Introduction

Species of the Miscanthus genus have advantages for biomass production. This perennial grass is a C4 plant with a high productivity and low input requirements, particularly for pesticides and nitrogen fertiliser [1]. Miscanthus produces more biomass per hectare than other energy crops such as maize. Furthermore, this crop also fixes more atmospheric carbon in its biomass [2], and it sequesters the carbon present in the soil [3], which is beneficial for greenhouse gas reduction.

Research in Europe has mainly focused on a single species, M. x giganteus, which is a natural hybrid between M. sacchariflorus and M. Sinensis [4]. This species presents little genetic variability [5, 6], and can be difficult to establish in a field. Despite its high biomass potential, M. x giganteus is sterile and propagated by rhizome, so that establishing this crop is expensive. It is also sensitive to lack of water [7, 8] and has a poor frost tolerance, especially during the first year of growth with a peak of sensitivity during the first winter [9, 10]. Potential improvement of the species could come from the M. sinensis, which has a diverse genetic pool for tolerance to water stress and frost [11], while still being high-yielding and adapted to biomass production.

In agronomy and plant breeding, there are models that can predict the distribution of crop yields from meteorological data, and models for assessing growth characteristics. Several models, such as MISCANFOR [12], MISCANMOD [13], or ecological modelling [14] have been in use to extrapolate Miscanthus yields, in particular M. x giganteus, to other environments. They use daily or monthly mean temperature, precipitation, photosynthetically active radiation, potential evapo-transpiration and irrigation time series for multiple or single years, and soil data for single or multiple locations [13].

However, no model has yet been proposed in Miscanthus to characterize the genetic variability of traits related to plant growth dynamics (e.g., growth rate, growth duration, maximal growth). An attractive trait for the comparison of genotypes for their growth is the canopy height: this trait is simple to measure, and canopy height at maturity is strongly positively correlated with aboveground biomass (between 0.82 and 0.93 depending on year and harvest date) [15]. Monitoring plant height during the plant growth cycle could thus inform us about biomass production. As the potential biomass yield of a crop can be defined by the product of growth rate and growth duration [16], measuring the growth rate and duration of canopy height of Miscanthus clones may allow estimation of their potential biomass production. Emergence date is another trait of interest in Miscanthus, as this species is frost-sensitive. An early emergence exposes the crop to late frosts, in spring, which may kill the first shoots, and affect biomass production.

To characterise the variability in aboveground biomass growth of different Miscanthus clones and the effect of harvest date and year on this variability, we studied crop emergence and canopy height growth characteristics, particularly rates, durations, and maximum values. One question was how to best estimate these variables to allow comparison among clones. A function that takes time into account can estimate these variables. Various equations describe the non-linear sigmoid relationship between growth and time [17, 18]. Miguez et al. [19] used a logistic curve to describe biomass yield as a function of thermal time in M. x giganteus. However, it seems they chose this function arbitrarily. Very few studies on other plants have compared different functions to describe growth. Robert et al. [18] and Khamis et al. [20] suggest observing the scatter of the residuals to test how well non-linear models fit. The value of the mean square error (MSE) is useful to test the model performance [20]. However, this measure can only compare functions that have the same number of parameters to estimate. Robert et al. [18] recommend comparing models using the Akaike information criterion (AIC), which formalises the parsimony principle and is a compromise between likelihood and the number of parameters. This criterion has the advantage of allowing direct comparison between models and accounting for the difference in parameter number.

Our aims were therefore to identify the ‘best’ function for describing the dynamics of crop emergence and of height growth for different Miscanthus clones, in order to estimate the corresponding parameters and to compare the clones accordingly. We considered one main hypothesis. We predicted that in Miscanthus, the best function would be specific of the trait under consideration.

