Predicting root biomass for semiarid grassland species of the southern Chihuahuan Desert

Hernández Gómez, Miguel Á.; Pando Moreno, Marisela; Mata González, Ricardo; González-Rodríguez, Humberto; Chacón Hernández, Julio; Gutiérrez, Maritza; Hernández Gómez, Miguel Á.; Pando Moreno, Marisela; Mata González, Ricardo; González-Rodríguez, Humberto; Chacón Hernández, Julio; Gutiérrez, Maritza

doi:10.29298/rmcf.v9i50.226

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Revista mexicana de ciencias forestales

versión impresa ISSN 2007-1132

Rev. mex. de cienc. forestales vol.9 no.50 México nov./dic. 2018

https://doi.org/10.29298/rmcf.v9i50.226

Articles

Predicting root biomass for semiarid grassland species of the southern Chihuahuan Desert

Miguel Á. Hernández Gómez¹

Marisela Pando Moreno¹^*

Ricardo Mata González³

Humberto González-Rodríguez¹

Julio Chacón Hernández²

Maritza Gutiérrez¹

^¹Facultad de Ciencias Forestales. Universidad Autónoma de Nuevo León. México.

^²Instituto de Ecología Aplicada. Universidad Autónoma de Tamaulipas. México.

^³Department of Animal and Rangeland Sciences. Oregon State University. USA.

Abstract:

Most of carbon in grasslands comes from underground biomass, particularly in arid grassland ecosystems. However, estimation of root biomass in these ecosystems has been poorly studied. In this study was analyzed the correlation between above ground plant variables and root biomass to develop statistical models for reliable root biomass estimations. Twenty-six plant species were collected within grazing-excluded grasslands. Linear, exponential and logarithmic regression models were performed for each species and for the whole data set to determine the variables that best predicted root biomass. Only Frankenia gypsophila and Dalea gypsophila showed root/shoot ratio (RSR) higher than one. Enneapogon desvauxii and Atriplex acantocarpha had a RSR close to one. Eight species showed statistical significance in at least one of the correlation analyses but only Tiquilia canescens, Bouteloua gracilis, Machaerantera pinnatifida, Lesquerella fendleri, and Atriplex acanthocarpa had both statistical significance and acceptable coefficient of determination (r² ≥0.50). Using the Marquardt exponential method, 14 out of 15 studied species showed a high determination coefficient and statistical significance. This method was adequate (r²=0.853) to estimate root biomass for the whole set of plants from plant height and crown diameter.

Key words: Plant biomass; arid ecosystems; allometric equations; Marquardt method; regression model; northeastern Mexico

Resumen:

La mayor parte del carbono en los pastizales proviene de la biomasa subterránea, particularmente en pastizales áridos. A pesar de ello, la estimación de la biomasa radicular en esos ecosistemas ha sido poco abordada. En el presente estudio se analizó la correlación entre variables aéreas de la planta y su biomasa radicular para desarrollar modelos estadísticos que permitan la estimación confiable de esta última. Se recolectaron 26 especies vegetales dentro de pastizales sin pastoreo. Se diseñaron modelos de regresión lineal, exponencial y logarítmica para cada taxon y para todos en su conjunto con el fin de determinar las variables que mejor predijeran la biomasa radicular. Solo Frankenia gypsophila y Dalea gypsophila mostraron relación raíz/tallo (RBR) >1. Enneapogon desvauxii y Atriplex acantocarpha tuvieron una RBR cercana a 1. Ocho especies mostraron significancia estadística en al menos un análisis de correlación, pero solo Tiquilia canescens, Bouteloua gracilis, Machaerantera pinnatifida, Lesquerella fendleri, y Atriplex acanthocarpa registraron tanto significancia estadística como un coeficiente de determinación r² ≥0.50. Mediante el método Marquardt en la regresión exponencial, 14 de las 15 especies de interés alcanzaron coeficiente de determinación alto y significancia estadística; este método fue el adecuado (r²=0.853) para estimar la biomasa radicular de las especies analizadas en su conjunto, a partir de la altura de la planta y el diámetro de la copa.

