## RGR factorization

We applied a two-component factorization of RGR in aboveground biomass at the community scale,

$$RGR=NP x \left[N\right]$$

1

where RGR is relative growth rate, the rate of change in aboveground biomass over the growth interval per unit of biomass (g biomass/g biomass/d), NP is N productivity, the rate of change in aboveground plant biomass divided by the mean value of plant N content (g biomass/g N/d; Ingestad 1979), and [N] is plant N concentration expressed as the ratio of aboveground plant N content per unit of area to aboveground biomass per unit of area (g N/g biomass). NP is a component of nitrogen use efficiency, the latter defined as the product of NP and the mean residence time of plant N (Hirose 2011). Mean values of RGR and its N components were calculated over each growth interval as follows (Hunt 1982):

$$RGR=\text{ln}(b2-\text{ln}b1)/(t2-t1)$$

2

$$NP=\left[\left(\frac{b2-b1}{t2-t1}\right)x \right((\text{ln}N2-\text{ln}N1)/(N2-N1\left)\right)]$$

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$$\left[N\right]=(\frac{N2}{b2}+\frac{N1}{b1})/2]$$

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where b, N, and t are aboveground biomass (g/m2), aboveground N content (g/m2), and time in days (d), respectively, for final (2) and initial (1) measurement dates. RGR derived as the product of NP and mean [N] will not equate exactly to calculated values of mean RGR (Hunt 1982) but the correlation in data we analyzed was > 0.99.

Links between RGR and its N components also were investigated using ‘scaling relationships’ derived from an additive factorization of RGR (Wright and Westoby 2001), where:

$$\text{log}RGR=\text{log}NP+\text{log}\left[N\right]$$

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Slopes of log-log relationships between RGR and each of its components indicate the proportionality in change between variables. The anticipated value of ‘scaling slopes’ is 1.0, such that RGR changes in direct proportion to change in NP or [N]. Negative correlation between NP and [N] will reduce values of ‘scaling slopes’ between RGR and NP or [N] to < 1.0 and thereby reduce the fractional change in RGR per unit of change in NP or [N].

## Site

RGR and its N components were estimated during spring for mixture and switchgrass communities located at Temple, Texas, USA (31◦10′ N, 97◦34′ W) (Long-term Biomass Experiment; LTBE). Eight randomly selected stands in a former agricultural field were planted with a seed mixture containing 38 native perennial forb and grass species (Polley et al. 2020a). Remaining stands (16) were planted to a monoculture of switchgrass (cultivar Alamo). Stands were planted 6 years prior to measurements (2010). Each was 17 m wide and 137–218 m long (0.26–0.37 ha). Annual precipitation averages 905 mm (50 years record) with peaks in spring and autumn. Monthly maximum temperatures vary between 15.3 and 35.4 ◦C in January and August, respectively. LTBE contributes to the USDA Long-Term Agroecosystem Research (LTAR) network (https://ltar.ars.usda.gov/).

We calculated RGR and its N components at the spatial scale of a 7-m diameter circular patch. Thirteen patches were permanently located along the length of each mixture stand and in switchgrass stands located immediately to the south of each mixture (n = 8 stands), resulting in 104 patches per community. Mixture and switchgrass communities are not grazed or fertilized. Both communities are hayed following each growing season and both include not-seeded native and exotic species that are considered ‘invaders’. Prominent invaders of mixture communities include annual grass and forb species that complete growth during spring. Included are the grass *Bromus japonicus* Thunb. ex Murray (Japanese brome) and forb *Gaillardia pulchella* Foug (Indian blanket). Prominent invaders in switchgrass include two exotic C4 perennial grasses, *Panicum coloratum* L. (Klein grass) and *Sorghum halepense* (L.) Pers. (Johnson grass). Annual grasses and forbs are locally abundant where switchgrass failed to establish.