Materials and Methods

Field Experiment

We planted a randomized complete block trial at Estrées-Mons, in France (49°53 N, 3°00 E) in spring 2007. It consisted of six blocks, each with 21 clones on plots of 16 m². Clones of four species were planted: three M. x giganteus clones, 15 M. sinensis clones, two M. sacchariflorus clones, and one M. floridulus clone. Table 1 gives the code, name, and species of each of them. Most of the species names corresponded to those given at the ornamental plant nurseries where the rhizomes came from, excepting for those we bought from U Jorgensen (University of Aarhus in Denmark), from Nordic Biomass (Denmark) and from ADAS (UK). We considered H8, a hybrid between M. sacchariflorus and M. sinensis [21], as a clone of M x giganteus. The clone named “Flo” belonged to M. floridulus species, according to the ornamental plant nursery where we bought it (Table 1). Using the genetic similarity based on 328 AFLP markers, the 21 clones belonged to several distinct clusters [22]. All the clones of M. sinensis clustered together. The two clones of M. sacchariflorus were together. For the remaining clones, it appeared that the clone of M. floridulus was close from those of M. x giganteus. For more detailed descriptions of plant material characteristics, see Zub [22] and Zub et al. [15]. The “autumn harvest” always occurred on the three same blocks in autumn, at the end of the growing period. The winter harvest always took place on the three remaining blocks at the end of winter, at over-maturity. Each plot consisted of four rows of eight plants at a rhizome-planting density of two plants per m². There was a border row on either side of the plot using the same genotype, M. sinensis Malepartus, to edge all plots. A detailed description of the trial is given in Zub et al. [15].

Table 1 The 21 Miscanthus clones used in the trial: code, species, clone name, ploidy level, and acquisition
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In the second and third years after planting (spring of 2008 and 2009, March–April–May), we recorded the date of emergence in the field every 2–3 days. We then monitored growth height weekly during the vegetative growth period, on all plants in the plot (8 to 32 plants per micro-plot). We used canopy height as a predictor for aboveground biomass because it is a non-destructive, easy to measure trait and has a strong positive inter-genotypic correlation with aboveground yield [15]. For each plant, canopy height corresponded to the height from the ground to the ligula of the last ligulated leaf.

To monitor temperatures around the rhizomes at 20 cm depth, four thermistances were set up at various points in the trial area. An air temperature sensor, installed at 10 cm, determined the difference in temperature experienced by shoots and rhizomes. Records took place every 15 minutes. These data were useful to determine cumulative degree days each day.

Determination of Ploidy Level

As the ploidy level was not available for most of the clones coming from the ornamental plant nurseries, it was measured by flow cytometry using nuclear suspensions of leaves from our field cultivated plants. To isolate and stain nuclei, we chopped about 40 mg of fresh leave tissue with a razor blade in a plastic Petri dish containing 2 ml of buffer [23] and 16 μl of a filter sterilized solution of 4’,6-Diamidino-2-Phenylindole (DAPI, Sigma D-9542) at a concentration of 250 μg.ml-1. Measurements were performed on a Partec PAS-II flow cytometer (Partec GmbH, 4400 Münster, Germany). Leaves of Pisum sativum cv Bilboquet corresponded to the internal standard. To estimate the ploidy level, we compared the position of peak of a given sample on a histogram with the reference of plants with known ploidy level. The clone H5 was tetraploid [21] and the clone of M x giganteus acquired from ADAS (GigB) was triploid [24]. No reference was available for the diploid clones, but the results showed differences clear enough among the peaks to separate the diploids from the triploids.

Statistical Methods

Estimation of Parameters of Emergence and Growth Dynamics

Based on the literature, we compared three functions for describing the dynamics of emergence and growth in Miscanthus:

  1. i.

    Logistic function with three parameters (a, b and c) assuming a lower asymptote of 0 (L3)

  2. ii.

    Logistic function with four parameters (a, b, c and d) assuming a lower asymptote other than 0 (L4)

  3. iii.

    Gompertz function

Based on the work of Robert et al. [18], who modelled the grain-filling period of winter wheat, we characterised the different emergence and growth dynamics obtained with the following three relative measurements: (i) upper asymptote corresponding to maximum emergence percentage and maximum height at maturity (respectively Emax and Hmax), (ii) maximum emergence rate (i.e., speed) and maximum growth rate (RateE and RateG), and (iii) time required to reach 0.95 of the upper asymptote (DurE and DurG).

For emergence, the Emax parameter was more representative of establishment success in the first year than of differences between clones. The parameters for emergence rate and time required to reach upper asymptote were strongly correlated with the environment of the rhizome. We therefore added a variable: time required to reach 50 % of final emergence. We call it date of emergence (DatE) and it reflected the relative earliness of each clone at emergence. In the context of looking for the variables that contribute to biomass yield, we used the DatE rather than Emax, RateE and DurE.

