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Ecosystems in which annual evaporative demand exceeds precipitation occupy about half of the Earth’s land surface (UNEP 1992), and plant productivity in them often increases linearly with mean annual precipitation or actual evapotranspiration (Rosenzweig 1968; Chong et al. 1993). The availability of water to individual plants in such systems depends in part on local climatic and edaphic factors and also on the depth, lateral spread and degree of overlap of plant root systems (Casper & Jackson 1997). Actual water use also depends on plant vascular architecture and on the balance of above- and below-ground plant dimensions (West et al. 1999).
Previous research in water-limited environments leaves little doubt that sizes and shapes of root systems differ among plants from arid to humid systems (Kutschera & Lichtenegger 1997). For example, plants are typically predicted to have larger root : shoot ratios in drier than in more mesic environments (Walter 1963; Pallardy 1981; Chapin et al. 1993). Nevertheless, absolute maximum rooting depths or lateral spreads might still be greater in wetter systems because plants are often bigger there. This distinction between absolute and relative plant dimensions is important for understanding ecological processes at different scales. For example, lateral root spreads and maximum rooting depths influence how many neighbours compete for resources and determine the potential pool of resources available to plants in an ecosystem (Caldwell & Richards 1986; Fitter et al. 1991; Canadell et al. 1996). Relationships between relative root and shoot size are important for studies of allocation and allometry in individual plants. As an example of the latter, plants of a given canopy size may need larger root systems in coarse textured soils, because such soils offer larger resistance to water flow and have smaller water-holding capacities and deeper infiltration depths (Sperry et al. 1998; Jackson et al. 2000b).
For predicting and modelling functions of natural ecosystems, plant diversity is sometimes reduced to a small number of plant functional types (Smith et al. 1993). Because there is little information about the functional ecology of many species, plant growth form categories are often used as proxies for such functional types (Box 1996; Sala et al. 1997). Data on maximum rooting depths and lateral root spreads could be useful for predicting functional differences between plant growth forms today and under future climate change scenarios. Moreover, many recent modelling studies have assumed that woody and herbaceous growth forms compete for resources in the upper soil layers, while woody plants have a larger proportion of roots in deeper layers, taking up significantly more soil water there (Jackson et al. 2000a). This assumption is known as the two-layer model and was first proposed by Heinrich Walter (1939) for tropical savannas, but its generality has been disputed (Seghieri 1995; Mordelet et al. 1997). Data on rooting depths of woody and herbaceous plants under a range of climates should be useful for determining under which climatic conditions and for which plant growth forms this model is most likely to apply.
The aim of this study, based on a new global dataset of > 1300 observations for individual plants, is to predict sizes and shapes of root systems from biotic and abiotic factors in water-limited environments. The study includes a comprehensive scaling analysis of relationships between above- and below-ground plant dimensions, to our knowledge the first such attempt.
In order to provide a framework for a priori predictions about relationships among climate, soil and plant dimensions, we developed a simple conceptual model based on the assumption that roots grow only as deeply as needed to fulfil plant resource requirements. This assumption is based on the idea that shallow root systems are generally favoured over deep root systems because (a) energy costs for construction, maintenance and resource uptake are lower for shallow roots (Adiku et al. 2000); (b) shallow soil layers are usually less likely to be oxygen-deficient (Hillel 1998); and (c) nutrient concentrations are often greater in the upper soil layers (Jobbágy & Jackson 2001). Our conceptual model links rooting depths largely to water availability, and predicts that rooting depths increase if water is available at depth and if there is transpirational demand for it.
This simple conceptual model allows us to test a set of predictions for water-limited ecosystems. One is that maximum rooting depth will be deepest in subhumid environments where evaporative demand slightly exceeds precipitation. Shallower rooting of individual plants is predicted for both arid systems, because precipitation and water infiltration depths decline in arid systems, and for more humid ones, where water is frequently re-supplied to the upper soil layers, making deeper roots potentially less important. Another prediction for water-limited environments is that rooting depths will not be strongly related to potential evapotranspiration (PET), because water infiltration depths will be more limiting than evaporative demands. As a corollary, for a given plant size, lateral root spreads will be largest in arid environments to take advantage of relatively shallow infiltration depths in such systems.
