# Non-destructive biomass estimation of herbaceous plant individuals: A transferable method between contrasted environments

Julien Pottier, Franck Jabot

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Julien Pottier, Franck Jabot. Non-destructive biomass estimation of herbaceous plant individuals: A transferable method between contrasted environments. Ecological Indicators, 2017, 72, pp.769 - 776. 10.1016/j.ecolind.2016.08.030. hal-01521547

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<figure><img src="image_1.png" /></figure>
1 **Title : Non-destructive biomass estimation of herbaceous plant individuals: a**

2 **transferable method between contrasted environments.**

3

4 **Author list: Julien Pottier and Franck Jabot**

5 Pottier, J. (Corresponding author, julien.pottier@clermont.inra.fr)¹

6 Jabot, F. (franck.jabot@irstea.fr)²

7 ¹INRA, UR874 (Unité de Recherche sur l’Ecosystème Prairial), 5 chemin de Beaulieu, F-

8 63039 Clermont-Ferrand, France.

9 ²Irstea, UR LISC, Centre de Clermont-Ferrand, F-63178 Aubiere, France.

10

11
12 **Abstract**

Monitoring plant growth at the individual level in arrays of environmental conditions is key to
understanding plant functioning with strong implications for ecophysiology, population
biology and community ecology. This requires non-destructive methods for repeated
estimates of individual plant biomass in time. Although allometric equations have been
widely used for trees and shrubs, there is currently no general approach for herbaceous
species that can be applied across habitats, plant architecture, life stage and leading to
transferable equations between contrasted environments. Here we propose a method based on
three biometric measurements of the minimum volume occupied by aboveground plant
organs. A total of 36 equations were fitted and compared for twelve species of temperate
grasslands, corresponding to various volume shapes, scaling functions (linear or power) and
including (or not) a life stage effect. The accuracy of the selected equations was compared to
similar attempts reported in the literature. We further assessed the across-site transferability of
the best allometric equations. The goodness-of-fit of the best equations selected for each
species was high (R² = 0.83). The type of selected equations was species-specific,
emphasising the benefits of considering a wide range of plant volume shapes and both linear
and power functions. Using a comprehensive assessment of allometric equation
transferability, we found that site effects could be neglected for eleven out of twelve species.
Biomass equations based on the minimum volume proved accurate. The proposed method is
easy to implement in any type of habitat, copes with various plant architectures and reduces
risks of error measurement compared to previously developed approaches. The method
further allows, for the first time, to use a single equation for monitoring the growth trajectory
of herbaceous plant individuals in contrasted environments.

**Keywords:** Grasslands; allometry; canopy volume; individual-based monitoring; plant biomass; growth trajectory.
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# 1. Introduction

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Monitoring plant growth in arrays of environmental conditions is critical for understanding plant functioning with strong implications for ecophysiology, population biology and community ecology. Tree growth monitoring is naturally performed at the individual level (Peacock *et al.* 2007), and refined allometric models have been developed to deduce tree and shrub biomass from non-destructive biometric measurements (Henry *et al.* 2013; Chave *et al.* 2014; Zhang *et al.* 2016). In contrast, the growth monitoring of herbaceous plants has been mostly performed at the population (Hooper *et al.* 2005) or community levels (Sala *et al.* 1988). Consequently, non-destructive methods of herbaceous plant biomass estimation have been mainly developed at these organization levels (Catchpole & Wheelert 1992; Harmoney *et al.* 1997; Brathen & Hagberg 2004; Barkaoui *et al.* 2013).

This focus of plant ecologists on population and community levels for herbaceous plants can be explained by the huge number of herbaceous individuals, even in small-sized monitoring plots, and by the uncertainty surrounding the definition of herbaceous individuals due to the varying levels of physiological integration between plant ramets (Harper 1977). Still, clearer understanding of herbaceous plant demographical processes requires conducting studies at the individual level because plant responses to abiotic factors and plant-plant interactions are processes operating at the level of plant individuals (Damgaard *et al.* 2002; Purves & Law 2002; Kraft *et al.* 2015).

The dynamics of individual plant biomass has traditionally been assessed through destructive sampling of replicates (e.g. Shipley & Meziane 2002). This approach has several drawbacks. First, it is time consuming and costly, which represents a strong limitation for collecting data of suitable frequency and/or number of replicates. Second, and most importantly, such a destructive method does not allow the monitoring of growth trajectories of single individuals
but rather average trajectories of populations of individuals. Non-destructive methods are
therefore required for repeated estimates of individual plant biomass in time.

