S Moindjie

J L Autran

D Munteanu

G Gasiot

P Roche

Multi-Poisson Process Analysis of Real-Time Soft-Error Rate Measurements in Bulk 65nm SRAMs

Altitude and underground real-time soft error rate (SER) measurements on SRAM circuits have been analyzed in terms of independent multi-Poisson processes describing the occurrence of single events as a function of bit flip multiplicity. Applied for both neutron-induced and alpha particle-induced SERs, this detailed analysis highlights the respective contributions of atmospheric radiation and alpha contamination to multiple cell upset mechanisms. It also offers a simple way to predict by simulation the radiation response of a given technology for any terrestrial position, as illustrated here for bulk 65nm SRAMs.

Introduction

Real-time soft error rate (RTSER) technique is an experimental reliability method to determine the soft error sensitivity of a given component, circuit or system [START_REF] Autran | Soft Errors: from particles to circuits[END_REF]. The methodology consists in a direct observation of a large number of devices working in parallel under standard operating conditions and exposed to ambient background radiation at ground level. From the detection and counting of single events upsets occurring during the experiment, one can estimate the soft error rate (SER) of the devices under test. In case of SRAM circuits, the result can be given in terms of "event" SER, "total bit flip" SER, "multiple cell upset" (MCU) SER, and can be numerically expressed in FIT/Mbit (one FIT equals one failure per 10 9 hours of operation) [START_REF] Autran | [END_REF].

For modern CMOS circuits at terrestrial level, SER is the result of a weighting of two main components due to: i) the atmospheric particle flux and particularly the high-energy neutrons interacting with IC materials; ii) the traces of radioactive elements present in the circuit materials, mainly U or Th contaminations at sub-ppb concentrations. These two SER components are respectively labeled neutron-SER (n-SER) and alpha-SER (α-SER). Neutron-SER is proportional to the intensity of the high-energy neutron flux at test location whereas alpha-SER is fixed and linked to the concentrations of radioactive impurities.

The measured SER at a given test location is generally expressed as [START_REF] Autran | [END_REF][START_REF]Measurement and Reporting of Alpha Particles and Terrestrial Cosmic Ray-Induced Soft Errors in Semiconductor Devices[END_REF]:

SER test location = AF × n-SER NYC +α-SER (1) ( (
where AF is the so-called acceleration factor [START_REF]Measurement and Reporting of Alpha Particles and Terrestrial Cosmic Ray-Induced Soft Errors in Semiconductor Devices[END_REF] which define the relative neutron flux at test location with respect to sea-level (reference New York City, NYC) and n-SER NYC is the value of the neutron-SER normalized for NYC conditions. From Eq. (1), it is obvious that α-SER can be directly measured during an underground experiment (AF = 0) and that measurements at two different locations is sufficient for determining the two unknown quantities n-SER NYC and α-SER.

In this study, altitude (on the ASTEP platform [START_REF] Autran | [END_REF]) and underground (at LSM, Modane [START_REF] Kingman | Poisson Processes[END_REF]) real-time soft error rate (SER) measurements on bulk 65nm SRAM circuits have been analyzed in terms of independent multi-Poisson processes describing the occurrence of single events as a function of bit flip multiplicity. This approach has been applied for estimating the event rates induced by atmospheric neutrons and alphaparticle emitters as a function of event multiplicity. We used these extracted results to predict by simulation the radiation response of the 65nm SRAMs for a third test location at sea-level (Marseille, France), illustrating the advantage of this method not only to evaluate the global SER value but also to accurately estimate the occurrence of MCU events as a function of their event multiplicity.

Theory

The occurrence of soft errors in electronics is a continuous time stochastic process. The principle of a RTSER experiment is to count the number of random events N(t) that have occurred up to some point t in time over a large population of circuits (the number of events is therefore small relative to the number of memory elements considered in the test). In such a real-time approach, soft errors are not permanent because they are eliminated when new data is written after detection: a RTSER test is thus equivalent to a life-test with replacement, i.e. in which a failing device is replaced with a new device immediately upon failure detection. Assuming that soft errors are also random in space (within the circuits), independent of each other and occur with a fixed event rate λ, the counting process {N(t), t ≥ 0} in a finite interval of time t consequently obeys the Poisson(λt) distribution [START_REF] Kingman | Poisson Processes[END_REF]:

P(N(t) = n) = e -λt (λt) n n! , n = 0, 1, 2 (2)
The maximum likelihood estimate for λ is simply the number of detected events N divided by the experiment duration T and eventually normalized with respect to the number of units on test. Expressing this later quantity in Mbit for a memory test and time in MBit×h, λ can be directly estimated from:

λ = N/ Σ ( 3
)
where Σ is the number of MBit×h cumulated at time T given by:

Σ = MEM (t)dt 0 T ∫ (4)
where MEM(t) represents the number of Mbit under test at time t. This quantity may be variable in case of device automatic disconnection by the system due to abnormal current consumption or other anomaly detected at device, daugthercard or mothercard levels.

The counting process, previously introduced, can be applied to "single events" (whatever the type of these events), or more specifically to single bit upsets (SBU) or to multiple cell upsets (MCU) defined by a given event multiplicity (noted MCU(q), q = 2, 3,.. corresponding to the number of bitcells simultaneously upset during a same particle interaction event). Let N 1 (t), N 2 (t),…. N i (t), … N M (t) be M independent Poisson processes with event rates λ 1 , λ 2 ,…, λ i ,… λ M respectively corresponding to the counting of SBU, MCU(2), …, MCU(i),… MCU(M) events. The total event counting process N(t) = Σ N i (t) will be the merging of all these Poisson processes and will be also a Poisson process with rate λ = λ 1 + λ 2 +…+λ i … + λ M , as illustrated in Fig. 1. Performing such a multi-Poisson process decomposition of the global "single event" process occurring during a RTSER experiment will allow us to reveal the respective contributions of atmospheric neutrons and alpha-particle emitters in the MCU SER response of the technology under test, as illustrated in the following.

Process 1, N 1 (t), SBU Process 2, N2(t), MCU(2) Process 3, N3(t), MCU(3) . . . Process M, NM(t), MCU(M) Merged process, N(t) t! t! t! t! t!

Real-time experiments

For the purpose of this study, we considered raw data of three RTSER experiments performed on 3,226 Mbit of bulk 65nm Single-Port SRAMS (using two identical test setups) between 2008 and 2017. Details about these experiments can be found in Refs. [START_REF] Autran | [END_REF][START_REF] Autran | [END_REF][START_REF] Autran | IEEE Radiation Effects Data Workshop (REDW)[END_REF][START_REF] Autran | [END_REF].

