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1. We tested the hypothesis that the net partitioning of dry mass and dry mass:area relationships is unaltered when plants are grown at elevated atmospheric CO2 concentrations.
2. The total dry mass of Dactylis glomerata, Bellis perennis and Trifolium repens was higher for plants in 700 compared to 350 μmol CO2 mol–1 when grown hydroponically in controlled-environment cabinets.
3. Shoot:root ratios were higher and leaf area ratios and specific leaf areas lower in all species grown at elevated CO2. Leaf mass ratio was higher in plants of B. perennis and D. glomerata grown at elevated CO2.
4. Whilst these data suggest that CO2 alters the net partitioning of dry mass and dry mass:leaf area relationships, allometric comparisons of the components of dry mass and leaf area suggest at most a small effect of CO2. CO2 changed only two of a total of 12 allometric coefficients we calculated for the three species: ν relating shoot to root dry mass was higher in D. glomerata, whilst ν relating leaf area to total dry mass was lower in T. repens.
5. CO2 alone has very little effect on partitioning when the size of the plant is taken into account.
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There are three ways of separating effects of treatment from ontogeny: harvest plants at the same stage of development, examine plants that have similar total dry mass, and the use of allometry. In this paper we shall concentrate on the last two methods; the former will be addressed separately (and see Gunn, Bailey & Farrar 1996).
Growth of roots and shoots are often related through the allometric formula S = bRk, where S is shoot dry mass, R root dry mass, and b and k are constants (Troughton 1955). Remarkably, and usefully, this relationship tends to remain linear for substantial periods of time for plant growth in an unchanging environment, although curvilinear relationships are also found (Pearsall 1927; Troughton 1955; Causton & Venus 1981; Coleman et al. 1995). Although the allometric coefficient (k) is often used to refer to the relationship between shoot and root dry mass it can also be used to examine relationships such as those between leaf area and total dry mass, leaf mass and total dry mass, and leaf area and leaf dry mass (LAR, LMR and SLA when expressed as ratios; Coleman et al. 1995; Barrett & Gifford 1995). A change in the partitioning of carbon between, for example, the shoot and the root, will be shown as a change in the value of k. k is generally calculated by a linear regression, using the method of least squares. However, this is not a suitable model as there are not an independent and a dependent variable (that is, it is as justifiable to plot ln S as the x variable as the y variable). A better model is the geometric mean regression or reduced major axis (Ricker 1984).
Baxter et al. (1994) found no change in k in the relationship between shoot and root dry mass (calculated after removal of total non-structural carbohydrates), for Agrostis capillaris or Poa alpina due to a twofold difference in the CO2 concentration (340 and 680 μmol CO2 mol–1). However, k is increased in Festuca vivipara so that more dry matter is partitioned towards the shoot than towards the root at elevated CO2. k is unchanged in barley and Picea sitchensis at elevated CO2 (Farrar & Williams 1991; Hibberd, Whitbread & Farrar 1996) but decreases in Lolium perenne (Nijs & Impens 1997). Barrett & Gifford (1995) found that there was an increase in the allometric constant relating leaf mass and plant mass in plants grown at elevated CO2 whilst CO2 had no effect on the relationship between leaf area and leaf mass in cotton. Growth CO2 concentration had no effect on the allometric relationship between root and plant mass in Yellow Birch (Berntson, Wayne & Bazzaz 1997).
In this study we examined the hypothesis that growth at elevated CO2 will increase plant dry mass but that partitioning between shoot and root, leaf area and total dry mass, leaf mass and total dry mass, and leaf area and leaf dry mass will be unaffected when size and ontogeny are taken into account. Our studies differ from others both because we compare three ways of data presentation (ratios, and both allometry and a procedure that scales by dry mass, as two different ways of avoiding ontogenetic effects), and because we grew the plants so that CO2 was the only variable. Thus the plants were grown hydroponically so that roots had ready access to nutrients (avoiding nutrient deficiencies that decrease S:R) and so that the water status of the rooting medium was identical in both CO2 treatments, unlike experiments in solid media where decreased transpiration in elevated CO2 can result in moister soil than in the ambient treatment.