Palabras clave: Biomasa vegetal; ecosistemas áridos; ecuaciones alométricas; método Marquardt; modelo de regresión; noreste de México

Introduction

A substantial proportion of the carbon (C) assimilated by plants through photosynthesis is transferred to roots, usually exceeding the amount allocated in the above ground components. This flux of C has a strong impact on the regulation of major soil processes that affect productivity and bio-chemical cycles of ecosystems (^{Jansson et al., 2010}).

Estimation of carbon (C) stocks and emissions of greenhouse gases have received increasing attention in the last decade (^{Maniatis and Mollicone, 2010}; ^{Asner, 2011}). However, temperate and tropical forests have been studied more thoroughly (^{Saatchi et al., 2011}; ^{Asner et al., 2012}) and other ecosystems that might contain substantial amounts of C have been neglected (^{Scurlock et al., 2002}; ^{Gibbon et al., 2010}).

Covering almost 39 million km² (about 25 % of the continental surface of the Earth), grasslands represent one of the most extensive ecosystems in the world and provide numerous environmental services (^{D'Atri, 2007}).

Grasslands are potential C sinks to reduce atmospheric CO₂ (^{Jones and Donnelly, 2004}; ^{Acharya et al., 2012}). Studies on C storage suggest that most of the C in grasslands originates from below ground biomass (^{Jackson et al., 2002}) and total allocated C increases with plant species richness (^{Adair et al., 2009}), particularly in arid systems where grass root growth can be much higher than grass shoot growth (^{Evans et al., 2013}).

Also, it is common that under adverse environmental conditions such as water or nutrient deficit in the root zone, the relationship between root biomass and shoot biomass (RSR= Root/Shoot ratio) tends to increase (^{Wan et al., 1993}; ^{Mata et al., 2002}; ^{Mata and Meléndez, 2005}; ^{Sainju et al., 2017}). However, root biomass in arid grasslands has been poorly investigated and it has frequently been underestimated in determining C pools in different ecosystems, even though roots can be the main biomass source in some species (^{Evans et al., 2013}; ^{Hernández-Gómez et al., 2013}).

Several studies have reported results for the quantification of above ground biomass through allometric equations in arid systems (^{Navar et al., 2004}; ^{Flombaum and Sala, 2007}; ^{McClaran et al., 2013}). Some other studies have estimated root biomass in cultivated temperate pastures (^{Vinther, 2006}; ^{Rasmussen et al., 2010}; ^{Acharya et al., 2012}; ^{Eriksen et al., 2012}) although most of them have assessed biomass by sampling soil at a standardized depth and without differentiating species.

Also, it has been worked on determining the proportion of root biomass that is produced or that dies annually (root turnover coefficients) using environmental and above ground plant characteristics to determine below ground net primary productivity of grasslands (^{Gill et al., 2002}). None of these studies has attempted to develop a statistical model that allows a quick estimation of root biomass from easy measurable plant variables. There is a definite lack of experiences to document allometric equations for the estimation of root biomass in arid and semiarid natural grasslands, perhaps because of the difficulty involved in quantifying below-ground production.

Allometric equations require an initial extensive destructive biomass sampling, but they can be used later as a consistent and non-destructive method for estimating below-ground root biomass. Species differences in biomass allocation should be considered in land management and conservation practices. Species-particular information on root and shoot biomass is also important in parameterizing ecological models that are used to support land and environmental management (^{Mata et al., 2008}). In this case, it was hypothesized that root biomass can be reliably estimated from above ground plant parameters. Hence, speciﬁc species-allometric equations were developed for 26 native taxa of the Chihuahuan desert as well as multispecies equations for all them as a whole.

Materials and Methods

Study area

The study was carried out in two cattle-excluded semiarid grasslands of the southern part of the Chihuahuan Desert in northeastern Mexico. Mean annual temperature for the region is 17.2 °C with a minimum of -1.8 °C in January and maximum of 35.1 °C in May. Average annual rainfall is 386.43 mm. March and July are considered the driest (8.43 mm) and wettest (58.06 mm) months, respectively (^{SMN, 2012}). Sampling areas were between 1 800 and 2 000 masl at the localities of La Soledad in the state of Nuevo León and El Salado in the state of San Luis Potosí.

