Assimilation and Transpiration Capabilities of Rhyniophytic Plants from the Lower Devonian and Their Implications for Paleoatmos

Palaeogeography, Palaeoclimatology, Palaeoecology 202 (2003) 153^178 www.elsevier.com/locate/palaeo

Assimilation and transpiration capabilities of rhyniophytic plants from the Lower Devonian and their implications for paleoatmospheric CO2 concentration Anita Roth-Nebelsick , Wilfried Konrad

Institut fu«r Geowissenschaften der Universita«tTu«bingen, Sigwartstr. 10, D-72076Tu«bingen, Germany Received 23 April 2002; received in revised form 13 August 2003; accepted 5 September 2003

Abstract

The characteristic basic construction of early land plants with an upright posture is represented by a simple leaf- and rootless axis system with a central conducting bundle (‘rhyniophytic habit’). Variations of this simple architectural principle in different early land plant taxa probably reflect different ecophysiological requirements. In this contribution, the assimilation and transpiration of three different Rhynie Chert taxa (Pragian, Lower Devonian) which show this fundamental construction are analyzed in detail: Aglaophyton major, Rhynia gwynne-vaughanii and Nothia aphylla. The analysis was conducted by applying a simulation method based on diffusion through a porous material. The results demonstrate that the capability of gaseous exchange increases from A. major to R. gwynne- vaughanii to N. aphylla. A. major shows the most strict water-conserving strategy of the three taxa. The results are consistent with data from the fossil record concerning ecophysiological strategies and life styles. Furthermore, the results indicate clearly that the structural properties of early land plants reflect an optimization strategy with a fine- tuning of gaseous exchange. The rhyniophytic habit is strongly adapted to and dependent on high atmospheric CO2 concentrations. The results provide evidence that the atmospheric CO2 concentration of the Lower Devonian amounted to roughly 120 mmol/m3. ß 2003 Elsevier B.V. All rights reserved.

Keywords: Lower Devonian; Plantae; Photosynthesis; Paleoecology; Paleoclimatology

1. Introduction sporangia and a central conducting bundle (see, for example, Stewart and Rothwell, 1993). This The earliest land plants which possessed an up- ‘telomic’ system represents very probable the con- right posture showed a rather uniform body struc- structional basis leading to modern cormophytes ture. They consisted of a system of dichotomously (extant plants composed of roots, stem and branching leaf- and rootless axes with terminal leaves) after several morphological transforma- tions. It is widely accepted that all land plants including mosses, lycophytes and horsetails repre- * Corresponding author. Tel.: +49-7071-2973561; Fax: +49-7071-295217. sent descendants of early land plants with such a E-mail address: [email protected] rhyniophytic habit (Zimmermann, 1959; Kenrick (A. Roth-Nebelsick). and Crane, 1997; Bateman et al., 1998). The sys-

PALAEO 3216 24-11-03 154 A. Roth-Nebelsick, W. Konrad / Palaeogeography, Palaeoclimatology, Palaeoecology 202 (2003) 153^178 tematic a⁄nities of early land plants are complex ground rhizome system than Aglaophyton and and there is clear evidence that plants with a rhy- Rhynia. An important question which will be niophytic habit belonged to di¡erent systematic addressed in this paper is whether or not these groups. A rhyniophytic organization was ex- di¡erences indicate signi¢cantly di¡erent ecophys- pressed, for example, by the Rhyniopsida and sev- iological requirements which re£ect di¡erent eco- eral basal members of the Lycophytina (see thor- logical niches settled by Rhynie Chert taxa. ough discussion in Kenrick and Crane, 1997). The Any attempt to approach early land plant eco- term ‘rhyniophytic’ will thus be used here not in a physiology has to take paleoenvironmental condi- systematic sense but in order to denote the telo- tions into account. One of the outstanding aspects mic organization. of the early and lower middle Paleozoic climate is Despite fundamental di¡erences between rhy- represented by the high atmospheric CO2 concen- niophytic plants and extant cormophytes, certain trations, compared to the Recent conditions. Dur- tissues of rhyniophytic plants are similar to tissues ing the Lower Devonian, for example, the atmo- of modern land plants (Edwards, 1993; Remy and sphere contained about 10 times more CO2 than Hass, 1996; Edwards et al., 1998). Rhyniophytic today, although the error range concerning this plants show parenchyma with intercellular air value is considerably high (Berner and Kothvala, spaces, stomata, cuticle and water transport tissue 2001). Since the rhyniophytic habit represents the which is arranged within the central protostele. starting point of modern plants and because it Rhyniophytic plants were thus equipped with all evolved under ^ compared to Recent conditions devices necessary for maintaining a homoiohydric ^ extremely high atmospheric CO2 concentrations, state (Raven, 1984, 1993; Edwards et al., 1998). an improvement of our knowledge about possible At ¢rst glance, the typical and uniform structure ecophysiological pro¢les of these archaic plants is of ‘characteristic’ rhyniophytic plants appears to valuable. One aspect of this consideration is the suggest correspondingly uniform ecophysiological fact that stomatal densities of early land plants properties. Recent ¢ndings of macrofossils of including rhyniophytic plants were utilized as early land plants document, however, that early proxy data of past atmospheric CO2 concentra- land plants were able to colonize various habitats tions (McElwain, 1998). with numerous survival strategies and functional In this contribution, a detailed study of gaseous adaptations (for example, Edwards, 1998; Ed- exchange of rhyniophytic plants is presented. wards et al., 2001; Gerrienne et al., 2001). It Since experimental studies on fossil plants are was, for example, suggested by Gerrienne et al., impossible, theoretical methods are necessary. 2001, that unusual spines on the axes of Lower Calculations or simulations of assimilation and Devonian plants existing in higher paleolatitudes transpiration of early land plants were under- were involved in freezing avoidance. taken in some earlier studies. Raven (1984, 1993), Well preserved plants of the Rhynie Chert also for example, carried out calculations of gaseous document numerous di¡erences in tissue ¢ne exchange of early land plants. Beerling and structure and morphology as well as in the hab- Woodward (1997) applied an approach which itats which were settled by di¡erent taxa (Ed- couples photosynthesis and CO2 in£ux. Descrip- wards et al., 1998; Kerp et al., 2001). Aglaophy- tion of molecular £uxes in analogy to electrical ton, for example, produced more massive axes networks is a widely used concept. This method, than Rhynia. The aerial axes of the systematically however, produces correct results only if the path- problematic Nothia aphylla, which was originally ways of the molecules can be described as straight placed within the Rhyniopsida and is now classi- lines (as is the case with £at leaves) and if no ¢ed as a plesiomorphic member of the Lycophy- molecules are extracted from the di¡usional gas tina, shows a rough surface strewn with protuber- £ow. Rhyniophytic plants are however axisym- ances (Kerp et al., 2001). The stomata are located metric and CO2 is removed from the gas £ux on the summit of these protuberances. Further- along the cortex tissue due to the process of as- more, Nothia shows a much more intense under- similation.

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An alternate approach using a porous model di¡erential equation results which cannot be approximation based on an approach of Par- solved analytically in its most general form. khurst and Mott (1990) and Parkhurst (1994) Therefore, some approximations were introduced: was thus formulated and applied in the present (1) the system is supposed to be axially symmetric, study. It allows for detailed considerations of dif- (2) only the stationary state is considered, and (3) ferences in tissue organization and systematic pa- the tissue is treated as a porous medium. Approx- rameter variations. The following taxa are consid- imation (1) is reasonable, because a telome of a ered in this paper: Aglaophyton major, Rhynia rhyniophytic plant shows axial symmetry. Ap- gwynne-vaughanii and Nothia aphylla. The limits proximation (2) has the consequence that rapid and ranges of their gaseous exchange are explored temporal changes in gaseous exchange cannot be and compared. Implications for the atmospheric calculated exactly. Due to the typical dimensions CO2 concentrations of the Lower Devonian are of rhyniophytic plants, however, any ‘di¡usional also regarded. state’ remaining constant for at least W1032 s can be treated as stationary with high accuracy. Ap- proximation (3) averages the discontinuous sys- 2. The model system tem of single cells and voids of a certain tissue into a ¢ctitious continuous tissue with uniform 2.1. The mathematical approach porosity and tortuosity. After application of all approximations, the fol- A thorough presentation and discussion of the lowing ordinary di¡erential equation results: theoretical approach is provided in Konrad et al. 1 d dC Q (2000) and only a short explanation will thus be r ¼ 3 S ¼ const: C ¼ CðrÞ r dr dr S given here. The system of equations is based on Fick’s ¢rst law of di¡usion: Q ¼ Qðr; CðrÞÞ ð3Þ ! j ¼ 3D grad C ð1Þ and ! where j (in mol/m2/s) denotes the di¡usional dCðrÞ £ux, D (in m2/s) the constant of di¡usion, C (in jðrÞ¼3S ð4Þ dr mol/m3) the concentration and grad the di¡erential operator grad fn(Df/Dx, Df/Dy, Df/Dz). In order to solve Eq. 3 we have to specify the If a gas di¡uses through a tissue, then the di¡u- sink term Q = Q(r,C(r)), which represents in the sional pathways represent a complex network, be- case of CO2 the photosynthesis model. A widely cause molecules can only di¡use through the void used photosynthesis model introduced by Farqu- spaces between cells. This e¡ect can be included har et al. (1980) will be used for this purpose. It is into Eq. 1 by substituting D by the parameter S, shortly presented in the Appendix. A detailed dis- the conductance: cussion of the mathematical aspects of the model n (including the solution procedure) is provided in SnD ð2Þ d 2 Konrad et al. (2000). A model of stomatal closure is not included in with porosity n = Vp/V (Vp = pore volume of tis- the system. A stomatal regulation mechanism sue, V = total volume of tissue). The tortuosity which optimizes transpirational water loss and d represents the ‘averaged’ increase of the molec- CO2 in£ux appears to be realized in many angio- ular pathway due to the existence of hindrances sperms (Cowan and Farquhar, 1977). Several (i.e. cells) which cannot be crossed by the mole- models of stomatal behavior exist (Ball et al., cules and have to be by-passed. 1987; Jones, 1992; Aphalo and Jarvis, 1993; The desired mathematical solution of the Beerling and Woodward, 1995). These models present problem is given by insertion of Eq. 1 are, however, only applicable to angiosperms. In into the principle of mass conservation. A partial more ancient plant groups, such as ferns or coni-