The equations for the functions concerning maximum height, growth rate, growth duration, and emergence date are presented for each function in Table 2.

Table 2 Equations of the three functions used to estimate emergence and plant height growth of Miscanthus and references of authors who applied these functions on other plants
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For crop emergence, the thermal time was expressed as cumulative degree days since the last negative soil temperatures (Miscanthus rhizomes cannot emerge when the temperature is below 0 °C). For canopy height growth, thermal time was expressed as cumulative degree days since emergence. We calculated the sum of daily temperatures with the following formula, in particular already used for maize, sorghum, peas, and wheat [25]. In our study, we used the optimum temperature (Topt) of 32 °C and the maximum temperature (Tmax) of 45 °C obtained with sugar cane [26], and the corresponding maximum growth rate (Rmax) of 0.04691 dd-1:

$$ TT = \frac{1}{{{R_{{max}}}}} * \frac{{{T_{{max}}} - T}}{{{T_{{max}}} - {T_{{opt}}}}} * {\left( {\frac{T}{{{T_{{opt}}}}}} \right)^{{\frac{{{T_{{opt}}}}}{{{T_{{max}}} - {T_{{opt}}}}}}}} $$
(1)

where TT is the daily thermal time experienced by the plants, T is the mean daily temperature, Tmax is the maximum temperature for sugar cane and Topt the optimum temperature for sugar cane development. The base temperature defined from this equation is 6.8 °C.

For each non-linear model considered, the following equation described the curve of emergence and canopy height growth of each genotype in each plot:

$$ {{{\text{Y}}}_{{\text{i}}}} = {\text{f}}({\text{T}}{{{\text{T}}}_{{\text{i}}}},\theta ) + {{\varepsilon }_{{\text{i}}}} $$
(2)

where Yi is either the % emergence on the plot i or the mean height of the plants in the plot i; TT is an independent variable representing the thermal time as previously defined; and θ is a vector of parameters to be estimated (3 or 4); εi is the error term.

Thus, to describe the relationships between emergence percentage and thermal time and between mean height in cm of a plot and its age in thermal time, we adjusted the data by three non-linear functions using the using the PROC NLIN non-linear regression procedure of the SAS system [27]. We obtained 63 parameter vectors per harvest date and per year.

Determination of the Best Function for Describing the Emergence and Plant Growth Dynamics

We used several statistical procedures to test the fit of the different non-linear models: observation of residual curves, comparison between the model mean square errors (MSE), and comparison between the model performance indices according to the Akaike criterion [28].

Determination of Relationship Between Parameters Estimated for Emergence, Plant Growth, and Height at Maturity

For each harvest date and each year of growth, we determined the intergenotypic coefficients of correlation between mean values for each clone of final canopy height at maturity (Hmax), mean emergence date (DatE), mean growth rate (RateG), and mean growth duration (DurG). We also estimated the intergenotypic coefficients of correlation between emergence and each of the growth parameters (growth rate, growth duration, and final canopy height).

Estimation of the Effects of Clone, Harvest Date, and Year of Growth on Parameters of Emergence and Growth Dynamics

We performed an analysis of variance using a fixed-effects model to study the effects of clone, harvest date, and year of growth on the parameters derived from the emergence and growth dynamics using the SAS GLM procedure [27]. The ANOVA model was as follows:

$$ {Y_{{ijkl}}} = \mu + {g_i} + {a_l} + {h_j} + g{a_{{il}}} + g{h_{{ij}}} + a{h_{{lj}}} + b{(h)_{{kj}}} + ga{h_{{ilj}}} + gb{(h)_{{ikj}}} + ab{(h)_{{lkj}}} + {\varepsilon_{{ijkl}}} $$

where μ is the general mean of a given Y parameter studied for the clone i grown in block k for harvest date j during the year l; g i is the clone main effect ; a l is the year main effect (corresponding to the crop age and environmental effects such as climate, soil…); h j is the harvest date main effect; b(h) kj is the effect of block k for the harvest date j ; ga ilj is the interaction between clone and year; gh ij is the interaction between clone and harvest date; ah jl is the interaction between year and harvest date; gah ijl is the interaction between clone, year, and harvest date; gb(h) ikj is the interaction between clone and block for harvest date; and ab(h) lkj is the interaction between year and block for harvest date. ɛ ijkl corresponds to the model residual error. We considered all terms as fixed effects.