A review of the literature (appendix A, see methods) reveals 15 studies that have developed
non-destructive methods for individual herbs. These studies generally rely on the use of
allometric equations relating various biometric plant measures to individual biomass (but see
Tackenberg 2007). The most widely used biometric measure is plant height (e.g. Guevara et
al. 2002), but other measures have also been used in isolation or in combination with plant
height, including plant cover (Röttgermann et al. 2000), basal area (Guevara et al. 2002),
canopy width (Assaeed 1997), or various volume formulations (Johnson et al. 1988;
Damgaard et al. 2002). These studies report overall good fits of allometric equations ($R^2$ =
$0.82 \pm 0.12$). However, the universality of this approach remains to be evaluated for
herbaceous species since i) mostly (semi-)arid or artificial systems (i.e. pot experiments like
Damgaard et al. 2002) have been considered in which plant individuals are strongly spatially
segregated; ii) the dependence of allometric relationships on environmental conditions and
plant life stages have not been thoroughly investigated, so that the transferability of calibrated
allometric equations across study sites is to be demonstrated and iii) the influence of plant
architecture on the usefulness of the different biometric measures remains poorly
documented.

Here, we calibrate a set of allometric equations for estimating the biomass of individual plants
for twelve typical species of temperate grasslands of various architectural types and sizes. Our
primary objective is to compare alternative allometric equations regarding their across sites
transferability. We also compare the gain in accuracy associated with the use of three
biometric measurements (instead of simply one or two), and with the inclusion of
phenological stage and site effects in the allometric equations. To do so, a set of allometric
equations were calibrated using destructive samples collected in contrasted environments.
Before destruction the samples were first measured according to three biometric measurements: plant height, basal and mid-height circumferences (Fig. 1). Based on the reported results, we provide some guidelines for optimising the predictive accuracy and transferability of the proposed non-destructive method of biomass estimation of herbaceous plant individuals.

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**Figure 1** The biometric measurements being considered. The apparent volume (left panel) is difficult to estimate accurately because the spatial arrangement of organs of herbaceous species, especially leaves, strongly depends on external factors. The minimum volume (right panel) corresponds to the volume that an individual plant occupies when all aboveground organs are joined together and uncoiled along the plant longitudinal axis. We consider height, basal circumference and circumference at mid height to estimate the minimum volume (see Table 3 for formulations).

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## 2. Material and Methods

### 2.1. *Literature review*

A search was conducted in ISI® Web of Science with the timespan 1950 to 2015 using the keywords "non-destructive" AND "biomass" AND "plants". This resulted in 430 references.

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Articles focusing on trees, shrubs and aquatic species were excluded. Finally, we considered only the minority of studies, and associated references, estimating biomass of plant individuals and not stand or population levels in open habitats. This evaluation resulted in a set of 15 references reporting allometric equations for a total of 76 species. These studies were either located in arid habitats or were pot experiments (Appendix A).

## 2.2. Site and species characteristics

We selected twelve species that are typical of temperate grasslands of Western Europe: six grass species (*Dactylis glomerata*, *Arrhenaterum elatius*, *Poa pratensis*, *Agrostis capillaris*, *Elymus repens*, *Lolium perenne*), four forbs (*Plantago lanceolata*, *Taraxacum officinale*, *Achillea millefolium*, *Veronica chamaedrys*) and two legumes (*Trifolium pratensis*, *Lotus corniculatus*). The selection of species was based on their plant traits and aimed at testing our method over a large variety of plant growth strategy and morphology (Table 1). We thus considered fast growing exploitative species like *Arrhenatherum elatius*, slower growing and more conservative species like *Achillea millefolium* and species of various canopy architecture and size. Indeed, we sampled all shoot growth forms, types of leaf distribution, and a large proportion of the plant height distribution referenced in the LEBA trait database for herbaceous plants (Kleyer *et al.* 2008; Appendix B).