Materials and methods
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- Materials and methods
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Data on rooting depths (n = 1305) and lateral root spreads (n = 965) of individual plants from water-limited ecosystems (≤ 1000 mm mean annual precipitation (MAP) and MAP : PET ratios < 1) were collected from the literature for deserts, semi-deserts, scrublands, grasslands and shrub- and tree-savannas (see Appendix 1). Within these climatic limits, the only records that were excluded from the present study were those from sites with a continuous cover of woody plants, such as forests and dense sclerophyllous shrublands, which are addressed in a separate study of rooting depths in humid to per-humid systems (Schenk & Jackson, unpublished data). We define rooting depth (Di) of an individual plant i as the deepest soil depth reached by the roots of an individual plant (i.e. maximum rooting depth) and lateral root spread (Li) as the maximum linear distance (one-sided) from the stem of an individual plant reached by its roots. Where available, canopy heights (Hi; n= 502) and widths (Wi; n= 466) were also recorded. Data were often determined from scale-drawings of whole plants or root systems. Where possible, canopy volumes were estimated assuming an ellipsoid shape: Vi[m3]=π × Hi[m] × (Wi[m])2/6. Data for Di, Li, Hi and Wi in the original literature almost never included error estimates, and therefore the inevitable sources of error could not be quantified.
Species were classified into seven growth forms: trees, shrubs, semi-shrubs (including suffrutescent forbs), perennial grasses, perennial herbaceous forbs, annuals and stem succulents. Shrub species that rarely reach heights above 1 m were classified as semi-shrubs, but small individuals of species that tend to grow taller than 1 m were classified as shrubs. The classifications generally followed those given in the papers; if none was provided, one was assigned based on information from local floras or databases (see below). In a few cases, some records for the same species were assigned to different growth forms because some species are polymorphic across their range, but for most species only a single record was found. Taxonomic nomenclature was updated using such databases as the IOPI Global Plant Checklist (http://www.bgbm.fu-berlin.de/IOPI/GPC/), the PLANTS database (USDA NRCS 2001) and local floras. We also recorded data on plant life span and growth habit (e.g. rhizomatous, stoloniferous or caespitose; stem and/or leaf succulence; prostrate or cushion habit; bulbous or tuberous morphology). For all statistical analyses, biennials and facultative annuals were lumped into their respective perennial categories and, because of limited sample sizes, annual grasses and annual forbs were combined into one category.
Mean annual precipitation (MAP) and its seasonal distribution were recorded from each publication or, where not recorded, were estimated from the nearest available weather station. Precipitation regimes were divided into four classes: winter, summer, all year, and tropical seasonal for seasonally dry climates lacking a cold season. Temperate and subtropical precipitation regimes were classified as summer regimes when the ratio of the precipitation during the 6 warmest months of the year to that during the 6 coldest months was ≥ 1.25, and as winter regimes when this ratio was ≤ 0.75. Estimates for mean annual potential evapotranspiration (PET) calculated by the Penman-Monteith method were taken from the global 0.5° gridded data set of Choudhury (1997). Soil texture data were also included when provided in the papers.
Statistical analyses had to take into account several issues. Root data for different plant growth forms were not randomly distributed over the range of climates studied, some environmental variables were correlated, and certain combinations of environmental factors were underrepresented (Fig. 1). In consequence, some statistical analyses were restricted to climatic ranges (as indicated below) that included a sufficient number of all categories of plant growth forms, soil texture and seasonality. Root data for all growth forms were also strongly and positively skewed (see table in Appendix 2). The data were fitted to statistical distributions using Crystal Ball software version 4.0 (Decisioneering, Denver, Colorado, USA), followed by comparisons of chi-square goodness of fit statistics between distributions. The best fits for both rooting depth and lateral root spread data were attained by fitting the data to lognormal distributions. Consequently, the best measure of central tendency for these data is the mean of the log-transformed data, or its back-transformed version, which is the geometric mean. As expected for lognormal distributions, geometric means did not differ significantly from medians (table in Appendix 2).
Figure 1. Characteristics of the data base used in this study. The upper graph shows the relative proportions of plant growth forms in the data base as a function of mean annual precipitation (MAP). The bottom graph shows the distribution of root data in the data base in relation to mean annual potential evapotranspiration (PET) and MAP. Humidity zones are defined by MAP : PET ratios (UNEP 1992) as hyper-arid (MAP : PET 0.05), arid (MAP : PET > 0.05 to = 0.2), semiarid (MAP : PET > 0.2 to = 0.5), subhumid (MAP : PET > 0.5 to = 0.65) and humid (MAP : PET > 0.65). The symbol shapes represent different types of seasonality as indicted in the legend.