PALAEO 3216 24-11-03 156 A. Roth-Nebelsick, W. Konrad / Palaeogeography, Palaeoclimatology, Palaeoecology 202 (2003) 153^178 fers, stomatal behavior is di¡erent from typical transpiration, which was therefore neglected in angiosperm characteristics (see Robinson, 1994 the model. and citations therein). The fern Pteridium aquili- The entire system of Eqs. 3^9 is applied to con- num, for example, shows a very slow stomatal centrically arranged layers representing the cross- movement with a strong endogeneous rhythm sectional model of a rhyniophytic axis and in- (Jarvis and Penny, unpublished results, discussed cludes the boundary layer, stomatal layer, hypo- in Robinson, 1994). P. aquilinum and Osmunda dermal layer (if present) and outer cortex layer regalis do not react instantaneously by rapid sto- (see Fig. 1) (for Eqs. 5^9 see the Appendix). The matal closure on variations in leaf-to-air vapor ¢nal layer speci¢c versions of Eqs. 3 and 4 are pressure de¢cit as is the case with many angio- solved for each layer in such a way that the over- sperms (Franks and Farquhar, 1999). Edwards all solution becomes a continuously di¡erentiable et al. (1996) suggested that rhyniophytic plants function of r. The calculations were performed probably did not show control mechanisms of with the commercial computer code MAPLE. A stomatal closure which are identical to control detailed representation and discussion of the so- systems in extant angiosperms. No data are avail- lution procedure is provided by Konrad et al. able about the mechanism of stomatal closure in (2000). rhyniophytic plants (Edwards et al., 1998). Re- garding these considerations, the formulation of a reasonable model concerning stomatal closure in early land plants is currently not feasible. The model simulations include, however, a study on the e¡ect of stomatal closure on gaseous exchange of the rhyniophytic axis. Gaseous exchange was assumed to occur only by di¡usion through the stomatal pores. Di¡usion through the cuticle was not considered. The pos- sibility cannot be excluded that the cuticle of rhyniophytic plants permitted a certain amount of gaseous exchange. Although Aglaophyton, for example, shows a distinct cuticle of several Wm, this does not necessarily imply impermeability with respect to H2O di¡usion, because the permeance of a cuticle is more dependent on content and distribution of waxes and thus on its biochemical composition than on its thickness (Becker et al., 1986; Edwards et al., 1996). In extant plants, it was shown that low rates of gaseous exchange can occur via the cuticle (Kerstiens, 1996). It was, however, suggested that in many of these experi- ments a signi¢cant portion of gas £ow occurred through incompletely closed stomata (Kerstiens, Fig. 1. Schematic representation of the tissue layer structure 1996). The actual permeance of extant cuticles of the plant models. Only the tissue layers which are consid- thus appears to be very low in general. In rhynio- ered by the mathematical model are shown. Note that the ra- phytic plants, the extremely low stomatal density dial dimensions of the layers in this illustration do not indi- together with the occurrence of a hypodermal cate real layer thickness. The z-axis (longitudinal axis) is orientated perpendicularly to the illustration. Black: bound- channel (in the case of Rhynia and Aglaophyton) ary layer (R^r3, R: plant radius); hatched: stomatal layer suggest a constructional principle of severely con- (r2^R); ruled: hypodermal layer (r1^r2); dotted: assimilation trolled gaseous exchange and thus low cuticular layer (r0^r1). After Konrad et al., 2000.

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2.2. Determination of parameters and sensitivity Nobel, 1999). The amount of visible light which is analyses then absorbed by the plant axis is calculated according to the elevation of the sun and by taking The simulations require several parameters of the cylindric shape into account (see method in di¡erent classes: environmental, anatomical and the Appendix)(Niklas and Kerchner, 1984). biochemical. All parameters are listed in Tables Most of the anatomical parameters are ob- 1^3 together with their sources. The values sum- tained from the literature dealing with excellently marized in Tables 1^3 are termed ‘initial data set’ preserved specimen from the Rhynie Chert, Scot- throughout the rest of the paper. The values of land or from our own measurements. These per- several parameters have to be derived from other mineralized specimen allow for reliable recon- parameters. These parameters are specially structions of axis diameter, geometric properties marked in the tables and the calculation methods or thickness of tissue layers, such as width of are provided in the Appendix. For several param- stomatal pore or thickness of epidermis, as well eters, the chosen values will be shortly discussed as the determination of tissue porosity. Since in the following section. All other parameter val- chloroplasts are, however, not preserved by fossil- ues will be discussed in Section 4.1. ization processes, the surface factor of the chlo- The atmospheric CO2 content is derived from roplasts has to be estimated on the basis of data model simulations which indicate RCO2 values from extant plants (see description in the Appen-

(RCO2 = fossil CO2 concentration/Recent CO2 con- dix). centration) of the Lower Devonian between 10 All biochemical parameters have to be taken and 15 (Berner and Kothvala, 2001). For the Pra- from corresponding literature data obtained for gian (age of Rhynie Chert) a value of RCO2 =12is extant plants. Vmax and Jmax, for example, were suggested by Berner and Kothvala (2001). For the taken from the range of values found for extant initial data set, a CO2 concentration 12 times conifers and then ¢ne-tuned in such a way that higher than the Recent value was thus chosen. the ratio between internal and external CO2 con- The best ¢t curve of past CO2 concentrations is, centration amounts to Ci/Ca = 0.7. It is generally however, enveloped by an error range of consid- assumed that this ratio represents ^ at least on an erable size (Berner and Kothvala, 2001). Possible averaging long-term scale ^ a common value real- implications of the present results for estimations ized in land plants (Ku«rschner, 1996; Beerling of Lower Devonian CO2 concentrations are dis- and Woodward, 1997). The values of Vmax and cussed in Section 4.4. Jmax are in this case at the lower range of values The irradiance value is based on the Recent found in extant conifers (see Appendix). The reli- solar constant and the various processes of scat- ability of the biochemical parameters is discussed tering and re£ection of electromagnetic radiation in Section 4. back into space (see, for example, Gates, 1980 or The present contribution contains several sensi-

Table 1 The environmental parameters of the simulation model Parameter Value Source

Wind velocity uatm (m/s) 0.8 arbitrary 33 Boundary layer thickness dbl (10 m) derived 3 Atmospheric CO2 content Ca (mmol/m ) 168 Berner and Kothvala, 2001 H2O 3 a Atmospheric H2O content Catm (mmol/m ) 843 arbitrary Air temperature T (‡C) 30 Beerling et al., 2001 2 Irradiance I3 ¼45 (Wmol/m /s) 620 arbitrary In the case of the derived parameters, the method of calculation is provided in the Appendix. a Parameter is varied, see text.

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Table 2 The anatomical parameters of the simulation model Parameter Aglaophyton Rhynia Nothia Radius of plant R (1033 m)a 2.25 1.0 1.050b 33 c;d;e Depth of stomatal pore dst (10 m) 0.03 0.015 0.03 33 c;d Long axis of stoma hst (10 m) 0.039 0.029 0.021 33 c;d Short axis of stoma wst (10 m) 0.0105 0.01 0.0025 310 2 c;d;e Area of stomatal pore ast (10 m ) 3.216 2.278 0.412 6 2 d;f Stomatal density Xst (10 /m ) 1.0 1.75 3.35 33 f;g Porosity of stomatal layer nst (10 ) 0.32 0.399 0.357 33 f;g Tortuosity of stomatal layer dst (10 ) 1.34 1.57 1.12 h d2 33 g;h ‘Conductivity’ of stomatal layer nst/ st (10 ) 0.18 0.16 0.28 33 c;d;f Thickness of hypodermal layer dhc (10 m) 0.075 0.105 ^ 33 c;d;e Long axis of hypodermal channel hhc (10 m) 0.04 0.03 ^ 33 c;d;e Short axis of hypodermal channel whc (10 m) 0.03 0.02 ^ 310 2 c;d;e Area of hypodermal channel ahc (10 m ) 9.42 4.71 ^ 33 f;g Porosity of hypodermal layer nhc (10 ) 0.96 0.87 ^ 33 f;g Tortuosity of hypodermal layer dhc (10 ) 1.0 1.0 ^ h d2 33 f;g ‘Conductivity’ of hypodermal layer nhc/ hc (10 ) 0.96 0.87 ^ 33 c;d i Thickness of assimilation layer das (10 m) 0.25 0.1 0.42 Cortex cell radius c (1036 m)c;d 55 50 45 g Speci¢c surface of cortex cell (aas/vas) (1/m) 36 364 40 000 44 444 g Surface factor of chloroplasts (achl/aas) (^) 2.345 2.345 2.345 33 j Porosity of assimilation layer nas (10 ) 0.35 0.35 0.35 33 g Tortuosity of assimilation layer das (10 ) 1.571 1.571 1.571 h d2 33 f;g ‘Conductivity’ of assimilation layer nas/ as (10 ) 0.142 0.142 0.142 In the case of the derived parameters, the method of calculation is provided in the Appendix. a Various sources. b In the case of Nothia this indicates the ‘outer’ radius of the plant (i.e. including Nothia’s emergences). The ‘inner’ radius (measured at the bases of the emergences) amounts to 0.72 1033 m. c Edwards et al., 1998. d Kerp et al., 2001. e Kerp and Hass, personal communication. f Parameter is varied, see text. g Parameter is derived. h The conductance S = Dn/d2 splits up into a factor D containing properties of the di¡using substance and a factor n/d2 de- scribing the morphology of the medium. The term ‘conductivity’ stands for the second factor. i In the case of Nothia the emergences are supposed to contain assimilating tissue. j Parameter was obtained by own measurements.