Species and ploidy-level effects then partitioned the clone effect and its various interactions with the effects of harvest date and year as follows:

$$ {g_i} = {e_m} + {p_n} + g{\prime_i} $$

where e m is the species effect and p n the ploidy level effect within the species. g′ i is the remaining clone effect (not explained by species or ploidy level).

The percentage partitioning the sum of squares of the clone effect by each of these newly introduced effects then estimated the efficiency of this partitioning by the successive effects of species and ploidy level.

To determine which factors have the most determinant effects, we took into account the highest F values for the effects that showed the greatest variability.

Results

Ploidy level is a very important factor to consider when analysing productivity and related traits. Hence, results on the determination of ploidy level by flow cytometry will be presented first. Secondly, we determined which of the non-linear models tested best suited for emergence date and growth dynamics. We then analysed the effects of year, species and ploidy level on observed differences among clones for emergence date on the one hand, and for growth parameters on the other. Lastly, we analysed the relationships between emergence date and growth parameters.

Determination of Ploidy Levels by Flow Cytometry

To estimate the ploidy level of the 21 studied Miscanthus clones, we compared the peak position for each clone sample on the histogram with the peak of a reference clone with known ploidy level. Clones could thus be classified in three clusters corresponding to 2x, 3x, and 4x ploidy levels: (i) clones with peaks overlaying the peak of the tetraploid H5 clone were declared tetraploid (Fig. 1c), (ii) clones overlaying the peak of the clone of M. x giganteus acquired from ADAS (GigB), were considered as triploid (Fig. 1b), and (iii) clones with peaks corresponding to less fluorescence intensity and that clearly separated from the triploid and tetraploid peaks (Fig. 1d shows a mixture of diploid, tetraploid and internal standard) were considered as diploid (Fig. 1a). In total, 14 were found to be diploid (Table 1), which encompassed 12 M. sinensis (Aug, Fla, Grz, Mal, Rot, Sil, Str, Fer, Her, Punk, Pur and Yak), one M. sacchariflorus (Sac), and one M. x giganteus (H8). Three clones were triploid (M. x giganteus (GigB), M. sinensis (H6) and M. floridulus (Flo)), and four clones were tetraploid clones (M. sacchariflorus (H5), M. sinensis (Gol and GolD) and M. x giganteus (GigD)) (Table 1). We then used this information about the ploidy level to perform further statistical analyses by species and ploidy level.

Fig. 1
figure 1

Histograms of flow cytometric analysis that were used to determine nuclear DNA content in leaves of different Miscanthus clones. a A diploid plant of M. sinensis var Punktchen (Punk). b A triploid hybrid M. x giganteus (GigB). c A tetraploid hybrid of M. sacchariflorus (H5). d A mixture of a diploid plant Miscanthus sacchariflorus (Sac), a tetraploid M. sacchariflorus (H5), and the internal standard Pisum sativum

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Best Models to Estimate Emergence Date and Growth Parameters

Three non-linear models were tested to describe the dynamics of the crop emergence and plant growth in each micro-plot for each year of growth and each harvest date. The scatter graphs of the residuals helped to detect possible deviations from the model. No heterogeneity of variance was observed for any model in any of the tested situations. The best models were those providing the lowest mean square error (MSE) and Akaike criterion (AIC) values (Table 3).

Table 3 Comparison of three functions for estimating emergence and growth dynamics in Miscanthus in the second and the third year of growth at two harvest dates
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The Gompertz function best described emergence dynamics for the second and third years of development for both harvest dates, according to MSE and AIC (Table 3).

For growth dynamics, the L4 function was the only function that converged for all clones, at each harvest of each year. In contrast, the Gompertz function algorithm did not converge for data collected on 23 cases (a “case” correspond to one clone in one harvest date in one year) during the autumn harvest of the third year (Table 3). To a lesser extent, it also failed to converge with autumn harvest for both years of development. The function L3 failed to converge with autumn harvest in both years of development and winter harvest in the third year.