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Statistical analyses were designed to test the effects of biotic and abiotic factors on rooting depths, lateral root spreads and their ratios. Allometric relationships between above-ground plant sizes and root system dimensions were examined by reduced major axis (RMA) regression analyses of log-transformed Li and Di against log-transformed canopy volumes (Vi) for growth form categories expected to differ in allometry: woody plants, forbs and grasses. The linear RMA regression procedure is recommended for allometric analyses when both the dependent and independent variables are estimated with error (Niklas 1994; Sokal & Rohlf 1995), and was calculated using the program PAST, version 0.65 (Øyvind Hammer, Palaeontological Museum, University of Oslo, Oslo, Norway).
All other statistical analyses were conducted using systat 9.0 (SPSS Science, Chicago, Illinois, USA), with data for Di, Li and Li/Di log-transformed to normalize the distributions. Data for MAP, PET and canopy volumes were also log-transformed to reduce positive skew and variance in the data. All parametric analyses of root system dimensions as a function of climate excluded the MAP * PET interaction term, because its inclusion did not significantly improve the models and caused problems of multicollinearity among MAP, PET and MAP * PET (Zar 1996). Temperature was also not included as a climatic variable because it is highly confounded with PET (Thornthwaite 1948; Budyko 1974).
To quantify relationships of root system dimensions with climate, the variables Li, Di and Li/Di were analysed in linear regressions that included either MAP or MAP and PET as independent variables. Analyses were restricted to climates with > 50 mm MAP because few data were available from extreme, drier climates. Goodness of fit for regressions containing only MAP as the independent variable was compared with regressions with both MAP and PET by comparing their adjusted r2 values. To estimate differences in overall rooting depths between humidity zones, we combined Di values for all growth forms for each humidity zone (Fig. 1; UNEP 1992) and calculated their geometric means and 95% confidence intervals (CI95%). Stem succulents were not included in these analyses because data for them were available from only a very limited range of climatic conditions.
Effects of the seasonality of the precipitation regime on Li, Di and Li/Di in temperate and subtropical environments were analysed in generalized linear models containing seasonality (winter, all year, summer), growth form, MAP, PET and interaction terms (excluding MAP * PET) as independent variables. These analyses were restricted to climates with > 50 mm and < 500 mm MAP, because data sets with summer rainfall regimes were scarce from drier climates and over-represented from wetter climates. Tropical climates were excluded from these analyses because they normally lack a cold season. Significant effects of seasonality were further examined by comparing root dimensions for each plant growth form in Bonferroni adjusted multiple pairwise comparisons between seasonality categories.
The prediction that allometries between above- and below-ground plant sizes change along climatic gradients was examined in multiple, linear regressions with below-ground to above-ground size ratios as dependent variables and MAP and PET as independent variables. The two allometric ratios examined were the rooting depth/canopy volume (Di : Vi) and lateral root spread/canopy volume (Li : Vi) ratios for three broad growth form categories: forbs, grasses and woody plants. Both ratios were log-transformed for the analyses.
To examine effects of soil texture on the relationship between root system and canopy size, the log-transformed allometric ratios Di : Vi and Li : Vi were further analysed in generalized linear models containing the independent variables soil texture, growth form (forbs, grasses, woody plants), MAP, PET, and all interaction terms except those containing MAP * PET (see above). Soil texture classes were reduced to two broad categories (coarse = gravel, sand to loamy sand; fine = sandy loam and finer) to ensure adequate sample sizes of all growth forms over the entire climatic gradient.
Because MAP and plant growth form are likely to be factors that are strongly related to absolute rooting depths in water-limited ecosystems, these variables were chosen to develop predictive rooting depth models. The models were tested against geometric means of rooting depths (Di) calculated for 20 geographical test locations at which more than 15 rooting depths for individual plants of different species had been measured. Data from these test locations were not used anywhere in model development. The geometric mean (or median) of individual plant rooting depths measured in a given ecosystem may be viewed as an estimate for a geometric mean (or median) ecosystem rooting depth (De).