tivity analyses. During a sensitivity analysis, one 3. Results or two parameters are varied systematically, while the others are kept constant. Sensitivity analyses 3.1. Local £uxes of H2O and CO2 with initial data are valuable in order to, (1) analyze system be- set havior, and (2) check the reliability and limitations of the model approach. If a sensitivity anal- The £ux of H2O is caused only by the water ysis is carried out, then the varied parameters potential gradient between plant tissue and atmo- are explicitly described in the corresponding sec- sphere whereas for CO2 the £ux is generated by tions, while the other parameters show the values the assimilation process. Fig. 2 shows the local provided in the initial data set listed in Tables £uxes of CO2 and H2O for Aglaophyton, Rhynia 1^3. and Nothia for the initial data set, plotted against

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Table 3 The biochemical parameters of the simulation model Parameter Picea Aglaophyton Rhynia Nothia 33 2 E¡ective conductance through a cortex cell gliq (10 mmol/m /s/Pa) 0.5 0.5 0.5 0.5 33 2 a Light-saturated rate of electron transport Jmax (10 mmol/m /s) 2.048 1.047 2.884 0.792 Michaelis^Menten constant for carboxylation Kc (Pa) 189 189 189 189 Michaelis^Menten constant for oxygenation Ko (Pa) 42 382 42 382 42 382 42 382 33 2 a Local maximum carboxylation rate Vmax (10 mmol/m /s) 0.842 0.430 1.185 0.325 Partial pressure of oxygen at chloroplasts po (Pa) 20 260 20 260 20 260 20 260 E⁄ciency of light conversion K (^) 0.2 0.2 0.2 0.2 Speci¢city factor for Rubisco a (^) 1 906 1 906 1 906 1 906

The values of the local maximum carboxylation rate Vmax and of the light-saturated rate of electron transport Jmax labeled Aglao- phyton, Rhynia and Nothia, respectively, are calculated in such a way that the condition Ci/Ca = 0.7 is ful¢lled. The data are compiled from the following sources: Harley and Sharkey, 1991; Harley et al., 1992; Kirschbaum and Farquhar, 1984; Parkhurst and Mott, 1990; Wullschleger, 1993. a Parameter is varied, see text.

Fig. 2. Local £uxes of H2O and CO2 plotted against radial coordinate for Aglaophyton major (A), Rhynia gwynne-vaughanii (R) and Nothia aphylla (N). as, hc, st and bl are abbreviations for assimilation layer, hypodermal channel, stomatal layer and boundary layer, respectively.

PALAEO 3216 24-11-03 160 A. Roth-Nebelsick, W. Konrad / Palaeogeography, Palaeoclimatology, Palaeoecology 202 (2003) 153^178 the distance r from the symmetry axis (listed in concentrations of H2O and CO2. Strong gradients Tables 1^3). For Aglaophyton and Rhynia, the are visible along: (1) the stomatal pore and (2) the £uxes of H2O and CO2 (outside the assimilation hypodermal channel (in the cases of Aglaophyton layer) are smooth functions of r. This is due to, and Rhynia). In the case of CO2, a gradient along (1) the axial symmetry of the plant, and (2) the the assimilation layer has established. It is, how- principle of conservation of mass which forces the ever, weak if compared to the stomatal and hypo- £uxes to increase or decrease inversely propor- dermal gradient. The initial values of Vmax and tional to r if sources or sinks are absent. In the Jmax lead to values of intercellular CO2 concen- case of Nothia, the £uxes behave somewhat less tration of about Ci/Ca = 0.7 (see Section 2.2). As- smoothly, because Nothia’s emergences destroy similation is saturated under these conditions. the complete axial symmetry of the plant axes. Inside the assimilation layer, the CO2 £ux changes 3.2. Transpiration and assimilation rates with for all three species from an increase to a strong initial data set decrease due to the consumption of CO2 during the assimilation process. Fig. 3 shows the local The transpiration rate (i.e. the e¥ux of H2O

Fig. 3. Local concentrations of H2O and CO2 plotted against radial coordinate for Aglaophyton major (A), Rhynia gwynne-vaughanii (R) and Nothia aphylla (N). as, hc, st and bl are abbreviations for assimilation layer, hypodermal channel, stomatal layer and boundary layer, respectively.

PALAEO 3216 24-11-03 A. Roth-Nebelsick, W. Konrad / Palaeogeography, Palaeoclimatology, Palaeoecology 202 (2003) 153^178 161 out of the axis surface per unit surface area) for Aglaophyton, Rhynia and Nothia is plotted as a histogram in Fig. 4. Aglaophyton and Rhynia show similar transpiration rates. Nothia shows the highest transpiration rate. The transpiration is low for all three taxa compared to common values of extant plants. Aglaophyton, for example, transpires 0.087 mmol/m2/s whereas for leaves of mesophytic trees values of 3 mmol/m2/s are common (see, for example, Larcher, 1997). It is, however, more reasonable in the case of rhyniophytic plants to relate their water loss to their volume (see underlying ideas in Section 4.2). This is ac- complished by calculating T = jH2O(R)U2ZRL/ (ZR2L)=2/RUjH2O(R) where L denotes the axis length. The results are included in Fig. 4. In this case, Aglaophyton shows the lowest transpiration rate, Nothia develops again the highest rate, while Rhynia lies in between these two values. Fig. 5 shows the values of CO2 in£ux per unit surface area into the plant axes for Aglaophyton, Fig. 5. Assimilation rates of Aglaophyton major, Rhynia gwynne-vaughanii and Nothia aphylla, obtained with Vmax and Jmax from the initial data set. White columns: assimilation rate per surface area (Wmol/m2/s). Black columns: assimilation rate per volume (mmol/m3/s).

Rhynia and Nothia.TheCO2 in£ux values represent the assimilation rates. Assimilation is highest for Nothia and lowest for Aglaophyton with Aglaophyton and Rhynia showing similar values. Note that the CO2 in£ux is not related to projected surface area as is usual for assimilation rates of extant plants. Converting assimilation rates per projected surface area to allow for the direct comparison with literature data of extant plants requires the multiplication of the presented values with the factor 4.44 (because of 2ZRL/(2RL cos 3)=Z/cos 3 = 4.44, if the sun is elevated 3 = 45‡ above the horizon and with an axis of length L). If the assimilation is, however, related to volume by the same procedure as was applied in the case of the water e¥ux (see above and underlying ideas in Section 4.2), then Aglaophyton shows a distinctly lower value than Rhynia while Nothia develops again the highest value (see Fig. 4. Transpiration rates of Aglaophyton major, Rhynia gwynne-vaughanii and Nothia aphylla. White columns: tran- Fig. 5). The formal de¢nition of the assimilation CO spiration rate per surface area (Wmol/m2/s). Black columns: rate per volume is given by A = j 2 (R)U2ZRL/ transpiration rate per volume (mmol/m3/s). (ZR2L)=2/RUjCO2 (R)).

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The parameter of WUE (‘water use e⁄ciency’) have been transformed according to rhyniophytic gives the ratio between the numbers of assimilated anatomical structure, see Appendix). These values CO2 molecules and transpired H2O molecules. It were chosen, because Vmax and Jmax of conifers is usually expressed as Wmol CO2 ¢xed per mmol are rather low and it is reasonable to assume H2O lost. The value of WUE represents the in- that Vmax and Jmax of rhyniophytic plants were stantaneous water loss during photosynthesis and located at the lower range of the extant spectrum is therefore strongly dependent on various param- of assimilation parameters (see Section 4.1.2). eters, such as the degree of stomatal closure, tem- With these values, Aglaophyton exhibits dis- perature or relative humidity. In a real plant, the tinctly higher assimilation rates per surface area WUE thus represents a strongly £uctuating pa- than Rhynia (see Fig. 6). If related to axis volume, rameter whose instantaneous value changes with however, Aglaophyton and Rhynia show almost various factors. In order to obtain a long-term identical values (see Fig. 6). The assimilation value of net carbon gain, long-term parameters, rate of Nothia approximately doubles on replac- such as the seasonal amount of water transpired ing the Vmax and Jmax values of the initial data set per dry matter produced, are often used especially by the Picea abies values and attains again the in agricultural studies (Kramer, 1983). It is, how- highest value of all three taxa, both with respect ever, possible to obtain ‘characteristic’ WUE val- to surface area and to volume (see Fig. 6). The ues of extant and unstressed C3 plants with their WUE values change in accordance with the assim- stomata fully opened (Nobel, 1999). With the ini- ilation rates, because the transpiration rate is not tial data set, the calculated assimilation and tran- in£uenced by the values of Vmax and Jmax (see spiration rates of Aglaophyton, Rhynia and Nothia Fig. 7). The ratios of internal CO2 concentration yield values around WUEW37, which is about 18 to external CO2 concentration now amount to times higher than the ‘typical’ extant value. Sim- ilar WUE values for all three plants under the conditions of the initial data set are to be expected as the WUE depends ^ at least approximately ^ not on the morphology of a plant but rather on the ratio of the (free air) di¡usional constants with respect to CO2 and H2O times the ratio of the concentration gradients of CO2 CO H O H O H O and H2O, i.e. WUE = D 2 /D 2 UvC 2 /vC 2 (Farquhar et al., 1989).

