2012, matching the most appropriate time of the year for the performance of each crop.

The two accessions (domesticated plant and wild progenitor) belonging to each pair were simultaneously grown at the same spatial location within the greenhouse (located in Móstoles, central Spain, 40º18´48´´N, 3º52´57´´W). To avoid plants from becoming severely pot-bound [START_REF] Poorter | Pot size matters: A meta-analysis of the effects of rooting volume on plant growth[END_REF], we built special long containers to allow the growth of root systems for several weeks before reaching the bottom of the container. A round plastic cylinder (42 cm deep, 8 cm diameter) was embedded inside, and down to the bottom end of a 25 cm long Jumbo Rootrainer (Haxnicks Ltd., Wiltshire, UK), resulting in a final container of 42 cm depth x 50 cm² area (2.1 L, Fig. S1). The bottom of this final container was removable without

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root or substrate disturbance, to analyze the depth of the deepest root (Fig. S1).

Containers were filled with pure sand to facilitate recovery of the complete root system. Finally, plants were fertilized twice a week with 50 mL of a complete nutrient solution to allow normal development in the sandy substrate and watered through regular automatic water sprinkling as needed to maintain plants under optimal growth conditions.

Plant root harvest and trait measurements

Every second day we checked the depth of the roots in the container by opening the removable bottom. As soon as the roots of a given species reached the bottom of the container, the complete set of individuals belonging to a species pair were harvested. At that time, plants were 30 -40 days old after germination, the exact time depended on the crop pair. We harvested 5-10 (median 9) healthy and well developed plants per accession (wild progenitor and domesticated plant), and carefully cleaned the whole root system. The whole root system of each individual was transferred to a transparent tray filled with water, where the root branches were carefully spread out to avoid overlapping. Then the root system was scanned as greyscale images at a resolution of 400 dpi (Epson scan GT 15000). Total root length (m), root mean diameter (mm), and root volume (cm 3 ) were determined for the whole root system using a scanner-based, digital image analysis system (WinRHIZO; Regents Instruments, Quebec City, Canada; Arsenault, Poulcour, Messier & Guay, 1995). Following root scanning, roots and the aboveground part of each plant were oven dried (60ºC) and weighed to estimate: total plant dry mass (g), root tissue density (RTD, g root ml root), specific root length (SRL, m root g -1 root), root mass fraction (RMF, g root g -1 plant) and root length ratio (RLR, m root g -1 plant) (Table 1). A total of 527 plants were phenotyped.

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Data gathering

To test whether the roots of domesticated plants and wild progenitors were different to those of other wild herbaceous species, we compiled root data from two global databases of root traits of wild herbaceous species. In both databases, we selected data of herbaceous species from diverse botanical families and excluded data from tree species, crop species and species belonging to the same genus as our crops. In addition, the data selected from both databases belong to plants grown in conditions similar to our experiment: pots in controlled conditions (indoors or outdoors), to ensure the comparability with the data of the 30 domesticated plants and wild progenitors. The Rhizopolis-db, a global database of fine root traits (details in Freschet et al., 2017) was used for comparisons of MRD (145 species; 53% forbs, 30% grasses and 17% legumes), RTD (141 species; 54% forbs, 30% grasses and 16% legumes) and SRL (99 species; 43% forbs, 36% grasses and 20 % legumes). The RMF database (398 species; 49% forbs, 42% grasses and 9% legumes) was taken from Poorter et al. (2015).

Statistical analyses

Prior to hypotheses testing we imputed missing values (1.6%), which were randomly distributed along the data, using multivariate imputations with chained equations [START_REF] Nakagawa | Missing inaction: the dangers of ignoring missing data[END_REF][START_REF] Penone | Imputation of missing data in life-history trait datasets: which approach performs the best?[END_REF] with the R package "mice" [START_REF] Buuren | mice: Multivariate imputation by chained equations in R[END_REF]. In addition, five individuals with extreme trait values were excluded from the data. Finally, all subsequent analyses were ran with 522 individuals, and trait data were log 10 -transformed to meet normality assumptions and homogeneity of variance of models´ residuals. All statistical analyses were performed with the R software (R Core Team, 2014).