**Field measurements, variable calculation, and statistics**

RGR, NP, and [N] were estimated using measurements of canopy reflectance on two dates during spring (late March-April) separated by 14–38 d in each of 5 years (2016 − 2019, 2021). Aboveground biomass reaches its spring peak in late April in mixture (Polley, Collins and Fay 2020). We measured reflectance from a rotary-wing, unmanned aerial vehicle (UAV; S1000; DJI; Shenzhen, China) using an ASD HandHeld2 spectroradiometer (spectral range of 350–1050 nm; ASD Inc., Boulder, CO, USA). We flew the GPS-guided UAV to a stationary position at 15.8 m height (25⁰ field of view) above each patch prior to each measurement. Three consecutive measurements of reflectance per patch were averaged for each sample. We measured reflectance within 2 h of solar noon on cloudless days and referenced measurements to a Spectralon® white reference panel at ~ 15-min intervals. Reflectance was calculated by dividing radiance reflected from the plant canopy by radiance incident on the canopy. We considered incident radiation to be the radiant flux reflected from a Spectralon® white reference panel exposed to full sunlight.

Aboveground biomass per patch (g/m2) for each sample date was calculated as an exponential function of the enhanced vegetation index (EVI) (adj. r2 = 0.83, P < 0.0001; Polley et al. 2020b).

$$EVI=G x \left(\frac{NIR-Red}{NIR+C1 x Red-C2 xB lue+L}\right)$$

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where NIR, red, and blue are reflectance in near-infrared, red, and blue wavelengths, respectively, L is an adjustment for canopy background, G is a gain factor, and coefficients C1 and C2 correct for the influence of aerosols (L = 1, C1 = 6, C2 = 7.5, G = 2.5).

Community N content (g N/m2) per patch was estimated using a linear regression fit to the relationship between observed values of aboveground N content and the red edge chlorophyll index (CIred edge), where CIred edge was calculated by subtracting 1 from the ratio of reflectance in the NIR (840 nm) to reflectance in a waveband in the red edge of the spectrum (717 nm) (Gitelson et al. 2005; Li et al. 2012). The N content-CIred edge regression was developed from ground-level ‘calibration’ measurements of aboveground N content and reflectance. Calibration data were collected across a series of 30-cm diameter rings (n = 61) positioned in mixture and switchgrass communities to span a wide range in aboveground N content. Reflectance was measured using an ASD HandHeld2 spectroradiometer. Vegetation then was harvested to 5 cm height, dried (65 C), and weighed. Samples of dried plant material from each ring were analyzed for [N] using inductively coupled plasma atomic emission spectroscopy (Isaac and Johnson 1998). Aboveground N content (g N/ m2) per ring was calculated by multiplying biomass/m2 by [N] (g N/g biomass). Linear regression explained 80% of the variance in community N content in calibration data (Supplementary Fig. 1).

We used this regression model to estimate N content at the patch scale (7-m diameter). Regression consistency in predicting N content across spatial scales was evaluated by comparing N content calculated using patch-scale reflectance to the average value of N content calculated using ground-level measurements of reflectance from eight 76-cm diameter plots randomly located in each of 16 patches. The slope of a linear regression between patch N content and the mean N content of plots per patch that was fit through the origin (Supplementary Fig. 2) did not differ significantly from 1 (t15 = -1.50, P > 0.10). The regression model thus adequately predicted patch-scale N content using measurements collected at smaller spatial scale.

We used linear regression to calculate log-log scaling slopes between community RGR and its N components and to assess relationships between spatial variation in RGR in each community and year and the unique (independent) effects of each of its N components. RGR was regressed on residuals from a regression of community NP on community [N] (statistically independent effects of NP) and residuals from a regression of community [N] on community NP (independent effects of [N]). Results of simple bivariate regression of RGR on each of its N components are influenced by shared contributions of the two N components to RGR. Correlation between community NP and [N] was assessed using Pearson correlation.

Precipitation effects on NP-[N] correlation coefficients and community N were investigated by regressing mean values of Pearson correlation coefficients and community N per year on precipitation summed over the 120-day period prior to RGR measurement each year. Precipitation sums were calculated for all possible time intervals with a minimum duration of 15 days (e.g., 31–45 days) and maximum duration of 120 days (e.g., 1-120 days) each year. The precipitation value that exhibited strongest correlation (highest r2 value) with each dependent parameter was selected. Regressions were fit using SAS 9.4.