<table><thead><tr><th>Species</th><th>Height (mm)</th><th>LDMC (mg/g)</th><th>SLA (mm²/mg)</th><th>SeedMass (mg)</th><th>Leaf distribution</th><th>Shoot growth form</th></tr></thead><tbody><tr><td>Achillea millefolium</td><td>472</td><td>194.4</td><td>12.02</td><td>0.132</td><td>Semi-rosette</td><td>Stem erect</td></tr><tr><td>Agrostis capillaris</td><td>669</td><td>266.3</td><td>31.28</td><td>0.064</td><td>Regular distribution along the stem</td><td>Stem ascending to prostrate</td></tr><tr><td>Arrhenatherum elatius</td><td>1177</td><td>255.1</td><td>29.18</td><td>3.079</td><td>Semi-rosette</td><td>Stem erect</td></tr><tr><td>Dactylis glomerata</td><td>1075</td><td>258.8</td><td>22.80</td><td>0.911</td><td>Regular distribution along the stem</td><td>Stem erect</td></tr><tr><td>Elymus repens</td><td>746</td><td>273.5</td><td>25.08</td><td>2.375</td><td>Regular distribution along the stem</td><td>Stem erect</td></tr><tr><td>Lolium perenne</td><td>801</td><td>207.7</td><td>24.68</td><td>1.975</td><td>Semi-rosette</td><td>Stem erect</td></tr><tr><td>Lotus corniculatus</td><td>286</td><td>206.0</td><td>27.67</td><td>1.403</td><td>Regular distribution along the stem</td><td>Stem ascending to prostrate</td></tr><tr><td>Plantago lanceolata</td><td>567</td><td>181.5</td><td>17.32</td><td>1.617</td><td>Rosette</td><td>Stem erect</td></tr><tr><td>Poa pratensis</td><td>608</td><td>288.0</td><td>16.25</td><td>0.273</td><td>Semi-rosette</td><td>Stem ascending to prostrate</td></tr><tr><td>Taraxacum officinale</td><td>489</td><td>159.7</td><td>23.40</td><td>0.532</td><td>Rosette</td><td>Stem erect</td></tr><tr><td>Trifolium pratense</td><td>667</td><td>205.0</td><td>23.33</td><td>1.581</td><td>Regular distribution along the stem</td><td>Stem erect</td></tr><tr><td>Veronica chamaedrys</td><td>250</td><td>312.1</td><td>20.39</td><td>0.206</td><td>Regular distribution along the stem</td><td>Stem ascending to prostrate</td></tr></tbody></table>
124 **Table 1.** Study species characteristics. Trait values are extracted from the LEDA trait database (Kleyer *et al.* 2008).

126 We aimed at calibrating allometric equations that would hold for an array of environments,
127 plant size and phenological stages. To do so, we applied a double sampling procedure on plant
128 individuals collected in contrasted habitats. This procedure involved measuring and
129 harvesting ten individuals in four different sites for each of the twelve species studied
130 (resulting in a total of 40 individuals per species). We selected plants covering a wide range of
131 plant sizes and phenological stages. Since all species were not present at each site, we
132 collected data in a total of 15 sites located in the Sancy massif in Central France with
133 contrasted characteristics in terms of altitude, climate, topography, soil type and agricultural
134 use (Table 2). Field sampling was performed from early June to late July 2015 (Appendix C).
135 Sampling ten individuals of twelve species in four sites resulted in biometric measurements,
136 harvesting and weighing of 480 individual plants.

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<table><thead><tr><th>Sites</th><th>Elevation (m a.s.l)</th><th>Sum DDEG5 (°C)</th><th>Annual precipitation (mm)</th><th>Parent material</th><th>Agricultural use</th></tr></thead><tbody><tr><td>A</td><td>1358</td><td>942</td><td>1000</td><td>Volcanic</td><td>Grazed</td></tr><tr><td>B</td><td>1254</td><td>1051</td><td>964</td><td>Volcanic</td><td>Abandoned</td></tr><tr><td>C</td><td>1454</td><td>840</td><td>1038</td><td>Volcanic</td><td>Mown</td></tr><tr><td>D</td><td>1384</td><td>915</td><td>1012</td><td>Plutonic</td><td>Grazed</td></tr><tr><td>E</td><td>1179</td><td>1134</td><td>934</td><td>Volcanic</td><td>Abandoned</td></tr><tr><td>F</td><td>1088</td><td>1250</td><td>890</td><td>Volcanic</td><td>Mown</td></tr><tr><td>G</td><td>1056</td><td>1283</td><td>881</td><td>Volcanic</td><td>Grazed</td></tr><tr><td>H</td><td>1000</td><td>1350</td><td>859</td><td>Volcanic</td><td>Mown</td></tr><tr><td>I</td><td>1059</td><td>1279</td><td>880</td><td>Volcanic</td><td>Mown</td></tr><tr><td>J</td><td>858</td><td>1552</td><td>791</td><td>Volcanic</td><td>Grazed</td></tr><tr><td>K</td><td>629</td><td>1894</td><td>700</td><td>Marl</td><td>Mown</td></tr><tr><td>L</td><td>730</td><td>1720</td><td>749</td><td>Basalt</td><td>Grazed</td></tr><tr><td>M</td><td>765</td><td>1668</td><td>763</td><td>Basalt</td><td>Grazed</td></tr><tr><td>N</td><td>606</td><td>1929</td><td>691</td><td>Marl</td><td>Mown</td></tr><tr><td>O</td><td>389</td><td>2247</td><td>625</td><td>Marly limestone</td><td>Mown</td></tr></tbody></table>

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## 2.3. Biometric measurements and allometric equations

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**Table 2.** Site characteristics and locations. Temperature and precipitation are derived from 100 m raster maps downscaled from the 1km Worldclim grids (Hijmans et al 2005) following the procedure of Dullinger et al (2012). DDEG5 stands for the annual sum of degree days above 5 °C. Soil data are derived from the European Soil Data Base V2.0 (2004). Agricultural use is deduced from field observations.