3.3. Sensitivity analyses

3.3.1. Variation of Vmax and Jmax With the present Vmax and Jmax values, small variations of these two parameters lead to strong changes of the assimilation rate. In order to per- form a sensitivity analysis with respect to Vmax and Jmax, di¡erent values of these two parameters were inserted. By doing this, the concept of Ci/ Ca = 0.7 is dismissed. For this sensitivity analysis, Vmax and Jmax values of a certain extant conifer (Picea abies, Wullschleger, 1993) are applied Fig. 6. Assimilation rates of Aglaophyton major, Rhynia W 2 W gwynne-vaughanii and Nothia aphylla, obtained with Vmax (Vmax = 0.842 mol/m /s and Jmax = 2.05 mol/ and J from Picea abies. White columns: assimilation rate 2 max m /s) instead of the values of the initial data set per surface area (Wmol/m2/s). Black columns: assimilation (see Table 3, note that the original literature data rate per volume (mmol/m3/s).

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All other values correspond to the initial data set. The graph illustrates the threshold behavior of the assimilation rate with respect to the parameter Xst. Below the threshold value of Xst, the assimilation rate decreases strongly with decreasing Xst and changes with dhc in a non-linear manner. Above the threshold value, an increase in Xst has

Fig. 7. Values of WUE of Aglaophyton major, Rhynia gwynne-vaughanii and Nothia aphylla. Values of Vmax and Jmax from Picea abies lead to di¡erent values of WUE for each species (left three columns). Values of Vmax and Jmax from the initial data set (derived via the condition Ci/ Ca = 0.7) result in a common WUE value for all three species (right column).

Ci/Ca = 0.42 for Aglaophyton, Ci/Ca = 0.79 for Rhynia and Ci/Ca = 0.35 for Nothia. The reason for the strong e¡ect of this moderate variation of Vmax and Jmax is illustrated by Fig. 8 which Fig. 8. a: Sensitivity analysis: dependence of assimilation shows the CO2 in£ux as depending on Vmax and rate per volume on Vmax and Jmax for Aglaophyton major Jmax. The initial values of Vmax and Jmax are lo- plotted in a three-dimensional representation. The position of cated at the critical ‘£ank’ and small variations of the result obtained with the initial data set is indicated in the these two values thus result in strong changes of graph by the mark ‘Ag’. b: Sensitivity analysis: dependence of assimilation rate per volume on Vmax and Jmax for A. ma- the CO2 in£ux. jor plotted in a two-dimensional representation (contour plot). The graph can be described as top view of Fig. 8a. 3.3.2. Variation of stomatal density, thickness of The lines are lines of constant assimilation rate per volume. hypodermal channel and stomatal opening The lines marked i to iv represent the following assimilation 3 3 3 3 3 The assimilation rate plotted against length of rates per volume: 1.5 mmol/m /s, 6 mmol/m /s, 7 mmol/ m3/s and 38 mmol/m3/s, respectively. Values of adjacent the hypodermal channel dhc and stomatal density lines di¡er by 0.5 mmol/m3/s. The position of the result ob- Xst for Aglaophyton is shown in Fig. 9a. The tained with the initial data set is indicated in the graph by 2 ranges are dhc =0T1.05 mm and Xst =0T20/m . the mark ‘Ag’.

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represents thus fully opened stomata). Fig. 9b demonstrates that the assimilation rate increases strongly when the pore begins to open and reaches a plateau at a degree of stomatal opening of about 0.3 ( = 30%). Further increase in stomatal opening does not result in increasing assimilation rates. Fig. 10a depicts how the transpiration rate of Aglaophyton depends on dhc and Xst. dhc and Xst are varied across the same ranges as in the sensitivity analysis of the assimilation rate. For 2 dhcC0.2 mm and for XstC1.5/mm , the transpira-

Fig. 9. a: Sensitivity analysis: assimilation rate per volume plotted against length of hypodermal channel dhc and stomatal density Xst for Aglaophyton major. The position of the result obtained with the initial data set is indicated in the graph by the mark ‘Ag’. b: Sensitivity analysis: assimilation rate per volume plotted against degree of stomatal closure, expressed as ratio between pore area and total pore area. This ratio can take values between 0 ( = fully closed stomata) and 1 ( = fully opened stomata). no signi¢cant e¡ect on assimilation, whereas the assimilation rate increases approximately linearly with decreasing dhc. The same behavior can be observed for Rhynia and Nothia (data not shown). Fig. 10. a: Sensitivity analysis: transpiration rate per volume For all three plants, the (calculated) threshold val- plotted against length of hypodermal channel dhc and stoma- ues of Xst are close to the (measured) values which tal density Xst for Aglaophyton major. The position of the re- were used in the initial data set. sult obtained with the initial data set is indicated in the Fig. 9b shows the change of assimilation rate graph by the mark ‘Ag’. b: Sensitivity analysis: transpiration rate per volume plotted against degree of stomatal closure, during stomatal closure which is provided in the expressed as ratio between pore area and total pore area. ¢gure as ratio between the pore area and the area This ratio can take values between 0 ( = fully closed stomata) of the completely opened pore (the value of 1 and 1 ( = fully opened stomata).

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segments (i.e. parallel to the abscissae) of the curves photosynthesis is saturated, in the inclined parts it is undersaturated. Under the conditions of the initial data set, saturation of photosynthesis 3 starts at CaW120 mmol/m (Fig. 12a). For Vmax and Jmax of Picea, starting points of saturated 3 photosynthesis are located at CaW106 mmol/m 3 (Rhynia), CaW166 mmol/m (Aglaophyton), and 3 CaW193 mmol/m (Nothia)(Fig. 12b). In another sensitivity analysis, Ca and Xst are varied simultaneously. With the other values cor- Fig. 11. Sensitivity analysis: WUE plotted against length of responding to the initial data set, Fig. 13a,b X hypodermal channel dhc and stomatal density st for Aglao- shows the result for Aglaophyton. A large, plain phyton major. The position of the result obtained with the in- X itial data set is indicated in the graph by the mark ‘Ag’. ‘£oor’ represents combinations of Ca and st which lead to saturation of photosynthesis, while tion rate varies strongly and in a non-linear manner on both Xst and dhc. With higher values of the stomatal density, the transpiration reacts more moderately on changes in Xst and dhc. Inspection of Fig. 10a reveals that the ‘actual’ transpiration rate of Aglaophyton is located at the upper end of the steep £ank. The same behavior can be observed for Rhynia and Nothia (data not shown). In Fig. 10b the change of transpiration rate during stomatal closure is represented. It can be seen that ^ contrary to the change in assimilation rate, shown in Fig. 9b ^ the transpiration rate increases smoothly with increasing stomatal opening. At a degree of stomatal opening of roughly 0.3 ^ which su⁄ces for achieving maximum assimilation rate ^ the transpiration rate amounts to about half the value of transpiration with fully open pores. The WUE (which can, by de¢nition, be viewed as combining e¡ects of assimilation rate and transpiration rate) is shown as a function of dhc and Xst in Fig. 11. A steep £ank develops for XstC1.5/ 2 mm and dhcC0.2 mm. The WUE value obtained with the initial data set is seated at the bottom of this £ank.

3.3.3. Variation of atmospheric CO2 concentration The assimilation rates are plotted against the atmospheric CO2 concentration Ca for the range Fig. 12. Sensitivity analysis: assimilation rate per volume 3 plotted against atmospheric CO2 concentration Ca for Aglao- Ca =10 250 mmol/m in Fig. 12a,b. Vmax and T phyton major (A), Rhynia gwynne-vaughanii (R) and Nothia Jmax values correspond to the initial data set aphylla (N). a: Jmax and Vmax of the initial data set (leading (Fig. 12a) or are taken from extant Picea abies to Ci/Ca = 0.7). b: Jmax and Vmax of an extant plant (Picea (Fig. 12b) (see Section 3.3.1). In the horizontal abies).

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value of Ca has little in£uence on saturation, pro- 2 vided Xsty0.1/mm is satis¢ed. Variation of the photosynthesis parameters Vmax and Jmax changes the positions, where the ‘undersaturated’ walls raise from the ‘saturated’ £oor, but not the qual- itative features of the graph. If, for example, Vmax and Jmax of Picea abies are used, then Xsty1.5/ 2 3 mm requires CaW160 mmol/m to saturate photosynthesis, and Ca loses its in£uence on satura- 2 tion only for values of Cay650 mmol/m (again 2 under the premises Xsty0.1/mm ). Rhynia and Nothia show similar behavior.

