Modeling ﬂuid ﬂow in Medullosa, an anatomically unusual...

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Paleobiology, 34(4), 2008, pp. 472–493

Modeling fluid flow in Medullosa, an anatomically unusualCarboniferous seed plant

Jonathan P. Wilson, Andrew H. Knoll, N. Michele Holbrook, andCharles R. Marshall

Abstract.—Medullosa stands apart from most Paleozoic seed plants in its combination of large leafarea, complex vascular structure, and extremely large water-conducting cells. To investigate thehydraulic consequences of these anatomical features and to compare them with other seed plants,we have adapted a model of water transport in xylem cells that accounts for resistance to flow fromthe lumen, pits, and pit membranes, and that can be used to compare extinct and extant plants ina quantitative way. Application of this model to Medullosa, the Paleozoic coniferophyte Cordaites,and the extant conifer Pinus shows that medullosan tracheids had the capacity to transport waterat volume flow rates more comparable to those of angiosperm vessels than to those characteristicof ancient and modern coniferophyte tracheids. Tracheid structure in Medullosa, including the largepit membrane area per tracheid and the high ratio of tracheid diameter to wall thickness, suggeststhat its xylem cells operated at significant risk of embolism and implosion, making this plant un-likely to survive significant water stress These features further suggest that tracheids could not havefurnished significant structural support, requiring either that other tissues supported these plantsor that at least some medullosans were vines. In combination with high tracheid conductivity, dis-tinctive anatomical characters of Medullosa such as the anomalous growth of vascular cambium andthe large number of leaf traces that enter each petiole base suggest vascular adaptations to meetthe evapotranspiration demands of its large leaves. The evolution of highly efficient conductingcells dictates a need to supply structural support via other tissues, both in tracheid-based stemseed plants and in vessel-bearing angiosperms.

Jonathan P. Wilson. Department of Earth and Planetary Sciences, Harvard University Cambridge, Mas-sachusetts 02138. E-mail: [email protected]

Andrew H. Knoll, N. Michele Holbrook, and Charles R. Marshall. Department of Organismic and Evolu-tionary Biology, Harvard University Cambridge, Massachusetts 02138

Accepted: 21 July 2008

Introduction

Fluid flow in plants is governed by thephysical properties of conducting cells. Be-cause of this close relationship between ana-tomical structure and function, fossilized xy-lem tissues permit inferences to be drawnabout fundamental physiological properties ofancient plants. Cichan (1986a) pioneered theestimation of transport rates through fossilstems, but progress in biophysical modelingnow allows more accurate quantification offossil plant function in ways that are readilyunderstood and easily compared with that ofmodern plants (Tyree and Sperry 1989; Com-stock and Sperry 2000; Roth-Nebelsick et al.2000; Hacke et al. 2001, 2004; Roth-Nebelsickand Konrad 2003; Sperry and Hacke 2004).

In this paper, we develop a model of watertransport in the late Paleozoic seed fern Med-ullosa, a plant that was widely distributed in

tropical ever-wet lowlands of North Americaand Europe, and compare it with modeledtransport rates through the late Paleozoic co-niferophyte Cordaites and the living pine, Pi-nus. Medullosa’s unusual anatomy has attract-ed paleobotanical attention for many years.Our conclusion that Medullosa’s tracheids en-abled high-throughput fluid transport similarto that of angiosperm vines has importantconsequences for interpreting its anatomy,vascular development, and paleoecologicaldistribution.

Water Transport in Plants

Photosynthesis and water transport havefundamental and far-reaching impacts onplant form and function. More than 95% of thewater drawn upward from roots into the plantstem evaporates from actively photosynthe-sizing surfaces (Taiz and Zeiger 2002). Plants

473FLUID FLOW IN MEDULLOSA

open their stomata in response to a variety ofbiochemical cues, allowing carbon dioxide todiffuse into the stomatal aperture, where it isultimately dissolved in water and transportedinto the internal cells of leaves or other sites ofphotosynthetic carbon fixation. Open stomata,however, expose well-hydrated interior tis-sues of plants to the drying power of the at-mosphere, resulting in water loss by evapo-ration. Water supply indirectly determines theamount of photosynthesis that can occur bylimiting stomatal opening and, hence, rates ofcarbon assimilation; water supply can alsolimit cell expansion in developing leaves (Kra-mer and Boyer 1995; Taiz and Zeiger 2002).

Evaporation of water from leaves generatesa tension that causes water to move via bulkflow from the soil into roots. Water is trans-ported to the leaves through a network ofdead cells, the xylem, which in many plantsalso provides significant structural support.For water to ascend through the xylem, thewater column must remain continuous fromroot to leaf; this is made possible by strong hy-drogen bonding between water molecules.Gas bubbles called embolisms can developwithin conducting cells when air is pulled inthrough the relatively porous wall regionsthat allow interconduit water movement,breaking the stream and jeopardizing watertransport. Photosynthetically produced sug-ars and other solutes move down the plantfrom their synthesis sites through a secondnetwork, consisting of highly modified livingcells called phloem. Flow of photosynthatewithin the phloem may be coupled to watertransport through the xylem (Thompson andHolbrook 2003), but unlike xylem, phloemcells provide little, if any, structural support inmost terrestrial plants and rarely preserve inthe fossil record. Water flows through the lu-men of xylem conduits approximately at Poi-seuille flow, a rate proportional to the fourthpower of the radius of the conducting cell, soa small increase in tracheid or vessel diametercan have a large effect on the amount of watertransported through the xylem (Tyree andZimmermann 1983; Sperry 1989; Comstockand Sperry 2000). Water flows between xylemconduits through pits, regions where the sec-ondary cell wall is not deposited, such that

water need only pass through the remainingprimary cell wall, called the pit membrane(Pesacreta et al. 2005). Pit morphology anddensity have a strong effect on xylem flowrates and thus whole-plant hydraulics (Zim-mermann 1983; Carlquist 2001).

It has been known for decades that in seedplants xylem cell morphology reflects opti-mization for two mutually exclusive tasks:transport and mechanical support (Esau 1977;Mosbrugger 1990; Rowe and Speck 2004). Xy-lem cells optimized for maximum water trans-port are wide, open-ended, and covered withnumerous pits, for example, vessel elements inangiosperms. In contrast, xylem cells opti-mized for support are long and thin, withwalls that are thick relative to lumen diameter,e.g., conifer tracheids. This dichotomy extendseven to the chemistry of xylem cell walls.Heavily lignified cells provide support, butthis is hypothesized to reduce the ability tomodulate fluid flow (Boyce et al. 2004). In con-trast, lightly lignified xylem cells may be ableto regulate the rate of water flow on a minute-by-minute basis, owing to the presence of pec-tins in the compound middle lamella that actas hydrogels, expanding and contracting inresponse to changes in sap ion concentration(Zwieniecki et al. 2001; Boyce et al. 2004).These cells, however, may be compromised intheir ability to provide structural support.Other recent research has shown that the abil-ity of xylem cells to resist implosion at hightensions is related to wood density and thethickness-to-span ratio of individual xylemcells (Hacke et al. 2001). Because of these well-understood and well-quantified relationshipsbetween structure and function, water trans-port and tracheid strength in ancient plantscan be reconstructed by using models of xy-lem hydraulic and mechanical function (Esau1977; Carlquist 2001; Sperry and Hacke 2004).