In this study, we define an individual plant as a ramet or collection of clumped ramets with the highest degree of physiological integration. Following this definition, an individual of a grass species may be represented by a single tiller or several adjacent and physiologically
149 integrated tillers forming a tussock. The mass *B* of a plant individual can be estimated from its
150 volume *V* following *B* = *V* x *D* where *D* is the bulk density. The apparent volume of a plant is
151 a combination of plant tissue and void. Bulk density is therefore a complex quantity that
depends both on tissue characteristics and plant architecture (Figure 1-A). The void
152 component of the plant apparent volume is an important source of inter-individual variability
153 in estimated biomass. The spatial arrangement of leaves, stems and reproductive organs is
154 highly dependent on external factors such as wind and neighbouring plants because of tissue
flexibility. This makes any measurement of the apparent volume highly uncertain. Previous
156 studies using measures of a plant apparent volume have mostly been located in arid habitats
157 where plants are spatially segregated, thereby decreasing this nuisance variability (see e.g.
158 Johnson et al. 1988). To avoid difficulties of intertwined plants in the field, we consider the
159 minimum volume of the canopy, rather than its apparent volume (Figure 1-B). We define the
160 minimum volume as the volume that an individual plant occupies when all aboveground
161 organs are joined together and uncoiled along the plant longitudinal axis. This requires hand
162 manipulation of plants but does not alter their tissues nor their future growth.
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164 We considered three simple biometric measurements to estimate the minimum volume of
165 each plant: the maximum height, the basal circumference and the circumference at mid height
166 (Figure 1-B). Both circumferences were measured with a graduated tape by tightening organs
167 until first signs of resistance in order to avoid plant tissue damages. This procedure
168 minimizes measurement error by reducing inter-individual variations in standing volume
linked to neighbourhood conditions (Fig. 1). Furthermore, there is very little potential
169 variation in circumference measurement linked to the tightening force exerted by the
170 observer, since large tightening forces are avoided to preserve the plant from tissue damage.
171 These biometric measurements were recorded in the field for the 480 plant individuals
172 considered. The plants were then clipped to ground level. In the lab, we sorted dead material,
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174 green tissues and reproductive organs. All plant samples were oven-dried at 60°C during 48
175 hours and weighed. The total plant biomass including dead material was used for subsequent
176 analyses.

177 Based on the three basic measurements introduced above, we formulated allometric equations
178 for nine possible shapes of the minimum volume (Table 3). Shapes like cylinder, double
179 cylinder, cone, double cone or ellipsoid were first considered as having a unique value of bulk
180 density. We further considered the possibility that the lower and upper parts of shapes like
181 double cylinder and double cone may show different bulk density. This was justified by the
182 uneven distribution of different organs (leaves, stems, reproductive organs) along the
183 longitudinal axis of plants. Finally, we also considered basic allometric models where the
184 plant biomass is a simple function of height (stick) or height and basal circumference
185 (reversed nail) or height and circumference at mid-height (spinning-top). We considered both
186 linear and power relationships between the measured plant biomass and the patterns presented
187 above. Both types of relationship correspond to two distinct hypotheses. The linear model
188 assumes that the bulk density of plant individuals does not vary with plant size. Conversely,
189 the power model assumes bulk density to vary with plant size as a result of non-isometric
190 allocation between organs of different density during plant ontogeny (Weiner 2004; Poorter et
191 al. 2015).
<table><thead><tr><th rowspan="2">Shape</th><th rowspan="2">Name</th><th colspan="2">Formula</th></tr><tr><th>linear</th><th>power</th></tr></thead><tbody><tr><td></td><td>Stick</td><td>B = dH</td><td>B = dH<sup>z</sup></td></tr><tr><td></td><td>Reversed nail</td><td>B = d<sub>1</sub>H + d<sub>2</sub>C<sub>basal</sub></td><td>B = d<sub>1</sub>H<sup>z<sub>1</sub></sup> + d<sub>2</sub>C<sub>basal</sub><sup>z<sub>2</sub></sup></td></tr><tr><td></td><td>Spinning-top</td><td>B = d<sub>1</sub>H + d<sub>2</sub>C<sub>half</sub></td><td>B = d<sub>1</sub>H<sup>z<sub>1</sub></sup> + d<sub>2</sub>C<sub>half</sub><sup>z<sub>2</sub></sup></td></tr><tr><td></td><td>Homogeneous double cylinder</td><td>B = d<sup>H</sup> / 2 (A<sub>basal</sub> + A<sub>half</sub>)</td><td>B = d<sup>H</sup> / [2(A<sub>basal</sub> + A<sub>half</sub>)]<sup>z</sup></td></tr><tr><td></td><td>Inhomogeneous double cylinder</td><td>B = H / 2 (d<sub>1</sub>A<sub>basal</sub> + d<sub>2</sub>A<sub>half</sub>)</td><td>B = [H / 2 (d<sub>1</sub>A<sub>basal</sub> + d<sub>2</sub>A<sub>half</sub>)]<sup>z</sup></td></tr><tr><td></td><td>Simple cone</td><td>B = d<sup>H</sup> / 3 A<sub>basal</sub></td><td>B = d<sup>H</sup> / (3A<sub>basal</sub>)<sup>z</sup></td></tr><tr><td></td><td>Homogeneous double cone</td><td>B = d<sup>H</sup> / 6 (A<sub>basal</sub> + 2A<sub>half</sub> + &radic;[A<sub>basal</sub>A<sub>half</sub>])</td><td>B = d<sup>H</sup> / [6(A<sub>basal</sub> + 2A<sub>half</sub> + &radic;[A<sub>basal</sub>A<sub>half</sub>])]<sup>z</sup></td></tr><tr><td></td><td>Inhomogeneous double cone</td><td>B = d<sub>1</sub><sup>H</sup> / 6 (A<sub>basal</sub> + A<sub>half</sub> + &radic;[A<sub>basal</sub>A<sub>half</sub>]) + d<sub>2</sub><sup>H</sup> / 6 A<sub>half</sub></td><td>B = [d<sub>1</sub><sup>H</sup> / 6 (A<sub>basal</sub> + A<sub>half</sub> + &radic;[A<sub>basal</sub>A<sub>half</sub>])]<sup>z</sup> + d<sub>2</sub><sup>H</sup> / 6 A<sub>half</sub></td></tr><tr><td></td><td>Ellispoid</td><td>B = d<sup>4</sup> / 3 &pi;Hr<sub>half</sub><sup>2</sup></td><td>B = d<sup>4</sup> / (3&pi;Hr<sub>half</sub><sup>2</sup>)<sup>z</sup></td></tr></tbody></table>