3.3.4. Variation of other photosynthesis parameters and chloroplast density There are some other parameters, which in£u- ence assimilation: the e¡ective conductance through the interior structures of the cortex cells gliq, the speci¢city factor for Rubisco a, the irradiance I, the e⁄ciency of light conversion K and the chloroplast surface factor achl/aas. In order to ¢nd out whether any of these parameters are critical (in the sense, that small de- viations from their exact values result in high changes of the results) we performed sensitivity analyses by plotting the assimilation rate as a function of each of these variables while keep- Fig. 13. a: Sensitivity analysis: assimilation rate per volume ing the other variables constant. These graphs plotted against atmospheric CO2 concentration Ca and sto- (not shown) have several features in common: X matal density st for Aglaophyton major. The position of the (1) when the independent variable approaches result obtained with the initial data set is indicated in the zero, the assimilation rate disappears as well, graph by the mark ‘Ag’. b: Sensitivity analysis: assimilation (2) the assimilation rate increases continuously rate per volume plotted against atmospheric CO2 concentration Ca and stomatal density Xst for A. major in a two-di- with increasing independent variable, and (3) all mensional representation (contour plot). The graph can be curves behave asymptotically, i.e. the assimilation described as top view of Fig. 13a. The lines are lines of con- rate is saturated for su⁄ciently high values of the stant assimilation rate per volume. The lines marked i and ii independent variable. According to the positions, represent values of assimilation rate per volume of 32.75 mmol/m3/s and 0 mmol/m3/s, respectively. Values of adjacent which are occupied by the parameter values of lines di¡er by 0.25 mmol/m3/s. the initial data set, we draw the following conclusions: (1) gliq and a are uncritical, because their initial data set values are positioned on the the two ‘walls’ result from strong variations of the asymptotic segment of the curves, (2) I and K are assimilation rate for (Ca,Xst)-pairs which are too ‘semi-critical’ in the following sense: their initial low to allow for saturation of photosynthesis. For data set values lie at the ‘beginning’ of the asymp- 2 Xsty1.4/mm , saturation is nearly independent of totic segment, i.e. if their ‘true’ values would be 3 Xst and is given as long as Cay120 mmol/m is higher than the values assigned to them in the 2 ful¢lled. XstC1.4/mm , however, requires increas- initial data set, then this error would not in£uence ingly high values of Ca in order to keep photo- the assimilation rate, but if the ‘true’ values would 2 synthesis saturated. For Cay400 mmol/m , the be lower, the initial data set would produce mis-

PALAEO 3216 24-11-03 A. Roth-Nebelsick, W. Konrad / Palaeogeography, Palaeoclimatology, Palaeoecology 202 (2003) 153^178 167 leadingly high results, (3) the chloroplast surface ilar to air temperature. The justi¢cation for this factor achl/aas is critical: its initial data set value assumption is as follows. Heat transfer via con- lies on the segment of the curve which exhibits the vection (sensible heat) and evaporative cooling steepest gradient. due to transpiration (latent heat) represent important mechanisms for heat transfer in plants (see, for example, Gates, 1980; Monteith and Uns- 4. Discussion worth, 1990). Evaporative cooling is, however, of little importance for rhyniopyhtic plants due 4.1. Reliability of input parameters to the high stomatal resistance leading to low transpiration rates and it is therefore to be ex- 4.1.1. Humidity, wind speed and temperature pected that convective cooling dominates heat Humidity and wind speed were arbitrarily chos- transfer in rhyniophytic plants (Roth-Nebelsick, en, because it is very probable that these param- 2001). During low wind speed or calm air, the eters showed a similar wide range of values during temperature of the plant axis, if exposed to direct the Lower Devonian as they do today. Humidity sunlight, can reach values which are several de- (i.e. atmospheric H2O concentration) in£uences grees higher than air temperature (Roth-Nebel- the results via the transpiration rate, because the sick, 2001). Higher wind speeds (uatmy0.5T1 evaporative water loss is proportional to the gra- m/s) lead to e¡ective convective cooling of the dient of the water vapor concentration between cylindrical plant axis, because the intensity of the intercellular spaces of the plant and the atmo- this exchange process varies inversely to the sphere (see, for example, Jones, 1992 or Nobel, boundary layer thickness, which is small for a 1999). More precisely, transpiration rate is a lin- body with a low characteristic dimension (Beer- ear function of the atmospheric H2O concentra- ling et al., 2001; Roth-Nebelsick, 2001). Thus, tion CH2O. In a plot, the two quantities are related under the conditions of the initial data set, the by a straight line. The slope of this line depends temperature of the rhyniophytic plant axis should on the details of the plant morphology. That is, at approach the air temperature. a given humidity, the studied species lose water at di¡erent rates. 4.1.2. Biochemical parameters The wind speed in£uences the results via the All biochemical parameters have to be taken boundary layer thickness, which decreases with from extant plants. These parameters, together decreasing characteristic dimension (for a cylin- with the chloroplast surface factor (see Section drical structure its radius) and increasing wind 2.2 and Appendix), represent an outstanding fac- speed. The boundary layer thickness governs the tor of uncertainty. The extent of uncertainty to be boundary layer conductance both for gaseous ex- faced depends on whether a parameter is ‘critical’, change and heat transfer (see review by Schuepp, that is, whether small changes of the parameter 1993). The main resistance to gaseous exchange, have signi¢cant in£uence on the results or not. In however, is contributed not by the boundary the latter case, an accurate knowledge of the value layer, but by the low stomatal density of rhynio- of this parameter is less crucial. Such sensitivity phytic plants, and variation of wind speed has analyses show that the chloroplast surface factor thus a low or even no e¡ect on the gas £uxes {achl/aas} as well as Vmax and Jmax represent crit- through the stomata (see Section 4.2). Convective ical parameters whereas the other parameters heat transfer (heat is carried away by air move- are far less crucial (see Sections 3.3.1, 3.3.4 and ments), however, does not depend on stomatal Fig. 8). conductance and is therefore strongly in£uenced The values for Vmax and Jmax of the initial data by wind speed. set are chosen according to two criteria: they are The process of heat transfer was not included in typical for plants belonging to phylogenetic older the present simulations. We assumed instead from groups, such as conifers or cycads. In order to the outset that the temperature of the axis is sim- narrow this range, we ¢ne-tuned Vmax and Jmax

PALAEO 3216 24-11-03 168 A. Roth-Nebelsick, W. Konrad / Palaeogeography, Palaeoclimatology, Palaeoecology 202 (2003) 153^178 in such a way, that the ratio between the internal suggested that steeper gradients of CO2 from the and the external CO2 concentrations amounts to outside to the intercellular air spaces may have Ci/Ca = 0.7. How reliable this choice is, if applied been maintained by plants living under higher at- to rhyniophytic plants, will be discussed in the mospheric CO2 concentrations than today. None- following. theless, applying the Ci/Ca = 0.7 criterion to early (1) It is generally assumed that rhyniophytic land plants results in reasonable assimilation rates plants were C3 plants (Raven, 1993). Further- (see Section 4.3). According to these considera- more, the properties of photosynthetic enzymes tions, we choose the values of Vmax and Jmax in appear to be rather similar among extant plants the initial data set such that a ratio Ci/Ca = 0.7 is (Badger and Andrews, 1987; Bowes, 1993). It is maintained. Substituting instead values from Pi- therefore to be expected that the kinetic properties cea abies for Vmax and Jmax leads in the case of of Rubisco in early land plants were similar to Rhynia to a ratio which hardly deviates from Ci/ those being measured in extant C3 plants. It ap- Ca = 0.7. For Aglaophyton and Nothia, however, pears thus justi¢ed to use values of the extant the P. abies values lead to steep CO2 gradients: spectrum. the ratios Ci/Ca amount to Ci/Ca =0.42 (Aglao- (2) The question arises which values of Vmax phyton) and Ci/Ca = 0.35 (Nothia), and the assim- and Jmax of the extant spectrum should be used. ilation rates are twice as high as is the case for Ci/ Rhyniophytic plants evolved in an atmosphere Ca = 0.7 (see Fig. 6). The rather constant values of 13 with outstandingly higher atmospheric CO2 con- N C of terrestrial organic matter since the Devo- centrations compared to Recent conditions. nian, however, indicate that the ratio of Ci/Ca was Under extant atmospheric conditions, the Rubis- more or less constant through time (Edwards et co of those plants utilizing mechanisms which real., 1998). sult in higher CO2 concentrations at the carboxylation site (such as C4 and CAM plants or 4.2. Transpiration of the rhyniophytic axes aquatic plants with CO2 concentrating mechanisms) shows a lower a⁄nity to CO2 than the Signi¢cant di¡erences in transpiration rate exist Rubisco of C3 plants with lower CO2 concentra- between the considered taxa (Fig. 4). These di¡er- tions at the carboxylation site. It is thus not to be ences are only due to anatomical and morpholog- expected that early land plants which evolved ical properties. Nothia shows the highest water under high CO2 showed assimilation parameters loss rate due to the high stomatal density and of high performance C3 plants which evolved the lack of narrow hypodermal channel under- under much lower atmospheric CO2 concentra- neath the stomata. Relating transpiration rate to tions. Using values located at the lower range of surface area, however, does not provide any in- the extant spectrum thus appears to be justi¢ed. formation about the di¡erences in the degree of (3) Ci/Ca = 0.7 is generally considered as repre- water loss in cylindrical plant axes with di¡erent senting a common value among vascular plants radii. With the same transpiration rate per surface (Robinson, 1994; Beerling and Woodward, 1997; area, the parenchyma of a thicker axis loses a Larcher, 1997). Numerous species do actually smaller fraction of water than the parenchyma show this value during photosynthesis (von of a thinner axis. This is because the volume of Caemmerer and Evans, 1991; Franks and Farqu- a plant axis increases with the radius squared har, 1999). It is, however, not strictly obeyed by while the transpiring surface area increases pro- plants and in many cases the Ci/Ca ratio can de- portional to the radius. If the transpiration rate is viate signi¢cantly from 0.7 (Farquhar et al., 1989; related to volume, then the transpiration rate of Franks and Farquhar, 1999). It is not clear Aglaophyton is signi¢cantly lower than that for whether Ci/Ca = 0.7 was also obeyed by early Rhynia and much lower than that for Nothia. land plants which evolved and existed under com- Aglaophyton thus shows a signi¢cantly more strict pletely di¡erent external CO2 concentrations if water conservation strategy than Rhynia and No- compared to Recent conditions. Robinson (1994) thia.