The models were parameterized by linear regression of Di against MAP for three plant growth form categories: annuals, herbaceous perennials and woody perennials (excluding trees and succulents, which did not occur at any of the test sites). These three categories were chosen because the limited data set (n = 803) used to develop these models did not allow us to distinguish between perennial grasses and forbs or between shrubs and semi-shrubs. Predicted rooting depths for the test locations were calculated for each growth form as a function of MAP, and the geometric mean ecosystem rooting depth De for each location was calculated by weighting the estimated Di for each growth form by the number of replicates from that growth form originally measured at the site. Predictions and measurements were compared by calculating the r2 coefficient to determine the percentage of the variance explained by the model. We also examined whether modelled and measured data both showed the same relationship with MAP. Modelled and measured geometric means of ecosystem rooting depths were linearly regressed against MAP, and regression slopes and intercepts were compared by analysis of covariance (Sokal & Rohlf 1995). Data from humid sites with MAP : PET ratios ≥ 0.75 were not used for model development because data from such sites were few (Fig. 1) and because none of the 20 test locations had such a humid climate.
To test whether plants from some families are more likely to be either more shallowly or more deeply rooted than the average herbaceous or woody plant, we compared log-transformed Di for families against log-transformed Di for the whole data set minus the family being tested. These comparisons were conducted separately for woody and herbaceous plants and were restricted to families that had at least 20 data sets of Di in the category (woody/herbaceous) that was analysed. Comparisons were done by t-tests and P-values were adjusted for multiple comparisons using the modified Bonferroni procedure of Jaccard & Wan (1996).
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Absolute rooting depths (Di) and lateral root spreads (Li) generally increased for plant growth forms as their size and life span increased (Figs 2 and 3, table in Appendix 2), with values greatest in trees and smallest in annuals. Perennial grasses and forbs did not differ in root dimensions, and shrubs had significantly larger Di and Li than semi-shrubs. Succulents had very shallow rooting depths but large lateral root spreads (Figs 2 and 3). There were also clear differences among growth forms in the shape of the root systems, with succulents having the largest ratios of lateral spread to rooting depth (Li : Di), a geometric mean of 4.5 (vs. c. 3 for trees, c. 1 for shrubs, c. 0.5 for semishrubs, and 0.3–0.35 for all herbaceous plants, see table in Appendix 2).
Figure 2. Maximum rooting depths of plant growth forms. Geometric means marked by different letters were significantly different according to one-way anovas (see table in Appendix 2 for statistical parameters).
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Differences in root system sizes (Di and Li) were explained partly by above-ground size differences (Vi), with significant correlations for woody plants, forbs and grasses (Fig. 4). Differences in canopy sizes accounted for c. 10% of the variance of Di in woody plants, c. 41% in forbs and c. 24% in grasses (Fig. 4), and rooting depths increased more strongly (as measured by the adjusted r2-values) with canopy size in forbs than in grasses or woody plants. Canopy sizes accounted for c. 53% of the variance of Li in woody plants, c. 38% in forbs and c. 33% in grasses (Fig. 4). Thus in woody plants, the relationship between Vi and Li was much stronger than the relationship between Vi and Di.
Figure 4. Allometric relationships between above-ground canopy volume and root dimensions (maximum rooting depth and lateral root spread). The regression lines and equations are based on reduced major axis regressions performed on log-transformed data, using the general equation log10 (Di or Li) = a + b log10 (Vi), with Di and Li expressed in m and Vi in m3.
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Absolute rooting depths showed a number of significant relationships with climatic variables. Positive relationships between Di and mean annual precipitation (MAP) were observed for all growth forms except shrubs and trees (Table 1). Rainfall was a much stronger predictor for Di than mean annual evapotranspiration (PET) in all growth forms, as adding PET into the regression models increased adjusted r2 values by only 0.001–0.033 (Table 1). Annuals had the strongest and steepest relationships of Di with MAP, and woody plants had the weakest. Positive relationships between PET and Di were observed in perennial grasses and forbs, while a negative relationship was observed in woody plants (Table 1).