with
A<sub>basal</sub> = C<sub>basal</sub><sup>2</sup> / 4&pi;
A<sub>half</sub> = C<sub>half</sub><sup>2</sup> / 4&pi;
r<sub>half</sub> = C<sub>half</sub> / 2&pi;

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**Table 3.** Allometric equations based on various volume shapes. These equations make use of a plant's maximum height (*H*), basal circumference (*C*<sub>basal</sub>) and circumference at mid-height (*C*<sub>half</sub>). *B* indicates total dry biomass of aboveground organs. Volumes with both white and gray parts indicate that two different bulk densities (*d*) are estimated.

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Eighteen allometric models were initially tested for each species (i.e. total plant biomass regressed against nine patterns following either a linear or power function). We further tested the robustness of these allometric equations against environmental or life stage effects. To do so, we fitted 36 additional models where life stage or life stage and site were added as
202 independent variables. Sites were considered as factors with four levels. Plant developmental
203 stage was considered as a binary factor representing the presence or absence of reproductive
204 organs. We assessed model performance following three criteria. First, we quantified the
205 model goodness-of-fit to the full dataset (n = 40 for each species) using the coefficient of
determination. Second, we computed model predictive accuracy using a repeated split-sample
206 procedure (100 iterations). Seventy five per cent of the full dataset were used for model
207 calibration (n = 30) and 25% for model evaluation. The splitting procedure aimed at
208 uniformly sample evaluation data within the range of species total biomass. We then
209 calculated the average Normalized Root Mean Square Error of predictions (NRMSE) across
210 the 100 iterations. Third, we assessed the across-site transferability using a 4-fold cross-
211 validation procedure where sites were used for data splitting. Therefore, the models were
212 calibrated for all but one site (n = 30) and evaluated on the remaining site. We then calculated
213 the average Normalized Root Mean Square Error of predictions (NRMSE) across the 4
214 possible iterations (one per site).

215 We compared the 54 models based on these three criteria (i.e. goodness-of-fit, predictive
216 accuracy and between-site transferability), but selected the best equation for each species as
217 the one showing the best between-site transferability.

219 All statistical analyses were performed under the R environment (R Core Team 2015). Scripts
220 and basic data are provided in Appendices C-D.

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**3. Results**

223 Among the 54 allometric equations, the most transferable one was selected for each of the 12
224 investigated species. The normalized errors reported for model transferability ranged between
225 0.11 and 0.35 with *NRMSE*<sub>transf</sub> = 0.20 (Table 4). Differences in predictive accuracy
226 between the most accurate and the selected models were low (ΔNRMSE ranging between 0
and 0.09), meaning that most transferable models were also the most accurate or close to the most accurate (Table 4). Overall, the selected equations showed high goodness-of-fit with $R^2$ ranging from 0.63 to 0.95 and $\bar{R}^2 = 0.83$ (Figure 2) and good predictive accuracy with NRMSE ranging from 0.10 to 0.23 and $\overline{NRMSE} = 0.16$ (Table 4). These good performances are in line with the results retrieved from the few previous studies having documented allometric equations for herbaceous species in open habitats (Figure 2). Goodness-of-fit and predictive accuracy did not differ between plant functional groups and was not significantly correlated with the plant traits considered here (Table 1).