Materials and methods
Seeds of Trifolium repens L. cv Kent (Emorsgate Seeds, Norfolk, UK), Dactylis glomerata L. cv Sylvan (IGER, Aberstwyth, UK) and Bellis perennis L. (Chiltern Seeds, Cumbria, UK) were germinated and grown at either 350 (ambient) or 700 μmol CO2 mol–1 (elevated) in controlled-environment chambers (Sanyo Gallenkamp PG660, Leicester, UK), at 20 °C with a 16 h photoperiod, a photon flux density of 420 μmol m–2 s–1 at plant height, supplied by HQI bulbs supplemented with tungsten filament bulbs and a vapour pressure deficit of 0·7 kPa. Air was drawn into the cabinets through a modified inlet port from a fan (Type-3MS11, Air Control Installations, Chard, UK) providing a flow of 60 litres min–1 which produced 5·5 complete changes of air per hour in each cabinet. Air was enriched to 700 μmol CO2 mol–1 using CO2 supplied from vapour-withdrawal cylinders (BOC Ltd, Manchester, UK) and this concentration was controlled using an infrared gas analyser (IRGA) to within ± 5 μmol CO2 mol–1 CO2 (EGM-1, PP-Systems, Herts, UK).
Thirty plants were grown in 7 dm3 of solution aerated at 1 dm3 min–1. The temperature of the solution was not controlled but was ± 1 °C of the air temperature. Solutions were changed every 3 or 4 days. Dactylis glomerata was grown in full strength and T.repens in half strength Long Ashton solution (mol m–3, full strength); KNO3 (4), Ca(NO3)2. 4H2O (4), NaH2PO4·2H2O (1·33), MgSO4·7H2O (1·5), FeEDTA Na (0·1), MnSO4·4H2O (0·01), CuSO4·5H2O (0·001), ZnSO4·7H2O (0·001), H3BO3 (0·05), Na2MoO4·2H2O (0·004), NaCl (0·1). Sodium metasilicate was added at the rate of 10 mg dm–3. Bellis perennis was grown in a solution containing (mol m–3): KNO3 (0·2) (NH4)2SO4 (0·06), Ca(NO3)2. 4H2O (0·15), KH2PO4·2H2O (0·95), K2HPO4 (0·05), MgSO4·7H2O (0·11), Na2EDTA·2H2O (0·02), FeSO4·7H2O (0·02), MnSO4·4H2O (0·008), CuSO4·5H2O (0·00016), ZnSO4·7H2O (0·006), H3BO3 (0·0018), Mo7O24(NH4)6·2H2O (0·000008), NaCl (0·02).
Plants of D. glomerata were harvested between 20 and 42 days old, B. perennis 21 and 50 days old and T.repens 16 and 33 days old. At each harvest five replicate plants of each species were taken randomly. Plants of B. perennis and T. repens were divided into leaves (excluding petioles), rest of shoot and root, whilst those of D. glomerata were divided into (1) main stem leaf blades which were fully expanded, (2) rest of main stem (leaf sheaths plus expanding leaf blades of the primary tiller plus bases of secondary tillers), (3) tillers and (4) root. Leaf area was measured on a leaf area meter (Delta T, type TC2014/X video camera with electronic control unit, Cambridge, UK) and dry mass of all parts was determined after drying in a ventilated oven at 80 °C.
A stepwise regression procedure was used to determine if first- or second-order polynomials were the best fit for a natural-log transformation of shoot or root dry mass plotted against time (days) for all plants (Hunt 1982). t-tests were used to determine if the quadratic term differed significantly from zero (Zar 1996), using the computer package SPSS (version 7, SPSS, Chicago, IL, USA).
A quadratic equation best described the data for root and shoot growth of B. perennis and all except shoot dry mass of plants of D. glomerata grown at ambient CO2 which was best described as a linear regression: quadratic equations only will be shown. A linear regression best described the data of shoot and root dry mass of T. repens, except for roots of plants grown at elevated CO2: linear equations only will be shown. The first differential of the equations was used to calculate relative growth rates. The time of the earliest harvest was used in the quadratic equations for D. glomerata and B. perennis.
RATIOS DESCRIBING NET PARTITIONING
LAR (leaf area/total plant dry mass, cm2 mg–1), LMR (mass of leaves used for leaf area measurements/total plant dry mass), S:R (shoot dry mass/root dry mass) and SLA (leaf area/leaf mass, cm2 mg–1) were calculated for each harvest. Dry mass is the sum of both structural and non-structural material.
