Comparing the Predictive Capacity of Allometric Models in Estimating Grass Biomass in a Desert Grassland

ABSTRACT Allometric models provide a rapid, nondestructive means for estimating aboveground biomass (AGB) of perennial grass species. In the absence of site-specific models, allometric relationships developed at other sites at other times are often used. This implicitly assumes that size-biomass relationships are highly robust. In this study, we assess the comparability of allometric relationships developed at two points in time (2005 and 2015) on different soils on a Sonoran Desert savanna in southern Arizona. We used peak growing season field measurements to develop single-species and multispecies regression models using basal diameter and height to predict the current year's AGB for seven perennial grass species. Basal diameter exhibited the strongest relationship with AGB among single-species (adjusted R2 = 0.54 to 0.87) and multispecies models (adjusted R2 = 0.73). Inclusion of height did little to improve biomass predictions. Our models generally underestimated observed 2015 AGB on the loamy site, whereas models developed in 2005 on a sandier site overestimated the 2015 AGB. Results suggest site-specific allometric models should be used when possible. However, in lieu of such models, relationships developed at other sites or at other times may be appropriate depending on the level of precision needed to address a specific research question.


Introduction
Quantitative estimates of aboveground biomass (AGB) and net primary productivity ( Scurlock et al. 2002 ) of perennial grasses are germane to rangeland conservation and management issues related to grazing, woody plant invasion, and other disturbances.However, direct site-specific estimates of AGB and its spatiotemporal variation requires time-intensive destructive plant harvesting and processing procedures ( Sala et al. 20 0 0 ) that may influence root growth ( Derner et al. 2006 ) and competitive interactions ( Holthuizjen and Veblen 2016 ).Nondestructive assessments of AGB using dimensional analytic techniques ( Niklas 1994 ) and allometric relationships circumvent these problems.Morphologic variables such as basal diameter, height, canopy diameter, and volume have been used to estimate biomass of diverse plant functional types ( Etienne 1989 ;Lambert et al. 2005 ).
Species-specific and multispecies allometric models provide a means for estimating AGB.When site-or species-specific models are not available, generalized allometric relationships may be used under the assumption they are reasonably robust (e.g., Pastor et al. 1984 ).However, these models may underperform if climate ( Rudgers et al. 2019 ), disturbance ( Johnson et al. 1988 ;Harrington and Fownes 1993 ) and topoedaphic factors alter plant biomass allocation and architecture (e.g., Koerper and Richardson 1980 ).Our objective here was to determine the extent to which allometric relationships developed for grasses at one Sonoran Desert grassland site in 20 05−20 06 would be compatible with those developed in conjunction with a 2015 study on a different ecological site.In addition, we sought to determine whether there was a difference in size-biomass relationships between plants under and away from mesquite canopies.

