## Introduction

Increased atmospheric carbon dioxide concentration usually increases plant dry mass (Patterson & Flint 1980; Baxter *et al.* 1994). It is less clear whether the partitioning of dry mass and leaf area has changed. Distribution of dry mass and leaf area is of considerable importance because it both determines future growth (*LAR* and hence *LWR* and *SLA* are components of RGR) and because the flux of C below ground is of major significance for C sequestration (Arnone & Körner 1995; Gifford, Lutze & Barrett 1996). Growth at elevated CO_{2} may increase, decrease or not affect the shoot:root (*S:R*) ratio (Patterson & Flint 1980; Oberbauer, Strain & Fetcher 1985; Cure & Acock 1986; Koch *et al.* 1986; Rogers *et al.* 1992, 1996; Ferris & Taylor 1993). Both *SLA* and *LAR* generally decrease with growth at elevated CO_{2} (Goudriaan & de Ruiter 1983; Oberbauer *et al.* 1985; du Cloux, Daguenet & Massimino 1987; Bazzaz *et al.* 1989; Newton 1991; Ferris & Taylor 1993; den Hertog, Stulen & Lambers 1993; Pettersson, McDonald & Stadenberg 1993) whilst *LMR* is unaffected (du Cloux *et al.* 1987; Stulen & den Hertog 1993; Pettersson *et al.* 1993). Plant development as well as growth is faster at elevated CO_{2} as shown by time to flowering (Mortensen 1987) and leaf development (Cure, Rufty & Israel 1989). Consequently many experiments may be measuring ontogenetic, not treatment, effects as they involve comparing treatments at the same age of plant.

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).

It has long been recognized that in order to assess the effect of a treatment on traits that exhibit size-dependent changes during growth, such as *S:R* ratios, comparisons must be made on plants of a common size (Evans 1972; Coleman, McConnaughay & Ackerly 1994; Coleman & McConnaughay 1995). Roumet *et al.* (1996) found that *LMR* was unaffected by growth at elevated CO_{2} whilst *SLA*, calculated on a total rather than a structural leaf mass basis, was decreased.

Growth of roots and shoots are often related through the allometric formula *S* = *bR ^{k},* 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 CO_{2} concentration (340 and 680 μmol CO_{2} 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 CO_{2}. *k* is unchanged in barley and *Picea sitchensis* at elevated CO_{2} (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 CO_{2} whilst CO_{2} had no effect on the relationship between leaf area and leaf mass in cotton. Growth CO_{2} 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 CO_{2} 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 CO_{2} 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 CO_{2} treatments, unlike experiments in solid media where decreased transpiration in elevated CO_{2} can result in moister soil than in the ambient treatment.