We next used our morphological development time series data to demonstrate how growth stage progression can be determined using two metrics: cumulative abundance of a stage and development rates between stages. For the former, we followed and recommend the method developed by Schirone et al. (1991) to estimate onset duration and abundance of morphological growth stages. Cumulative abundance is calculated as the number of stems that have passed a defined developmental threshold, and presents abundance as a proportion of the total stems measured. At each sampling date, the cumulative abundance of a considered stage is estimated as the number of stems at the threshold stage or higher, divided by the sample size. When graphed, this temporal series describes a sigmoid curve, which can be modeled with a logistic function. The onset date is estimated by modeling a curve through the measured data points, then identifying the point in time at which the frequency of individuals at the threshold stage equals 50%. Onset dates for each secondary growth stage should be calculated separately within each principal growth stage to elucidate overlapping M. × giganteus stages.

Principal growth stage development rate (PGSDR) was calculated as the rate of appearance of new secondary stages over time. This rate specifies the time required to develop morphologic structures (e.g., leaves, nodes). If the relationship of development to time is linear, PGSDR is the slope of the linear regression between secondary growth stage progression and time. In case of a non-constant rate during the growing season, multiple linear regressions for multiple constant rates or non-linear models can be used. In the latter case, the derivate of the function may be more informative.

In principal growth stage 1, PGSDR corresponds to leaf appearance rate and its inverse is equivalent to the phyllochron, or accumulated time (in days or thermal time) required for the appearance of successive leaves on a stem (Xue et al., 2004). Leaf appearance rate and phyllochron have direct application to crop modeling, crop management, assessment of abiotic stress, and cultivar selection.

Leaf duration, defined as the time between leaf emergence and senescence, is another important parameter in plant phenology, crop management and modeling. When principal growth stage senescence is described in terms of number of senesced leaves and secondary growth stages attributed in the same mode as in leaf development (one every two senesced leaves), leaf duration can be estimated as the difference in onset dates for same secondary growth stage between principal growth stage 1 and 9.

We used our explanatory data set to demonstrate calculation of leaf appearance rate and phyllochron as a function of both calendar days and thermal time. Thermal time was measured in growing degree days (GDD, °C day) as: GDD= [Tmax- Tmin2]- Tb Where T_max and T_min are daily maximum and minimum air temperature, respectively, and T_b is the base temperature below which development does not occur. We used 6°C as the base temperature for leaf expansion (Farrell et al., 2006) and considered [(T_max − T_min)/2] = T_b when [(T_max − T_min)/2] < 0 [see McMaster and Wilhelm, 1997, for further detail on the importance of clarifying how to deal with [(T_max − T_min)/2] < 0]. Cumulative degree days were calculated as the sum of daily GDD across the growing season.

For a complete and concise description of principal growth stage progression, the cumulative thermal time should be reported for each principal stage. This could be calculated as the difference between first and last secondary growth stage onset dates. Also, using the development rate approach, it can be estimated as the difference between time at the last secondary growth stage and the first one. This approach has the advantage that it allows estimation of the beginning of the principal growth stage as the root of the describing polynomial.

Summary statistics allow the scaling of stem-based observations to the field or population level. The method presented here has been modified from Kalu and Fick (1981) and Moore et al. (1991). Since M. × giganteus may have multiple principal growth stages running in parallel, summary statistics can be calculated separately for each stage (Equations 1, 2). Based on a sample of N stems, the average morphological stage at growth stage i (BBCH¯i) is calculated as: (1)BBCH¯i=∑j = 1NBBCHijN Where BBCH_ij represents the BBCH code for the jth stem in the ith principal growth stage. Essentially, BBCH¯i estimates the average BBCH code for each individual principal stage. The complete developmental stage (BBCH_complete) would be presented as all the average codes for each stage separated by oblique strokes. Alternatively, if users stop tracking one stage once the next begins, the complete code is the two digit code associated with most developed stage.

The variability across samples is determined for each principal growth stage individually as the standard deviation for principal growth stage i (S_BBCHi), calculated as:

S_BBCHi is useful to estimate the variability that exists within an M. × giganteus stand at each principal growth stage and help to compare the progression of each stage. A small S_BBCHi indicates the majority of stems are at similar level of progression within a given principal growth stage, while a large S_BBCHi indicates that there is a wide range of maturity within a growth stage.