Emergence Date was Largely Influenced by the Crop Year

An analysis of variance was performed to analyse the effects of clone, harvest date, and year on emergence date (DatE) estimated with the Gompertz function (Table 4). The variance model explained 93 % of total variation in emergence date, with a low residual coefficient of variation (CV) of 12 % (Table 4). The main effects of clone and year and the clone × year and clone × harvest date interactions were significant (at the 0.05 probability level). Grouping the clones by species and then by ploidy level resulted in partitioning 52 % of the total variation due to the clone effect. Similarly, partitioning the interaction between clone effect and year effect by species and then by ploidy level explained up to 70 % of the interaction.

Table 4 (a) Analysis of variance for emergence dates (DatE in degree days (dd)) estimated by the Gompertz function and (b) analysis of variance for growth rate (RateG), growth duration (DurG) and final canopy height (Hmax) estimated by the 4-parameter logistic function. Spec refers to species. %SS; percentage of sum of square
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Among the main effects, the year effect was more variable than the others (F value of 582 in Table 4). This was mainly due to an earlier emergence the third year compared to the second year (106 dd compared to 154 dd respectively).

Regarding the interactions, the clone × year interaction was slightly higher than the clone main effect (Fig. 2a). Emergence date ranged between 138 dd for Flo and 169 dd for Punk in the second year, and from 79 dd for Punk to 146 dd for GigB in the third year. Grouping the clones by species explained a high part of this interaction (63 %). The interaction was clearly due to the earlier emergence dates the third year regardless of the harvest date (although the triple interaction clone × year × harvest date was significant): most M. sinensis clones, one M. sacchariflorus clone (Sac) and one M. x giganteus clone (H8), less distant to the bisecting line, contributed the most to this interaction (with circle on Fig. 2a), whereas the M. floridulus clone, two M. x giganteus clones (GigB and GigD), one M. sacchariflorus clone (H5) and two M. sinensis clones (Fer and Fla) (Fig. 2a), showed similar emergence dates in the second and third years for both autumn harvest and winter harvest.

Fig. 2
figure 2

Emergence date (in degree days, dd) as a function of year (a) and harvest date (b). Root mean square error = 15 dd. a The clone × year interaction was due to the fact that (i) two clones of M. x giganteus¸ one of M. floridulus, one of M. sacchariflorus and two of M. sinensis had similar emergence dates in their second and third years of growth, while (ii) the other clones emerged much earlier in the third year. b The interaction between clone effect and harvest date in the third year was due to the later emergence of M. sinensis Fla after winter harvest than after autumn harvest, and to the earlier emergence of one clone of M. x giganteus, one of M. sacchariflorus and two of M. sinensis after winter harvest than after autumn harvest

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Finally, there was a significant interaction between the effects of clone and harvest date, which was mainly due to the third year of growth (Fig. 2b). In the second year, the different clones broadly showed the same emergence date for both harvest dates (Fig. 2b). In contrast, five clones stood out in the third year: one M. sinensis clone (Fla) showed a much later emergence date with winter harvest than with autumn harvest and one clone of M. sacchariflorus (H5), two of M. sinensis (Fer and Rot) and one of M. x giganteus (GigD) showed emergence dates at least 26 dd earlier with winter harvest than with autumn harvest (Fig. 2b).

Note that the different species involved different numbers of clones, as did the different ploidy levels, which could introduce a bias into the results. However, the differences observed among species and ploidy levels were fairly marked, so we can assume that the broad trends among species and ploidy levels can be identified.

Crop Growth was Highly Influenced by the Year, Species, and Ploidy Level within the Clone Effect

Table 4 shows the results of the analysis of variance of the height growth dynamics parameters (growth rate, growth duration, and final canopy height) of Miscanthus estimated from function L4. Since most of the effects and the corresponding interactions were significant (at the 0.05 probability level), only the most important ones regarding the F values are pointed out here.

Firstly, the year had the greatest main effect (compared to harvest date and clone), whichever growth parameter was considered: the mean growth rate was slower in the third year than in the second year (0.18 cm.dd-1 compared to 0.23 cm.dd-1 on average), the growth duration in dd was almost twice as long in the third year than in the second year (mean value of 717 dd and 362 dd respectively), and finally the plants were 30 cm taller in the third year.