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The position of the stomata in Nothia, on the fully assessed. Mycorrhizal fungi are usually inter- summits of the emergences, and the surface preted as improving the nutrient supply as is the roughening due to these emergences were inter- case in extant mycorrhizas (Harley and Smith, preted as increasing transpiration rate, because: 1983; Taylor et al., 1992; Taylor and Taylor, (1) the exposed position of the stomata would 1997). There is evidence that in some cases extant cause the pore to be positioned outside the low mycorrhizae may contribute also to the water velocity region of the boundary layer, and (2) a supply of the host plant (Ruiz-Lozano and Az- rough surface promotes a turbulent boundary con, 1995). It is, however, unclear whether this layer (Kerp et al., 2001). The boundary layer also occurred in rhyniophytic plants to a signi¢- does, however, not represent the main di¡usive cant amount. resistance for gaseous exchange. The following The role of mycorrhizae on gaseous exchange ratios of resistances res (inverse of conductance in rhyniophytic plants ^ except of decreasing the S) are valid for di¡usion of both CO2 and H2O: size of intercellular voids by settlement of fungal (bl = boundary layer, st = stomatal layer, hy = hyphae ^ is di⁄cult to estimate until more studies hypodermal layer, if present, as = assimilation are made. At any rate, water conservation was layer) resbl :resst :reshy :resas = 1:5560:1037:7 for very probably of utmost importance for rhynio- Aglaophyton, 1:6166:1144:7 for Rhynia and resbl : phytic plants (Edwards et al., 1998). resst :resas = 1:73 682:5 for Nothia. Reducing the The higher transpiration rate of Nothia (which boundary layer resistance (i.e. increasing the is still low compared to common transpiration boundary layer conductance) thus does not in£u- rates of extant plants) is also supported by fossil ence gaseous exchange signi¢cantly, neither in data. Nothia showed an extensive underground Aglaophyton and Rhynia nor in Nothia. It is there- rhizom system. This massive rhizomatous system fore improbable that the rough surface of Nothia of Nothia shows clusters of rhizoids being directly increased gaseous exchange. An unequivocal in- connected to the stele of the aerial axes (Kerp et terpretation of possible functional features of the al., 2001). This indicates that Nothia probably had emergences of Nothia is di⁄cult at present. It a better water-absorbing capacity than Aglaophy- could be speculated that these structures possibly ton and Rhynia and could thus sustain the com- played a role in heat transfer because heat trans- paratively high transpiration rate of the aerial sys- fer is (1) mainly independent of stomata and the tem. Additionally, the aboveground axes probably gas £uxes through them, and (2) sensitive to had a short life span and were shedded during boundary layer thickness and turbulence. unfavorable (dry?) periods whereas Aglaophyton The strict water-conserving strategy of Aglao- and Rhynia possessed more long-living axes. phyton and ^ to a lower extent ^ in Rhynia is in This is indicated by the poorer preservation po- accordance with information available about the tential of the aerial axes of Nothia compared to growth form of these plants. Aglaophyton and Aglaophyton and Rhynia. Rhynia do not show massive underground rhizom systems and the ability of Aglaophyton and Rhy- 4.3. Assimilation of the rhyniophytic axes nia with respect to water absorption was probably severely restricted despite the fact that both taxa With the initial data set, the assimilation rates occurred in more humid habitats (there is, for of Aglaophyton, Rhynia and Nothia (related to example, evidence that Aglaophyton was able to projected surface area) are 14.4 Wmol/m2/s (Aglao- survive £ooding events, see Remy and Hass, phyton), 16.1 Wmol/m2/s (Rhynia) and 23.1 Wmol/ 1996). Transpiration rate could additionally be m2/s (Nothia), respectively. That is, they lie in the decreased by stomatal closure during, for exam- lower to middle range of values of net photosyn- ple, periods of high plant-to-air vapor pressure thesis usually found in extant plants (see, for ex- de¢cits, as shown in Fig. 10b. ample, Long et al., 1993; Larcher, 1997). Extant The e¡ects of mycorrhizal fungi which are plants with very low assimilation rates, such as present in many rhyniophytic taxa cannot yet be the ferns Osmunda regalis and Pteridium aquili-

PALAEO 3216 24-11-03 170 A. Roth-Nebelsick, W. Konrad / Palaeogeography, Palaeoclimatology, Palaeoecology 202 (2003) 153^178 num, show values in the range 10T12 Wmol/m2/s the plants since both taxa show neither an exten- under optimal conditions (Franks and Farquhar, sive rhizome system which has to be supported by 1999). Typical values of conifers lie in the range the aerial axes nor costly support tissues, because of 6T10 Wmol/m2/s and the morphological and rhyniophytic plants were turgor-stabilized (Speck anatomically similar extant species Psilotum nu- and Vogellehner, 1988). In perennial plants, half dum shows characteristic assimilation rates of of the carbohydrate products are consumed by 2.5 Wmol/m2/s (Long et al., 1993; Larcher, 1997). the root system and by building tissues for struc- The rhyniophytic values are caused by the high tural support (Givnish, 1979; Raich and Nadel- external CO2 concentration leading to saturation ho¡er, 1989). Nothia shows a massive rhizom sys- of photosynthesis. Calculations carried out by tem representing a carbohydrate sink which Raven (1993) who also demonstrated that satu- indicates a demand for higher assimilation rate rated photosynthesis occurred in rhyniophytic in Nothia. Moreover, the apparently seasonal oc- plants, arrived at even higher values of about 94 currence of the aerial axes of Nothia can be inter- Wmol/m2/s and he described this value as repre- preted as intensifying a demand for their high senting a possible maximum. This value is based, productivity. That Nothia exhibits in all cases however, on maximum photosynthesis rate per the highest assimilation rate is therefore corrobo- exposed internal cell area of extant leaves and is rated by information provided by the fossil rec- thus not fully comparable to the present ap- ord. proach. Beerling et al. (2001) presented values of For all three taxa, saturation of photosynthesis about 10 Wmol/m2/s. It is, however, not clear was probably important in order to obtain su⁄- whether these are expressed on a projected surface cient carbohydrate gain. Saturation of photosyn- area basis. The high WUE values of the three taxa thesis is dependent on: (1) the external CO2 con- which are about 20 times higher than typical centration, and (2) anatomical parameters, mainly WUE values of extant mesophytic plants are stomatal density Xst. It is obvious from Fig. 9a due to the low transpiration rates. (assimilation rate per volume plotted against dhc More germane to rhyniophytic plants than as- and Xst) that with the initial data set (and also similation per surface area, however, is the CO2 with the Picea abies set of Jmax and Vmax) the in£ux per plant volume. The energetic demand of (calculated) threshold values of Xst leading to sat- the plant is not proportional to its surface but to urated photosynthesis in Aglaophyton are close to the amount of living tissue and thus to the volume their actual stomatal densities which are obtained of the plant. The assimilation process has to take from fossilized specimen. Decreasing Xst signi¢- place at the peripheral region of the cylinder, be- cantly would strongly decrease the assimilation cause light and gas cannot penetrate further than rate, because photosynthesis would no longer be to a certain depth of the tissue (Niklas, 1997). For saturated. Fig. 11 shows that the WUE value of the cylindric shape, the volume (proportional to the initial data set is seated at the beginning of the the amount of energy consuming tissue) increases steep £ank leading to maximum WUE. In the with the radius squared while the surface (propor- light of Fig. 10a (showing transpiration rate plot- tional to the amount of energy producing assim- ted against dhc and Xst), the ‘actual’ stomatal den- ilation tissue) increases proportional to the radius sity of Aglaophyton appears to represent a com- (see also Section 4.2). The energy-consuming vol- promise between transpiration and assimilation, ume thus increases stronger with radius than the leading to an optimized gaseous exchange. Simu- energy producing surface. If assimilation rates ob- lation of stomatal closure for Aglaophyton dem- tained with the initial data set are represented as onstrated that ^ with the initial data set ^ tran- rates per volume then Aglaophyton shows the low- spiration can be strongly reduced by closing the est and Nothia the highest value (see Fig. 5). stomatal pore while assimilation remains largely In the case of Aglaophyton and Rhynia, the as- una¡ected (Figs. 9b and 10b). Actual WUE val- similation rates obtained during the calculations ues could thus be even larger in rhyniophytic appear to be more than su⁄cient for maintaining plants, with photosynthesis being saturated.