Study site
The 210 km 2 Santa Rita Experimental Range (SRER) is on the west side of the Santa Rita Mountains 45 km south of Tucson, https://doi.org/10.1016/j.rama.2024.01.004 1550-7424/© 2024 The Author(s).Published by Elsevier Inc. on behalf of The Society for Range Management.This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ) Figure 1.Relationship (and adjusted R 2 ) between aboveground plant biomass (g) and basal diameter (cm) in 2015 for seven grass species growing in the vicinity of velvet mesquite canopies.Diameter-only multispecies model detransforms to biomass (g) = e 0.2044 • diameter (cm) 1.1736 ."ANCOVA SS vs. MS * * * " denotes significant ( α < 0.001) differences in slopes on single-species and multispecies regression lines.
Arizona.Elevation ranges from 900 to 1 400 m; climate is subtropical semiarid with precipitation (PPT) dominated by the North American Monsoon ( Adams and Comrie 1997 ).Mean annual PPT and temperature ranges from 330 mm/18.9°C at lower elevations (978 m) to 430 mm/17.2°C at higher (1 293 m) elevations ( Wheeler et al. 2007 ).Our study was conducted on instrumented, rotationally grazed watersheds ( Polyakov et al. 2010 ) in the 990-1 200-m elevation zone, where vegetation is dominated by velvet mesquite ( Prosopis velutina Woot.) and a ground layer of lovegrass ( Eragrostis lehmanniana Nees.).Soils were sandy clay/sandy clay-loams in the Sasabe-Baboquivari soil complex ( Breckenfield and Robinett 2003) .Long-term (1987Long-term ( −2015) ) mean annual PPT and monsoon (July-September) PPT on the watersheds is 398 mm and 229 mm, respectively (ARS Rain Gauge 8) (Fig. S1, available online at …).We conducted field measurements from 1 September through 10 October 2015 during the period of peak herbaceous AGB ( Cable 1975 ) and preceding seasonal grazing.The cattle stocking rate of our site in 2014 before harvest (0.02 animals ha −1 yr −1 ) was comparable with that of the Nafus et al. ( 2009) site (0.03 animals ha −1 yr −1 ) ( Mashiri et al. 2008 ;Nafus et al. 2009 ).The methodology described in the next sections follows that of Nafus et al. (2009) , the only study providing allometric models for perennial grasses in southern Arizona of which we are aware.
We measured basal diameter using cloth tapes (0.1-cm increments) on plants > 0.3 cm BD and digital calipers (0.1-mm increments) on plants ≤ 0.3 cm BD.Regarding the latter, we recorded the average of two orthogonal measurements.Plant height (0.1-cm increments) was measured from the soil surface to the uppermost leaf collar.The height of bush muhly, with its spherical architecture, was based on an average peak height of tillers.After measurements, we clipped plants 1 cm above the soil surface, bagged them, and transported them to the laboratory to dry at 60 °C for 48 h.Previous years' AGB was removed, and samples were weighed to the nearest 0.1 g.

Allometric models
We used natural log (ln) transformations of AGB and size metrics to model relationships between grass size and AGB to ensure comparability with models defined by Nafus et al. (2009) .Our equations are of the form ln y = a + b (ln x), which detransform to y = e a x b (e.g., Andariese and Covington 1986 ;Northup et al. 2005 ).Explanatory size variables included basal diameter (BD, ln [cm]) and height (H, ln [cm]).Models were not corrected for logarithmic bias ( Baskerville 1972 ) to avoid confounding comparisons with Nafus et al. (2009) .We used linear regression to predict AGB for each species separately (single species model) and all species combined (multispecies model) using R v. 3.6.3( R Core Team 2020 ).We used the resulting equations to compare our modeled AGB estimates to 1) observed (measured) AGB and 2) AGB values generated by the Nafus et al. (2009)   Models of plant size-biomass relationships for grasses based on 2015 data.Size variables include basal diameter (BD, cm) and height (H, cm).Column headers include sample size (number of plants), regression intercepts, coefficients, adjusted R 2 , standard error of the estimate (SEE), correction factor , and root mean square errors (RMSE) of natural log-transformed plant BD ( X BD ) and height ( X H ) for single-species and multispecies models to solve for the natural log of the current year's biomass.Rows show results for unique combinations of explanatory variables.The BD-only multispecies model detransforms to biomass (g) = e 0.20 • diameter (cm) 1.17 .