Results and discussion

From raw data on Figs. 2 to 4 and because the three experiments involved the same quantity of memory [START_REF]Measurement and Reporting of Alpha Particles and Terrestrial Cosmic Ray-Induced Soft Errors in Semiconductor Devices[END_REF]226 Mbit), we first extracted in Tables 2 to 4 the event rate per hour (number of events divided by the experiment duration) of single events as a function of the event multiplicity (an event of unit multiplicity corresponding to a single bit upset). From Eq. (1) also valid in terms of event rate, one can consider that for a given test location:

λ i = AF × n-λ i +α-λi (5)
where λ i , n-λ i and α-λ i are respectively the total, neutron and alpha event rates for events of multiplicity i (i=1, 2,…). Considering Eq. ( 5) for both ASTEP (AF = 6.5) and LSM (AF = 0) experiments, it is then possible to extract these n-λ i and α-λ I values for the 3,226 Mbit of tested devices. This extraction is reported in Table 5 and illustrated in Fig. 4. These results show that, for this particular bulk 65nm technology, soft errors are dominated by the contribution of alpha-particle radioactivity present in IC materials up to events of multiplicity equal to 6. In particular, the alpha event rate is 6 times larger than neutron event for SBU, 7 times larger for MCU(2), 5 times larger for MCU(3) and 4 times larger for MCU [START_REF] Autran | [END_REF] and MCU [START_REF] Autran | IEEE Radiation Effects Data Workshop (REDW)[END_REF]. Neutrons and alphas have finally similar event rate for MCU(4) whereas neutrons seems to dominate for larger MCUs.

In order to verify the validity of such extractions, we use on more time Eq. ( 5) to estimate the alpha and neutron event rates for Marseille location from data of Table 5 extracted by the combination of ASTEP and LSM results. Taking AF = 0.9 for Marseille, Table 6 shows the results of the so-called "predicted" event rates using this procedure. These values are compared to the experimental (i.e. measured) event rates and are used to "predict" the number of events vs. multiplicity for a fixed duration of 17,233 h corresponding to the measurements. Table 5 shows that these predicted values are very close to the measured ones, demonstrating here the interest of such a multi-Poisson process analysis to calculate not only the global event rate of the circuits but also to quantify the respective contributions of MCU events as a function of event multiplicity. In the conference presentation and in the final paper, a similar analysis will be applied to bulk 40nm SRAMs for which results extracted from altitude and sea-level experiments [START_REF] Autran | International Reliability Physics Symposium (IRPS'2012)[END_REF] will show more contrasted results between neutron and alpha contributions to MCU events with multiplicities ranging up to 22. Table 5. Extracted values of neutron and alpha event rates from data of Tables 2 and3 5.

Figure 1 .

 1 Figure 1. Merging M Poisson processes corresponding to the occurrence of single events of different cell upset multiplicities.

Figures 2 to 4

 4 Figures 2 to 4 show the cumulative bit flips distributions versus test duration obtained for the three experiments. Test has been conducted under nominal operating conditions: V DD = 1.2V, room temperature, standard checkerboard test pattern. These results will serve as raw data for the multi-Poisson process analysis conducted in the next section.

Figure 2 .Figure 3 .Figure 4 .

 234 Figure 2. Cumulated distribution of bit flips versus time for the altitude experiment on the ASTEP platform.

  [START_REF] Autran | International Reliability Physics Symposium (IRPS'2012)[END_REF].87 × 10 -5

  1 = 3.06 × 10 -4 α-λ 1 = 1.91 × 10 -3 2 n-λ 2 = 3.08 × 10 -5 α-λ 2 = 3.33 × 10 -4 3 n-λ 3 = 3.59 × 10 -5 α-λ 3 = 2.10 × 10 -4 4 n-λ 4 = 3.55 × 10 -5 α-λ 4 = 3.51 × 10 -5 5 n-λ 5 = 8.25 × 10 -6 α-λ 5 = 3.51 × 10 -5 6 n-λ 6 = 8.25 × 10 -6 α-λ 6 = 3.51 × 10 -5 7 n-λ 7 = 1.36 × 10 -5 α

Figure 4 .

 4 Figure 4. Neutron and alpha event rates as a function of event multiplicity as extracted in Table5.

Table I

 I

	summarizes these experiments conducted on
	the ASTEP platform (2,255 m of altitude) in 2008-09,
	at the underground laboratory of Modane (LSM)
	between 2008 and 2015 and at sea-level in Marseille
	(IM2NP laboratory) since 2014. This last experiment is
	always running in 2017.

Table 1 .

 1 Summary of the 65nm SRAM RTSER experiments.

	Location	Acceler. factor AF	Start date Stop date	Effective cumulated hours of tests
	ASTEP	6.5	01/21/2008 05/07/2009	11,278
	LSM	0	04/11/2008 01/25/2015	57,058
	Marseille	0.9	10/16/2014 Ongoing *	17,233

Table 2 .

 2 Event rate extraction from RTSER data for the altitude experiment on ASTEP platform.

	Event	Number of	Event rate
	multiplicity	Events	(h -1 )
	1	44	λ 1 = 3.90 × 10 -3
	2	7	λ 2 = 6.21 × 10 -4

Table 3 .

 3 Event rate extraction from RTSER data for the underground experiment at LSM.

	Event	Number of	Event rate
	multiplicity	Events	(h -1 )
	1	109	λ 1 = 1.91 × 10 -3
	2	24	λ 2 = 4.21 × 10 -4
	3	12	λ 3 = 2.10 × 10 -4
	4	2	λ 4 = 3.51 × 10 -4
	5	2	λ 5 = 3.51 × 10 -5
	6	2	λ 6 = 3.51 × 10 -5
	7	0	λ 7 = 0

Table 4 .

 4 Event rate extraction from RTSER data for the sealevel experiment at Marseille.

	Event	Number of	Event rate
	multiplicity	Events	(h -1 )
	1	36	λ 1 = 2.09 × 10 -3

Table 6 .

 6 Event rate extraction from RTSER data for the sealevel experiment at Marseille.

	Event

multi- plicity Number of Events Event rate (h -1 )

		Measured Predicted Measured Predicted
	1	36	38	2.09 × 10 -3	2.18 × 10 -3
	2	9	6	5.22 × 10 -4	3.72 × 10 -4
	3	4	4	2.32 × 10 -4	2.42 × 10 -4
	4	0	1	0	6.67 × 10 -5
	5	1	1	5.80 × 10 -5	4.24 × 10 -5
	6	0	1	0	4.24 × 10 -5
	7	0	0	0	1.21 × 10 -5
	TOTAL	50	51


D Munteanu

J L Autran

S Moindjie

Single-Event-Transient Effects in Junctionless Double-Gate MOSFETs with Dual-Material-Gate investigated by 3D Simulation

The Junctionless Double-Gate MOSFET combined with a Dual-Material Gate (JL-DMDG) is interesting for future ultra-scaled devices thanks to a simplified technological process (no junctions), reduced leakage currents and capability to reduce SCEs and HCEs (due to the step in the potential profile). In this work, we investigate the bipolar amplification and charge collection in JL-DMDG submitted to heavy-ion irradiation. We show that JL-DMDG is more sensitive to radiation than more conventional devices with single-material-gate or operating in inversion-mode.