Cochran's test was used to test for the equality of variances before an analysis of variance was carried out. Significant interactions were compared using Tukey's honestly significant test. Data are shown as means of five replicates + one standard error of the mean.
To remove the effect of size, ratios were expressed against dry mass. Discriminant function analysis (Cooper & Weekes 1983; Tabachnick & Fidell 1996 using SPSS statistical package) was used to assess whether it was possible to distinguish between the group of plants grown at ambient from the group grown at elevated CO2 on the basis of S:R ratio and total dry mass, LAR and total dry mass, LMR and total dry mass or SLA and total dry mass for each species. Prior to analysis the data were assessed for the presence of outliers by Mahalanobis distance and homogeneity of variance–covariance using Box's M-test (Tabachnick & Fidell 1996). Using all plants from all harvests the variance–covariance matrices were heterogenous. After removal of plants of B. perennis and D.glomerata with a total dry mass > 2000 mg and T.repens > 500 mg (see Fig. 1), the variance–covariance matrices were homogenous and discriminant analysis was then carried out on these plants.
We shall use the symbol ν with subscripts to denote allometric coefficients calculated by geometric mean regression; thus νSR, νAM, νLM, and νAL are the allometric analogues of the ratios S:R ratio, LAR, LMR and SLA, respectively. Allometric coefficients were calculated for the relationships between shoot dry mass and root dry mass (νSR), leaf area and plant dry mass (νAM), leaf mass and plant dry mass (νLM), and leaf area and leaf dry mass (νAL) by geometric mean regression (Ricker 1984). In summary the natural log of Y was plotted against the natural log of X for all plants from all harvests. A straight line gave a better fit than a curvilinear relationship and so the equation:
ln Y = ln a + k ln X
was then fitted through the points, where X is root, leaf or total dry mass, Y is shoot or leaf dry mass or leaf area, and a and k are constants. Goodness of fit of the points to a straight line was assessed using the coefficient of determination (r2) (Zar 1996). The allometric coefficient for a geometric mean regression was calculated as ν = k/r, where r is the correlation coefficient. A comparison of the two correlation coefficients (350 and 700 μmol CO2 mol–1 within any one plot was carried out after a Fisher's z-transformation of r (Zar 1996). Only for one plot, leaf dry mass vs total dry mass for T. repens, was there a significant difference between the r-values for the two lines. No allowance for this was made in the final analysis. Comparisons of ν were carried out using a modified t-test and results are shown with 95% confidence limits (Ricker 1984). Where there was no significant difference between the slopes a comparison of the elevations (as opposed to the intercepts) of the regressions (i.e. a comparison of the vertical positions of the lines on the graphs) was carried out using a t-test (Zar 1996).
Maximum RGR ranged from 0·2 to 0·3 day–1 (Table 1). Total dry mass was higher in plants grown at elevated compared to ambient CO2, for all three species (values from the final harvest are shown in Table 1). The dry mass of the shoots of T. repens, D.glomerata and B. perennis, and the roots of T.repens and B. perennis grown at elevated CO2 were higher than for plants grown at ambient CO2 but [CO2] had no effect on the root dry mass of D. glomerata (Table 1).
Table 1. . The effects of [CO2] on growth of T. repens, D. glomerata and B. perennis in hydroponics. Dry mass and leaf area at the final harvest. Constants in the equations ln dry mass = a + b(time) or ln dry mass = a + b(time) + c (time)2 for shoot and root dry mass and maximum RGR (calculated at the earliest harvest for quadratic equations). Standard errors are in brackets. NS, no significant difference
Total leaf area was higher in plants of B. perennis and T. repens grown at elevated compared to ambient CO2 (Table 1). The CO2 concentration of growth had no effect on the total area of fully expanded leaves in D. glomerata (Table 1).
NET PARTITIONING OF DRY MASS AND LEAF AREA
S:R ratio was higher in plants grown at elevated compared to ambient [CO2] in T. repens and B. perennis (P < 0·01). However, there was a significant interaction between CO2 and harvest (P < 0·05) so that only at the final harvest was S:R ratio higher in D. glomerata (Fig. 1).
Plants grown at ambient CO2 could be distinguished from those grown at elevated CO2 on the basis of S:R ratio and total dry mass using discriminant function analysis for B. perennis but not D. glomerata or T. repens. On this basis the S:R ratio was higher in B. perennis grown at elevated CO2 (Table 2).