Medullosa

Medullosans are stem-group seed plants,sister to the clade that includes cycads, Ginkgo,conifers, Gnetales, and angiosperms (Crane etal. 2004). Ecologically, medullosans becameimportant constituents of floodplain commu-nities beginning in the Late Mississippian(Stewart and Delevoryas 1952; Phillips 1981;

474 JONATHAN P. WILSON ET AL.

Dunn et al. 2003) and expanded into coalswamp environments following a mid-Penn-sylvanian drying event (Phillips et al. 1974;Phillips 1981; DiMichele et al. 2001). Both per-mineralized and compressed medullosan re-mains occur widely in deposits from the Unit-ed States, Europe, and northwest Africa (Stidd1981; Wnuk and Pfefferkorn 1984; Galtier et al.1986; Galtier 1997). Reasonable whole-plantreconstructions are available (Andrews 1940;Pfefferkorn et al. 1984), although debate aboutthe habit of Medullosa persists (Pfefferkorn etal. 1984; Wnuk and Pfefferkorn 1984; Hamerand Rothwell 1988; Mosbrugger 1990; Dunn etal. 2003). In fact, there is little reason to believethat all medullosans had the same habit, butthey all exhibit the same unusual morphology,with massive, pinnately compound leaf sys-tems attached to slender stems characterizedby a distinctive vascular system (Andrews1940; Delevoryas 1955; Pfefferkorn et al. 1984;Wnuk and Pfefferkorn 1984; Arens 1997).Medullosans have several characters found in-dividually in other plant groups, both extinctand extant (e.g., Calamopityales, gigantopter-ids, cycads), but their overall architecture isunique.

Four genera of stems are recognized on thebasis of morphological characters: Medullosa,Sutcliffia, Quaestora, and Colpoxylon. The veg-etative structure of Medullosa species is bestknown, so we concentrate on them here. The11 described species of North American med-ullosans range in age from Late Mississippianto Early Permian.

Morphology and Anatomy. It has been notedfor almost two centuries that medullosans hadan unusual vascular system (Cotta 1832;Brongniart 1849; Solms-Laubach 1891; Scott1899). Like many other seed plants, the pri-mary xylem of medullosans developed as aeustele (Basinger et al. 1974). Secondary vas-cular development, however, was striking:multiple cylinders of vascular cambium de-veloped around one or more procambia, re-sulting in stems that, at the completion of sec-ondary growth, contained what look like mul-tiple vascular segments surrounded by abun-dant parenchyma, rather than the solidcylinder of secondary xylem typical of extantseed plants (Fig. 1). This anatomical arrange-

ment was originally thought to form throughfusion of separate stems (Delevoryas 1955),but is now understood to reflect anomalouscambial development (Basinger et al. 1974).Cambial development in Medullosa placedeach secondary xylem cell in close contactwith living cells of axial parenchyma, withlarge, multiseriate xylem rays, or with both.

Vascular segments anastomose throughoutthe stem of a typical Medullosa, generally sep-arating below a petiole insertion point and re-connecting above it (Stewart and Delevoryas1952). The degree of anastomosis and numberof segments varies along the length of indi-vidual stems as well as among species. In gen-eral, stems contain two to four segments, butas many as 23 have been documented in M.primaeva. One specimen of this species has twosegments near its base, divides apically intosix, and then 23, following which the xylemfuses back to two segments within less than 7cm of distance along the stem (Stewart andDelevoryas 1952). No other known plant dis-plays this amount of variability in the distri-bution and activity of its vascular cambium.

In medullosans, each petiole is vascularizedby multiple leaf traces that arise from severalsegments within the stem (Basinger et al.1974). Thus, each frond is connected to manyseparate but well-connected paths of waterthroughout the stem. Leaf traces depart fromthe primary xylem at the center of each seg-ment, dichotomizing repeatedly near thepoint of petiole insertion to form ten to morethan 100 individual vascular strands withinthe petiole base. This pattern of leaf trace de-velopment appears to extend, as well, to pro-tostelic representatives of the family; in theLate Mississippian medullosan Quaestora am-plecta, leaf traces that depart from multipleprimary xylem points across the stem all leadinto a single petiole (Mapes and Rothwell1980). Quaestora has been interpreted as an-cestral to eustelar medullosans (Mapes andRothwell 1980), but new finds in Arkansasshow that it coexisted with at least one speciesof Medullosa that contained a eustele, whichtherefore might represent the plesiomorphicmorphology (Dunn et al. 2003). In any event,this distinctive pattern of petiole vasculariza-tion constitutes a synapomorphy for the Med-


FIGURE 1. Morphology and anatomy of the Paleozoic seed plant Medullosa. A, Reconstruction of Medullosa thomp-sonii, from Andrews (1940), reprinted with permission. Because of the need to fit the drawing on one page, thefronds in this reconstruction are drawn as if the plant were wilting. For an alternative reconstruction, see Pfefferkornet al. (1984). B, A cross-section of Medullosa sp. from the Harvard University Paleobotanical Collections, with im-portant anatomical features labeled.

ullosaceae (Mapes and Rothwell 1980; Dunnet al. 2003). Cycads exhibit a similar pattern ofleaf vascularization, but their stems have con-centric vascular cylinders instead of multiplevascular segments (Norstog and Nichols1997).

Medullosan plants had narrow stems (gen-erally a few centimeters in diameter, but withaxes of one species reaching 0.5 m across) butmassive petioles (up to 5 m long) (Wnuk andPfefferkorn 1984). Most Medullosa species arethought to have grown as trees (Pfefferkorn etal. 1984; Stewart and Rothwell 1993; Taylorand Taylor 1993); however, buttressing largepetioles with a narrow stem presents a bio-mechanical problem: what supported theplant in an upright position? A number of ex-tant plants have large petioles borne on rela-tively narrow stems, including tree ferns, cy-cads, palms and some other monocots, andthe dicot Gunnera. Each of these groups has adedicated, low-resistance pathway for wateras its vascular system and differentiates load-bearing tissue elsewhere (Mosbrugger 1990,

Rowe and Speck 2004). In cycads, xeromorph-ic and fire-resistant leaf bases support thelarge petioles (Norstog and Nichols 1997). Adense cortex and fibers scattered throughoutthe stem provide mechanical support inpalms, whereas tree ferns such as Angiopterishave bands of sclerenchyma near the stem pe-riphery, as well as armored leaf bases. Deter-mining the role of vascular tissue in the struc-tural support of Medullosa will help determinethe best comparative model to use in efforts tounderstand its mechanical properties.