Introduction

Double-Gate (DG) MOSFET technology is recognized as a promising solution to meet the roadmap requirements in the nanometre scale, namely due to its excellent control of short channel effects (SCE) ensured by the presence of an additional gate electrode which enhance the potential control of the channel [1]. The DG MOSFET technological process can be simplified by using a junctionless (JL) structure [2][3], with the same type of semiconductor throughout the entire silicon film (Fig. 1a). This device has some interesting advantages: there is no doping concentration gradients in the device and the junction leakage currents are totally suppressed, so the off-state current is uniquely controlled by the gate which could be very attractive for ultra-scaled devices. Another interesting concept is to use a dual-material-gate (DM) in order to reduce the hot-carrier induced effects (HCE) and drain-induced barrier lowering (DIBL) phenomena [4]. The junctionless DG MOSFET with dual-material-gate (JL-DMDG) has two materials in the gates (Fig. 1b), with different workfunctions, Φ M1 and Φ M2 . This configuration induces a step in the surface-potential profile (see Fig. 2) which, for Φ M1 >Φ M2 , simultaneously provides transconductance increase and DIBL reduction. The step function profile of the surface potential ensures screening of the channel region on the source side (under the material M1) from drain-potential variations. In addition, the electric field peak at the drain is considerably reduced, which suppresses HCEs [5][6]. JL-DMDG is then a promising structure for which extensive modelling works have been reported in the literature [7][8] in the last years. However, at the best of our knowledge, radiation-sensitivity studies of these devices have not been performed. In this paper we investigate by 3-D numerical simulation the response to single-event of JL-DMDG through a detailed comparison with more usual inversion-mode (IM-DMDG [9], Fig. 1c single-material-gate devices (JL-SMDG [10] and IM-SMDG [11]). The impact of several technological parameters on single-event transients and bipolar amplification is also addressed.

Φ M1 Φ M2 Gate L 1 L 2 Φ M1 Φ M2 Gate oxide Φ M1 (b) (c) Gate N-typ e

Simulated devices and models

Four types of devices have been considered: JL-DMDG, IM-DMDG, JL-SMDG and IM-DMDG. All devices are designed with the same geometrical dimensions: channel length L G =20 nm, 100 nm gate width, 6 nm-thick silicon film and 1 nm-thick gate oxide, similar to real devices reported in [12]. In junctionless devices, the entire silicon film is uniformly n-type doped at 10 19 cm -3 . The inversionmode devices (IM-DMDG and IM-SMDG) have an intrinsic channel; source and drain regions are highly n-type doped and the doping profile in these regions is uniform. In single-gate devices (JL-SMDG and IM-SMDG), a single-material M1 is used for the gates. In dual-material-gate devices (JL-DMDG and IM-DMDG) the gates consists of dual materials, M1 (Φ M1 ) and M2 (Φ M2 ), of lengths L 1 and L 2 , respectively (L 1 +L 2 =L G ). In a first time we considered L 1 =L 2 =L G /2, Φ M1 =4.8 eV and Φ M2 =4.1 eV.

3-D numerical simulations have been performed with the DESSIS device simulator from Synopsis Inc. [START_REF]Synopsys Sentaurus TCAD tools[END_REF]. The main models used in simulation are the Shockley-Read-Hall and Auger recombination models, the Fermi-Dirac carrier statistics and the hydrodynamic model was used for the carrier transport equations. The impact ionization model depends on carriers energy. The mobility model includes the dependence on the carrier energy, lattice temperature and doping level. The ion strike was simulated using the DESSIS HeavyIon module [START_REF]Synopsys Sentaurus TCAD tools[END_REF]. The electron-hole pair column created in the device by the ion strike is modeled using a carrier-generation function which has a Gaussian radial distribution with a characteristic radius of 20 nm, a Gaussian time distribution, centered on 10 ps and having a characteristic width of 2 ps. In a first time, the ion strikes in the channel center (x=30nm). Other hit locations will be considered next. Devices are biased in the off state (V G =0V). The drain is constantly biased at a power supply voltage equal to 1 V.

Static characteristics

The surface potential profile in junctionless and inversion mode devices is plotted in Figure 2. As expected, the surface potential in dual-material-gate devices has a step-function profile, which is not

Single-Event-Induced Transients

Drain current transient

Figure 4 shows the drain current transient resulting from an ion hit in the channel center of the simulated devices, the ion having a linear energy transfer (LET) of 0.1 MeV.cm 2 /mg. The highest drain current transient peak is obtained for JL-DMDG device. Dual-material-gate device have higher transient peaks and wider transients that single- material gate devices. The reason is probably a higher bipolar gain for dual-material-gate devices due to the step-function profile of the channel potential.

Collected charge and bipolar amplification

Figures 5a and 5b show the variation of the collected charge (Q COLL ) and bipolar amplification as function LET. Q COLL is obtained by integrating the simulated drain current over the transient duration. The deposited charge, Q DEP , is calculated considering the Gaussian distribution of the ion track and the exact 3-D geometry of the silicon body. The bipolar gain is then given by the ratio between the Q COLL and Q DEP . The LET range considered here corresponds to the LET range of a neutron-induced ion in silicon in the terrestrial environment [START_REF] Fang | [END_REF]. Dual-material-gate devices have higher parasitic bipolar amplification than the single-material-gate counterparts. This can be explained by the reduction of the effective channel length in dual-material-gate devices induced by the presence of a gate material with lower workfunction on the drain side of the gate, which induces a stepfunction potential profile. Then the collected charge and the bipolar gain values are higher in these devices than those obtained in single-material-gate devices. Concerning the dual-material-gate devices, JL-DMDG exhibits a higher bipolar gain than IM-DMDG because of more important floating body effects in the channel of the junctionless device having a higher doping level than the channel of inversion-mode device which is intrinsic. The difference between the four devices is important at low LET, but it gradually weakens when the LET increases. The explanation is that at high LET the electric field is collapsed and then potential variations in the channel have less impact on the parasitic bipolar amplification. The bipolar gain then becomes nearly the same for all devices.

Device sensitivity to ion hit location

We consider in the following different ion hit locations along the x-axis between the source contact (x=0) and the drain contact (x=60 nm). The drain current peak (Fig. 6) and the transient width increase as the ion strike location moves from source to drain with a maximum value at x=40 nm for LET=10 MeV.cm 2 /mg. The collected charge and the bipolar gain as a function of the strike location are shown in Fig. 7. The deposited charge, Q DEP, is also reported for comparison. Q DEP is highest in the middle of the channel and decreases toward the source and drain sides of the silicon film, because a reduced part of the ion track is contained in the active region [10]. Q COLL has a bell-shaped profile with a maximum at x=40 nm. For all x locations Q COLL is higher in junctionless than in inversion-mode devices. For ion strikes in the source of IM-DMDG and IM-SMDG, Q COLL is lower than Q DEP . This indicates that the bipolar amplification (Fig. 7b) is very low and that there is a strong recombination of the deposited charge in the device [10]. The bipolar gain is always higher in junctionless than in inversion-mode devices, but has similar dependences on ion hit location for the four structures. The bipolar gain maximum is located at the channeldrain junction in IM-DMDG and IM-SMDG and at x=50 nm for JL-DMDG and JL-SMDG.

Impact of technological parameters on transient response of JL-DMDG devices

We also investigated the impact of several technological parameters on the transient response of JL-DMDG. Simulations have been performed on dualmaterial-gate devices with various lengths of the highgate workfunction region, L 1 , in order to evaluate the impact of this parameter on the transient response of JL-DMDG devices. workfunction region is reduced. The JL-DMDG structures with L 1 >0.8×L G have bipolar gains close to that of the JL-SMDG structure, which is very interesting for obtaining hardened JL-DMDG devices.