Table 2. . The effect of [CO2] on the mean of all plants from all harvests, for the variables total plant dry mass (mg), S:R ratio, LAR (cm2 mg–1), LMR and SLA (cm2 mg–1) in T. repens, D. glomerata and B. perennis grown in hydroponics. Prior to analysis plants were selected on the basis of total dry mass of plants from all harvests (B. perennis and D. glomerata total dry mass ≤ 2000 mg, T. repens total dry mass ≤ 500 mg). Standard errors are shown in brackets. NS, no significant difference; *P≤ 0·05, **P≤ 0·01
Leaf area ratio
LAR was lower in D. glomerata (P < 0·01), B. perennis (P < 0·01) and T. repens (P < 0·001) grown at elevated compared to ambient [CO2] (Fig. 1).
Plants grown at ambient CO2 could be distinguished from those grown at elevated CO2 on the basis of LAR and total dry mass using discriminant function analysis for T. repens but not B. perennis or D. glomerata. On the same criterion, LAR was lower in T. repens grown at elevated CO2 (Table 2).
Leaf mass ratio
LMR was higher in D. glomerata (P < 0·05) and B.perennis (P < 0·001) grown at elevated compared to ambient CO2;LMR was unaffected by [CO2] in T.repens (Fig. 1).
Plants grown at ambient CO2 could be distinguished from those grown at elevated CO2 on the basis of LMR and total dry mass using discriminant function analysis for B. perennis, but not D. glomerata or T. repens. On the same criterion LMR, was higher in B. perennis grown at elevated CO2 (Table 2).
Specific leaf area
SLA was lower in D. glomerata and T. repens (P < 0·001) grown at elevated compared to ambient CO2 and in B. perennis at the first harvest (Fig. 1).
Plants grown at ambient CO2 could be distinguished from those grown at elevated CO2 in all three species on the basis of SLA and total dry mass using discriminant function analysis. On the same criterion, SLA was lower in plants grown at elevated CO2 (Table 2).
Shoot vs root dry mass (νSR)
The allometric coefficient, νSR, relating shoot and root dry mass was unaffected by CO2 concentration in T.repens and B. perennis but was higher in D. glomerata grown at elevated compared to ambient CO2: there was increased partitioning towards the shoot. There was a significant difference between the elevations of the regressions in B. perennis (P < 0·01) but not in T. repens. Elevations were not compared in D. glomerata. The graphs of ln shoot dry mass vs ln root dry mass for the three species are given in Fig. 3 as examples of allometric plots. The remaining coefficients are given as values only (Table 3).
Table 3. . The effect of [CO2] on the allometric coefficient relating shoot and root dry mass, leaf area and total dry mass, leaf mass and total dry mass, and leaf area and leaf mass of T. repens, D. glomerata and B. perennis. The allometric coefficient was calculated by plotting the natural log of Y against the natural log of X for all plants from all harvests and fitting a linear regression where X is root, leaf or total dry mass, Y is shoot or leaf dry mass or leaf area, ln a is the intercept and k is the slope; r is the correlation coefficient. The allometric coefficient, ν, was then calculated as k/r. Values are shown with 95% confidence limits. NS, no significant difference; *P≤ 0·05, ***P≤ 0·001
Leaf area vs total dry mass (νAM)
The allometric coefficient, νAM, relating leaf area to total dry mass was unaffected by CO2 in B. perennis and D. glomerata but was lower in T. repens grown at elevated compared to ambient CO2 (Table 3) with less leaf area being produced per unit of total plant mass at elevated CO2. CO2 concentration had no effect on the elevations of the regressions in B. perennis or D.glomerata. Elevations were not compared in T.repens.
Leaf mass vs total dry mass (νLM)
CO2 concentration had no effect on the allometric coefficient, νLM, relating leaf dry mass to total dry mass in any species (Table 3). CO2 concentration had a significant effect on the elevations of the regressions in B. perennis and D. glomerata (P < 0·001), but not in T. repens.
Leaf area vs leaf dry mass (νAL)
CO2 concentration had no effect on the allometric coefficient, νAL, relating leaf area to leaf dry mass in any species (Table 3). CO2 concentration had a significant effect on the elevations of the regressions in T.repens (P < 0·01) but not in B. perennis or D. glomerata.