The selected model was very variable among species in terms of shape, type of function and importance of stage effect. The shapes of the selected models had non-evident relationships with species traits. Reversed nail was selected as the best shape for *Trifolium pratensis* only, simple cone for *Plantago lanceolata*, spinning-top for three species (*Achillea millefolium*, *Elymus repens*, *Lotus corniculatus* and *Veronica chamaedrys*), homogenous double cone for *Poa pratensis*, homogeneous double cylinder for three species (*Agrostis capillaris*, *Lolium perenne* and *Taraxacum officinale*), homogeneous ellipsoid for *Arrhenatherum elatius*, and inhomogeneous double cylinder for *Dactylis glomerata*.
<figure><img src="image_4.png" /></figure>

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**Figure 2.** Goodness-of-fit of the allometric equation selected for each species from this study (gray boxes) and results extracted from the literature (white boxes; Appendix A).

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The stick model based solely on plant height was never selected as the most transferable model (Table 4, Figure 3-A). It was further found to be the worst model for all species except *Veronica chamaedrys*. Shapes relying on basal circumference and height (reversed nail and simple cone) were selected for two out of twelve species. Shapes further including mid-height circumference were selected for the ten remaining species. The improvement in goodness-of-fit provided by this third biometric measure ranged between 0 and 18% (Figure 3-B). These results highlight that the complementary biometric measurements proposed in this study make a critical contribution to the predictive ability of the allometric equations.

Models including life stage effects were selected for seven out of twelve species (Figure 3-C).

Although inclusion of life stage resulted in strong improvement for linear models (increase in $R^2$ up to 40%), it did not improve power models by more than 7.2% except for *Lolium perenne*, which showed an increase of 17%. Power functions were selected for seven out of
twelve species. These results highlight that power functions are useful, but not essential, for predicting the biomass of temperate individual herbs at various stages of their life cycle.

Finally, we calibrated allometric equations including site effects. Although one may expect elevation to show a unidirectional influence, we did not find a clear pattern of site effects among the twelve species (Appendix E). We further assessed the gain in goodness-of-fit associated with the use of a site effect in the allometric equation, and found that this gain was limited for all species except *Lolium perenne* (Figure 3-D). For this peculiar species our results encourage to devise site specific allometric equations to recover a good predictive accuracy.

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<figure><img src="image_5.png" /></figure>

269

**Figure 3.** Goodness-of-fit of the selected models compared to A) the most accurate stick model without site effect, B) the most accurate model that relies on plant height (*H*) and basal circumference (*C*<sub>basal</sub>) without site effect, C) the most accurate model without stage effect and D) the most accurate model including site effects. Letters indicate the species: Am (*Achillea*)
274 *millefolium*); Ac (Agrostis capillaris); Ae (Arrhenaterum elatius); Dg (Dactylis glomerata);