Vegetation is conformed by communities of short halophytic/gypsophyllus grasslands (between 0.05 and 0.2 m height) associated with microphyllous and rosetophyllous desert scrub (^{Estrada et al., 2010}) where the most abundant species are Muhlenbergia villiflora Hitchc., Scleropogon brevifolius Phil., Zinnia acerosa (DC.) A. Gray, Dasyochloa pulchella (Kunth) Willd. ex Rydb., Bouteloua chasei Swall., Frankenia gypsophila I. M. Johnst., Calylophus hartwegii (Benth.) P.H. Raven, Dalea gypsophila Barneby and Bouteloua gracilis (Willd. ex Kunth) Lag. ex Griffiths. These grasslands embrace several endemic plants (Dalea gypsophila, D. radicans S. Watson, Frankenia gypsophila, Machaeranthera heterophylla R. L. Hartm. and M. crutchﬁeldii B.L. Turner) (^{Estrada et al., 2010}) and animals such as the Mexican prairie dog (Cynomys mexicanus Merriam, 1892) that is a regionally endemic species with a status of globally endangered (^{Baillie and Groombridge, 1996}). This ecosystem also provides an important refuge for resident and migratory animals (^{Day and Ludeke, 1993}).

Soils in the area are mainly Solonchack and calcaric Phaeozem, and smaller areas of chromic Vertisol and luvic Chernozem (^{INEGI, 1981}).

Sampling and data analysis

26 plant species were sampled for the analysis of biomass estimation. Sampling was done during July, August, and September 2011-2013, about a month after the even scarce rainy season. Plants were collected from 240 randomly established plots (1 m² each); out of which 144 were located in El Salado and 96 in La Soledad. The number of plant samples per species varied between 8 and 18 according to the availability in the field and covered a broad range of heights and diameters for each species.

Samples were extracted from wet soil (during the rainy season), either immediately after a rain or after manual watering the soil to allow root extraction as complete as possible. Roots were washed out with distilled water and plants measured for shoot height, mean crown diameter and root length. Roots were separated from the aerial part of the plant and both were dried at 70 °C with a Riossa HCF-102-D digital drying oven until dry weight remained constant. The stems and roots were measured with an Urrea graduated plastic measuring tape. These values were used to assess the relationship between shoot and root biomass (RSR) and to develop a non-destructive model to determine root biomass.

Data complied with statistical assumptions (multivariate normality, no multicollinearity, no auto-correlation and homoscedasticity). Then, linear, exponential and logarithmic regression models were performed for each species (Table 1) and individual plant traits such as plant height (H), mean crown diameter (D) or a combination of them (H*HD, H+HD and H,D) were used as independent variables that best estimate root biomass, which was the dependent variable. Linear regression analysis was carried out by the least-square method while the exponential model was performed using the Marquardt (non-linear minimum square) procedure (^{Marquardt, 1963}). Analyses were performed by using SPSS and PROC NLIN SAS/STAT (^{SAS Institute, 2004}).

Table 1 Regression analyses models to estimate root biomass (RB) as a function of plant crown diameter (D) and plant height (H) in 26 plant species from the southern Chihuahuan desert.

Model	Variable	Mathematical expression
Linear	Diameter (D)	RB= B0+B1D
	Height (H)	RB= B0+B1H
	HeightDiameter (HD)	RB= B0+B1HD
	Height + Diameter (H+D)	RB= B0+B1H + B2D
Logarithmic	Diameter (D)	RB=β0+β1ln⁡D
	Height (H)	RB=β0+β1ln(H)
	HeightDiameter (HD)	RB=β0+β1ln⁡HD
	Height + Diameter (H+D)	RB=β0+β1ln⁡(H)+β2ln⁡(D)
Exponential	Diameter (D)	BR= B0eB1D
	Height (H)	BR= B0eB1H
	HeightDiameter (HD)	BR= B0eB1HD
	Height, Diameter	BR= B0eB1H+BZD
	Height + Diameter (H+D)	BR= B0eB1H+D

B₀ = Y-axis intercept of the regression model; B₁ and B₂ = The slopes of the regression models; Log and e = The base 10 logarithmic and the exponential function value.