Table 1. Regression parameters for the relationships between root system dimensions, mean annual precipitation (> 50 to ≤ 1000 mm) and mean annual potential evapotranspiration. The parameters are for the linear equations log10Y= a1 + b1 log10 MAP and log10Y= a2 + b2 log10 MAP + c log10 PET, where Y is the respective root variable (rooting depth (in m), lateral root spread (in m), or lateral spread/rooting depth), MAP is mean annual precipitation in mm, and PET is mean annual evapotranspiration in mm. Statistically significant parameters are marked by *(P < 0.05), **(P < 0.01) or *** (P < 0.001)
| Annuals||−2.312|| 0.809***||0.265***||−0.713|| 0.720***||−0.449||0.267***|
| Perennial forbs||−1.603|| 0.629***||0.136***||−2.590|| 0.620***|| 0.334||0.137***|
| Perennial grasses||−1.053|| 0.409***||0.111***||−2.662|| 0.392***|| 0.543**||0.135***|
| Semi-shrubs||−0.316|| 0.178*||0.018*|| 1.280|| 0.157*||−0.504**||0.041**|
| Shrubs||−0.053|| 0.158||0.007|| 1.192|| 0.152||−0.395||0.014|
| Trees|| 1.000||−0.208||0.019|| 4.967||−0.086||−1.323*||0.099*|
|Lateral root spread|
| Annuals||−3.096|| 0.919***||0.253***||−4.301|| 0.991***|| 0.336||0.248***|
| Perennial forbs||−1.029|| 0.196||0.009||−3.057|| 0.160|| 0.702||0.019|
| Perennial grasses||−0.020||−0.180||0.008||−4.304||−0.168|| 1.395***||0.136***|
| Semi-shrubs|| 1.273||−0.638***||0.171***|| 0.524||−0.646***|| 0.252||0.171***|
| Shrubs|| 0.279|| 0.020||0.000||−2.426||−0.046|| 0.918*||0.049|
| Trees||−0.089|| 0.383||0.057||−1.998|| 0.224|| 0.708||0.082|
|Lateral : depth ratio|
| Annuals||−0.684|| 0.056||0.000||−2.026|| 0.136|| 0.374||0.000|
| Perennial forbs|| 0.585||−0.434***||0.064***||−0.448||−0.453***|| 0.358||0.065***|
| Perennial grasses|| 1.040||−0.589***||0.132***||−1.808||−0.581***|| 0.928**||0.183***|
| Semi-shrubs|| 1.316||−0.701***||0.192***||−0.414||−0.721***|| 0.583**||0.208***|
| Shrubs|| 0.679||−0.287||0.008||−4.286||−0.364|| 1.651***||0.121***|
| Trees||−1.405|| 0.747||0.108||−4.606|| 0.447|| 1.213||0.143|
Geometric means of absolute rooting depths increased from hyper-arid to the subhumid climatic zones for all growth forms combined (hyper-arid: 0.67 m, CI95% 0.46–0.93 m; arid: 0.96 m, CI95% 0.86–1.06 m; semiarid: 1.08 m, CI95% 1.00–1.17 m; subhumid: 1.63 m, CI95% 1.47–1.80 m). Geometric mean rooting depths were also more shallow in the humid zone (1.24 m, CI95% 1.02–1.48 m) than in the subhumid zone. These results support the prediction that rooting depths in water-limited ecosystems should be deepest in subhumid climates.
Lateral root spreads had generally weaker relationships with climatic variables than did maximum rooting depths (Table 1, Fig. 5). Significant relationships were not detected between Li and MAP in perennial grasses, forbs and shrubs, but Li increased with increasing MAP for annuals (perhaps paralleling a size increase above-ground) and decreased for semi-shrubs. Lateral root spreads increased with increasing PET in perennial grasses and shrubs (Table 1). Root system shapes also changed along climatic gradients, as Li : Di ratios decreased with increasing MAP in perennial herbaceous plants and semi-shrubs, and increased with increasing PET in perennial grasses, semi-shrubs and shrubs (Table 1). This suggests that general shapes of root systems tend to change from relatively shallow and wide in arid climates to deeper and narrower in subhumid to humid climates.
Figure 5. Absolute maximum rooting depths and lateral root spreads for five plant growth form categories as a function of mean annual precipitation (MAP). Significant linear trends are indicated by solid regression lines, non-significant ones by dashed lines. Regression parameters are listed in Table 1. Data for trees are not shown, because the sample size for trees was rather small and because their root system sizes showed no significant relationships with MAP.