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Fig. 13a,b shows that saturation can be 4.4. Implications of the results for atmospheric achieved over a wide range of combinations of CO2 concentration of the Lower Devonian Ca and Xst values. Higher Ca values than in the initial data set allow lower values of Xst while The structure of Fig. 13a ^ an extended plain assimilation stays saturated. It is usually di⁄cult lowland representing saturated photosynthesis to detect stomata on fossilized axes of early land framed on two sides by the continuously ascend- plants dating further back than to the Lower De- ing slopes of undersaturated photosynthesis ^ vonian (Edwards, 1998). Since the atmospheric contributes additional information for determin- CO2 content during the Silurian was even higher ing the CO2 concentration of the Lower Devonian than during the Lower Devonian (Berner and atmosphere. Kothvala, 2001), the results summarized in Fig. Consider a hypothetical plant X with stomatal 13a,b suggest that plant axes of this ancient density XX living in an atmosphere with CO2 con- age could survive with a very low stomatal den- centration CX. If the values of XX and CX give X sity, drastically reducing the probability of their a position somewhere within the ‘lowland of sat- detection. Fig. 13a,b also shows that decreas- uration’, X has reached its optimum conditions ing Ca leads eventually to a regime in which a with respect to assimilation. Its performance strong increase in Xst is necessary in order to with respect to transpiration, however, would ob- allow for saturated photosynthesis. The strong viously be better at smaller values of XX, as can be decrease of atmospheric CO2 content during the seen from Fig. 11. Therefore, we may expect that Middle Devonian may thus be involved in the X exhibits a tendency to occupy a position with as disappearance of rhyniophytic plants during this low XX values as possible without impairing pho- time period, because they were probably not able tosynthesis saturation. This evolutionary opti- to adapt their stomatal densities to these new con- mum is obviously realized by a XX value on the ditions. borderline between the ‘lowland of saturation’ The results summarized so far indicate that the and the ‘slopes of undersaturated photosynthesis’. actual values of stomatal density (together with In order to determine the CO2 concentration of the depth of the hypodermal channels, if present) the Lower Devonian atmosphere from the known represent a ¢ne-tuning of gaseous exchange which stomatal density Xrhyniophyte of the rhyniophytes, integrates maximum carbon gain and minimum we can turn this argument around (see Fig. transpiration rate to a compromise solution of 13b): on the premises that the rhyniophytes optimized gas £uxes. This optimum also re£ects were well adapted to their environment the Lower the limited capacity of water absorption in rhy- Devonian CO2 concentration can be found niophytic plants. Rhyniophytic plants represent from the position where a straight line at Xst = an ancient construction originating in the coloni- Xrhyniophyte parallel to the abscissa intersects the zation process of terrestrial environments by borderline separating saturated and undersatu- green plants (Edwards, 1998). The low and opti- rated photosynthesis. This ‘cut’ through Fig. 13b mized values of gaseous exchange are very prob- is represented by Fig. 12a. The shape and extent ably a consequence of the restricted water-absorb- of the area of saturated photosynthesis in Fig. ing capacity, and it is therefore possible that the 13a,b depend, however, on the choice of the as- high atmospheric CO2 concentrations were re- similation parameters, especially of Jmax and quired in order to ‘permit’ the evolution of up- Vmax. The sensitivity analysis described in Section right terrestrial plants (Edwards et al., 1998). On 3.3.1 demonstrates the e¡ects of changing Jmax the one hand, rhyniophytic plants were, as indi- and Vmax. In this sensitivity study, values of cated by the results, excellently adapted to early Jmax and Vmax of an extant plant (Picea abies) Paleozoic conditions. On the other hand, the high were inserted (e¡ect on assimilation shown by atmospheric CO2 conditions were probably the Figs. 6 and 12b); then the construction just given fundamental precondition for the evolution of leads to three di¡erent optimum values for the the rhyniophytic habit. atmospheric CO2 concentration: CaW166 mmol/

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3 3 m (Aglaophyton), CaW193 mmol/m (Nothia) 5. Conclusions 3 and CaW106 mmol/m (Rhynia, see Fig. 12b). In this case, the range of plausible atmospheric (1) The three considered taxa di¡er in transpi- CO2 concentrations is thus CaW106T193 mmol/ ration and assimilation rate and show the fol- m3. The assimilation parameters of Picea result, lowing order of increasing gaseous exchange pro- however, in extremely low values of Ci/Ca :0.42 vided the condition Ci/Ca = 0.7 is applied: for Aglaophyton and 0.35 for Nothia. It is there- Aglaophyton major 6 Rhynia gwynne-vaughanii 6 fore reasonable to assume that the values of the Nothia aphylla. The transpiration rates of all three initial data set which result in Ci/Ca = 0.7 repre- taxa are markedly lower than the rates which sent a good approximation. If we thus impose ^ in are usually attained by extant plants. The assim- view of the discussion in Section 4.1.2 ^ the initial ilation rates are seated at the lower to middle data set in order to ¢ne tune the values of Jmax range of the extant spectrum due to photosynthe- 3 and Vmax, then we obtain CaW120 mmol/m sis saturation under Lower Devonian CO2 con- which is about 8.5 times the Recent value. It is centrations. lower than the value provided by the standard (2) The fact that Nothia aphylla shows the high- curve of RCO2 returned by GEOCARBIII, which est rates of gaseous exchange is consistent with is about 12 times the Recent value (Berner and the fact that this species developed a massive rhi- Kothvala, 2001). McElwain (1998) provided two zom system which represented very probably a estimations of atmospheric CO2 of the Lower De- carbon sink on one hand while providing a vonian based on stomatal densities of the Lower much better source of water supply than was Devonian plants Sawdonia ornata and Aglaophy- present in Aglaophyton major and Rhynia ton major: the ¢rst one amounts to a range gwynne-vaughanii on the other hand. The fossil

RCO2 =7T10 (by using a ‘Recent standard’) and evidence of seasonally shedding of the aerial the second one gives a range RCO2 = 9.5T12.5 (by axes of N. aphylla additionally indicates a demand using a ‘Carboniferous standard’). The estimation for higher productivity of these axes during their obtained by the present contribution is thus lifetime. seated within the ¢rst range. It should, however, (3) The protuberances at the axis surface of be noted that the method applied by McElwain Nothia aphylla did not increase gaseous ex- (1998) is based on producing ratios between the change. stomatal densities of the fossil taxon and an ex- (4) The di¡erences in gaseous exchange of the tant plant species termed ‘NLE’ (nearest living three taxa thus probably re£ect di¡erences in their equivalent) whose ecological and structural prop- lifestyles and ecophysiological properties. erties are claimed to be similar to those of the (5) The results indicate on one hand that the fossil taxon. Additionally, the value of stomatal construction of rhyniophytic plants is strongly density of Aglaophyton which were used by McEl- adapted to a high atmospheric CO2 concentration 2 wain (1998) (Xst = 4.5/mm ) is much higher than by producing optimized gaseous exchange. This the stomatal density which was applied in this means, however, on the other hand that the evo- contribution (McElwain and Chaloner, 1995; lution and existence of rhyniophytic plants ^ and McElwain, 1998, see also Edwards et al., 1998). therefore the prototype of land plants with an The data of stomatal density available so far show upright posture ^ was dependent on such high some variation. As indicated in Table 2, the ana- CO2 concentrations. tomical parameters provided by Edwards et al. (6) The results concerning interrelationship be- (1998) and Kerp et al. (2001) as well as their tween ¢ne-tuning of gaseous exchange, assimila- data on stomatal density were used in order to tion rate, anatomical properties and external CO2 create a consistent data set. A direct comparison concentration suggest that the Lower Devonian of the present results and the results of McElwain CO2 concentration amounted roughly to about 3 (1998) thus appears to be problematic. CaW120 mmol/m .

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6. Glossary whc short axis of hypodermal channel Xst stomatal density b e¡ective pore radius see also Tables 1^3. c radius of cortex cell Environmental and physical parameters and dst tortuosity of stomatal layer constants

A assimilation rate per volume C gas concentration Photosynthesis parameters Ci intercellular CO2 concentration Ca atmospheric CO2 concentration gliq e¡ective conductance through a cortex cell CO2 C atmospheric CO2 concentration J current of molecules H O C 2 atmospheric H2O concentration, humidity j £ux into plant surface D free air di¡usional constant jas £ux into assimilating tissue CO2 D free air di¡usional constant for CO2 jchl £ux into chloroplast H O D 2 free air di¡usional constant for H2O J(I) potential rate of electron transport dbl thickness of boundary layer Jmax light-saturated rate of electron transport grad gradient operator K Michaelis^Menten constant of carboxylation ! c j di¡usional gas £ux Ko Michaelis^Menten constant of oxygenation CO j 2 assimilation rate per area po Partial pressure of oxygen at assimilating site H O j 2 transpiration rate per area q partial pressure of CO2 at assimilating site I irradiance Vmax local maximum carboxylation rate l path length Wc carboxylation rate limited by Rubisco activity le path length around hindrance Wj carboxylation rate limited by Rubisco regeneration n porosity K e⁄ciency of light conversion Q gas sink a speci¢city factor of Rubisco r radial coordinate

RCO2 fossil CO2 concentration/Recent CO2 concentration Rgas universal gas constant S e¡ective conductance Acknowledgements Sh solar constant d tortuosity T absolute temperature This work was supported by the German Sci- T transpiration rate per volume ence Foundation (DFG: Mo 412/13;c-1). We uatm wind velocity want to thank H. Kerp and H. Hass for many helpful discussions and J.H. Nebelsick for crit- Anatomical and morphological parameters ically reading the English manuscript.