We also vary the metal-gate M2 workfunction in JL-DMDG devices and investigate its influence on the bipolar gain. These additional simulations and a detailed discussion will be included in the full paper.

Fig. 1 .

 1 Fig. 1. Schematic description of the simulated symmetrical JL-SMDG, JL-DMDG and IM-DMDG devices. For a better view, spacers and isolation oxides are not shown.

Fig. 2 .Fig. 3 .

 23 Fig.2. Surface potential profiles at V G =0V and V D =1V.

Fig. 4 .

 4 Fig.4. Drain current transients for an ion hit in the center of the channel (LET=0.1 MeV.cm 2 /mg).

Fig. 5 .

 5 Fig. 5. Collected charge and bipolar amplification as function of LET for an ion hit in the center of the channel.

Fig. 6 .Fig. 7 .

 67 Fig. 6. Peak of the drain current transient as a function of the ion hit location (LET=10 MeV.cm 2 /mg).

Figure 8 Fig. 8 .

 88 Fig. 8. Bipolar gain as function of the length of the highgate workfunction region, L1, for LET=1 MeV.cm 2 /mg in DMDG devices (the ion hit location is x=30 nm).


Laurent Hardion
email: laurenthardion@unistra.fr

Régine Verlaque

Gisèle Haan-Archipoff

Daniel Cahen

Michel Hoff

Bruno Vila

Cleaning up the grasses dustbin: systematics of the Arundinoideae subfamily (Poaceae)

Keywords: Arundo, Crinipedeae, Phragmites, Phylogeny, Pratochloa, Taxonomy

Among the 12 subfamilies currently considered in the systematics of Poaceae, the Arundinoideae have long been considered as a dustbin group, with a diversity of forms putatively hiding incertae sedis.

Because this subfamily has been poorly investigated using molecular markers for the last two decades, the present study provides the first complete phylogeny of the Arundinoideae based on five plastid DNA loci sequenced for 12 genera, and analysed with and without plastome data from previous studies. The refined Arundinoideae appear to be a robust evolutionary lineage of Poaceae, divided into three tribes with some biogeographical patterns: (1) tribe Arundineae, the most heterogeneous tribe, including Eurasian Arundo, Australian Amphipogon and Monachather, and South African Dregeochloa; (2) tribe Crinipedeae (described here), including Crinipes, Elytrophorus, Styppeiochloa and Pratochloa (described here), with a South and East African distribution; and (3) tribe Molinieae, including Hakonechloa, Molinia and Phragmites, with a Eurasian distribution. Despite reduction in size, this small subfamily conserves a high diversity of morphological forms, with several small but highly differentiated genera. Finally, the molecular dating approach provides an evolutionary framework to understand the diversification of Arundinoideae, refuting Gondwanan vicariance between genera and suggesting capability for long distance dispersal.

Introduction

Poaceae Barnhart is one of the most fascinating plant families by its usefulness for humans and its ecological and taxonomic diversification. Although several angiosperm families possess higher species richness, grasses exceed all others by their ecological significance [START_REF] Kellogg | The grasses: a case study in macroevolution[END_REF]. Thanks to numerous adaptive strategies such as C-4 metabolism (GPWG II 2012), Poaceae occur in almost all terrestrial ecosystems and dominate grassland biomes covering a quarter of land surfaces [START_REF] Shantz | The place of grasslands in the Earth's cover[END_REF]). In addition, about half of the annual production of global agriculture is due to the domestication of four of the c. 12,000 grass species (http://faostat.fao. org/). In this context, the understanding of grass evolutionary history represents a major scientific challenge. Since the groundwork studies by [START_REF] Brown | Prodromus florae Novae Hollandiae et insulae Van-Diemen[END_REF][START_REF] Brown | Prodromus florae Novae Hollandiae et insulae Van-Diemen[END_REF], Poaceae have been periodically revised in several subfamilies and tribes (a synthesis in [START_REF] Prat | Vers une classification naturelle des Graminées[END_REF][START_REF] Clayton | Genera graminum: grasses of the world[END_REF]. For the last two decades, molecular studies have accelerated this systematics resolution [START_REF] Clark | A phylogeny of the grass family (Poaceae) based on ndhF sequence data[END_REF][START_REF] Duvall | Molecular phylogenetics of Poaceae: an expanded analysis of rbcL sequence data[END_REF][START_REF] Hilu | Phylogeny of Poaceae inferred from matK sequences[END_REF][START_REF] Hsiao | A molecular phylogeny of the grass family (Poaceae) based on the sequences of nuclear ribosomal DNA (ITS)[END_REF]GPWG 2001), with the current consideration of 12 subfamilies, 51 tribes and 771 genera [START_REF] Soreng | A worldwide phylogenetic classification of the Poaceae (Gramineae)[END_REF], structured in two main lineages, the BOP and PACMAD clades (Fig. 1).