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The seasonality of precipitation affected absolute rooting depths (Di) of shrubs very differently than other growth forms (Fig. 6). Only shrubs had shallower rooting depths in environments dominated by summer precipitation compared with non-seasonal or winter precipitation (P < 0.05; Fig. 6). No significant relationship between Di and seasonality was observed for herbaceous perennials and semi-shrubs, while annuals were slightly more deeply rooted in summer rainfall climates (P < 0.05). In net effect, overall differences in rooting depths between growth forms were least pronounced in summer rainfall climates and most pronounced in winter rainfall climates, a result with implications for climate change scenarios (Fig. 6). Seasonality did not appear to have an effect on lateral root spreads or on root system shapes (Table 2).
Figure 6. Geometric means (± 1 SE) of absolute maximum rooting depths for five plant growth form categories in climates with > 50 and < 500 mm mean annual precipitation (grouped by seasonality). See Table 2 for the corresponding statistical analysis.
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Table 2. Statistical parameters of generalized linear models of root dimensions as a function of plant growth form (annual, perennial forb, perennial grass, semi-shrub, shrub), seasonality of rainfall (winter, even, summer), MAP and mean annual PET. Models were developed for climates ranging from > 50 mm to < 500 mm MAP
|Model: r2 of model||Rooting depth 0.369||Lateral root spread 0.537||Lateral root spread/rooting depth 0.300|
|Growth form|| 1.446|| 4||3.211||0.013|| 0.162|| 4||0.262||0.902|| 1.065|| 4||1.887||0.111|
|Seasonality|| 0.441|| 2||1.958||0.142|| 0.273|| 2||0.885||0.413|| 0.244|| 2||0.865||0.422|
|MAP|| 0.924|| 1||8.213||0.004|| 0.026|| 1||0.166||0.684|| 0.093|| 1||0.658||0.418|
|PET|| 0.748|| 1||6.648||0.010|| 0.015|| 1||0.096||0.757|| 1.353|| 1||9.582||0.002|
|Seasonality × growth form|| 2.316|| 8||2.572||0.009|| 0.408|| 8||0.330||0.954|| 2.066|| 8||1.830||0.069|
|Growth form × MAP|| 1.004|| 4||2.230||0.064|| 1.563|| 4||2.534||0.039|| 1.820|| 4||3.224||0.012|
|Growth form × PET|| 1.626|| 4||3.612||0.006|| 0.473|| 4||0.767||0.547|| 0.803|| 4||1.422||0.225|
|Seasonality × MAP|| 0.244|| 2||1.084||0.339|| 0.116|| 2||0.375||0.688|| 0.444|| 2||1.573||0.208|
|Seasonality × PET|| 0.441|| 2||1.958||0.142|| 0.366|| 2||1.186||0.306|| 0.349|| 2||1.234||0.292|
|Seasonality × growth form × MAP|| 1.613|| 8||1.791||0.075|| 1.254|| 8||1.017||0.422|| 2.772|| 8||2.455||0.013|
|Seasonality × growth form × PET|| 2.247|| 8||2.496||0.011|| 0.446|| 8||0.361||0.941|| 2.221|| 8||1.967||0.048|
|Error||90.391||803|| || ||97.474||632|| || ||88.505||627|| || |
Analyses of relative rooting depths showed that herbaceous plants of a given canopy size tended to have deeper roots in drier than in wetter climates. The allometric size ratios Di : Vi and Li : Vi decreased with increasing MAP in forbs and grasses. In contrast, for woody plants, Di : Vi increased with increasing MAP and Li : Vi showed no significant relationship with MAP (Table 3). Both of the allometric ratios Di : Vi and Li : Vi decreased with increasing PET in all growth forms (Table 3), suggesting that plants of a given above-ground size tend to have smaller root systems in warmer climates (high PET) than in colder climates. The fact that both allometric ratios changed with MAP and PET also suggests that the effects of climate on plant size differ above- and below-ground.