Although briefly noted by others (Andrews1940; Cichan 1986a,b), little attention has beenpaid to the fact that tracheids found in Med-ullosa are among the widest and longest everreported from seed plants, living or extinct.Andrews (1940) measured 17.5 and 24.0 mmlong tracheids in Medullosa, noting that thecells were so long it was difficult to find acomplete cell shorter than a thin section andsuggesting that his measurements, thus, un-derestimated the tracheids’ true lengths. Sec-ondary xylem tracheids commonly exceed 200


FIGURE 2. A, Light micrograph of Medullosa sp. tracheid; scale bar is approximately 130 �m. B, Surface view of atorus-margo pit from Tsuga canadensis (Lancashire and Ennos 2002). C, Surface view of homogeneous pit membraneof Fraxinus (modified from Choat et al. 2006). D, Diagram of idealized water flow through tracheids, showing thelocation and simplified cross-sectional view of torus-margo and homogeneous pit membranes.

�m in diameter, wider than those of any ex-tant gymnosperm (Schopf 1939; Andrews andMamay 1953). In addition to their large size,medullosan tracheids have a high density ofpits covering their walls (Fig. 2). Increased pitdensity decreases total resistance in the tra-cheid; pits are analogous to parallel resistorsin a circuit.

Pinus and Cordaites

We chose to compare Medullosa with twoother seed plants, the Carboniferous conifer-ophyte Cordaites and the living conifer Pinus.Cordaites contains xylem cells that are mor-phologically similar to those of many other ex-tinct seed plants, including the dominant treeof Gondwana, Glossopteris. Pinus tracheidstypify those of conifers and several othergymnosperms in their size, shape, and type ofpits. Medullosan tracheids, in their extremesize and number of pits, represent a third typeof xylem found in a small number of Paleozoicseed plants, including the Late Permian gi-gantopterids (Li and Taylor 1998). These threetaxa are, thus, representative of the widerange of tracheid diversity evolved through-out the history of vascular plants.

Pinus evolved during the middle Mesozoic

and currently forms extensive boreal foreststhat appear to have expanded since the Oli-gocene Epoch (Axelrod 1986; Millar 1993). Pi-nus trees are characterized by crowns of nee-dlelike foliage atop trunks of dense woodcomposed of short tracheids with torus-mar-go pits—an arrangement characteristic of ex-tant conifers in general (Bannan 1965; Bauchet al. 1972; Greguss and Balkay 1972; Judd etal. 2007). Torus-margo pits allow for high po-rosity in pit membranes and provide somecavitation protection, endowing conifers witha conducting efficiency comparable to that ofsmall-vesseled angiosperms (Sperry and Ty-ree 1990; Pittermann et al. 2005; Pittermann etal. 2006).

The cordaites are a group of woody plantsconsidered to be stem-group conifers on thebasis of ovulate branches aggregated intoloose, conelike structures and saccate pollen(Florin 1950, 1951; Crane 1985; Stewart andRothwell 1993; Taylor and Taylor 1993; Falcon-Lang and Scott 2000). In North America, cor-daites were widely distributed in mire anddryland environments from the Late Missis-sippian through the Early Permian. Cordaitescan generally be described as a group of smallshrubs to tall (�30 m) trees bearing strap-


shaped leaves 10 cm to 1 m long that were at-tached to stems bearing broadly conifer-likewood. Unlike extant conifers, cordaite tra-cheids did not contain a single row of torus-margo pits; instead they contained two orthree rows of pits bearing homogeneous pitmembranes. In this paper, we use the leaf ge-nus Cordaites to represent tracheid morpholo-gy for the whole plant.

Methods

Early models of water transport in plantsfocused on the nature of individual xylemcells as hollow tubes and used the Hagen-Poi-seuille equation to estimate flow rates (Zim-mermann 1983; Cichan 1986a). These modelstreated xylem in the stem as a single set of un-obstructed pipes extending from roots toleaves and thus overestimated flow volumesthrough stems. In vivo, fluids flowing throughthe xylem are impeded by resistance associ-ated with the movement between cells. Amore accurate model of water transport in xy-lem cells, based on an Ohm’s Law analogy(van den Honert 1948) that takes into accountthe structures that link xylem cells, allows aquantitative and anatomically accurate evalu-ation of xylem hydraulic properties (Hacke etal. 2004; Sperry and Hacke 2004).

We have used this approach to model tra-cheid-level hydraulic capacity of medullosanhydraulic architecture by adapting a moregeneralized model of single-cell hydraulicsthat was developed and described in detail byJohn Sperry, Uwe Hacke, and colleagues(Hacke et al. 2004; Sperry and Hacke 2004).This model is based upon Hagen-Poiseuilleflow through tubes (Vogel 1994) that have a fi-nite length and are closed at the ends (Com-stock and Sperry 2000), and which containpits through which water moves from one cellto another (Hacke et al. 2004; Sperry andHacke 2004). Two versions of the tracheidmodel were implemented in MATLAB, one forxylem cells with homogeneous pit membranes(Medullosa, Cordaites) and another for thosewith torus-margo pit membranes (Pinus).

Ohm’s Law models are based on the anal-ogy between the flow of current through a cir-cuit and water flow through the conductivetissue of a plant (Comstock and Sperry 2000;

Hacke et al. 2004; Sperry and Hacke 2004).Tracheids are modeled as resistors in a circuitwith total resistance (R), with flow rate (Q)analogous to current (I) and pressure drop(�P) to voltage drop (�V) (eqs. 1 and 2):

�VI � (1)

R

�PQ � (2)

R

Conductance (K) is the inverse of resistance inan individual tracheid (eq. 3) and specific con-ductivity, Ksp—K normalized by tracheidlength and wall area—is calculated in themodel by dividing cell length (L) by the prod-uct of the cell wall area (Awall) and total resis-tance (Rtot) (eq. 4).

1K � (3)

R

LK � (4)sp R Atot wall

Measuring flow in terms of conductance, rath-er than flow rate, allows quantitative compar-isons of different plants independent of thepressure gradient within each plant. Pressuregradient reflects the ambient environment andcan vary widely, depending on temperature,time of day, soil moisture, and other factors.

Wall area is found by dividing the cell wallvolume (V) by the tracheid length (eq. 5). Forthe cell wall volume, we modeled the tracheidas two concentric cylinders, with the samelength and different radii corresponding tothe outer wall and lumen, wall volume beingthe difference between the two. Awall equalsthe amount of wall material per unit length;normalizing conductance to this term gives ameasurement of cell wall invested per tra-cheid. This is a nonstandard normalization,but it has been used in previous modelingstudies (Hacke et al. 2004; Sperry and Hacke2004). A more standard normalization is con-duit conductivity per cross-sectional area (Ksc,eq. 6), calculated by substituting cross-sec-tional area of the tracheid, including both thecell wall and the lumen, into equation (4).Conduit area (Aconduit) is calculated from the


area of a circle with radius equal to the sumof the lumen radius and wall thickness.