Arundinoideae Kunth ex Beilschm. were dissociated from these two historical lineages early on, due to apically reduced florets and laterally compressed spikelets-specific to the 'festucoid' type-versus subtropical distribution and epidermal features-specific to the 'panicoid' type (Avdulov 1931;[START_REF] Jacques-Félix | IX -Notes sur les graminées d'Afrique tropicale[END_REF][START_REF] Stebbins | A suggested classification of grass genera of North America based on modern criteria[END_REF][START_REF] Prat | Vers une classification naturelle des Graminées[END_REF]Fig. 1a). Arundinoideae included incertae sedis taxa, which sometimes led to consider it to be a basal clade of Poaceae, or even a taxonomic 'dustbin group' [START_REF] Prat | Vers une classification naturelle des Graminées[END_REF][START_REF] Auquier | Critères anciens et modernes dans la systématique des Graminées[END_REF][START_REF] Clayton | Genera graminum: grasses of the world[END_REF]. Consequently, Arundinoideae have included up to 736 species and 72 genera [START_REF] Conert | Dregeochloa, eine neue Gattung der Gramineen (Gramineae, Arundinoideae, Danthonieae)[END_REF][START_REF] Conert | Dregeochloa, eine neue Gattung der Gramineen (Gramineae, Arundinoideae, Danthonieae)[END_REF][START_REF] Renvoize | The sub-family Arundinoideae and its position in relation to a general classification of the Gramineae[END_REF][START_REF] Soreng | A worldwide phylogenetic classification of the Poaceae (Gramineae)[END_REF], but its molecular polyphyly [START_REF] Barker | Polyphyly of Arundinoideae (Poaceae): evidence from rbcL sequence data[END_REF](Barker et al. , 1998;;[START_REF] Hsiao | A molecular phylogeny of the subfamily Arundinoideae (Poaceae) based on sequences of rDNA[END_REF]) led to its drastic reduction by the description of Danthonioideae H.P.Linder & N.P. Barker (GPWG 2001) and the reinstatement of Micrairoideae Pilg. [START_REF] Sánchez-Ken | Reinstatement and emendation of subfamily Micrairoideae (Poaceae)[END_REF]. Following these treatments, Arundinoideae have become one of the smallest grass subfamilies, with 15 genera and about 42 species (Table 1). But these taxa show a surprising ecological and morphological heterogeneity, from helophyte reeds such as Phragmites australis (Cav.) Trin. ex Steud., one of the most cosmopolitan plant species, to dwarf xerophytes such as Dregeochloa pumila (Nees) Conert, the only succulent grass living in Southern African sandy deserts. Repeated morphological analyses of Arundinoideae provided some interesting insights but failed to clearly resolve their classification. This is partly due to the diversity of forms and few evident synapomorphies in such a small subfamily [START_REF] Renvoize | The sub-family Arundinoideae and its position in relation to a general classification of the Gramineae[END_REF][START_REF] Linder | Phylogeny and evolution in the Crinipes group of grasses (Arundinoideae: Poaceae)[END_REF] ). In addition, several taxa currently in the Arundinoideae may be erroneously included. In return, some apparent Arundinoideae may be misplaced in other subfamilies, such as 'Eragrostis walteri Pilg.' previously considered as the only non-C 4 Chloridoideae, but recently placed in the Arundinoideae based on molecular data [START_REF] Ingram | Molecular phylogenies disprove a hypothesized -C 4 reversion in Eragrostis walteri (Poaceae)[END_REF]. Finally, several species and genera (Dichaetaria Nees ex Steud., Leptagrostis C.E.Hubb., Nematopoa C.E.Hubb. Piptophyllum C.E.Hubb., Zenkeria Trin.) of Arundinoideae have never been studied in a molecular phylogeny, due to their rarity and restricted distributions, some of them being represented only by a few herbarium specimens [START_REF] Linder | Phylogeny and evolution in the Crinipes group of grasses (Arundinoideae: Poaceae)[END_REF]. The present study attempts to provide the first complete phylogeny of the Arundinoideae subfamily. The main challenges are (1) to test the monophyly of taxa currently included in Arundinoideae, (2) to resolve the phylogenetic relationships within this subfamily in order to identify putative tribes and (3) to initiate the understanding of the evolutionary history of this small but heterogeneous sub-family. To address this, we used five plastid DNA loci previously investigated to resolve the systematics of Poaceae. We also added previously published plastomes (complete plastid genomes) of several species, in order to increase the resolution of phylogenetic reconstructions and improve the calibration of molecular dating. Finally, we provide a taxonomic treatment to improve the classification of Arundinoideae.

Materials and methods

DNA extraction and plastid DNA sequencing

Sampling includes samples from BM, CANB, ETH, K, MARS, P, PRE and STR Herbaria (Online Resource 1). For each sample, about 1 cm 2 of leaf material was crushed by two metallic marbles in 2-mL tubes treated with liquid nitrogen and placed in a ball mill. Total DNA was extracted following [START_REF] Doyle | A rapid DNA isolation procedure for small quantities of fresh leaf tissue[END_REF] with a modification for herbarium material: incubation of ground material with CTAB isolation buffer (4% CTAB) for 120 min. DNA concentrations were estimated using a NanoDrop ND-1000 spectrophotometer (Labtech, Uckfield, UK) and diluted to 50 ng/µL for recent collections, or used at the initial concentration for old specimens with degraded DNA. Plastid DNA diversity was screened on five loci using primer couples as described in the literature and newly designed internal primers for specimens with degraded DNA: trn K-matK, matK, rbcL, rbcL-psa I, ndhF (Online Resource 2). Polymerase chain reactions (PCRs) were performed with 5 mL of DNA solution, 1× of GoTaq Flexi Buffer, 0.25 µM of each primer (Eurofins Scientific, Luxembourg), 1.0 mM of MgCl 2 , 0.2 mM of dNTP and 1 unit of GoTaq G2 Flexi DNA polymerase (Promega, Fitchburg, Wisconsin, USA) in a final volume of 50 µL. The thermal cycling profiles followed indications from the previously cited literature for each locus. Purification and sequencing of PCR products were carried out by Eurofins.

Phylogenetic analyses

First, each plastid DNA locus was manually checked and aligned in MEGA 6.0 [START_REF] Tamura | MEGA6: molecular evolutionary genetics analysis version 6.0[END_REF]). In addition, we added corresponding sequences from four plastomes of Arundinoideae, three of Micrairoideae, four of Danthonioideae and five of Chloridoideae sequenced in a previous study [START_REF] Cotton | Resolving deep relationships of PACMAD grasses: a phylogenomic approach[END_REF] . Two nucleotide datasets were used: (1) the loci dataset including the five dissociated locus alignments and (2) the loci + plastome dataset gathering every locus in one large alignment with the 16 whole plastome sequences (Online Resource 3). In the second dataset, we combined the plastid sequences of Arundo donax L. with transcriptomic data from a previous study (GenBank accession GBRH01000000; [START_REF] Barrero | Shoot transcriptome of the giant reed, Arundo donax[END_REF], using the mapping function in Geneious v.7 and using the P. australis plastome as a reference (GenBank accession KF730315). The online program MAFFT v.7 was used for loci and plastomes alignments (http://mafft.cbrc.jp/alignment/server/ ; [START_REF] Katoh | MAFFT multiple sequence alignment software version 7: improvements in performance and usability[END_REF]. Phylogenetic relationships and dating divergences were estimated using Bayesian inferences in Beast v.1.8.1 [START_REF] Drummond | BEAST: Bayesian evolutionary analysis by sampling trees[END_REF]. The Arundinoideae + Micrairoideae cluster was treated as the ingroup, and its monophyly was enforced as for the remaining outgroup and for the Danthonioideae and the Chloridoideae (GPWG II 2012). The molecular dating of phylogenetic divergences was led by a secondary calibration of basal nodes using dates and uncertainties estimated in previous analyses of angiosperm-wide datasets [START_REF] Christin | Molecular dating, evolutionary rates, and the age of the grasses[END_REF]). These dates were obtained using several angiosperm fossils, with additional consideration of 67 Ma fossilized phytoliths giving a lower age for the stem of Oryzeae [START_REF] Prasad | Late Cretaceous origin of the rice tribe provides evidence for early diversification in Poaceae[END_REF][START_REF] Christin | Molecular dating, evolutionary rates, and the age of the grasses[END_REF] ). Time constraints were set on the root of the tree by a normal distribution of mean 57.304 ± 5.5 and on the crown of Arundinoideae + Micrairoideae by a normal distribution of mean 47.509 ± 8.5. For each locus of the first dataset, unlink site models were estimated following substitution models indicated in jModelTest v.2.1 [START_REF] Darriba | jModelTest 2: more models, new heuristics and parallel computing[END_REF], and unlink clock models were estimated under a log-normal relaxed clock with a normal distribution with the prior for the distribution of node ages approximated by a Yule speciation process (Table 2). The second dataset was analysed as a single alignment, following a general time-reversible substitution model with a gamma shape parameter and using a proportion of invariants (GTR + G + I), and a log-normal relaxed clock with a Yule speciation process. The MCMC tree searches were run for 10,000,000 generations, sampling a tree every 1000 generations after a burn-in period of 1,000,000 generations. The adequacy of the number of generations, sampling frequency and burn-in period was confirmed through a visual inspection of the traces and ESS for all parameters using Tracer v.1.6 [START_REF] Rambaut | Tracer, version 1.6[END_REF]. Finally, the two maximum clade credibility (MCC) trees were summarized in TreeAnnotator 17.4 [START_REF] Drummond | Relaxed phylogenetics and dating with confidence[END_REF].