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To test whether the roots of domesticated plants and wild progenitors were different to those of other wild herbaceous species, we performed phylogenetic generalized least squares models (PGLSs) comparing wild progenitors and domesticated species with databases of root traits of wild herbaceous species. The root traits: MRD, RTD, SRL and RMF were included as response variables in the PGLS models. Plant type (wild progenitor, domesticated plant or other wild species) was included as explanatory variable. Additionally, we analyzed whether differences in the root traits along plant types varied for grasses, legumes and forbs (functional group). For doing so, we included functional group and the interaction with plant type as explanatories in the models. PGLS models incorporate phylogenetic correlation structure in model residuals to account for phylogenetic non-independence of species data points (Symonds & Blomberg, 2014). To run the PGLS regressions, we built a phylogenetic tree for each root trait containing the species of each database and the 30 crops pairs. To do so, each phylogenetic tree was derived from a largest reference tree of the angiosperms (Zanne et al., 2014), with the drop.tip function of 'phytools' package (Revell, 2012). Species not represented in the reference tree were replaced by other species of the same genus presented in the reference tree, only when there was one or two species representatives of the genus in the data set; or removed from the data sets when there were more species representing the genus. The resulting trees did not have polytomies. PGLSs were implemented using the gls function of the 'picante' package (Kembel et al., 2010).

Finally, post hoc test with pairwise comparison among levels of the fixed effects factors and the interaction were conducted using the phylANOVA function of the 'phytools' package (Revell, 2012).

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To assess the effect of domestication on each root trait separately, we used linear mixed effect models. The dependent variables were the five root traits and total plant dry mass (TDM). In all models, domestication status (domesticated plant or wild progenitor) was included as fixed factor. Crop identity (30 crops, Table 2) was included as a random effect over the intercept of the model, and as a random effect over domestication status (random slope effect, analogous to an interaction term in fixed effects models). In addition, we analyzed whether domestication effects were different for grasses, legumes, and forbs. For doing so, we included functional group and its interaction with domestication status as fixed effect terms in the models. All models were run with the lme function of the "nlme" R package [START_REF] Pinheiro | nlme: Linear and Nonlinear Mixed Effects Models[END_REF]. The significance of the fixed factors was tested with type III analysis of variance, with the mixed function of the 'afex' package (Singmann, Bolker, & Westfall, 2015). The mixed function fits the complete model and creates reduced versions removing a single effect, then compares the reduced model to the complete model. In order to assess goodness of fit, we obtained the conditional R 2 (variance explained by random and fixed factors) and marginal R 2 (the variance explained by fixed factors) of the models following Johnson (2014), using the R package "MuMIn" (Bartón, 2013).

Finally, to test how domestication changed root traits and the consequences thereof for the whole root phenotype, we used the multivariate model proposed by [START_REF] Poorter | The limits to leaf and root plasticity: What is so special about specific root length?[END_REF], and tested it using path analyses (Shipley, 2009). The original model predicts the response of root traits to nutrient availability (Fig. 1a), but since we hypothesized that evolution under domestication occurs in high fertility habitats (Denison, Kiers & West, 2003), we replaced "nutrient availability" by "domestication status" (Fig. 1b). To test whether our data fit the [START_REF] Poorter | The limits to leaf and root plasticity: What is so special about specific root length?[END_REF] model, we