275 Er (*Elymus repens*); Lp (*Lolium perenne*); Lc (*Lotus corniculatus*); Pl (*Plantago lanceolata*);

276 Pp (*Poa pratensis*); To (*Taraxacum officinale*); Tp (*Trifolium pratensis*); Vc (*Veronica chamaedrys*).

278

279
<table><thead><tr><th rowspan="2">Species</th><th rowspan="2">Shape</th><th rowspan="2">Function</th><th rowspan="2">Stage</th><th colspan="7">Fit with full dataset</th><th colspan="2">Predictive accuracy</th><th>Between site Transferability</th></tr><tr><th>R<sup>2</sup></th><th>d</th><th>d<sub>1</sub></th><th>d<sub>2</sub></th><th>z</th><th>z<sub>1</sub></th><th>z<sub>2</sub></th><th>Δ R<sup>2</sup></th><th>NRMSE</th><th>ΔNRMSE</th><th>NRMSE<sub>transf</sub></th></tr></thead><tbody><tr><td>Achillea millefolium</td><td>Spinning top</td><td>Power</td><td>yes</td><td>0.86</td><td>-</td><td>2E-08</td><td>0.75</td><td>-</td><td>4.06</td><td>2.26</td><td>0.008</td><td>0.15</td><td>0</td><td>0.15</td></tr><tr><td>Agrostis capillaris</td><td>Homogeneous double cylinder</td><td>Power</td><td>no</td><td>0.81</td><td>5.95</td><td>-</td><td>-</td><td>0.53</td><td>-</td><td>-</td><td>0.029</td><td>0.16</td><td>-0.012</td><td>0.24</td></tr><tr><td>Arrhenaterum elatius</td><td>Homogeneous ellipsoid</td><td>Power</td><td>no</td><td>0.91</td><td>2.27</td><td>-</td><td>-</td><td>0.76</td><td>-</td><td>-</td><td>0.004</td><td>0.1</td><td>0</td><td>0.14</td></tr><tr><td>Dactylis glomerata</td><td>Inhomogeneous double cylinder</td><td>Power</td><td>no</td><td>0.95</td><td>-</td><td>0.03</td><td>0.16</td><td>0.92</td><td>-</td><td>-</td><td>0.021</td><td>0.12</td><td>-0.035</td><td>0.15</td></tr><tr><td>Elymus repens</td><td>Spinning top</td><td>Linear</td><td>yes</td><td>0.8</td><td>-</td><td>1.96</td><td>230.64</td><td>-</td><td>-</td><td>-</td><td>0.074</td><td>0.17</td><td>-0.027</td><td>0.17</td></tr><tr><td>Lolium perenne</td><td>Homogeneous double cylinder</td><td>Power</td><td>yes</td><td>0.63</td><td>0.44</td><td>-</td><td>-</td><td>0.81</td><td>-</td><td>-</td><td>0.176</td><td>0.23</td><td>-0.094</td><td>0.35</td></tr><tr><td>Lotus corniculatus</td><td>Spinning top</td><td>Linear</td><td>yes</td><td>0.79</td><td>-</td><td>1.31</td><td>31.20</td><td>-</td><td>-</td><td>-</td><td>0.070</td><td>0.18</td><td>-0.019</td><td>0.30</td></tr><tr><td>Plantago lanceolata</td><td>Simple cone</td><td>Power</td><td>no</td><td>0.96</td><td>2.85</td><td>-</td><td>-</td><td>0.72</td><td>-</td><td>-</td><td>0.006</td><td>0.1</td><td>-0.011</td><td>0.11</td></tr><tr><td>Poa pratensis</td><td>Homogeneous double cone</td><td>Linear</td><td>yes</td><td>0.83</td><td>0.11</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.035</td><td>0.18</td><td>-0.035</td><td>0.29</td></tr><tr><td>Taraxacum officinale</td><td>Homogeneous double cylinder</td><td>Linear</td><td>no</td><td>0.84</td><td>0.03</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.040</td><td>0.16</td><td>-0.004</td><td>0.17</td></tr><tr><td>Trifolium pratensis</td><td>Reversed nail</td><td>Linear</td><td>yes</td><td>0.82</td><td>-</td><td>5.3</td><td>60.17</td><td>-</td><td>-</td><td>-</td><td>0.025</td><td>0.15</td><td>0</td><td>0.17</td></tr><tr><td>Veronica chamaedrys</td><td>Spinning top</td><td>Power</td><td>yes</td><td>0.75</td><td>-</td><td>0.03</td><td>3E-07</td><td>-</td><td>1.55</td><td>13.4</td><td>0.007</td><td>0.19</td><td>-0.017</td><td>0.20</td></tr></tbody></table>

**Table 4.** Selected allometric equations for each species. The selection procedure is based on the lowest Normalized Root Mean Square Error of the between-site transferability analysis (NRMSE<sub>transf</sub>) among models that do not account for potential site effects. The selected models were compared to the most accurate ones with ΔR<sup>2</sup> depicting the difference of goodness-of-fit and ΔNRMSE the difference of predictive accuracy.
284 **Discussion**

285 The method proposed here is accurate, easy to implement and leads to equations that are
286 generally transferable between contrasted environments. The selected allometric equations
287 for each species showed high prediction accuracy and goodness of fit, similar to the results
288 reported in the literature (Appendix A). The main difference is that our method relies on the
289 minimum volume whereas other studies have used the apparent volume (e.g. Johnson et al.
290 1988, see Appendix A). The apparent volume can be easily estimated in systems where plants
291 are spatially segregated such as in arid habitats where all previous studies have been
292 conducted. However, in intricate vegetation, such as in temperate grasslands, the plant canopy
293 cannot clearly be delineated at the individual level. We here demonstrated that biomass
294 estimations based on the minimum volume efficiently circumvent this problem, making the
295 proposed method relevant to any herbaceous community.

296 Results from the present study show that the three investigated biometric measurements
297 (height, basal circumference and mid-height circumference) are complementary (Fig. 3A-B).

298 They allow to select for the best shape among nine possible formulation of the minimum
299 volume. Our investigation was based on a modest number of species but covered a large range
300 of canopy architecture, size and leaf traits of the Western European flora. Six out of nine
301 shapes, which made use of two to three biometric measurements were selected as the best
302 formulations (Table 4). These results provide evidence of the flexibility of the method, which
303 can cope with different plant architectures and grassland types.