Species
No
Using Wilcoxon rank sum tests, we determined that sizebiomass relationships of grasses under velvet mesquite canopies were comparable with those obtained for those away from canopies ( P > 0.05; Fig. 1 ).Our allometric models therefore reflect data pooled from plants under and away from mesquite canopies.Among our single-species models, BD alone accounted for 54%−87% of the variation in AGB (see Fig. 1 ); height alone accounted for 6%−45% of the variance ( Table 1 ).Including height along with diameter did little to improve biomass predictions ( R 2 increases of 0.04 to 0.14).Pooled across species, BD and height accounted for 73% and 42% of the variance in AGB, respectively, with the two variables combined explaining 79% of the variance.In comparison, Nafus et al. (2009) accounted for 80−91% of variation in AGB in their single-species models.With the exception of Boer lovegrass, our single-species models, like theirs, were within the 95% prediction interval of the multispecies models.Regression line slopes of our single-species and multispecies models differed significantly (analysis of covariance [ANCOVA], P < 0.001).
Our models underestimated observed AGB for plants with larger BDs (see Fig. 1 ), whereas those of Nafus et al. (2009) overestimated AGB ( Fig. 2 ).Boer lovegrass was an exception, where equations from both studies predicted AGB well.ANCOVA revealed that differences between our single-species models and those of Nafus et al. (2009) were significant ( P < 0.001).

Discussion
Our results are consistent with previous work on grass sizebiomass relationships (e.g., Andariese and Covington 1986 ;Guevara et al. 2002 ) in that inclusion of height did little to improve the predictive capacity of either single-species or multispecies allometric models.The additional time investment associated with recording and processing height data may therefore not be justified ( Nafus et. al 2009 ).Smith et al. (2021) noted that while effectiveness of multispecies allometric models varies depending on the species used for model development, such models may be useful in areas with mixtures of species.Our multispecies models performed similarly to our single-species models.
We observed different results using models developed for the same species at different points in time and applied to individuals occurring 3 km apart.This reinforces findings by Rudgers and colleagues (2019) , who determined that spatiotemporal changes in precipitation, temperature, and drought influence allometric relationships between AGB and plant morphometrics.Plants at our site had a greater maximum BD than those at the Nafus et al. (2009) site.This reflects, in part, the higher annual and monsoon PPT at our site the year of and preceding our AGB measurements (e.g., Adar et al. 2022 ) (see Fig. S1).Models for Boer lovegrass may be more robust given they performed well in both studies.
Given that woody plants enhance soil nutrient pools and alter microclimate underneath their canopies (e.g., Throop and Archer 2007 ), grass size-mass relationships might be expected to differ between individuals growing under and away from velvet mesquite canopies.As this was not observed here, grass allometric relationships in this system may be robust.This is consistent with Gower et al. (1993) , who found that fertilization did not influence plant allometry.Accordingly, differences in intershrub zone sampling schemes or microclimate do not likely explain differences in allometric relationships between our site and that of Nafus et al. (2009) .The soil complex characterizing our site is finer textured than the soil at the Nafus et al. ( 2009) site (Table S1; available online at [ doi:10.1016/j.rama.2024.01.004 ]).However, while this may account for the differences in plant size at the two sites, it does not explain why their multispecies and single-species models overestimated AGB at our site.Additional information would be required to characterize the spatiotemporal differences in environmental characteristics on the two sites.
Our results and those of Buech and Rugg (1989) suggest sitespecific models should be used when possible.Reliability and robustness of future allometric models could ostensibly be improved by incorporating variables relating to precipitation, soil properties, and disturbance histories (e.g., stocking rates).In lieu of sitespecific models, relationships developed at other sites or at other times may be appropriate, depending on the level of precision that may be needed for a specific research question.For example, plantand small plot-scale experiments may require relatively precise information and one suite of dimension metrics ( Williamson et al. 1987 ), whereas a different suite of dimensional metrics may suffice for accurately assessing biomass at broader scales using terrestrial lidar scanning (e.g., Wachendorf et al. 2017 ;Anderson et al. 2018 ) and uncrewed aerial vehicles ( Zhang et al. 2022 ).

Figure 2 .
Figure 2. Grass biomass-basal diameter relationships for seven grass species on a Combate soil in 2005 ( Nafus et al. 2009 ) and those developed in 2015 (this study) for the same species on nearby Sasabe-Baboquivari soil.Line represents a 1:1 relationship.Note different x-and y-axis scales."ANCOVA * * * " denotes significant ( α < 0.001) differences in single-species regression line slopes for Nafus et al. 2009 and this study.