Results

Root-shoot biomass relation

Only two out of 26 plant species showed a higher root to shoot value higher than one. The two species are Frankenia gypsophila (2.27) and Dalea gypsophila (1.95). Enneapogon desvauxii and Atriplex acantocarpha had a root/shoot relation close to one, which means that they have a similar production of above and below-ground biomass (Table 2).

Table 2 Shoot and root biomass and RSR (Root/Shoot Relation) for 26 native plant species of the southern Chihuahuan Desert.

Species	Family	Life cycle	N	Shoot biomass (g)	Root biomass (g)	RSR
Frankenia gypsophila I.M. Johnst.	Frankeniaceae	Perenne	15	19.43±4.12	44.19±10.32	2.27
Dalea gypsophila Barneby	Fabaceae	Perenne	12	0.69±0.15	1.35±0.27	1.95
Enneapogon desvauxii P. Beauv.	Poaceae	Perenne	4	2.04±0.08	2.02±0.36	0.99
Atriplex acanthocarpa (Torr.) S. Watson	Chenopodiacea	Perenne	10	8.25±2.46	8.02±2.01	0.97
Scleropogon brevifolius Phil.	Poaceae	Perenne	4	1.34±0.18	1.01±0.37	0.76
Muhlenbergia arenicola Buckley	Poaceae	Perenne	5	0.87±0.13	0.52±0.11	0.60
Dieteria canescens (Pursh) A. Gray (Syn.: Machaeranthera canescens)	Asteraceae	Anual o Perenne breve	4	7.48±1.87	3.90±0.77	0.52
Bouteloua gracilis (Willd. ex Kunth) Lag. ex Griffiths	Poaceae	Perenne	10	11.37±2.51	5.82±1.12	0.51
Rumex crispus L.	Polygonaceae	Perenne	5	0.88±0.33	0.43±0.13	0.49
Aristida havardii Vasey	Poaceae	Perenne	10	1.28±0.15	0.63±0.09	0.49
Zinnia acerosa (DC.) A. Gray	Asteraceae	Perenne	18	3.77±0.69	1.71±0.48	0.45
Muhlenbergia repens (J. Presl) Hitchc.	Poaceae	Perenne	10	8.50±0.65	2.92±0.45	0.34
Machaeranthera pinnatifida (Hook.) Shinners	Asteraceae	Perenne	10	4.79±1.18	1.38±0.35	0.29
Muhlenbergia villiflora Hitchc.	Poaceae	Perenne	13	1.37±0.18	0.36±0.07	0.26
Dasyochloa pulchella (Kunth) Willd. ex Rydb.	Poaceae	Perenne	15	2.25±0.21	0.56±0.19	0.25
Bouteloua chasei Swall.	Poaceae	Perenne	10	1.42±0.21	0.35±0.05	0.25
Lepidium virginicum L.	Brassicaceae	Anual Bienal	13	9.30±1.90	2.19±0.55	0.24
Atriplex canescens (Pursh) Nutt.	Chenopodiaceae	Perenne	4	29.30±10.37	10.92±5.06	0.20
Croton dioicus Cav.	Euphorbiaceae	Perenne	5	22.58±2.53	2.87±0.31	0.13
Hoffmanseggia glaucas (Ort.) Eifert	Caesalpiniaceae	Perenne	5	0.50±0.10	0.06±0.03	0.11
Euphorbia prostrata Aiton	Euphorbiaceae	Perenne	5	2.00±0.50	0.20±0.12	0.10
Gaura coccinea Pursh	Onagraceae	Perenne	13	11.53±3.21	1.06±0.13	0.09
Lesquerella fendleri (A. Gray) S. Watson	Brassicaceae	Perenne	15	3.40±0.57	0.27±0.02	0.08
Tribulus terrestris L.	Zygophyllaceae	Anual	5	1.01±0.27	0.07±0.03	0.07
Tiquilia canescens (DC.) A. Richardson	Boraginaceae	Perenne	8	63.20±9.20	4.45±0.58	0.07
Aristida adscencionis L.	Poaceae	Anual	5	2.75±0.39	0.08±0.02	0.03

Values represent the mean ± standard error.