Table 3. Regressions for the relationships between allometric ratios (below-ground to above-ground plant size), MAP (mm) and mean annual PET (mm). The two allometric ratios were the rooting depth to canopy volume ratio (Di : Vi in m−2) and the lateral root spread to canopy volume ratio (Li : Vi in m−2). The regression parameters listed are for linear equations of the format log10Y= a + b log10 MAP + c log10 PET, where Y is the respective allometric ratio. The regression coefficients a, b and c are listed with their standard errors. Allometric ratios were calculated separately for woody and herbaceous plants. Regression coefficients marked by different letters were significantly different between growth forms at P < 0.05. All regressions and regression coefficients were significantly different from zero at P < 0.05, except regression coefficient b for Li : Vi in woody plants
|Allometric ratio||a||b||c||adjusted r2||n|
|Di : Vi|
| Forbs||11.12a ± 2.64||−0.62b ± 0.23||−2.39a ± 0.78||0.046||208|
| Grasses||12.94a ± 3.09||−1.75b ± 0.42||−2.05a ± 0.82||0.132||108|
| Woody plants|| 7.87a ± 2.27|| 0.61a ± 0.22||−2.56a ± 0.69||0.129||178|
|Li : Vi|
| Forbs||12.72a ± 2.69||−0.90b ± 0.23||−2.88a ± 0.79||0.084||194|
| Grasses||14.73a ± 2.95||−2.11c ± 0.40||−2.47a ± 0.77||0.210||100|
| Woody plants|| 6.69a ± 1.86|| 0.09a ± 0.18||−1.86a ± 0.56||0.057||178|
There was no evidence for effects of soil texture on allometric below-ground to above-ground size ratios (data not shown). Maximum rooting depths and lateral root spreads also did not differ consistently for plants of a given size growing in soils of different texture.
Regression models were developed to predict geometric mean rooting depths for plants co-occurring at each of 20 geographical locations. The regression equations were calculated from all data (sample sizes n given below) excluding those from these 20 locations (see Methods). These models included only precipitation and broad growth form categories (annual, herbaceous perennial, woody perennial) as independent variables. The equations were:
Annual forbs and grasses: log10 Di = −1.9507 + 0.6730 log10 MAP; n = 57, adj. r2 = 0.340.
Perennial forbs and grasses: log10 Di = −1.6641 + 0.6621 log10 MAP; n = 212, adj. r2 = 0.150.
Woody shrubs and semi−shrubs: log10 Di = −0.3857 + 0.2412 log10 MAP; n = 282, adj. r2 = 0.044.
These models predicted geometric mean rooting depths at the 20 test locations quite well (Fig. 7). The general trend of increasing rooting depths with increased precipitation was predicted accurately, as neither the slopes (ancova, sum of squares 0.0081, d.f. = 1, F-ratio = 0.0698, P = 0.793) nor the intercepts (ancova, sum of squares 0.0010, d.f. = 1, F-ratio = 0.0089, P = 0.925) differed between linear regressions of measured and modelled data against MAP (Fig. 7). A comparison of predicted versus modelled data by linear regressions yielded a goodness of fit of r2 = 0.623 (n = 20; F-ratio = 29.682; P < 0.0001). This result provides further evidence that precipitation is an important factor governing rooting depths of plant growth forms in water-limited environments; it also suggests that these regression equations may be used to predict geometric means of plant rooting depths for sites in climates with MAP : PET ratios of < 0.75.
Figure 7. Geometric means of absolute maximum rooting depths for 20 geographical locations as a function of mean annual precipitation. Error bars represent 95% confidence intervals for the geometric means. Also shown are the geometric means predicted for each site by a regression model (see Results).
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Herbaceous plants from three plant families were especially likely to be deeply rooted. The geometric mean Di for all herbaceous plants in the data base was 0.85 m, compared with the following values for the more deeply rooted families: Fabaceae (Di = 1.27 m; n = 57; P = 0.0012), Asteraceae (Di = 1.17 m; n = 17; P = 0.0003), and Poaceae (Di = 1.02 m; n = 262; P < 0.0001) (with P-values indicating statistical differences from the mean for all plants excluding those being tested). For woody plants, the geometric mean Di in the entire data set was 1.47 m, and only woody plants in the Mimosaceae were significantly more deeply rooted than this value (geom. mean Di = 3.50 m; n = 38; P = 0.0012). Woody plants from two families were more shallowly rooted than the geometric mean for all woody plants: Asteraceae (Di = 1.24 m; n = 132; P = 0.034) and Cactaceae (Di = 0.29 m; n = 30; P < 0.0001).