304 In the present work, power functions often resulted in greater predictive power than linear
305 functions, indicating significant variations of plant bulk density with plant size. This is
306 consistent with the fact that power models without and with reproductive stage as independent
307 predictor showed similar goodness-of-fit whereas linear models without stage effect were
308 generally less accurate than models including stage effect. This can be interpreted as a
consequence of allometric biomass allocation between stems, leaves and reproductive organs
during plant ontogeny that do not have the same bulk densities (Niklas 2004; Weiner 2004;
Poorter et al. 2015). Although the power function is biologically justified by the allometric
scaling theory, it was not always associated with significant fit improvements in our study.

Four out of twelve studied species exhibited linear relationships and several studies reported good estimations of individual herb biomass from linear models (Gutierrez & Aguilera 1989; Assaeed 1997; Röttgermann et al. 2000; Guevara et al. 2002; Hirata et al. 2007; van der Eynden 2011). Isometric scaling between plant organs has been reported for small plants (Enquist & Niklas 2002; Enquist et al. 2007; Poorter et al. 2015), and is consistent with optimal biomass partitioning theory (Lohier et al. 2014). Our contrasted findings emphasize the need to systematically consider linear and non-linear functions when fitting biomass equations from biometric measurements of herbaceous individual plants, as currently recommended for other plant groups (Chave et al. 2014).

Most importantly, we found that a single equation can reasonably be used to successfully predict the biomass of individual plants in different habitats for the large majority of the investigated species, at least within the range of environmental conditions investigated here, which was already wide (Table 2). A notable exception was the perennial ryegrass (Lolium perenne). It is possible that we sampled different selected ryegrass genotypes with contrasted ecophysiological and morphological characteristics since different varieties of ryegrass are used for hay production and pasture (Beecher et al. 2015). The strong site effect for this species may therefore have been confounded with a genotype effect. To our knowledge this study is the most comprehensive assessment of the transferability of biomass equations between different environments for herbaceous species. A few previous studies have compared allometric equations fitted for different disturbance regimes, including fire (van der Eynden 2011) and grazing (Tausch et al. 1994; Nafus et al. 2009, but all were within
homogeneous abiotic conditions. Huenneke et al. (2001) and Andariese & Covington (1986) compared different sites varying in abiotic conditions. The most frequent conclusion of these studies is that biomass equations should be calibrated for each investigated site. Only Huenneke et al. (2001) and our findings contrast with this prevailing view. Despite the good across-site transferability of the allometric equations evidenced in this study, further investigation is needed where both approaches would be specifically compared.

Based on these findings we recommend the application of this method for most herbaceous species, except for very small (below 0.05 meters height) and tall species (above 2 meters height) for which the proposed measurements may be unpractical. We furthermore suggest the following guidelines for interested users:

1. Potential users should fit their own equations rather than using the reported parameters for two reasons: i) to minimize potential observer biases, and ii) because prediction errors when extrapolating models to distinct biogeographic areas have not yet been evaluated.

2. Large environmental gradients should be sampled when calibrating the allometric equations and equations should be used within the range of investigated environmental conditions.

3. In order to determine the best equation for each species, all possible equations reported here should be fitted; the most appropriate species-specific equations cannot be selected a priori using basic knowledge of species architecture and size. As a default model, we recommend using a power model for a homogenous double cone which showed on average the best performances, all criteria combined.

This non-destructive, cross-site estimation method of individual plant biomass opens new perspectives for research at the individual and community levels. At the individual level, monitoring biomass trajectories of plant individuals will allow the assessment of changes in
demographic rates in relation to environmental conditions. Such information can be used to better tease apart the respective influences of abiotic conditions and biotic neighbourhood in plant dynamics along their growth trajectories, and thus to enrich existing approaches based on biomass measurements at the end of a field experiment (e.g., Wilson & Keddy 1986; Goldberg et al. 1999; Freckleton & Watkinson 2001). These empirical assessments may feed dynamical models of plant dynamics at the population and community levels (Lande et al. 2003; Rees & Ellner 2009). With modern developments in theoretical ecology, dynamic modelling approaches have proved powerful in assessing the detailed nature of competition (Damgaard et al. 2002) and the importance of niche differentiation and fitness differences in the outcome of competition (Levine & HilleRisLambers 2009; Adler et al. 2010; Kraft et al. 2015). Coexistence theory of herbaceous plants has mainly be applied in arid systems where parameters like reproductive output, survival, cover and density are monitored (Sears & Chesson 2007; Adler et al. 2010; Kraft et al. 2015). The use of non-destructive estimates of individual biomass could help test this theory with models based on biomass production, which are more informative for systems like temperate grassland where population growth is mostly vegetative (Benson & Hartnett 2006).

375

376 Acknowledgement

This study received financial support from the French Auvergne Région and FEDER. We thank Juliette Bloor and two anonymous reviewers for insightful comments on an early version of the manuscript.

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