VA � (5)wall L

LK � (6)sc R Atot conduit

There are two components to resistance in thetracheid (eq. 7), one derived from resistance toflow through the tracheid, which is mathe-matically equivalent to resistance to flow in atube (Rlumen), and the other from resistance towater flow through the pits from one tracheidto another, where (Rpit) is equal to resistancethrough one pit. Because water will passthrough two sets of pits when moving fromthe lumen of one tracheid to the lumen of an-other, the resistance component from pits isdoubled.

RpitR � R � 2 (7)tot lumen Npits

Individual pits are modeled as resistors inparallel, so that the total resistance from pitsis inversely proportional to their number(Npits). Conifers often have a single row of pitsin each tracheid, usually between ten and 30,whereas Medullosa has large numbers of pits,commonly more than 200 per tracheid. Tocompensate, conifer pits are usually large,with a torus-margo structure that increasesflow but may impede refilling after embolism(Sperry and Tyree 1990).

Rlumen (eq. 8) is the inverse of the Hagen-Poi-seuille equation for flow across half of a tube’slength. Half-tube length is used because it rep-resents the mean distance that water flowsthrough any given tracheid, given that tra-cheids have closed ends with water flowing inand out via the pits; this reduces the numer-ator by a factor of two. As noted above, resis-tance to flow is inversely proportional to thediameter of a conducting tube (here, Dtracheid)to the fourth power. Therefore, a small in-crease in the dimensions of a xylem cell re-sults in a dramatic improvement in fluid flow.In addition, if all other variables are held con-stant, an increase in the length of a conductingtube (L) will decrease flow, albeit at a slowerrate than any change in diameter. As others

have pointed out (Comstock and Sperry 2000),this is not necessarily held constant in livingplants, because water will pass through fewersets of pits over a given distance when con-ducting cells are longer. Viscosity of waterflowing through the tracheid ( ) will vary�H O2

slightly depending on environmental factorssuch as temperature; we used the viscosity ofwater at 25�C for all our calculations.

64� LH O2R � (8)lumen 4(D )tracheid

Rpit, the pit resistance (eq. 9), consists of theresistance from the two apertures (Raperture)through which water flows at a given viscosity(eq. 10) plus resistance from flow through thepit membrane (Rmembrane; eq. 11). We modifiedthe pit membrane resistance by a constant (),described in detail below. The pit aperture hasa measurable thickness (tap) and diameter(Dap) and opens to the pit membrane (Fig. 2D).The pit membrane is modeled as a thin sheetwith a number of pores (Npore) in it, each witha given diameter (Dpore). The pores are alsomodeled as individual resistors in parallel,with the consequence that membrane itselfcan vary; in equation (11), we used a term tomodify the number of active pores per pit;F[porosity] varies from 0 to 1. Our default val-ue of 0.7 is based on literature estimates, rec-ognizing the possibility that some pit mem-brane pores may be obstructed by macromo-lecular gel-like compounds (Hacke et al. 2004;Sperry and Hacke 2004).

R � R � 2R (9)pit membrane aperture

128t � 24�ap H O H O2 2R � � (10)aperture 4 3D Dap ap

24�H O2R � (11)membrane 3N Dpore pore

We calculated the number of pores in the pitmembrane (eq. 12) by dividing the area of thepit membrane (the square of the pit membranediameter [Dmembrane]) by the square of the sumof a single pore’s diameter (Dpore) plus the av-erage thickness of a cellulose microfibril (tf).We chose 15 nm as our microfibril thickness(Taiz and Zeiger 2002) and simulated a rangeof pore sizes, from 5 to 65 nm, consistent with


FIGURE 3. Proportion of tracheid resistance from cellwall (pits) as a function of diameter and length. Pro-portion of resistance from tracheid lumen is the recip-rocal of the data shown. For tracheids as large as thosein Medullosa, most of the hydraulic resistance comesfrom pits. Black stars indicate proportions of wall resis-tance that were used as default values for the three taxaand were used to calibrate values for and Dpore. Tra-cheid dimensions: Medullosa, 142 �m, 25 mm; Cordaites,25 �m, 3.3 mm; and Pinus, 39 �m, 3.8 mm.

estimates in the literature based on vulnera-bility curves and direct measurement (Choatet al. 2003, 2004, 2006; Pesacreta et al. 2005).

2(D )membraneN � F [porosity] (12)pore 2(D � t )pore f

Value of . To adjust for discrepancies be-tween theoretical models and experimentaldata from fluid flow experiments (Brodribb etal. 2003, 2005; Brodribb and Holbrook 2004;Hacke et al. 2004; Sperry and Hacke 2004; Pit-termann et al. 2005; Sperry et al. 2005), the pitmembrane resistance (eq. 11) was modified bya constant to allow the membrane resistanceto vary (, ‘‘resistivity constant’’). Measure-ments on living angiosperms suggest that pitmembranes may have up to three orders ofmagnitude higher resistance than models pre-dict on the basis of first principles (Choat et al.2006). This may be due to uncertainty aboutthe role of pectins hypothesized to function ashydrogels in the overall retardation of fluidflow between adjacent xylem cells (Zwienieckiet al. 2001). Because the phylogenetic patternof pit membranes’ contribution to overall tra-cheid resistance is uncertain in living plants,this constant allows for more flexibility in in-terpreting the functional space of tracheidconductivity. We varied between 0.1 and1000 for Cordaites and Medullosa, but our de-fault values were 1 and 16, respectively. Thesevalues preserved the proportionality of lumento pit resistances at 67% and 77% respectivelyfor tracheids of average dimensions (Fig. 3).

Although neontological in its formulation,the approach outlined in the preceding para-graphs is valuable to paleobotanists becausemany of its stated parameters are constants orvary within well-defined environmental lim-its, and those that are not constants can be de-termined either from comparative biology ofliving plants and environmental data, or fromanatomical study of fossil plants.

Measurements and Sensitivity Analyses

To calculate medullosan tracheid conductiv-ity, we measured tracheid width, tracheidlength, pit density, and pit dimensions onspecimens from two species: M. anglica (Har-vard Paleobotanical Collection #24474), andan unnamed species (Medullosa sp. Harvard

Paleobotanical Collection #7791). We mademeasurements by using light microscopy forCordaites (Harvard Paleobotanical Collection#53824 and #7878) and SEM imaging of mac-erated tracheids from Medullosa. Further mea-surements of tracheid diameter were madefrom figures of two species described in theliterature to determine if dimensions were sig-nificantly different: M. noei (Delevoryas 1955;Cichan 1986b) and M. primaeva (Delevoryas1955) (see Table 1). For comparison, measure-ments were also taken from Andrews (1940)and Bannan (1965) of the same parameters forCordaites (Mesoxylon) and Pinus.