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conducted a phylogenetic confirmatory path analysis. Phylogenetic analysis was selected to account for non-independence of data due to phylogenetic relatedness of the crop species (González-Voyer & Von Hardenberg, 2014). In phylogenetic path analysis, the predicted relationships between the variables are translated into models and analyzed using PGLS with phylogenetic signal (Pagel's lambda) estimated with maximum likelihood. To conduct the PGLS we built a phylogenetic tree. To do so, we pruned the large dated angiosperm phylogeny tree (Zanne et al., 2014) to our set of genera using the "phytools" R package (Revell, 2012). The significance of the paths was calculated using a d-sep approach (Shipley, 2009), based on an acyclic graph that depicts the hypothetical relationships and independence claims between variables. The d-seps are translated into models and analyzed using PGLS. Likewise, we assessed the goodness of fit of the data to the path model using the associated p-values with the Fisher's C statistic (Shipley, 2009). The standardized path coefficients were obtained from PGLS (Grace & Bollen, 2005). In addition, we estimated the coefficients and significance of indirect and total effects of domestication on each trait in the path diagram (Grace & Bollen, 2005). The indirect effects were calculated by multiplying all the path coefficients that link the domestication variable with each variable of the model, and total effects were computed as the sum of direct and indirect effects (Grace & Bollen, 2005). The significance of the total effects of domestication on each root trait was calculated with the sum of the variance associated to each direct and indirect effect.

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RESULTS

Root functional differences between domesticated species, wild progenitors and other wild herbaceous species

To see how wild progenitors and domesticated plants were relative to wild species, we compared our data with large compilations from the literature. Wild progenitors and domesticated plants significantly differed from other wild herbaceous species for the four root traits analysed (plant type: P< 0.05, Fig. 2), irrespective of functional group (functional group: P> 0.05, Table S2). The wild progenitors and domesticated accessions of this experiment had thicker and less dense roots in comparison with the data from wild herbaceous species, with lower SRL scores, and greater allocation to root biomass (Fig. 2).

Domestication and crop identity effects on TDM and root traits

We found a general increase of total dry mass after domestication (Table 3, Fig. 3a).

TDM ranged from 0.2-4 g for wild progenitors and 0.5-8 g for domesticated accessions (Table S3). The response to domestication varied among crops, as indicated by the variance associated with crop identity (Table 3). In addition, the response to domestication was more positively pronounced for larger wild progenitors (correlation term: crop identity x domestication status = 0.63), such as bean or cucumber; and was even slightly negative for smaller progenitors, such as white clover or Rucola (Fig. 3a).

We also found a stronger response to domestication in legumes, which increased TDM after domestication more than grasses and forbs (Fig. 4a).

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None of the five root traits showed a significant response to domestication across species (Domestication effect P> 0.15, Table 3). The variance associated with the random structure indicated a wide variability in the response to domestication among the 30 pairs of crops (Figs. 3b-f). For example, RMF increased with domestication in crops such as soybean or chickpea, but decreased in others such as cabbage or oat (Table S3, Fig. 3e). MRD, SRL, RMF and RLR was significantly affected by functional group (Table 3, Fig. 3b, d, e andf). Nevertheless, the response to domestication of each functional group was insignificant for the five root traits (interaction domestication status x functional group, Table 3, Figs. 4b-f).

Multi-trait response of roots to domestication

Plants increased their total dry mass in response to domestication (path = 0.27, P= 0.004, Fig. 1b). However, MRD, RTD and RMF were not directly affected by domestication (P> 0.05, Fig. 1b). The overall goodness of fit of the data to the theoretical model was high (C-statistic of 20.6 and associated P 0.55, Fig. 1b). The relationships between TDM and root traits fitted the a priori model [START_REF] Poorter | The limits to leaf and root plasticity: What is so special about specific root length?[END_REF]; Fig. 1a), with the exception of the relationship between TDM and RTD (see significance and path scores in Fig. 1b). Larger plants had thicker fine roots (MRD, path = 0.33, P= 0.003, Fig. 1b). Both MRD and RTD had negative effects on SRL (path = -0.76 and P< 0.001 for MRD; path -0.5 and P< 0.001 for RTD, Fig. 1b) and RLR was more dependent on changes in SRL than in RMF (path = 0.95, P< 0.001, and path = 0.27, P< 0.001, respectively, Fig. 1b). In line with univariate analyses, domestication had negligible effects on root traits via indirect effects. The positive effect on plant size driven by domestication was not strong enough to trigger significant net effects on MRD, RTD, SRL and RMF (Fig. 5).