Estimation of root biomass from above ground plant parameters

Linear, exponential, quadratic and logarithmic regression analyses among above ground plant traits and root biomass were carried out for those species with a sample size larger or equal to 8 (15 species; Table 3). Eight species showed significance (P≤0.05) in at least one of the analyses but only five species (Tiquilia canescens, Bouteloua gracilis, Machaerantera pinnatifida, Lesquerella fendleri, and Atriplex acanthocarpa) had both significance and acceptable coefficient of determination (r² adjusted ≥0.50). A. acanthocarpa was the species that showed acceptable coefficient of determination for a higher number of variables (H, D and D+H) and types of regression analyses (linear, exponential, quadratic and logarithmic). A quadratic polynomial regression analysis was the most adequate model with a higher r² value for most of the species. The plant parameter that best explained root biomass was plant crown diameter.

Table 3 Equations derived from the regression analyses.

Species	Variable	n	r²Aj	Sig.	Regression model	Equation
Atriplex acanthocarpa	H	10	0.563	0.012	Lineal	BR=2.324 +0.729X
Atriplex acanthocarpa	H	10	0.562	0.013	Exponencial	BR=3.179 e0.084H
Atriplex acanthocarpa	D	10	0.832	0.000	Lineal	BR=1.019+0.038D
Atriplex acanthocarpa	D	10	0.577	0.011	Logarítmico	BR=-16.197+4.972 lnD
Atriplex acanthocarpa	D	10	0.838	0.002	Cuadrático	BR=1.900 +0.028D +1.782E-5D2
Atriplex acanthocarpa	D	10	0.735	0.002	Exponencial	BR=2.94 e0.004DH
Atriplex acanthocarpa	D+H	10	0.797	0.001	Lineal	BR=-19.713+0.873D+H
Atriplex acanthocarpa	D+H	10	0.740	0.001	Logarítmico	BR=-92.470+29.200 lnD+H
Atriplex acanthocarpa	D+H	10	0.841	0.002	Cuadrático	BR=14.375-1.108 D+H+0.028D+H2
Atriplex acanthocarpa	D+H	10	0.598	0.009	Exponencial	BR=0.396 e0.087D+H
Bouteloua gracilis	D	10	0.620	0.007	Lineal	BR=-0.975+0.763D
Bouteloua gracilis	D	10	0.794	0.004	Cuadrático	BR=7.322-1.213D+0.102D2
Bouteloua gracilis	D	10	0.573	0.011	Exponencial	BR=2.095 e0.101D
Bouteloua gracilis	DH	10	0.603	0.008	Lineal	BR=1.134+0.016DH
Bouteloua gracilis	DH	10	0.683	0.018	Cuadrático	BR=5.227-0.014DH +4.147E-5DH2
Bouteloua gracilis	DH	10	0.558	0.013	Exponencial	BR=2.767 e0.002DH
Lesquerella fendleri	D	15	0.723	0.000	Cuadrático	BR= -0.647+0.175D-0.008D2
Machaerantera pinnatifida	D	10	0.514	0.020	Exponencial	BR=0.155 e0.129D
Machaerantera pinnatifida	DH	10	0.689	0.017	Cuadrático	BR=-3.238+0.047DH-9.457E-5DH2
Machaerantera pinnatifida	D+H	10	0.672	0.020	Cuadrático	BR=10.932+1.135D+H-0.019D+H2
Tiquilia canescens	H	8	0.730	0.038	Cuadrático	BR=37.516-3.583H+0.092H2
Tiquilia canescens	D	8	0.512	0.046	Lineal	BR=-2.244+0.208D
Zinnia acerosa	H	18	0.509	0.005	Cuadrático	BR=8.717-0.743H+0.016H2
Zinnia acerosa	DH	18	0.533	0.003	Cuadrático	BR=7.032-0.043DH+6.349E-5DH2
Zinnia acerosa	D+H	18	0.502	0.001	Logarítmico	BR=18.572-5.150 lnD+H
Zinnia acerosa	D+H	18	0.536	0.003	Cuadrático	BR=13.171-0.661D+H+0.008 D+H2

Only those plant species that meet the significance criterion (P≤0.05) and determination coefficient (adjusted r² ≥0.50) are shown in the Table. D = Plant crown diameter; H = Plant height.