Growth at elevated CO2 had little effect on partitioning when CO2 was the only factor varying (nutrient and water status were unaltered by CO2 treatment) and size or ontogeny were taken into account: of the 12 relationships examined allometrically only two were significantly affected by CO2 concentration. In sharp contrast the conclusions that would be drawn from a comparison of ratios at particular harvests would be that growth at elevated CO2 resulted in increases of the shoot:root and leaf mass ratios and decreases of the leaf area ratio and specific leaf area (Table 4). Such conclusions would be wrong: they are based on a lack of appreciation of the way in which ratios such as S:R may change with ontogeny (Farrar & Gunn 1996).
Table 4. . Summary of the effects of [CO2] on the relationships between shoot and root dry mass, leaf area and total dry mass, leaf mass and total dry mass, and leaf area and leaf dry mass expressed as (A) ratios vs time (from Fig. 2), (B) ratios vs total dry mass (from Table 2) and (C) allometric coefficients, ν (from Table 3). ↓, decrease; ↑, increase; NS, no significant effect of [CO2] of growth
Although any scaling procedure can be used as the basis on which to compare treatments here we use two, dry mass and allometry. Each has advantages and disadvantages. Only 50% of the discriminant function analyses gave the same result as the allometric analysis (Table 4). This apparent discrepancy may be due to the smaller range of plants assessed when comparing ratios on the basis of dry mass to the number used for allometry: a better experimental procedure would be to compare ratios from plants harvested when of similar dry mass. The discrepency may also be due to the statistical difficulties in comparing ν between treatments where any differences may be small and variation large, a problem which is especially acute when using native species. Also changes in partitioning, assessed by allometry, are determined only by changes in ν; no account is taken of differences in the second term in the regression equation, the intercept (ln a). For example, S:R ratios calculated from the allometric equations relating shoot and root dry mass will be different for treatments which differ in the value of the intercept alone and not in the allometric coefficient. In these experiments, however, there was generally no significant difference in the intercepts (statistical results not shown). Overall, for these rather variable native species, we consider allometry to be a better comparator than discriminant function analysis; not only does it have clear biological meaning, but also, in spite of the caveats above, it is statistically more robust.
The method used to analyse any data must be matched to the question being asked. Allometry answers the question—does treatment change partitioning (of area, mass, carbon, etc.)? If however, the question relates to the relative ability of different parts of the plant to capture resources (e.g. shoot for capturing light and root for capturing water or nutrients) then ratios must be assessed (Farrar & Gunn 1998).
Although CO2 concentration had little effect on the allometric coefficient, ν, it had more effect on the elevations of the regressions. Changes in elevations, without changes in the slopes, can only have occurred owing to early changes in the growth pattern of plants grown at the two CO2 concentrations because common seed was used for plants grown at ambient and elevated CO2. These early changes have never been detected in any experiments, owing partly to the difficulties associated with measuring very small plants and partly to the large number of replicates that would be required to pick up such small changes in v.
Farrar & Gunn (1996) predicted that the partitioning of carbon between root and shoot should be unchanged by growth at elevated CO2 when CO2 is the only variable (i.e. non-limiting nutrients and water) because there is no reason why sinks in shoots and roots should be differentially sensitive to the increased availability of reduced carbon. ν, relating shoot and root dry mass, was unchanged in B. perennis and T. repens, although it was increased in plants of D. glomerata grown at high CO2. This increase was, however, very small and may have been due to the differential accumulation of non-structural carbohydrates in the shoot and the root. Depending on the question, it may be better to assess changes in partitioning on a structural dry mass basis rather than on total dry mass because non-structural carbohydrates may account for a significant proportion of the dry mass of an organ (Baxter et al. 1995).
In conclusion this work has shown that it is impossible to assess the affect of a treatment on net partitioning of dry mass and area through the use of ratios calculated at any one time. It is necessary to at least assess the data graphically, as a plot of ratio vs total dry mass, or allometrically. Meanwhile many conclusions in the literature must be doubted and the data underlying the conclusions re-examined.
We would like to thank NERC for support under the TIGER programme (section IV/1). We are grateful to Bryan Collis for formative discussions, Peter L. Mitchell for discussions on geometric mean regression and Louise Thurlow for technical assistance.