Results

Our study presents 31 species with evidence from new plastid DNA sequences and includes two previously unsequenced genera, Crinipes Hochst. and Zenkeria. We failed to extract sufficiently preserved DNA or to find plant material in the visited herbaria for the monotypic genera: Dichaetaria (PRE980454), Leptagrostis (STR), Nematopoa (K) and Piptophyllum. The amplification of rbc L-psaI failed for Amphipogon caricinus F.Muell. and one sample of D. pumila (PRE581482).

Genetic variation of plastid DNA loci

The five loci covered 7150 bp, i.e. 4.9% of the 146,502 bp represented by the plastomes alignment. The mapping of the A. donax transcriptome on the plastome of P. australis created a partial plastome of 78,561 bp for A. donax, i.e. 53.6% of the plastomes alignment, but including only low variability coding regions. In the first nucleotide dataset, the five loci show different amounts of variation, from low variable genes with less than 20% of variable sites (matK, ndhF, rbcL), to the intergenic spacer rbcL-psaI containing a high proportion of variable sites (60.4%), among which a large portion of indels (37.2% of sites), with a median variability for the mainly intronic trnK5′-matK5′ (Table 2). The substitution varied from 3.55 to 7.56 × 10 -10 substitution per year for the three genes, and 1.18-1.28 × 10 -9 for the two other loci.

Phylogenetic relationships

The MCC trees generated from the two nucleotide datasets show almost identical and well resolved topologies, with nearly all nodes supported by posterior probabilities >0.95. In the Arundinoideae subfamily, walteri' is placed along a well-isolated stem as a sister group of the genus Elytrophorus , with a divergence estimated to 21.7 Ma (or 16.8 Ma, for the loci dataset). The Micrairoideae subfamily appears as sister to the Arundinoideae. Surprisingly, genus Zenkeria is not included in Arundinoideae, but rather as the nearest relative of Micraira F.Muell. within Micrairoideae.

The two calibration strategies, considering (1) the five loci without plastome under unlink site and clock models, or (2) the whole alignment with plastomes following unique site and clock models, show a significant difference in divergence dating, with plastome calibration inducing older node ages in the ingroup (and younger ones in the outgroup) than unlinked calibration of the five loci, with a difference of about 5 Ma (4-7 Ma) for a same node. The exception is the crown node of the whole chronogram supporting the dating calibration, remaining at 54.9 Ma (95% CI [45.4; 65]) for the loci + plastome dataset and 54.7 Ma 95% CI [44.6; 65] for the loci dataset, near the prior at 57.3 ± 5.5 Ma. The stem nodes of the three main clades previously described based on the loci + plastome dataset). Their crown nodes were estimated not so far from stem nodes, between 33 and38 Ma, expect for the crown node of clade Molinia-Hakonechloa-Phragmites, which is estimated around 15 Ma (95% CI [27.6; 6.3]). Despite a large 95% CI, every

Arundinoideae genus started its diversification before the Quaternary, during the Neogene (23-2.6 Ma).

Discussion

Resolution of Arundinoideae phylogeny

The Arundinoideae subfamily appears here to be a robust evolutionary lineage of Poaceae, with eleven genera forming a monophyletic and structured clade. However, the present study shows that Zenkeria is misplaced and should reside in the Micrairoideae. We provide new molecular data for 12 genera of which two have never been sequenced but failed to analyse four other ones. These remaining four genera are monotypic, rare and have not been collected for a long time, but recent plastome sequencing data seem to place Dichaetaria, Nematopoa and Piptophyllum in other grass subfamilies (Teisher, pers. comm.). To date, Leptagrostis, known from only a few Schimper specimens collected over a century ago, has yet to be sequenced. During the present study, [START_REF] Kellogg | Tracing the origin of Gulf Coast Phragmites (Poaceae): a story of long-distance dispersal and hybridization[END_REF] mentioned three other genera in Arundinoideae:

Alloeochaete C.E.Hubb., Danthonidium C.E.Hubb. and Phaenanthoecium C.E.Hubb., but these were placed as incertae sedis in the Danthonioideae by [START_REF] Soreng | A worldwide phylogenetic classification of the Poaceae (Gramineae)[END_REF].

Even if the present study somewhat clarifies Arundinoideae systematics, this smaller refined subfamily remains oddly heterogeneous, with a variety of morphological forms and deep evolutionary differentiation among taxa, as suggested by the weak ratio between the numbers of species(41-42) and genera (11)(12)(13)(14).

Indeed, most genera include only 1 or 2 (-3) species (Table 1), except Amphipogon (9) and the two reedy genera, Arundo (5) and Phragmites (5). [START_REF] Soreng | A worldwide phylogenetic classification of the Poaceae (Gramineae)[END_REF] suggested further division into subtribes might be needed within the Arundinoideae. However, we chose to stay at a tribe level considering the limited interest in describing mono-or di-generic subtribes. With regard to the present phylogeny (Fig. 2), the structuring of the Arundinoideae into three tribes is well supported:

1. Tribe Molinieae V.Jirásek includes genera Hakonechloa, Molinia, and Phragmites [START_REF] Jirásek | The systematics of cultivated plants and their taxonomic categories[END_REF].

Contrary to [START_REF] Soreng | A worldwide phylogenetic classification of the Poaceae (Gramineae)[END_REF], we chose to remove the Crinipoid group [START_REF] Barker | The relationships of Amphipogon , Elytrophorus and Cyperochloa (Poaceae) as suggested by rbcL sequence data[END_REF][START_REF] Linder | Phylogeny and evolution in the Crinipes group of grasses (Arundinoideae: Poaceae)[END_REF]) from Molinieae based on the phylogenetic and morphological similarities of Hakonechloa, Molinia and Phragmites (supported by their stem length, recent diversification, and lemma similarity; Fig. 2). The Sino-Japanese Moliniopsis Hayata is sometimes considered as a distinct genus [START_REF] Soreng | A worldwide phylogenetic classification of the Poaceae (Gramineae)[END_REF] or placed as a synonym of Molinia based on morphological similarity (as in the present study). However, the rpoC2, rbcL and atpF-atpH sequences deposited in GenBank for Ma) of Japanese Islands [START_REF] Jolivet | Japan Sea, opening history and mechanism: a synthesis[END_REF][START_REF] Taira | Tectonic evolution of the Japanese island arc system[END_REF][START_REF] Isozaki | New insight into a subduction-related orogen: a reappraisal of the geotectonic framework and evolution of the Japanese Islands[END_REF]. This late marine isolation may explain the parallel allopatric speciation of the three Japanese endemic taxa. The presence of long hairs on the callus (but not on the lemma) may be a synapomorphy characterizing Molinieae (Fig. 2), except for the short-haired or glabrous callus found in Molinia caerulea (L.) Moench.