The tracheids of Cordaites and Pinus are sim-ilar in length and diameter, but they differ in


TABLE 1. Measurements of tracheid length and diameter for fossil Medullosa and Cordaites specimens. Mean, stan-dard deviation, and maximum and minimum dimensions are given for six taxa. Because complete tracheid lengthin Medullosa is difficult to observe in thin section, the numbers are based on five measured xylem cells.

Diameter (�m)

Mean SD Max Min n

Length (mm)

Mean SD Max Min n

Medullosa noei 142 32 167 83 24 25.4 2.4 28 22 5Medullosa primaeva 170 63 263 100 11Medullosa sp. 121 39 165 74 19Medullosa anglica 146 45 237 100 13Cordaites sp. 25.0 8.7 42.4 10.6 21 3.3 1.4 5.0 1.5 11Cordaites sp. 30.2 5.8 42.4 21.2 21

pit morphology. Cordaite pits are ellipsoidalapertures bounded by a thin permeable mem-brane, whereas Pinus has circular-borderedpits that are differentiated into a porous meshof fibers, the margo, that surrounds a thick,non-porous primary wall segment, the torus.Because of this distinctive pit structure, weused a different set of values for Dpore in equa-tions (11) and (12) for Pinus to account for thetorus-margo pit membrane’s increased poros-ity (Sperry and Tyree 1990; Pittermann et al.2005), as described by Hacke et al. (2004). Brief-ly, the margo was modeled as a mesh contain-ing large pores up to 1 �m in diameter, andthe torus was modeled as a nonconductingcylinder in the center of the pit membrane. Pi-nus stem tracheids appear to have a single rowof torus-margo pits regardless of the tra-cheid’s diameter, whereas Cordaites tracheidsadd a second or third row of pits as tracheiddiameter increases. Extant conifer roots maycontain wider tracheids that have a secondrow of pits, but this condition is rare in stems.

We substituted anatomical values, as well asparameters based on estimations from extantmaterial, into the equations and then variedlength and diameter as sensitivity analyses,both to approximate the ranges of anatomicalmeasurements found in the fossils and tostudy the parameter space (Table 2). In partic-ular, the pore size (Dpore) in fossil plant pitmembranes is unknown, so we substituted avalue derived from analysis of cavitation vul-nerability in vessel-bearing angiosperm rainforest trees for Medullosa and Cordaites (40 nm;Choat et al. 2003). There is considerable vari-ation in pit membrane pore size; direct mea-surements of pore diameter via gold bead per-fusion (5–20 nm; Choat et al. 2004) differ from

estimates made on the analysis of vulnerabil-ity curves through application of the capillar-ity equation (50–200 nm; Choat et al. 2003,2004, 2006). We chose our value because it fallswithin the range bounded by the two esti-mates, although it increased the proportion ofmedullosan tracheid resistance from pitsabove the 40–60% threshold found in analysisof tracheids and vessels (Sperry et al. 2005,2006; Wheeler et al. 2005).

Pit Area Resistance. To assess our model ofpit membrane porosity and our values forDpore and , we calculated the flow resistanceper tracheid normalized on a pit membranesurface area basis. The pit area resistance (rp)is equal to the product of the cell wall resis-tance (Rwall) and one-half the pit area, which isthe product of the area of a single pit (Apit) andone-half the number of pits in a tracheid (Npits)(eq. 13).

NR pitswallr � A (13)p pit� �2 2

Wall resistance (eq. 14) is found by subtractingthe lumen resistance (Rlumen) from the total re-sistance (Rtot).

R � R � Rwall tot lumen (14)

We compared pit area resistance calculationsfor Cordaites and Medullosa with recent analy-ses showing that tracheids of conifers and ves-selless angiosperms and eudicot vessels formtwo statistically distinct populations with lowand high pit area resistances, respectively(Hacke et al. 2007). We calculated rp for a rangeof pit membrane pore diameters, from 5 to 65nm, and plotted the results against data fromHacke et al. (2007) both to compare our model


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with experimental data and to place Paleozoicseed plants in this context (Fig. 4).

Estimating Cavitation Vulnerability. The phys-ical structure that accounts for the wide vari-ability in cavitation resistance observed in xy-lem cells remains unknown. Two hypothesesthat describe the relationship between cavita-tion vulnerability and vessel size are the cap-illarity hypothesis and the pit area hypothe-sis. In both, the size of the largest pore in thepit membrane determines resistance to cavi-tation of the entire tracheid, operating underthe assumption that given a pressure gradientimposed across a xylem cell, the largest porewill be the likeliest place for air-seeding to oc-cur. In the former, the size of the largest poreis a function of interspecific variation in pitmembrane pore size and cannot necessarilybe predicted from first principles alone; eachplant species has its own distribution of poresizes within membranes, and this governs theplant’s tradeoff between conductivity and vul-nerability to cavitation. Such a view is sup-ported by calculated values of pore sizes thatcan vary tenfold among species (Choat et al.2003). In contrast, the pit area hypothesis isbased on an observed correlation between in-creasing pit area in a xylem cell and more pos-


itive cavitation pressure, suggesting that xy-lem cells with a larger proportion of their cellwall dedicated to pits will cavitate at moremodest pressures than cells with lower pit ar-eas. It has been hypothesized that the size dis-tribution of pit membrane pores is close touniform across all seed plants and that theprobability of an anomalously large pit mem-brane pore in contact with a neighboring air-filled tracheid or vessel element is what deter-mines cavitation pressure, and this latterproperty increases with increasing pit area.

We investigated the functional consequenc-es of Medullosa’s pit area according to both ofthese scenarios. First, using our estimatedpore size, we used the capillarity equation (eq.15) to estimate the pressure drop (�P) re-quired to pull air through a pit membranewith a single pore of this size, which is a func-tion of pore diameter (Dpore), the surface ten-sion of water ( ; 0.07 Nm�1), and the contact�H O2

angle between air and the lignocellulosicmembrane ( ; 0�):

� (cos )H O2�P � 4 (15)[ ]Dpore

Second, we used the pit area from an averagemedullosan tracheid with diameter 142 �mand length 25.4 mm to compare with Sperryet al.’s (2006) correlation between pit area andcavitation pressure, to estimate a cavitationthreshold. To compare the effect of pit area oncavitation vulnerability among the three taxa,we used a tracheid 41 �m in diameter and 5mm in length for both Pinus and Cordaites.