Stage 0 describes plant development beginning with rhizome buds. It is also applicable to axillary buds growing from aerial stems, which have also been proposed as propagules (Boersma and Heaton, 2014), as in sugarcane. Rhizome bud development goes from beginning of bud swelling (stage 01) through emergence when leaves break through the soil surface (stage 09). Bud swelling ends (stage 03, Figure 1) as buds break (stage 05), the first true leaves elongate past protective bud scales (Figure 1), and leaf laminae grow toward the soil surface (Table 2). In the establishment year, bud development typically begins in late spring, depending on planting date and weather conditions. In older stands, stem emergence typically begins when soil temperatures are consistently above 10°C or cumulative degree days above 0°C are higher than 650 (Hastings et al., 2009).

This principal stage is based on the total number of leaves present on the stem and does not differentiate between green or senesced leaves. Observers can choose to assess only green leaves or include senesced leaves, depending on their goals. The proportion of senesced leaves present at a given point is presented in stage 9, senescence. New leaves are not counted until fully expanded as indicated by a visible ligule. New leaves continue to emerge until the stem fully flowers and senesces, or is winter-killed. M. × giganteus typically has less than 20 leaves on a stem; therefore, we suggest here that secondary stages advance by every two leaves (Table 2). For example, a stem with two fully expanded leaves would be at growth stage 11, where the principal growth stage 1 (leaf development) is given in the tens place and the secondary growth stage is given in the ones place as 2 leaves/2 = 1. Similarly, a stem with 8 leaves would be at growth stage 14 (Figure 1). Should a stem have 15 leaves, a mesostage can be added using a decimal point, and the stem would be at growth stage 17.5. Although uncommon, especially if only following green leaves, stems that produce more than 19 leaves would be staged as 19.5, the maximal value for this growth stage.

Because this scale is applied to individual stems coming from a belowground rhizome network, tillering in this sense refers to new stems developed from axillary buds on the monitored stem. M. × giganteus stems are unbranched and rarely produce tillers, however, some swollen axillary buds could appear on the base of the stem, especially if the stem is damaged (e.g., from hail or herbivory). Rarely, these buds will produce new stems and it is even more seldom that these stems will reach the canopy level. Secondary stages in this case correspond to the number of tillers produced per stem. The norm is no tillers on a stem (stage: 20) though infrequently one or two tillers may be present (stage 21 or 22).

Presence of swollen buds could be recorded within this principal growth stage since it could have impacts on phenology and plant physiology. These stages would be included as decimal points; 20.1: presence of partially swollen axillary bud (~2 mm), 20.5: axillary bud fully swollen (~8–1.0 mm, Figure 1), 20.9: Bud breaking. Finally, in the case of tillering, the scale continues to be applied to the main stem (Table 2).

In M. × giganteus, stem elongation occurs soon after emergence and continues until the culm flowers or is winter-killed. This stage is of prime importance since it tracks the development of the principal harvestable structure. Stem elongation is addressed by counting the number of aboveground palpable nodes present on the stem, that is, the number of nodes that can be felt by gently pressing along the stem. We suggest that, as in leaves, secondary stages progress every two nodes (Table 2). For example, a stem with eight fully expanded leaves and four palpable nodes would be coded as 14/32 (Figure 1), indicating 4 ^* 2 = 8 leaves in principal growth stage 1 (leaf development) and 2 ^* 2 = 4 palpable nodes in principal growth stage 3 (stem elongation). If more detail is needed, odd number of nodes could be coded as mesostages using the tenths place. For example, if a stem has seven nodes it should be staged as 33.5, indicating 3 ^* 2 = 6 nodes and 0.5 indicating the presence of another node (giving a total of seven nodes). As in leaf development, stems with more than 19 nodes (biologically rare, Uwatoko et al., 2016) will all be staged as 39.5.

This principal stage refers to the progression of the inflorescence through the appearance of the flag leaf sheath. It starts when flag leaf is visible but lamina still rolled (stage 40). Stage 41 occurs when the flag leaf is fully expanded (Figure 1), indicating the end of leaf development. Booting ends when the inflorescence fills the entire flag leaf sheath and no florets are yet exposed (stage 49). Intermediate secondary stages distinguish the proportion of the sheath occupied by the inflorescence. Since this could be hard to identify and track we recommend using generic landmarks and assigning them in 25% increments. In consequence, only three secondary growth stages are required to allocate these morphological changes evenly: 43, 45, and 47 (Table 2, Figure 1). For instance, stage 43 occurs when the inflorescence fills 25% of the sheath, stage 45 when the inflorescence occupies 50% and so on. First florets may not appear through the collar of the flag leaf and may grow instead through the sheath. In this case the stem will still be staged as 49.