2. Tribe Crinipedeae Hardion is described here to include Crinipes, Elytrophorus, Pratochloa (described here), and Styppeiochloa. This tribe corresponds to the Crinipoid group as described by Linder et al. Elytrophorus spicatus(Willd.) A.Camus which spreads to southern Asia and Australia. This large distribution pattern might be due to floral adaptations for long distance dispersal, e.g. by ornitochory since the lemmas have short, scabrous awns, the paleas are winged and variously notched (adherent), and this species grows in wet sites (a suitable condition for bird occurrence). Since Crinipes-Styppeoichloa and Elytrophorus-Pratochloa form clades, it might be useful to eventually have this reflected in the classification, possibly as separate subtribes.

3. Tribe Arundineae Dumort. is also strongly supported in our phylogeny, even if supports of internal nodes among the four genera are weaker (Fig. 2). Initially included in the same genus due to their eco-morphological similarities, subtropical Eurasian reed genus Arundo does not belong to the same tribe as cosmopolitan reed genus Phragmites. Surprisingly, the taxa which are the closest relatives of Arundo are the two Australian-endemic herbaceous genera Amphipogon and Monachather [START_REF] Barker | Polyphyly of Arundinoideae (Poaceae): evidence from rbcL sequence data[END_REF]. The present study also places the South African genus Dregeochloa in Arundineae, and not in Molinieae as assumed by [START_REF] Soreng | A worldwide phylogenetic classification of the Poaceae (Gramineae)[END_REF]. The morphological similarities between Dregeochloa and Monachather (Fig. 2) and the biogeographical afnities between Amphipogon and

Monachather might justify the use of Amphipogoneae L.Watson and T.D.Macfarl., thus isolating

Arundo in the Arundineae. However, these assumptions need to be tested using other molecular markers, and specifically with nuclear genes that have been poorly investigated in this subfamily [START_REF] Hsiao | A molecular phylogeny of the subfamily Arundinoideae (Poaceae) based on sequences of rDNA[END_REF]. The Australian genus Amphipogon includes the highest species richness of Arundinoideae genera, with nine species radiating in the West Mediterranean zone of Australia, with several endemic taxa and some species with a broader distribution in Eurasia. It is noteworthy that Arundinoideae initially described on the basis of reedy genera such as Arundo, Phragmites and Molinia (also called the Phragmitiformes Avdulov 1931) cannot exclusively be considered a reedy group of grasses. The high number of small herbaceous taxa and the distant position of Arundo and Phragmites argue for the homoplasy of culm height and rigidity. However, most Arundinoideae taxa are associated with humid habitats, even when they occur in semi-arid biomes. Dregeochloa is a counterexample of this, with its distribution in arid zones, and several xerophyte adaptations (thickened cuticle, stomata protection, succulent leaves; accurate description in [START_REF] Ellis | Leaf anatomy of the South African Danthonieae (Poaceae). I. The genus Dregeochloa[END_REF].

In a global consideration, except for North American native P. australis subsp. americanus Saltonstall, P.M.

Peterson & Soreng [START_REF] Saltonstall | Recognition of Phragmites australis subsp. americanus (Poaceae: Arundinoideae) in North America: evidence from morphological and genetic analyses[END_REF], Arundinoideae are restricted to the Old World (including Australia). The biogeography of Arundinoideae looks like a Gondwanan legacy, with South and East African, Indian and Australian species. Consequently, hypotheses of vicariance and/or land dispersal have yet to be tested (e.g. [START_REF] Linder | Phylogeny and evolution in the Crinipes group of grasses (Arundinoideae: Poaceae)[END_REF]). However, the removal of Indian endemic, Zenkeria and our molecular dating shed new light on the subject. Indeed, these geological zones were clearly isolated by the Indian Ocean 100 Ma ago [START_REF] Crisp | How was the Australian flora assembled over the last 65 million years? A molecular phylogenetic perspective[END_REF], long before the stem node of the Arundinoideae. Consequently, the common ancestors of this subfamily had to possess some suitable traits for long distance dispersal, e.g. by anemochory, as illustrated by the long-haired lemma inclosing small caryopses and forming an efficient means for dispersal (e.g. Phragmites, Arundo, Fig. 2), or by ornitochory as suggested above for Elytrophorus spicatus or other species growing in wet sites; or by marine dispersal as sometimes hypothesized for Etymology: This new genus is named in tribute to Henri Prat (1902Prat ( -1981)), professor at the Universities of Marseille (France) and Montreal (Quebec, Canada). After a thesis on the systematic study of grass epidermises, he published several works on the systematics of Poaceae with an emphasis on their morphology, anatomy and organogenesis [START_REF] Prat | L'épiderme des Graminées. Étude anatomique et systématique[END_REF][START_REF] Prat | La systématique des Graminées[END_REF][START_REF] Prat | Vers une classification naturelle des Graminées[END_REF].

Fig. 1

 1 Fig. 1 Places of the Arundinoideae subfamily (in red ) in the historical representation of grass systematics, from an old literature synthesis of morphological and anatomical studies (modified from Prat 1936; a) to a recent molecular phylogeny (modified from GPWG II 2012; b). Clade sizes are proportional to their species richness (also indicated between brackets). BOP clade, Bambusoideae-Oryzoideae-Pooideae (in grey); PACMAD clade, Panicoideae-Aristidoideae-Chloridoideae-Micrairoideae-Arundinoideae-Danthonioideae (in white)

  three distinct and well supported clades can be identified: (1) the first one includes the Eurasian Arundo, the two Australian-endemic genera Amphipogon R.Br. and Monachather Steud., and the South African Dregeochloa Conert; (2) the second one includes sub-Saharan genera: Crinipes , Styppeiochloa De Winter, and Elytrophorus P.Beauv.; (3) the third one includes mainly Eurasian genera: Phragmites Adans., Molinia Schrank, and Hakonechloa Makino ex Honda. The only incongruence between the topologies generated by the two nucleotide datasets is located in the first clade, where the loci dataset describes early divergence of the Arundo-Monachather clade from the Amphipogon-Dregeochloa clade, whereas the loci + plastomes dataset shows the divergence of Amphipogon-Arundo from Monachather-Dregeochloa. In both phylogenies, these four putative clades are poorly supported (pp < 0.7). The species currently known as 'E.