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DISCUSSION

Based on the screening of root traits of a uniquely large set of crop species, our analyses revealed new correlates of plant domestication. Specifically, we found that the evolution towards larger plants during domestication implies correlated evolution of thicker roots.

However, since (i) the direct effect of domestication on plant size and of plant size on root thickness were modest, and (ii) indirect effects are small, due to their multiplicative nature; the overall effect of domestication on root thickness was of small magnitude.

Additionally, root trait responses to domestication were diverse among the several crop species. That variation was however unrelated to phylogenetic or peculiarities of domestication process of the 30 crops. More interestingly, we showed that root traits of domesticated plants and of their wild progenitors are not a random sample of global functional trait variation of other wild herbaceous species; they are biased towards trait scores indicative of plants adapted to highly fertile conditions. This result leads us to suggest that the crop root phenotypes, and their adaptability to agricultural habitats, were mainly determined by early selection of wild species which were already preadapted to highly fertile and frequently disturbed habitats, rather than by further evolution with domestication. These results have important implications for our understanding of resource acquisition strategies of crop roots and portend applied approaches to develop improved cultivars.

The roots of crop wild progenitors were pre-adapted to agricultural conditions

Current crop phenotypes are the outcome of centuries of selection under agriculture, but also reflect the choices of early farmers among available wild plants (Sauer, 1952;Preece et al., 2015;[START_REF] Mercuri | Plant behaviour from human imprints and the cultivation of wild cereals in Holocene Sahara[END_REF]. Although crop evolution under domestication exerted a modest impact on root traits in our study,

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as discussed below, early farmers already showed a bias on root phenotypes of agricultural plants. Specifically, roots of crops' wild progenitors, in comparison with those of other wild herbs, were less dense and thicker (Fig. S2), which is typical of fastgrowing species from fertile habitats (Kramer-Walter et al., 2016;Reich, 2014;Ryser, 1996). Furthermore, thicker but less dense roots are suggested to be caused by roots with more cortex area than stele (xylem vessels) area, because cortex area is less dense (Kong et al., 2014). Species with such a root phenotype rely more on mycorrhizal associations for mineral nutrition [START_REF] Brundrett | Coevolution of roots and mycorrhizas of land plants[END_REF][START_REF] Ma | Evolutionary history resolves global organization of root functional traits[END_REF] and indicate acquisitive strategies (Kong et al., 2016). Nevertheless, some evidences, from maize and bean, suggest that domestication triggered roots with larger vessel area (York, Galindo-Castañeda, Schussler, & Lynch, 2015;[START_REF] Peña-Valdivia | Anatomical root variations in response to water deficit: Wild and domesticated common bean (Phaseolus vulgaris L.)[END_REF][START_REF] Burton | Phenotypic diversity of root anatomical and architectural traits in Zea species[END_REF]. Future studies would be needed to test the proportion of vessel and cortex area of wild progenitors and domesticated plants in the context of botanical variation, and the effect of domestication.

Further, the high diameter and low SRL displayed by the roots of wild progenitors are consistent with a recent worldwide meta-analysis, where these attributes were generally associated with fertile environments (Freschet et al., 2017). Indeed, thicker, lower SRL roots may be generally found where plants are less dependent on soil exploitation by fine roots. Finally, larger biomass allocation to the roots of wild progenitors, as compared to that of other wild herbs, is more surprising in light of the typical species in fertile soils but fits the theory of balanced organ biomass and morphology above-versus below-ground, as postulated by Freschet, Kichenin, & Wardle (2015b). Specifically, since crops and their wild progenitors have relatively higher specific leaf area than average [START_REF] Milla | Plant domestication through an ecological lens[END_REF]Tribouillois et al., 2015), they rely

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less on leaf biomass investment to capture light and could therefore invest more biomass into belowground organs. Further studies comparing the biomass investment below and aboveground in domesticated plants with this in wild herbs would be necessary to test this hypothesis.