Since the tested models only allowed prediction of root biomass for five species, an exponential regression using the Marquardt method was also tested. The Marquardt procedure is a maximum neighborhood method that performs an optimum interpolation between linearization and the steepest-descent or gradient method (^{Marquardt, 1963}). This method uses an iterative process of non-linear equations by a minimum square method that minimize the square sum of residuals of the model, allowing the maximum possible value for the likelihood function according to the required precision (^{Aguirre, 1994}).

When using the Marquardt method, 14 out of the 15 studied species showed a high coefficient of determination (r²≥0.60) and significance (P≤0.05) (Table 4).

Table 4 Equations derived from the Marquardt method of exponential model analysis to estimate root biomass (RB) as a function of plant crown diameter (D) and plant height (H) by species.

Sspecies	Variable	n	r²Aj	Sig.	Equation
Aristida havardii	D	10	0.861	0.0004	RB=0.561e-0.0092D
	H	10	0.885	0.0002	RB=2.6465e0.0589H
	H+D	10	0.891	0.0009	RB=2.4733e-0.0134H+-0.0628D
	H*D	10	0.858	0.0004	RB=0.6256e-0.00001HD
Atriplex acanthocarpha	D	10	0.661	0.0133	RB=1.4789e-0.07D
	H	10	0.847	0.0006	RB=3.7664e-0.077H
	H+D	10	0.937	0.0001	RB=0.5382e(-0.0822H)+(0.077D)
	H*D	10	0.931	<0.0001	RB=3.9404e-0.00322HD
Bouteloua chasei	D	10	0.864	0.0003	RB=0.4416e0.0228D
	H	10	0.858	0.0004	RB=0.3616e0.00245H
	H+D	10	0.862	0.0004	RB=0.3973e0.0253H+(0.00905D)
	H*D	10	0.862	0.002	RB=0.4091e(0.00105HD)
Bouteloua gracilis	D	10	0.938	<0.0001	RB=1.4998e-0.1374D
	H	10	0.816	0.0012	RB=1.4682e-0.0433H
	H+D	10	0.940	0.0001	RB=1.8543e-0.1519H+(-0.0111D)
	H*D	10	0.917	<0.0001	RB=2.4597e-0.0026HD
Dalea gipsofila	D	12	0.743	0.0011	RB=0.5671e-0.1097D
	H	12	0.751	0.001	RB=0.2705e-0.2538H
	H+D	12	0.778	0.0027	RB=0.1994e(-0.0837H)+(0.196D)
	H*D	12	0.783	0.0005	RB=0.5556e-0.0171HD
Dasyochloa pulchella	D	15	0.419	0.0292	RB=0.1203e-0.1513D
	H	15	0.623	0.0018	RB=0. 0124e-0.4223H
	H+D	15	0.678	0.0028	RB=0.0127e(-0.2369H)+(0.6708D)
	H*D	15	0.505	0.0103	RB=0.1708e-0.0133HD
Frankenia gipsofila	D	15	0.612	0.0021	RB=25.5739e0.0338D
	H	15	0.605	0.0024	RB=30.4454e-0.0376H
	H+D	15	0.615	0.0079	RB=25.3009e(-0.0248H)+(0.0159D)
Lepidium virginicum	D	13	0.585	0.0079	RB=1.3999e-0.0149D
	H	13	0.612	0.0055	RB=1.1626e-0.0276H
	H+D	13	0.621	0.0175	RB=1.216e(0.0191H)+(0.0191D)
	H*D	13	0.588	0.0076	RB=1.7525e-0.0003HD
Lesquerella fendleri	D	15	0.941	<0.0001	RB=0.1593e-0.0553D
	H	15	0.937	<0.0001	RB=0.1633e-0.0428H
	H+D	15	0.944	<0.0001	RB=0.136e-0.0405H+0.0254D
	H*D	15	0.943	<0.0001	RB=0.1927e-0.00292HD
Machaeranthera pinnatifida	D	10	0.724	0.0058	RB=0.4364e-0.0766D
	H	10	0.635	0.0177	RB=1.4201e0.00241H
	H+D	10	0.738	0.0192	RB=0.5581e(-0.0876H)+(-0.0354D)
	H*D	10	0.656	0.014	RB=1.0422e-0.00158HD
Muhlenbergia repens	D	10	0.863	0.0004	RB=0.1317e-0.1864D
	H	10	0.875	0.0002	RB=0.1386e-0.1908H
	H+D	10	0.875	0.0015	RB=0.1423e(0.0119H)+(0.2015D)
Muhlenbergia villiflora	H	13	0.031	0.0002	RB=0.1345e-0.0769H
	H+D	13	0.805	0.0007	RB=0.1024e(-0.0705H)+(0.0504D)
	H*D	13	0.804	0.0001	RB=0.1847e-0.00553HD
Tiquilia canescens	D	8	0.951	0.0001	RB=1.1298e-0.0418D
	H	8	0.917	0.0006	RB=2.0123e-0.0402H
	H+D	8	0.952	0.001	RB=1.1462e(-0.0461H)+(-0.00795D)
	H*D	8	0.944	0.0002	RB=2.3945e-0.00093HD
Zinnia acerosa	D	18	0.631	0.0003	RB=31.5865e0.2417D
	H	18	0.693	<0.0001	RB=11.7601e0.1492H
	H+D	18	0.720	0.0002	RB=24.3341e(0.099H)+(-0.1114D)
	H*D	18	0.723	<0.0001	RB=8.6773e0.0101HD