Secondly, the clone main effect also explained a lot of the variability in height growth rate and final canopy height and, to a lesser extent, the variability in duration of growth. There was an almost five-fold difference in growth rate between the extremes (Fig. 3a), which ranged from 0.07 cm.dd-1 for clone Yak to 0.41 cm.dd-1 for clone Flo. This variability among clones was largely due to species and ploidy level (91 %), which successively partitioned 54 % and 37 % of the variability in growth rate (Table 4). Duration of growth also varied among clones, mainly because of one M. sinensis clone (Her) which had a significantly (P < 0.05) longer growth duration than the other clones (910 dd on average against 530 dd respectively) (Fig. 3b). Lastly, final canopy height varied threefold between the smallest clone, Yak (65 cm), and the tallest, H5 (220 cm). This variability among clones was largely due to species (56 %) and ploidy level (37 %). Taking into account the means assessed at the species level, the M. floridulus clone was the tallest, with a mean height of 204 cm, while the clones of M. x giganteus and M. sacchariflorus were significantly smaller, with a mean final canopy height of 175 and 172 cm respectively. The M. sinensis clones were significantly smaller, with a mean height of 105 cm. The M. sinensis 2x (M. sin_2x) clone was 45 % smaller than M. sin_3x and M. sin_4x, and the M. sacchariflorus 2x (M. sac_2x) clone was 45 % smaller than M. sac_4x.

Fig. 3
figure 3

a Comparison of growth rates (in centimetres per degree days, cm.dd-1) for the two harvest years. Root mean square error = 0.03 dd-1. The clone × year interaction was due to mean growth rates per clone being generally slower in the third year of growth for clones of M. sinensis, and being similar in both years for clones of M. x giganteus, M. floridulus and M. sacchariflorus. b Growth (in degree days, dd) was longer in the third year of growth than in the second year. Root mean square error = 79 dd

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With regard to the interactions, there was a strong interaction between the effects of clone and year for all growth parameters, in contrast to the interaction of clone with harvest date (Table 4). For duration of growth, for instance, this interaction was mainly due to species, which accounted for 60 % of the corresponding variation. The M. floridulus clone and the M. sinensis clones showed growth duration almost twice as short in the second year (319 dd and 357 dd respectively) as in the third year (526 and 809 dd respectively). By contrast, the mean growth duration of the M. sacchariflorus and M. x giganteus clones was similar between the two years (Fig. 3b).

Finally, the interaction harvest date × year affected mostly growth duration and final canopy height. The 9 % difference in duration of growth between autumn and winter harvests in the second year was not significant but duration of growth was significantly longer (22 %) for autumn harvest than for winter harvest in the third year of growth (Fig. 3b). Final canopy height did not significantly differ between the two harvest dates in the second year (110 cm), but in the third year plants were taller in winter harvest than in autumn harvest (150 cm versus 137 cm respectively).

Inter-genotypic Correlations between Emergence Date and Growth Parameters

We identified the main traits contributing to the final canopy height by studying the inter-genotypic correlations with emergence date and growth parameters. We calculated these intergenotypic correlations from the means per year and per harvest date for each clone, on the one hand, and the means of the different M. sinensis clones on the other hand (Table 5).

Table 5 Comparison for Pearson correlation coefficients of all clones studied (A) with M. sinensis clones (B) for their emergence date (DatE), final canopy heights (Hmax), growth rate (RateG) and growth duration (DurG) at the autumn and winter harvests of the second and third years
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Firstly, there was a significant positive correlation between final canopy height (Hmax) and emergence date irrespective of harvest date during the third year of growth (Table 5). Four clones (Flo, GigB, GigD and H5) strongly contributed to the correlation (Fig. 4): they stood out from the others by their late emergence dates and tall final canopy height (over 200 cm). But this correlation became non-significant (at the 5 % probability level) if we considered only the clones of M. sinensis.

Fig. 4
figure 4

In the third year of growth, the later a clone emerged, the greater the final canopy height was, irrespective of harvest date. Root mean square error (RMSE) = 8 cm for height and RMSE = 15 dd for emergence date

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Secondly, a significant positive correlation was found between final canopy height and growth rate irrespective of harvest date and growth year. Clones were was taller when their growth rate was higher. This correlation was stronger in the third year than in the second year, irrespective of harvest date. This was the case for all the clones and also for the clones of M. sinensis (Table 5).