A total leaf surface chl A total area of all chloroplasts Appendix A Ames total area of all mesophyll cells aas surface of cortex cell achl surface of all chloroplasts in a cell A.1. Photosynthesis model AR surface of a chloroplast ast area of stomatal pore The CO2 £ux into chloroplasts, jchl, is given by dst depth of stomatal pore dhc length of hypodermal channel po jchl ðq; IÞ¼ 13 minfW cðqÞ; W jðq; IÞg ð5Þ hhc long axis of hypodermal channel 2a q L axis length nas porosity of assimilation layer with n porosity of stomatal layer q st W ðqÞnV R radius of plant axis c max p q þ K 1 þ o Rc length of longer axis of chloroplast c K V tissue volume o Vp tissue pore volume q n R ratio of chloroplast thickness and chloroplast length W jðq; IÞ JðIÞ p ð6Þ 4 q þ o vas volume of cortex cell a

PALAEO 3216 24-11-03 174 A. Roth-Nebelsick, W. Konrad / Palaeogeography, Palaeoclimatology, Palaeoecology 202 (2003) 153^178 and jchl ¼ gliqðCðrÞRgasT3qÞð9Þ KI JðIÞn ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð7Þ KI where Rgas represents the universal gas constant, 1 2 þ T the absolute temperature and gliq the e¡ective Jmax conductance through the interior structures of the where q stands for the partial pressure of CO2 and cortex cells (see Fig. 14 for a schematic overview po for the local O2 concentration (the various of the model). other parameters are listed in Table 3 and in the glossary). The expression min{Wc(q),Wj(q,I)} denotes the A.2. Boundary layer smaller of Wc(q) (carboxylation rate limited by the activity of Rubisco) and Wj(q,I) (carboxyla- The thickness of the boundary layer (air layer tion rate limited by regeneration of Rubisco via with reduced wind velocity) adjacent to the axis electron transport). surface is determined according to an approxima- jchl is connected to Q by the following equation provided by Nobel, 1999: tion: rffiffiffiffiffiffiffiffiffiffiffiffi 2R 1 dbl ¼ 5:8 mm ð10Þ achl aas uatm s Q ¼ 3 ð13nasÞjchlðq; IÞð8Þ aas vas with dbl the thickness of boundary layer, R the with the ratio achl/aas between the sum of the sur- radius of the plant axis, and uatm the wind veloc- faces of all chloroplasts within one cortex cell to ity. the surface aas of this cell (termed ‘chloroplast surface factor’ throughout the text), the porosity nas of the assimilation layer and aas/vas as the sur- A.3. Stomatal layer face-to-volume ratio of a typical cortex cell. Eq. 8 thus states that the sink is produced by the chlo- Permineralized specimen of Aglaophyton, No- roplast layer located at the periphery of a cortex thia and Rhynia provide the necessary anatomical cell. A ¢nal step is required which converts the data: average area of stomatal pore ast, depth of partial pressure q of CO2 inside the chloroplasts stomatal pore dst and number of stomata per unit in Eq. 7 into the CO2 concentration C(r) in the surface Xst. These parameters are used in order to intercellular air spaces (Parkhurst and Mott, calculate porosity nst and tortuosity dst of the sto- 1990): matal layer:

Fig. 14. Schematic overview of the model.

PALAEO 3216 24-11-03 A. Roth-Nebelsick, W. Konrad / Palaeogeography, Palaeoclimatology, Palaeoecology 202 (2003) 153^178 175 l Z n ¼ a X ð11Þ d ¼ e ¼ W1:57 ð14Þ st st st as l 2 b st d st ¼ 1 þ ð12Þ dst The speci¢c surface (aas/vas) of a long cylindri- with bst the e¡ective pore radius (see Nobel, cal cortex cell with radius c reads as: 1999). The tortuosity stems from the fact that aas 2 lines of equal concentration within the boundary ¼ ð15Þ v c layer bulge out over the stomata so that molecules as di¡using out of the stomata still experience sto- The ratio (achl/aas) represents the sum of the matal conditions although they have already left surfaces of all chloroplasts achl within one cortex the stomatal layer (Nobel, 1999). cell to the surface aas of this cell. In a sense this value thus describes how much space of a cell is occupied by chloroplasts. The value is determined A.4. Hypodermal layer by two factors: (1) the orientation of the chloroplasts in the cell, and (2) the degree of (inner) A hypodermal layer is included in the system, if surface occupation of the cell by chloroplasts. hypodermal channels are present. These structures Typical chloroplasts of land plants are similar to are narrow channels beneath the stomata and can oblate spheroids. The surface of a chloroplast is be found in Aglaophyton and Rhynia. Nothia has then provided by pffiffiffiffiffiffiffiffiffiffiffiffiffi! R 2 1 13R 2 substomatal chambers. Hypodermal channels are Z 2 Z 2pffiffiffiffiffiffiffiffiffiffiffiffiffi þpffiffiffiffiffiffiffiffiffiffiffiffiffi AR ¼ 2 Rc þ Rc ln elliptical in cross-section with a longer axis hhc 13R 2 13 13R 2 and a shorter axis whc. Their number equals the ð09R 91Þð16Þ number of stomata. The porosity of the hypodermal layer reads as: with Rc the length of the spheroid’s longer axis and R the ratio of chloroplast thickness to chlo- Z 2R3dst nhy ¼ hhcwhcX st ð13Þ roplast length. The shorter axes of typical chlo- 4 2R3ð2d þ d Þ st hy roplasts of land plants are about half as long as their two longer axes. If the inner surface of a cortex cell would be completely occupied by these A.5. Assimilation layer chloroplasts, CO2 di¡using into one chloroplast would have to di¡use through a cortex cell area Z 2 It is generally assumed that assimilation took of Rc. The ratio (achl/aas) would then be given by place mainly in the outer cortex (see, for example, (achl/aas) = 2.760. Chloroplasts in land plants di¡er Edwards et al., 1998). The assimilation layer is in size. Typical values are, according to Moore et therefore represented by the outer cortex layer. al., 1998,4T8 Wm for the chloroplast diameter and Measurements carried out by using methods of 2T3 Wm for the chloroplast thickness (see also image processing on thin slices of fossil material Raven, 1993). We adopt the mean values of these yield an average value for porosity of nas =0.35 two intervals and arrive at (achl/aas) = 2.606 for for all three taxa. For measured thickness values R = 0.429. The inner cell surfaces of cells con- of the outer cortex layer of the three taxa see taining chloroplasts are, however, not completely Table 2. In order to calculate the tortuosity das, occupied by these cell organelles. According to a rough approximation is applied: a molecule dif- Parkhurst and Mott, 1990, a value of 90% which fusing around a cell has to move along a half is typical for mesophyll cells of extant leaves is circular path with a distance r to the cell center. adopted. A value of The pathlength l amounts to l = r and the direct e e ða =a Þ¼2:3454 ð17Þ travel distance is l =2r. The tortuosity is therefore chl as given by: thus results which was used in the calculations.

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A.6. Vmax and Jmax of this amount of radiation is within the range of photosynthetically valuable wavelengths. Values of Vmax and Jmax provided in the liter- If the sun is elevated above the horizon by an ature cannot be applied directly, because the angle 3, the projective absorption area of an up- £uxes usually given are related to a ¢ctitious ex- right plant axis with a radius of R and a height of ternal leaf area far away from the chloroplasts. In L is given by 2RL cos 3. On distributing the order to be used within the framework of our impinging light evenly onto the telome surface calculations, values from the literature have to 2ZRL, the factors R and L drop out and the mes be corrected for the actual A /A values of the number I3 of photons reaching the axis per unit rhyniophytic plant. Vmax and Jmax are thus rede- time and unit axis area is given by: ¢ned according to the following considerations. Wmol Consider a current of molecules J di¡using into I 3 ¼ cos 3 U877 ð22Þ m2 s or out of the chloroplasts under stationary conditions. Achl, Ames and A represent the total areas Assuming 3 = 45‡ and taking into account dif- of chloroplasts, of all mesophyll cells and of the ferences in the inner structures of Aglaophyton, total leaf surface. If the corresponding £uxes ^ the Rhynia and Nothia, we arrive at an expression symbol j stands for either Vmax or Jmax ^ are de- between I3 and the number I of photons at the ¢ned by assimilating sites per unit time and unit area, which is similar to the one obtained above for J J J jchln jmesn jn ð18Þ the relation between j and jchl : Achl Ames A A aas then elimination of J results in I ¼ I 3 mes ð23Þ A achl chl mes jchlA ¼ jmesA ¼ jA ð19Þ and thus References A A Ames j ¼ j ¼ j ð20Þ chl Achl Ames Achl Aphalo, P.J., Jarvis, P.G., 1993. An analysis of Ball’s empirical model of stomatal conductance. Ann. Bot. 72, 321^327. chl mes Since (A /A )=(achl/aas), we conclude Badger, M.R., Andrews, T.J., 1987. Co-evolution of Rubisco and CO2 concentrating mechanisms. In: Biggins, J. (Ed.), A aas Progress in Photosynthesis Research. Martinus Nijho¡, jchl ¼ j mes ð21Þ A achl Dordrecht, pp. 501^609. Ball, J.T., Woodrow, I.E., Berry, J.A., 1987. A model predict- Own measurements of (Ames/A) provided a val- ing stomatal conductance and its contribution to the control mes ue of (A /A) = 10 and (achl/aas) = 2.3454 has been of photosynthesis under di¡erent environmental conditions. Biggins, J. (Ed.), Progress in Photosynthesis Research. Mar- calculated above. The local values of Vmax and tinus Nijho¡, Dordrecht, pp. 221^224. Jmax can now be obtained by substituting the ap- Bateman, R.M., Crane, P.R., DiMichele, W.A., Kenrick, P., propriate literature data of Vmax or Jmax for j on Rowe, N.P., Speck, T., Stein, W., 1998. Early evolution of the right hand side of Eq. 21. land plants: phylogeny, physiology, and ecology of the pri- mary terrestrial radiation. Annu. Rev. Ecol. Syst. 29, 263^ 292. Becker, M., Kerstiens, G., Scho«nherr, J., 1986. Water perme- A.7. Irradiance ability of plant cuticles: permeance, di¡usion and partition coe⁄cients. Trends Ecol. Evol. 1, 54^60. The value of the Recent solar constant Sh Beerling, D.J., Woodward, F.I., 1995. Leaf stable carbon iso- 2 amounts to Sh = 1360 W/m (see, for example, tope composition records increased water-use e⁄ciency of Nobel, 1999). About 45% of this amount is ab- C3 plants in response to atmospheric enrichment. Funct. Ecol. 9, 394^401. sorbed in the upper atmospheric layers or re- Beerling, D.J., Woodward, F.I., 1997. Changes in land plant £ected back into space. On a global average, function over the Phanerozoic: reconstructions based on the 55% thus reaches the earth’s surface. About 45% fossil record. Bot. J. Linn. Soc. 124, 137^153.

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