Some species such as Tiquilia canescens and Lesquerella fendleri showed a highly significant (P<0.001) coefficient of determination (r²>0.90) for all included variables. The only species which showed a low coefficient of determination (r²≤0.319) and non-significance (P=0.275; not shown in Table 3) was Gaura coccinea.

Several regression analyses pursuing to estimate root biomass from above ground plant traits were run for data of all the species as a whole. The exponential regression models showed (Table 5) to be statistically significant in the estimation of root biomass as a function of plant variables, although with very low determination coefficient values (r²≤0.122). Only the exponential regression with the Marquardt method showed a high coefficient of determination and significance using the variable H, D (r²=0.853; P<0.001).

Table 5 Results and equations derived from linear, exponential and logarithmic analyses for all the species as a whole to estimate root biomass (RB) as a function of plant crown diameter (D) and plant height (H).

Regression model	Variable	n	r²	Sig.	Equation
Exponential	D	182	0.122	0.000 *	RB=0.445e0.64D
	DH	182	0.037	0.009 *	RB=-0.894e0.001DH
	D+H	182	0.067	0.000 *	RB=0.506e0.028D+H
Exponential using the Marquardt method	H	182	0.004	<0.0001 *	RB=6.2293e-0.0178H
	D	182	0.006	<0.0001 *	RB=3.1317e0.0266D
	D,H	182	0.8529	<0.0001 *	RB=7.7889e0.0145D+0.0298H

Equations are shown only for statistically significant results.

Discussion

Most species displayed low RSR values. Only Frankenia gypsophila (2.27) and Dalea gypsophila (1.95) showed RSR > 1. These two are endemic presumably highly adapted to the gypsophyllous characteristics of the local soil conditions. However, these values are considerably lower than that reported by ^{Evans et al. (2013)} for Sporobolus airoides (Torr.) Torr. whose RSR value was 5.5, thus denoting a much greater root production proportion. These authors found higher RSR values in grasses than in desert shrubs, where the last ones exhibited RSR numbers between 0.25 and 0.50.