In addition, there was a significant negative correlation between final canopy height and duration of growth (Table 5). This was observed for winter harvest in the second year and above all for both autumn and winter harvests in the third year. This negative correlation was also found in the third year between species and ploidy level, and within species M. sinensis.

Lastly, we found a significant negative power relationship between growth rate and duration, irrespective of harvest date and year (Fig. 5). The faster the growth, the shorter its duration was.

Fig. 5
figure 5

Negative power relation observed between duration of growth (in degree days, dd) and growth rate (in centimeters per dd), for the third year of growth. Root mean square error (RMSE) = 79 dd for growth duration and RMSE = 0.03 dd-1 for growth rate. It was identical for the two harvest dates

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Discussion

In Miscanthus, the use of the Akaike criterion, the mean square error and a graphical analysis of residuals led us to choose (i) the Gompertz function as the most efficient for describing the emergence data, and (ii) the 4-parameter logistic function as the best for describing canopy height growth. We have also shown the effects of clone and year on the different variables estimated by these functions, and also the interactions with the clone factor, the most important of these being clone × year. The clone effect was quite strong due to species and then, to a lesser extent, to ploidy level; the species × year effect strongly partitioned the clone × year interaction.

Which Functions for which Trait?

No previous study has been published that compares functions to describe aboveground growth in Miscanthus. On one hand, Miguez et al. [19] used the logistic curve to describe Miscanthus yield trends over the course of its growth cycle, but did not justify their choice. Robert et al. [29] compared the Gompertz, Weibull, and 3- and 4-parameter logistic functions for studying varieties of winter wheat for grain-filling dry matter as a function of time. They concluded that the 3-parameter logistic curve was best, based on the AIC criterion and analysis of residuals as an indicator of the quality and performance of the models. Khamis et al. [20] reached the same conclusion when comparing 12 models on palm-oil yield dynamics over the years following planting. On the other hand, Mohanty et al. [30] considered that rice emergence was best represented by a Gompertz function, based on an assessment of the fit with the root mean square error (RMSE). In accordance with all these studies, our results confirm the superiority of the logistic function for studying Miscanthus plant growth over time, and the superiority of the Gompertz function to analyse crop-emergence dynamics.

The convergence problems that arose particularly with the Gompertz function and the 3-parameter logistic function for growth dynamics may be due to the shape of the curves. The 4-parameter logistic function considers a period during which plant height varies little, followed by an acceleration of growth. The Gompertz and 3-parameter logistic functions, which have no lower asymptote, do not represent this phenomenon very well [31].

Species Comparisons for their Growth Dynamics

While the literature describes relatively well biomass production during the growth cycle of M. x giganteus [19, 21, 32], little is known about its genotypic variability. Riche et al. [33] compared the biomass output of four M. x giganteus clones, one M. sacchariflorus clone, five M. sinensis clones and five hybrids of M. sinensis over 11 consecutive growth cycles in England, but they did not compare the growth dynamics during the plants' annual cycle. Fifteen clones have also shown variability in plant height at maturity during the third year of the crop in five European sites [21] but there were no dynamic measurements taken during the growth period. Jorgensen et al. [34] showed the height growth dynamics of the same clones as above, in Denmark, but the comparisons of the clones corresponded only to the end of the growth period.

By studying the growth during two annual growth cycles, our study revealed that genotypic differences observed in plant height at maturity are due, at least partly, to difference in emergence date and growth rate (Fig. 4).

Effects of Clone, Year, and Harvest Date

Clone differences in emergence date, growth rate, and growth durations could be due to differences in the base temperatures for each clone. Farrell et al. [10] revealed differences in base temperatures between four Miscanthus clones of three species. M. x giganteus and M. sacchariflorus (Gig2 and H5) had a base temperature of 8.5 °C, which is equivalent to an hybrid between two M. sinensis (H9) but which is significantly higher than the 6 °C base temperature of a hybrid selected from a population of M. sinensis (H6). In our study, we assigned an identical base temperature for all the clones, of around 6.8 °C during the active growth phase (close to the base temperature observed in H6 [10]). These differences in base temperature could lead to a 1.7 °C difference in daily cumulative temperature, which would add up to a 150 dd overestimation in M. x giganteus and M. sacchariflorus for the emergence period of February–March–April, and a 300 dd overestimation for the active growth period from April to September. However, this should be nuanced, as final-height differences between clones were strongly correlated with yield differences (data published in [15]).