The M. × giganteus inflorescence is a panicle of racemose branches with paired and pedicellate spikelets (Hodkinson and Renvoize, 2001). This stage starts with upper spikelets coming out of the flag leaf collar (stage 51) and ends once the panicle is fully exposed and the peduncle is visible (stage 59). In general terms, secondary stages could be characterized by: upper branch exposure (borne on the upper half of the main axis, stage 53), lower branch exposure (borne on the lower half of the main axis lower branches, stage 56, Figure 1) and peduncle exposure (stage 59, Table 2, Figure 1). If more detail is required, secondary growth stages could be expressed as the exposed percentage of the panicle. This requires a trained observer to estimate the relative proportion of a partially exposed panicle. Note that stage 59 may not occur in environments where the growing season is not long enough or hard frost events are frequent in middle to late fall. In this case inflorescence emergence may stop before the panicle is fully exposed. Exposed florets may continue to open.

This stage is defined as the proportion of exposed florets with emerged anthers. It starts with sporadic exposed anthers (stage 60) until full flowering (stage 69) when anthers are present throughout the entire inflorescence; secondary stages are attributed in 10 percent increments (e.g., stage 65: 50% of anthers are exposed, Table 2, Figure 1). Flowering proceeds basipetally through the inflorescence. Anther exposure can occur while the inflorescence is still emerging and, consequently, the inflorescence could fully flower even though the inflorescence is not fully exposed.

M. × giganteus is a sterile clone and no seed is produced so flowering represents the last reproductive stage. In order to expand the scope of this scale to other varieties and Miscanthus spp., grain maturity stages were included. These stages were based on general grass descriptions from Meier (2001) as adapted to perennial grasses (e.g., P. virgatum) by Sanderson et al. (1997).

At the beginning of seed development (stage 71) the total number of cells in the endosperm is established and grains have a watery ripe consistency; first grains may have reached half their final size. Gradually, seeds increase solid (e.g., starch, protein) concentrations and reach their final size at medium milk stage (75). Seed development ends at late milk stage (77).

Most of the seed dry weight is accumulated during the ripening stage. Along with the continued increment in starch and protein concentration, water content decreases, increasing grain hardness. Secondary stages are characterized by pressing the grain with a fingernail. Stage 83 is when grain content is soft and the fingernail impression is not held; 85 is when a fingernail impression remains after the test. Stage 87 represents when the grain is hard and difficult to break with a thumbnail and finally stage 89 is when the grain cannot be dented.

This stage describes the senescence progression of the stem during a growing season and it is based on leaf senescence without differentiating between possible causes, e.g., stress or seasonal cues. In order to provide a better approach for comparative purposes it should be reported as the proportion of the total number of leaves present at any given point. A leaf is consider senesced once 50% or more of the laminae has senesced. For simplicity, it could also be quantified as a visual estimate of the senesced proportion of the entire plant. For instance, a plant with five senesced leaves out of a total of 25 could be considered 20% senesced and coded as 92 (Figure 1). Stages 91–99 represent the progressive senescence of leaves on the stem, from 10 to 90%, respectively, at 10% increments (Table 2, Figure 1). This stage could start very early in the growing season once the stand reaches canopy closure and low light quality triggers senescence in lower canopy leaves.

In 2016, morphological development was observed biweekly in 2-year-old M. × giganteus. Data were used to illustrate the steps required to estimate progression of morphological development stages using the cumulative abundance of a given stage (Table 3). For example on July 11 there were four stems at stage 15 or higher (2 at 15 and 2 at 15.5) and 0 stems at stage 18. By September 6 all sampled stems were at stage 15 or higher, and seven were at stage 18 or higher (4 at 18, 2 at 18.5 and 1 at 19). Note that abundance is expressed as a proportion and thus is not dependent on equal sample sizes between dates. Graphing cumulative abundance of growth stages 15 and 18 over time produced sigmoid curves that were used to derive the onset date of each stage (Figure 2). The onset date of stage 15 was July 13 (5282 GDD) and the onset date of stage 18 was August 19 (7963 GDD).

We also estimated PGSDR for principal growth stage 1 (leaf development; PGSDR₁) and 3 (stem elongation; PGSDR₃) as the slope of the linear regression between average principal growth stage per sampling date and thermal time in GDD (Figure 3). For example, PGSDR₁ = 0.00094 means that almost a thousandth of a secondary growth stage is developed per GDD. Its inverse (1053) represents the number of GDD required to complete a secondary growth stage. Given that secondary growth stages advance every two leaves, leaf appearance rate is double PGSDR₁ (0.00188 leaf GDD⁻¹) and the phyllochron is half of PGSDR₁ (526.5 GDD leaf ⁻¹).

The M. × giganteus morphological development data collected over the 2016 growing season was also used to demonstrate the calculation of the average and standard deviation of principal growth stages 1 and 3 (Table 4).