The fact that wild progenitors exhibit a root phenotype adapted to agricultural habitats is in line with the Dump Heap hypothesis. This hypothesis suggests that early domestication started with the species growing around human settlements, in anthropogenic environments which are characterized by relatively high nutrient availabilities and disturbance frequencies (Sauer, 1952;Zeven, 1973;Hawkes, 1983).

Fast growing and short-lived plants would become more abundant around settlements, would thrive better in early agricultural habitats, and thus would respond better to the early attempts of cultivation and further domestication (Hawkes, 1983;[START_REF] Mercuri | Plant behaviour from human imprints and the cultivation of wild cereals in Holocene Sahara[END_REF]. Although rigorous comprehensive tests are still pending, wild progenitors tend to show specific leaf area and nitrogen content of leaves typical of fast-growing species, when compared with other wild herbaceous plants [START_REF] Cunniff | Functional traits differ between cereal crop progenitors and other wild grasses gathered in the neolithic fertile crescent[END_REF][START_REF] Milla | Plant domestication through an ecological lens[END_REF]. Our screening of root analysis traits is in line with aboveground evidence that wild plants with nutrient acquiring strategies were more successful candidates for domestication by being pre-adapted to the cultivation conditions.

Root traits changed modestly and in idiosyncratic ways after domestication

We hypothesized that root morphology and allocation would change towards resourceacquisitive strategies alongside domestication processes. Contrary to our hypothesis, we found a wide diversity of root morphology and allocation responses to domestication.

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For most root traits, trait scores decreased in some species or increased in others, which is consistent with a generalized species-specific response, as observed in previous case studies that compared wild progenitors to domesticated species. For example, SRL decreases with domestication in beans [START_REF] Perez-Jaramillo | Linking rhizosphere microbiome composition of wild and domesticated Phaseolus vulgaris to genotypic and root phenotypic traits[END_REF] but not in maize (Gaudin, Mc Clymont & Raizada, 2011). Even case studies reporting on the same crop species show opposite responses to domestication depending on growth conditions or the identities of crop varieties under study. For instance, similar allocation to roots was reported for wild progenitors and domesticated species of wheat and maize (Gaudin, McClymont & Raizada, 2011;[START_REF] Nakhforoosh | Wheat root diversity and root functional characterization[END_REF], whereas others found lower allocation to roots in domesticated species for the same two species (Waines & Ehdaie, 2007;[START_REF] Burton | Phenotypic diversity of root anatomical and architectural traits in Zea species[END_REF]Szoboszlay et al., 2015;Roucou, Violle, Fort, Roumet, Ecarnot, & Vile, 2018). Our broader screening together with previous case studies, supports that the effects of domestication on root morphology and allocation are diverse. Nevertheless, to assess the generality of our results, it will be necessary to conduct similar experiments on root traits under more realistic field conditions [START_REF] Poorter | Pampered inside, pestered outside? Differences and similarities between plants growing in controlled conditions and in the field[END_REF]) and under contrasting growth conditions such as competition or fertilization level.