Graminoids tend to accumulate large quantities of carbon below ground, which make grasslands an attractive biome for carbon sequestration (^{Sharrow and Ismail, 2004}). However, a low below-ground carbon accumulation is typical of annual species, which represents a negative implication if they invade grasslands (^{Evans et al., 2013}). In this regard, the results of this study coincide since the perennial grass Enneapogon desvauxii had the highest RSR value (0.99) while Aristida adscencionis, which is an annual grass, had the lowest RSR (0.03). It could be said that, more often, perennial species may have greater root biomass than annuals as the they remain a longer time in the field, although phenology, climate, and characteristics of the plant need to be considered. For instance, ^{Snyman (2014)}, when studying two Opuntia species, found that root biomass decreased with water stress, although the opposite occurred with root length.

Eight species showed significance (P≤0.05) in at least one of the analyses but only five (Tiquilia canescens, Bouteloua gracilis, Machaerantera pinnatifida, Lesquerella fendleri and Atriplex acanthocarpa) were significant and had an acceptable coefficient of determination (r² ≥0.50). A. acanthocarpa showed adjusted r² >0.50 for a higher number of variables (H, D and D+H) and types of regression analyses (linear, exponential, quadratic and logarithmic).

A quadratic polynomial regression analysis was the most adequate model with a higher r² value for most of the species. The plant parameter that best explained root biomass was plant crown diameter. However, when using the Marquardt method, 14 out of the 15 studied species showed a high determination coefficient (r²≥0.60) and significance (P≤0.05).

The Marquardt exponential model was also adequate to estimate root biomass for the whole set of plants using the variable D, H which resulted in a high coefficient of determination (r²=0.853) and significance (P≤0.05). The equation developed with the exponential model could be very useful for pragmatic purposes (e.g., estimation of C sequestration below ground) since it allows estimation of root biomass avoiding the task of identifying plants at species level.

In a similar way, ^{Gill et al. (2002)} developed an algorithm using environmental and above ground plant characteristics for estimating below-ground net primary productivity in grasslands and they arrived at an equation that predicted below ground biomass with reasonable confidence (r²=0.54) although lower than the documented in this paper (r²= 0.853).

Also, ^{Kuyah et al. (2012)} analysed the relationship between DBH and root biomass of a mixture of tree species (Markhamia lutea, (Benth.) K. Schum., Mangifera indica L., Eucalyptus spp., Cupressus lusitanica Mill. and Acacia mearnsii De Wild.) along the Yala river basin in Western Kenya and found that a linear relationship (r²=0.90) was better to describe the correlation for larger trees (DBH>40 cm) compared to a power function relationship (r²=0.86). In both cases, coefficients of determination were higher than those reported in this paper for grassland species.

In the semiarid forests of the Argentine pampa, ^{Risio et al. (2013)} developed a model to estimate above and below-ground biomass of Prosopis caldenia Bukart. They found that the most adequate model to predict root biomass for the species with basal area (AB) and total height (h) as the independent variables was:

W= β*AB2+λ*h

And reported an adjusted r² value of 0.70, a lower coefficient of determination than the one presented in this paper.

Conclusions

The results of the actual study highlight, to some extent, that measurable above plant variables strong correlate with root biomass, which enabled to propose several reliable models to predict it.

The Marquardt method of the exponential model proved to be suitable to estimate root biomass of 15 species of semiarid grasslands of northern Mexico, both when they were analysed individually and the whole set of plants. The latter is a practical advantage of the method since it could allow estimation of root biomass of similar species without the need of identifying plants at species level.

Acknowledgements

The authors express their gratitude to the Universidad Autónoma de Nuevo León for all the logistic support for the development of this study.

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Received: March 08, 2018; Accepted: August 20, 2018

^{Conflict of interests}

The authors declare no conflict of interests.

^{Contribution by author}

Miguel Á. Hernández-Gómez: development of the research, fieldwork, capture and analysis of data, drafting of the manuscript; Marisela Pando Moreno: conceptual development of research, structuring of the manuscript and final editing; Ricardo Mata González: support in the understanding of results and drafting of discussion for the manuscript; Humberto González Rodríguez: support in the understanding of results and drafting of discussion for the manuscript; Julio Chacón Hernández^: support with the statistical analyses of data; Maritza Gutiérrez: fieldwork, review of the manuscript and final editing.

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