To assess the structural stability of tracheidsunder extreme tensions, we used the observedrelationship between tracheid wall thickness-to-span ratio and resistance to implosionfound in Hacke et al. (2001) to determine thethreshold at which tracheids in each of ourtaxa would implode. Others have observedthat the ratio of the thickness of xylem cellwalls to the span of the lumen is correlatedwith the ability to resist implosion. Cells withlarge lumens and thin cell walls are subject toimplosion under strong pressure gradients,whereas cells with thick walls and short lu-men diameters are not (Hacke et al. 2001), arelationship that holds across vessel elements

and tracheids, albeit with slightly differentwithin-group trends, reflecting different safe-ty margins between the groups. We measuredxylem cell wall thicknesses from Medullosa,Cordaites, and Pinus, calculated their thick-ness-to-span ratio for a given diameter, andplotted this value against tracheid diameter inorder to determine the size at which tracheidswould have been vulnerable to implosion at�2 MPa. We chose this value because �2 MPa,which can be reached at moderate environ-mental conditions, such as a temperate foreston a summer day, is a tension at which largevessels can be vulnerable to implosion but tra-cheids are not.

Results

Anatomical Measurements. Light micro-scope examination of tracheids maceratedfrom Medullosa specimens in coal balls andmeasurements from published figures showthat these cells have large diameters, rangingfrom 74 to more than 200 �m (see Table 1), inagreement with other published measure-ments of medullosan tracheid diameter (Ci-chan 1986a,b). In contrast, measurements ofsecondary xylem in two Cordaites specimensyielded average diameters of 25 and 30 �m (n� 21). Because flow rate is proportional to theradius of the conducting cell to the fourthpower, and tracheids of Medullosa are two tofive times as wide as those of contemporane-ous coniferophytes, they should yield a per-tracheid flow rate 16–625 times higher.

Medullosan tracheids macerated from coalballs had pits that covered approximately one-half of the cell’s surface and contained up tosix rows of 20-�m-diameter circular-borderedpits (Table 2). Cordaite tracheids maceratedfrom coal balls contained up to three rows ofcircular-bordered pits that covered slightlyless than one-fifth of the cell’s surface. Pinustracheids normally contained a single row oftorus-margo pits along the radial wall, butrare specimens have a second row. Pit frac-tions ranged from a maximum of 0.5 in Med-ullosa to a minimum of 0.05 in Pinus.

Hydraulic Conductivity. Our model produc-es two principal results, the first dealing withwater transport capacity and the second deal-ing with biomechanical tradeoffs resulting


from tracheid structure. First, at diametersand lengths common to both taxa in the fossilrecord, an individual tracheid of Medullosawould move far more water per pressure gra-dient and unit time than a coniferophyte tra-cheid, with or without torus-margo pits (Figs.5, 6). Conduit specific conductivity (Ksc) for amedullosan tracheid of average dimensions—142 �m in diameter and 25.4 mm long—is ap-proximately 0.3 m2/MPa·s. A large Pinus stro-bus tracheid, 39 �m in diameter and 3.8 mmlong, would have a Ksc of approximately 0.02m2/MPa·s, whereas a tracheid from Cordaitesof average dimensions (25.4 �m in diameter,3.3 mm long) would conduct at approximately0.01 m2/MPa·s. For size ranges simulated inour tests, even small medullosan tracheidshave higher Ksc than tracheids from Pinus andCordaites (Fig. 6).

Simulated conductivity and resistivity val-ues compare favorably with measurementsmade on living angiosperms and gymno-sperms (Figs. 4, 5). Resistance measurementsmade on conifer tracheids and angiospermvessels are broadly consistent with this mod-el’s predictions of conductivity in Cordaitesand Pinus and in Medullosa, respectively, whenthe dimensions are comparable between thefossil and living taxa (Choat et al. 2003; Sperry2003; Hacke et al. 2004, 2007; Sperry andHacke 2004; Pittermann et al. 2005). In termsof conductivity, then, medullosan tracheidsare more similar to angiosperm vessels thanthey are to conifer tracheids, despite originat-ing from a tracheid-like developmental pro-gram. The anatomy of medullosan tracheidsalone also puts to rest the suggestion thatthere are developmental limits to tracheid sizethat prevent them from reaching sizes com-parable to some vessels (Lancashire and En-nos 2002).

For a Medullosa noei tracheid 142 �m in di-ameter and 25 mm long, conductivity nor-malized to cross-sectional wall investment(Ksp) is approximately 9.5 m2/MPa·s (Fig. 7).A large Pinus tracheid 40 �m in diameter and4 mm long could conduct at approximately0.11 m2/MPa·s. Tracheids of Cordaites, withcircular-bordered pits, conduct water nearlyat values comparable to Pinus tracheids be-cause of the increased area of pits on each tra-

cheid, but have a lower conductivity than tra-cheids of Medullosa (data not shown).

When the size ranges of medullosan andpine tracheids are overlain and conductivity iscompared, it becomes clear that even the larg-est pine tracheids have a lower conductivityper cross-sectional wall investment than thesmallest medullosan xylem cells (Fig. 7). Thelargest medullosan tracheids conduct nearlytwo orders of magnitude more water than thelargest conifer tracheids, independent of pit-ting style, when normalized to cross-sectionalwall thickness.

The hydraulic conductivity of medullosanxylem per unit area is high. It is difficult tomake quantitative comparisons with experi-mental values for living plants, because of thedifferent methods in reporting data (Tyreeand Ewers 1991); however, virtually half of thecross-sectional area of a medullosan stem iscomposed of large tracheids, whereas angio-sperm xylem combines relatively few large,long vessels with numerous fibers. In this way,medullosan stems are constructed like coniferstems, except they contain tracheids with highconductivity rather than numerous low-con-ductivity tracheids. Given the large amount ofstem cross-sectional area devoted to medul-losan tracheids, we would expect per-areaconductivity to be comparable between a ves-sel-bearing eudicot and a tracheid-bearingMedullosa.

Pit Membrane Porosity and Morphology

Varying pit membrane porosity over threeorders of magnitude affects the magnitude ofour results but not the rank order of the dif-ferences between medullosan and conifero-phyte tracheids. Making individual pits lessporous in the model by increasing the resis-tance of the pit membranes had a stronger ef-fect on tracheids that have fewer pits than onthose that have many (Fig. 5). However, be-cause the resistance component from pitsmodels them as resistors in parallel, with ahigher number of pits lowering the total resis-tance, the porosity of the membrane is onlyone of many important considerations.