  Moliniopsis japonica (Steud.) Hayata support placement within Molinieae, and molecular data fail to resolve the monophyly of Molinia and Moliniopsis (analyses not shown). The nine species of this tribe are primarily distributed in the Old World, but each of the three genera possesses an endemic taxon from Japan and surrounding areas: Hakonechloa macra (Munro) Honda, Molinia japonica Hack. and Phragmites japonicus Steud. Compared to the wider distribution of the five other species, this biogeographical pattern positions the early origin of this tribe towards Eastern Asia, with the Miocene formation of the Japan Sea (since 20 Ma) progressively inducing the Pliocene isolation (5-3

(

  1997), except Zenkeria which we place in the Micrairoideae, and Dichaetaria, Nematopoa and Piptophyllum which should be moved to other subfamilies (Teisher, pers. comm.). Our new Crinipedeae poorly matches with subtribe Crinipinae Conert that included only Crinipes and Hakonechloa[START_REF] Conert | Dregeochloa, eine neue Gattung der Gramineen (Gramineae, Arundinoideae, Danthonieae)[END_REF]. Both phylogenetic data and lemma morphology support a close relationship between the East African Crinipes and the South African Styppeoichloa. E. walteri, recently placed in the Arundinoideae based on nuclear and plastid sequences[START_REF] Ingram | Molecular phylogenies disprove a hypothesized -C 4 reversion in Eragrostis walteri (Poaceae)[END_REF], is sister to Elytrophorus. However, phylogenetic divergence and deep morphological differentiation of the lemma(Fig.2) justify placement of this Namibian species in a new monotypic genus (see taxonomic treatment). The tribe Crinipedeae is mainly sub-Saharan (including Madagascar), except for

Fig. 2

 2 Fig. 2 Chronogram of Arundinoideae based on five plastid DNA loci(trnK-matK, matK, rbcL, rbcL-psaI, ndhF) and plastomes data (asterisk), and morphological diversity of lemmas within this small subfamily. Molecular clock secondarily calibrated using previous estimations from[START_REF] Christin | Molecular dating, evolutionary rates, and the age of the grasses[END_REF] for the two divergence nodes with outgroup Micrairoideae (Micr.) and outgroup Chloridoideae (Chlo.) + Danthonoideae (Dant.). Grey phylogeny indicated the same chronogram without plastome data and considering unlinked site and clock models for each locus. Nodes without value are supported by posterior probabilities of 1.0, and nodes with cross symbols (dagger) are supported by posterior probabilities between 0.7 and 1.0. Black bars, 5 mm.1 Partial plastome of Arundo donax (coding regions covering 53.6% of the plastome alignment) from transcriptome data[START_REF] Barrero | Shoot transcriptome of the giant reed, Arundo donax[END_REF]

  Phragmites (Lambertini et al. 2012). Taxonomic treatment subfam. Arundinoideae Kunth ex Beilschm. = Arundinoideae Tateoka = Phragmitoideae Parodi ex Caro = Arundinaceae Burmeist., unranked tribe Arundineae Dumort.-TYPE: Arundo L. = Amphipogoneae L.Watson & T.D.Macfarl. = subtribe Arundininae Miq. Genera included: Amphipogon R.Br. (= Diplopogon R.Br.), Arundo L., Dregeochloa Conert, Monachather Steud. tribe Molinieae Jirásek-TYPE: Molinia Schrank Genera included: Hakonechloa Makino ex Honda, Molinia Schrank (= Moliniopsis Hayata), Phragmites Adans. tribe Crinipedeae Hardion, trib. nov.-TYPE: Crinipes Hochst. = Crinipinae Conert pro parte. Description: Annual or perennial erect herbs, culms 10-150 cm long. Ligule a fringe of hairs or an membrane. Leaves mostly basal or cauline, non-auriculate. Leaf blades stiff, persistent or deciduous. Leaf sheaths persistent. Panicle open or glomerate. Fertile spikelets laterally compressed, 2-12 mm long, comprising 2-15 florets, breaking up at maturity, disarticulating below each fertile floret, with diminished florets at the apex. Rachilla internodes definite. Glumes persistent, shorter than spikelet, ovate or lanceolate. Lower glume shorter than to equal to upper glume. Glumes 1-keeled and 1-3-veined. Lemma membranous, with or without keel, 3-veined, entire or dentate bifid. Lodicules 2, Stamens 3. Genera included: Crinipes Hochst., Elytrophorus P.Beauv., Pratochloa Hardion, Styppeiochloa De Winter. Pratochloa Hardion, gen. nov. ≡ Eragrostis walteri Pilg.-TYPE: Pratochloa walteri (Pilg.) Hardion Pratochloa walteri (Pilg.) Hardion, comb. nov. ≡ E. walteri Pilg., Notizbl. Bot. Gart. Berlin-Dahlem 15: 452. 1940. -TYPE: NAMIBIA. Kleiner Naukluftrivier, 29 Oct 1937, Walter 458 (holotype: B [image B100272776!]; isotype: B [image B100272777!])

Table 1

 1 Genera, species richness (S) and geographical distribution of the subfamily Arundinoideae

	Genus	S	Distribution
	Amphipogon R.Br. (= Diplopogon R.Br.)	9	Australia
	Arundo L.	5	Tropical Eurasia
	Crinipes Hochst.	2	East Africa
	Dichaetaria Nees ex Steud.	1	India
	Dregeochloa Conert	2	South Africa
	Elytrophorus P.Beauv.	2	Africa-Asia-Australia
	Hakonechloa Makino ex Honda	1	Japan
	Leptagrostis C.E.Hubb.	1	East Africa
	Molinia Schrank (= Moliniopsis Hayata)	3	Eurasia
	Monachather Steud.	1	Australia
	Nematopoa C.E.Hubb.	1	South Africa
	Phragmites Adans.	5	Cosmopolitan
	Piptophyllum C.E.Hubb.	1	South Africa
	Styppeiochloa De Winter	3	South Africa
	*Zenkeria Trin.	5	India
	Total	42	Old World + Australia

* Genus removed from the subfamily based on the present study

Table 2

 2 Characteristics of the plastid DNA loci used for phylogenetic reconstructions. Site models were defined for each locus using jModel-Test 2.1.10

	Locus	Length Position	Site model	Substitution rate % Identical sites Pairwise %	% Indel sites
							identical sites
	trnK5′-matK5′ 736	3342-4078	TPM3uf + G 1.28 × 10 -9	72.4	92.4	11.3
	matK5′(-trnK3′) 1788	1553-3341	GTR + G	6.44 × 10 -10	82.9	96.9	1.19
	rbcL	1321	61,833-63,154	HKY + I + G	3.55 × 10 -10	90.8	98.0	1.74
	rbcL-psaI	1202	63,155-64,357	TrN + I + G	1.18 × 10 -9	39.6	84.2	37.2
	ndhF	2103	111,495-113,598 GTR + I + G	7.56 × 10 -10	84.8	97.1	0.57

Acknowledgements The authors thank staffs from BM, CANB, ETH, K, MARS, P, PRE and STR Herbaria for loans and material removal. LH addresses a special thanks to Pascal-Antoine Christin (University of Sheffield) for data and support in the calibration of the molecular phylogeny, and to Jordan Teisher (Washington University in St. Louis) for useful and sporting exchange views about the systematics of Arundinoideae. The authors are also grateful to Marianick Juin (IMBE) for contribution in the lab work, to Heather Lindon (RBG Kew) for expertise in botanical Latin, and to Paul M. Peterson (US, Smithsonian Institution) for his conscientious review which greatly improved the readability of the manuscript.

Compliance with ethical standards

Confict of interest The authors declare that they have no conflict of interest.

Ethical statement

The authors comply will all rules of the journal following the COPE guidelines; all authors have contributed and approved the final manuscript.

Information on Electronic Supplementary Material

Online Resource 1. Sampling information and GenBank accessions.

Online Resource 2. Primers used in PCRs and developed for the present study.

Online Resource 3. Loci + plastome alignment used for phylogenetic analyses.