Acknowledging that the response of root traits to domestication is species-specific, we further investigated other explanatory variables that might account for the diversity in the size and directionality of domestication effects among crops. First, we asked whether crops belonging to different functional groups showed contrasting responses to domestication. In accordance with the literature, grasses tended to allocate more biomass to roots than forbs (Fig. 4c;Roumet, Lafont, Sari, Warembourg, & Garnier, 2008;Poorter et al. 2015;Roumet et al. 2016). Similarly, legumes had lower SRL than

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forbs, also in line with previous evidence (Tjoelker, Craine, Wedin, Reich, & Tilman, 2005). However, the effect of domestication on root traits was generally insignificant among groups (Table 3, Fig. 4), ruling out that functional groups could account for the observed diversity in crop responses to domestication. Similarly, taxonomic affinities have been used to explain variation in root morphology among taxa previously (Kong et al., 2014;Valverde-Barrantes, Freschet, Roumet, & Blackwood, 2017). However, phylogenetic relationships did not contribute to explain the diversity in crop reactions to domestication (Table S4, Methods S1). Lastly, we explored whether the variation of reactions was explained by variability in domestication processes (timing of the domestication event and organ under focal selection). Interestingly, plant size has increased more in older than in younger crops (Table S4; Fig. S3), which is consistent with a longer selective pressure on size. However, the size of the domestication effect for root traits was not explained by those aspects of the domestication process (Table S4; Figs. S3-4). Further characteristics of the domestication processes such as intensity of the selective efforts or geographical location of domestication event may help to elucidate the observed diversity of root traits responses to domestication.

CONCLUSIONS

Our comparative analysis revealed that none of the root traits reacted to domestication in accordance with evolution towards faster-growth strategies. Root traits changed during most of the 30 domestication processes surveyed here, but this occurred in diverse directions, depending on the crop species, and irrespective of phylogenetic and functional group affiliations, or of variability in the domestication processes. The diversity of responses to domestication encountered here emphasizes the importance of studying multiple crops with a comparative focus. Finally, the less dense and thicker

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roots with low SRL of crop wild progenitors suggests that the root phenotype of the wild species selected by early farmers were already adapted to fertile and disturbed conditions, thereby supporting the Dump Heap hypothesis. Thus, the adaptation of root phenotypes to fertile soil appears to be largely determined by the choice of wild species by the first farmers rather than by further evolution under domestication.

Economic Botany, 58, 5-10.

Table 1

 1

		.
	Abbreviatio
		ns,
	definitions
	and units of
	the	traits

ACKNOWLEDGMENTS

We thank J.M. Alonso, J. Margalet and T. de la Fuente for assistance in data gathering.

We also thank all public seed banks that provided seeds for the project (complete list in Supplementary Table S1). This work was supported by MINECO (grants CGL2014-56567-R, BES-2012-054356, PCIN-2014-053).

DATA ACCESSIBILITY

The data belonging to the domesticated plants and wild progenitors will be available online as a part of Fine-Root Ecology Database (FRED; http://roots.ornl.gov). The dataset of mean root diameter, root tissue density and specific root length of wild herbs is available as a part of FRED. Finally, the dataset of root mass fraction of wild herbs can be found in Poorter et al. 2015.

AUTHOR CONTRIBUTION

R.M, and N.M-R. conceived the ideas and designed the methodology. Data were contributed by J.M-L, R.M., H.P., G.F., C.R.. Data analyses were discussed by all authors, and performed by N.M-R. N.M-R. led the writing of the manuscript with R.M.. All authors participated to the writing and provided critical reviews of each draft before giving approval for submission of the final version.

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Table 3. Effect of domestication on total plant dry mass (TDM) and root traits: mean root diameter (MRD), root tissue density (RTD), specific root length (SRL), root mass fraction (RMF) and root length ratio (RLR), resulted from the linear mixed-effect models. The table shows the F value and significance (*, P<0.05; **, P<0.01) of domestication effect, functional group and the interaction domestication status x functional group. The variance of the model explained by the fixed effects is indicated by R 2 marginal (R 2 m). The variances associated with the random effects are indicated by the terms: crop identity, the effect of crop identity on the response of domestication (i.e. random effect on the slope) and the residual variance. Finally, the variance explained by both: random and fixed effects are presented with the R 2 conditional (R 2 c).

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