Pit area resistance measurements for Cor-daites and Medullosa yielded values of 1.5 and23.2 MPa·s/m�1 for pit membrane pores 40


FIGURE 5. Conduit specific conductivity (Ksc) for Medullosa (asterisks), Cordaites (stars), and Pinus (open triangles)for given pit area resistivities (rp). Comparison is made with vesselless angiosperm and conifer tracheids with com-parable diameters for the two coniferophytes, and for a eudicot vessel with comparable diameter to Medullosa. Bold-ed characters identify values used as per-taxon standard throughout the paper. Values for vesselless angiospermtracheids, conifer tracheids, and a eudicot vessel are from Hacke et al. (2007). Vesselless angiosperm and conifertracheid diameters are presented next to crosses and squares. Owing to the lack of data for vessels with diameterscomparable to Medullosa, 142 �m vessel value is extrapolated from ‘‘67% optimum’’ line in their Figure 1B. Boldedvalue for Medullosa Ksc yields 77% of total hydraulic resistance from pits; bolded value for Cordaites has 67% ofhydraulic resistance in pits. Because tracheid resistivity is highly variable with respect to diameter, two values areshown for vesselless angiosperm and conifer tracheids.

nm in diameter (Fig. 4). These values placeCordaites within the group of living conifersand Medullosa between the vesselless angio-sperms and vessel-bearing eudicots (Hacke etal. 2007). Smaller pore sizes increase pit arearesistance for both taxa but do not change thisassociation.

Except for tracheids of extremely low di-ameters and lengths (less than 20 �m and 1mm, respectively), medullosan tracheidscould conduct higher volumes of water thanconifer tracheids, with or without torus-mar-go pits (Fig. 6). Tracheids of these sizes are ab-sent in our specimens of Medullosa (Table 1).The large number of pits in each medullosantracheid, compared with conifer tracheids (Ta-ble 2, Fig. 2), dramatically reduces the resis-tance to water flow through a xylem cell bygreatly increasing pit membrane area. This in-crease in pit area, in turn, decreases the total

resistance to fluid flow through the xylem cell.Large pit diameters in Medullosa further de-crease resistance in any individual pit.

Resistance to Implosion and Cavitation. Thesecond result concerns the biomechanicalfunctionality of medullosan tracheids. The ad-vantages these cells confer in conductivitycome at a physiological cost, making Medullosamore vulnerable than pycnoxylic seed plantsto implosion and cavitation induced by waterstress. Wood density, expressed as the thick-ness-to-span ratio of xylem cells, has beenshown to correlate positively with resistanceto implosion under tension (Hacke et al. 2001).Calculating this ratio for Medullosa and Pinuswhile varying the diameter of the tracheidsshows that medullosan tracheids would sufferirreversible damage at modest negative pres-sures (Fig. 8). Experimentally derived lines ofimplosion found by Hacke et al. (2001) suggest


FIGURE 6. Conduit specific conductivity (Ksc) in Medullosa, Pinus, and Cordaites tracheids versus diameter andlength. Note differences in scales in the three graphs. Color (z-axis values) is consistent across the three plots.

that the largest tracheids in Medullosa wouldhave imploded at tensions less than �2 MPa,a tension that can be reached in a temperateforest on a dry, sunny day. Indeed, medullo-

san tracheids would probably have embolizedat lesser tensions. The thicker, narrower tra-cheids of Pinus and Cordaites are unlikely toimplode at these tensions; their thickness-to-


FIGURE 7. Conductance normalized to cross-sectionalwall thickness (Ksp) in Medullosa and Pinus tracheids ver-sus diameter and length. Contours show lines of equalconductance (Ksp) in m2/MPa·s, and boxes outline sizeranges possible in extant plants (for Pinus) or the fossilrecord (for Medullosa). Conductance in medullosan tra-cheids always exceeds that of pine tracheids.

FIGURE 8. Medullosa (thick line), Cordaites (dotted line),and Pinus (thin line) thickness-to-span ratios versus tra-cheid diameter. Ranges are based on tracheid diametersand thicknesses found in fossils and the literature (Ban-nan 1965; Greguss and Balkay 1972). The hashed zoneis where given thickness-to-span ratios cause irrevers-ible implosion at �2 MPa (from Hacke et al. 2001).

span ratio lies far from the line of implosion.In fact, in some Pinus species, excised branchesdo not experience any loss of conductivity un-der tensions greater than �2 MPa (Pittermannet al. 2006). The thickness-to-span ratio ofmedullosan tracheids also suggests that thevascular system could not have been an im-portant source of structural support, as it wasalways at risk of cavitation, embolism, andsubsequent implosion.

As described above, our model also predictsthat most of the hydraulic resistance in a med-ullosan tracheid should come from the pits,rather than approximately 35% and 65% fromthe lumen and the tracheid wall, respectively,as experimental data suggest for both conifersand woody angiosperms in the Rosaceae(Wheeler et al. 2005; Sperry et al. 2006). To in-vestigate the cavitation resistance of a med-ullosan tracheid that, according to the capil-larity hypothesis, had 65% of its flow resis-tance coming from pits, we imposed an in-crease in the size of the pores in pitmembranes of an average medullosan tra-cheid (diameter � 142 �m, length � 25.4 mm)until the pits accounted for 65% of the tracheidresistance, rather than 87%. We used this porediameter to predict the pressure gradient thatwould have caused 50% loss of conductivity

from cavitation (P50) in medullosan wood, us-ing the capillarity equation (eq. 15). Pores 100nm in diameter caused pits to account for 65%of medullosan tracheid resistance, and thisvalue substituted into equation (15) suggeststhat a pressure gradient of �3 MPa couldcause air-seeding in medullosan tracheids. Itis possible that there are rare occurrences ofpores this size in medullosan pit membranes;they occasionally occur in vesselless angio-sperms (Hacke et al. 2007) but are rare in an-giosperm and fern pits (Carlquist 2001).

To estimate cavitation vulnerability in Pi-nus, Cordaites, and Medullosa according to thepit area hypothesis, we also calculated the pitarea of a tracheid from each of our three taxa.A medullosan tracheid of average diameterand length would contain pit area of approx-imately 3.3 mm2, whereas Pinus and Cordaitesare two to three orders of magnitude smaller:0.015 and 0.003 mm2, respectively. We plottedthese estimates of pit area against the experi-mentally derived correlations of pit area andcavitation resistance found by Sperry et al.(2006). Tracheids from Medullosa fell withinthe ranges of pit area per tracheid found with-in angiosperm vessels and yielded a cavitationpressure of �0.88 MPa. Cordaites and Pinus fellwithin the range of conifer stem tracheids, andyielded a cavitation pressure between �2 and�7.5 MPa, with uncertainty due to a poor r2

value for conifer tracheids (r2 � 0.33). Thesevalues are consistent with cavitation pressuresfound in experimental analyses of conifer and


angiosperm stem segments (Sperry and Tyree1990; Pockman et al. 1995; Hacke and Sperry2001; Pittermann et al. 2006; Sperry et al.2006).

Discussion

Advantages of Ohm’s Law Modeling. Themodel presented here represents water move-ment through plants more accurately thansimple Hagen-Poiseuille calculations becauseit incorporates factors such as tracheid length,pit density, and pit type into calculations ofconductivity. As many authors have dis-cussed, the type, number, and dimensions ofpits are strong determinants of conductive ca-pacity, especially at large tracheid diameters(Comstock and Sperry 2000; Hacke et al. 2004;Sperry and Hacke 2004; Sperry et al. 2005).Neglecting to incorporate the resistance toflow that occurs when water moves from onepit aperture to another overestimates theamount of water that passes through the vas-cular system. Hagen-Poiseuille models simu-late plants as continuous, empty tubes fromthe soil to the leaves, when they are better un-derstood as a series of short, discontinuous,connected tubes moving water in parallel.