M. sinensis clones had a slower growth rate during the third year of growth than during the second year, which might be due the higher sensitivity to water stress of this species compared to M. x giganteus and M. sacchariflorus. In the third year of growth, the plants had to cope with water stress from late July onwards, whereas no water stress occurred during the second year. M. sinensis is known to close its stomata more quickly when it lacks water in order to limit evapotranspiration [35], which increases its tolerance to water stress. In counterpart, this response could also slow its growth by reducing photosynthesis.

Further, the behaviour differences between clones varied between the second and third years after an autumn harvest, but not after a winter harvest: we found no significant differences in growth duration in the second year, but in the third year it was significantly longer with autumn harvest (22 %) than with winter harvest. Yet emergence dates were virtually identical for the two harvests, in both years (Fig. 2). It might be due to the fact that the winter harvest micro-plots flowered (or their panicles emerged) earlier than with an autumn harvest, particularly with M. sinensis [15].

Options for Genetic Improvement

The inter-species hybrid between M. sinensis and M. sacchariflorus (clone H8), which is of medium height, suggests an ideotype for genetic improvement. A high final plant height (Hmax) combined with a rapid growth rate and late emergence date could be the criteria for selecting most biomass productive plants at an early stage. The clones which associated late emergence dates, fastest growth, and tallest plants were mainly clones of M. floridulus, and of the M. x giganteus inter-species hybrid. This hybrid is actually the main source currently used for biomass production.

Nevertheless, the canopy height variable might be preferable to early emergence and growth rate, because it is by far the easiest to estimate. However, Hmax varied widely within the M. sinensis species, but not so much within M. x giganteus. These results are in accordance with Clifton-Brown et al. [21], who demonstrated the low variability in aboveground development (number of stems and plant height at end of growth period) among four clones of M. x giganteus. Vonwuhlisch et al. [5] and Hodkinson et al. [6], using isozymes, showed that M. x giganteus has a low genetic variability, suggesting that there is little room for genetic improvement in this species. Creating new hybrids would therefore be a significant breeding avenue to explore. It would increase genetic variability for traits of interest such as final plant or canopy height, while making use of the variability found within the species M. sinensis, as demonstrated from the small sample of 15 clones tested in our study.

In the M. floridulus species, some native clones appeared as highly productive in Chinese conditions [36]. Nevertheless, using 328 AFLP markers to measure the genetic similarity between our 21 clones, we found that the clone of M. floridulus that we studied was genetically close to M. x giganteus [22]. Therefore, this clone might be a hidden cv Floridulus from the M. x giganteus species. It appears that M. floridulus needs more investigation to be considered as a genetic improvement option for European conditions.

Conclusion

Our study has shown that Miscanthus vary in their emergence dates and growth dynamics as estimated by the Gompertz and 4-parameter logistic functions, respectively. We have also found that to obtain greater aboveground development, it would be useful to combine a late emergence date, a short duration of growth and a high growth rate. It seems that genetic improvement to increase aboveground biomass yield in Miscanthus should therefore focus on increasing the growth rate rather than increasing the duration of the growth cycle. This study also arose some perspectives to improve seasonal management of Miscanthus crops, as winter harvests cause growth to stop quicker than autumn harvests, especially in M sinensis.

Earlier studies had shown a strong correlation between plant height and aboveground biomass [15, 21]. To find new selection criteria for the genetic improvement of Miscanthus, it might be useful to study the relationship between aboveground biomass and the emergence and growth parameters estimated in our study [15]. Some of those traits might also be useful when studying the effect of stress, such as water deficit and nitrogen limitation. Other criteria might also be worth considering such as stem numbers and earliness of flowering (or earliness of panicle emergence). After that, a focus on the heritability of the most relevant traits would provide insights on existing possibilities for genetic improvement at the intra-species level.