Others have noted the difficulty of deter-mining the overall size, ecology, and habit offossil plants, especially given the possibilitiesof growth forms that lack living representa-tives (Rowe et al. 1993; Masselter et al. 2006).The approach taken in this paper sheds lighton these issues because our model is calibrat-ed against the maximum tension that a cellcan resist before imploding. As implosion riskis a function of cell size, which holds acrosstracheids and vessels, conductivity modelscan address the possibility that xylem tissueacted as structural support, aiding in the eval-uation of growth habit.

The size, distribution, and number of poresin pit membranes remain the largest uncer-tainties in the model presented here; however,our calculated values of pit area resistanceprovide support for our choice of pore sizeand number, owing to their correspondencewith the functional space of extant seed plantspresented by Hacke et al. (2007). The fossilrecord may be silent on the diameter of poresin the pit membranes of Medullosa or Cordaites

because of taphonomic factors, but simulationof their probable range in Figure 4 shows thatuncertainties in pore size do not have a qual-itative effect on our results.

The conductivity model presented here isversatile, permitting the simulation of xylemcells that do not currently exist or have neverexisted, in terms of both extreme morphologyand novel combinations of anatomical char-acters. This allows for a full exploration of pa-rameter space unconstrained by what is foundin living plants, and has the potential to an-swer broader questions about the evolutionaryhistory of water transport and plant ecophys-iology.

Medullosan Paleoecophysiology

Effects of Large Tracheid Size. Our modelpredicts that most of the resistance in a med-ullosan tracheid should come from the cellwall, given the extremely large diameter ofeach conducting cell (Fig. 3). In many of oursimulations, more than 80% of the resistancecame from the pits, except at very small tra-cheid diameters (�20 �m). Recent work hasshown that in vessel-bearing angiosperms, lu-men and pit resistances each account for ap-proximately half of the total resistance(Wheeler et al. 2005), and it is likely that ourmodel overestimates the size of pores in thepit membrane when compared with experi-mental hydraulic measurements, as has beenthe case with other first-principles-basedmodels (Hacke et al. 2004; Sperry and Hacke2004). In all of these cases, underestimation ofthe resistance component from pits is mostlikely due to variation in pore size distributionwithin the membrane (Choat et al. 2003, 2006;Wheeler et al. 2005) or to the distribution andabundance of lignin and pectin within themiddle lamella (Zwieniecki et al. 2001; Boyceet al. 2004).

Fluid Flow in Medullosa Stems. Of course,the dimensions of individual tracheids consti-tute only one of several factors that collective-ly determine fluid flow in the whole plant.Tracheids function as an integrated networkin active xylem tissues, and the anatomicalstructure of stem xylem and leaf traces deter-mines water supply to the leaves. Leaf area, inturn, governs the plant’s demand for water,


and the amount of carbon that can be assimi-lated. By any estimate, medullosan leaveswere large (Taylor and Taylor 1993); althoughit is difficult to reconstruct the exact numberof pinnules on any frond, many secondaryand tertiary pinnules have areas that exceed100 mm2 in both of the principal foliage typesassociated with medullosan stems (Mickleand Rothwell 1982; Beeler 1983; Pryor 1987,1990). Given that numerous pinnae of this sizewould be functional on any living frond, andgiven stomatal densities that are well withinthe ranges of both extant tree ferns and livingangiosperms (Arens 1997; Cleal et al. 1999),we suggest not only that the resulting highevapotranspiration demands of Medullosa areconsistent with high tracheid conductivity,but also that they may explain the other un-usual features of medullosan anatomy.

When the overall structure of medullosanxylem is considered as a network, it appearsto function as a highly redundant and well-connected system at all scales, from the indi-vidual cell and xylem tissue, up to the wholeplant. This is functionally important for threereasons: first, it ensures a robust supply of wa-ter to the photosynthetic surfaces; second, itleads to an elevated risk of embolism spreadingthroughout the wood; and third, it constrainsthe ecological distribution of medullosans thatcombine large leaf areas and large tracheids.

The high number of pits on each tracheidensures that any two neighboring xylem cellsare well-connected to each other through mul-tiple points. The anastomosing nature of thevascular segments within the stem allows formultiple pathways of water to exist throughthe stem, albeit on short spatial scales. Thismay prevent compartmentalization of waterdemand and the consequent buildup of largetensions in the stem, which could increase therisk of embolism which, once seeded, wouldspread.

Leaf Traces. The numerous leaf traces thatenter each petiole base may be analogous toanastomosing vascular segments in that doz-ens of discrete strands ensure a supply of wa-ter from many different sources within thestem. Leaf traces are known to be loci of ex-treme vulnerability in a plant’s vascular sys-tem, and it is known that petioles and small

branches will suffer cavitation before stem xy-lem cells (Zimmermann 1983; Tyree and Sper-ry 1989).

The sheer number of traces could also re-flect an unusual development of xylem cells inpetioles. The phytohormone auxin is synthe-sized at leaf margins and transported fromcell to cell by PIN proteins, and high auxinconcentration in a cell causes a signal cascadethat converts living parenchyma cells intodead xylem cells (Woodward and Bartel 2005).In this light, instead of having a single, largevascular strand comparable to that found inferns and most other seed plants (which de-velop from the canalization of auxin on a sin-gle path through the petiole), Medullosa mayhave had a mechanism by which many ofthese canals could develop simultaneously.The cycads may have a similar mechanism inplace today.

Although their precise phylogenetic posi-tion remains controversial, medullosans areoften associated with cycads because of thisdistinctive leaf vascularization—in bothgroups, a complex of traces connects the baseof each petiole to the stem’s vascular system.The similarity in leaf trace pattern has some-times been accepted as a synapomorphy forthe two groups (Stewart and Rothwell 1993;Taylor and Taylor 1993). It is possible, how-ever, to entertain two alternative hypotheses:(1) this character could be a plesiomorphy notshared by more derived seed plants, or (2) thesimilar anatomies could reflect functional con-vergence. The absence of complex leaf vascu-larization in other stem seed plants such as Ly-ginopteris, in other extinct seed plants such asGlossopteris, or in living seed plants placednear the base of modern molecular phyloge-nies (e.g., Ginkgo) suggests that complex leaftraces may well be convergent.

Other extant plants have similarly complexleaf traces, including tree ferns, palms, andthe Southern Hemisphere dicot Gunnera. All ofthese plants have large leaf areas supportedby small stems and/or a modest developmentof wood: leaves 3–4 m long are not uncommonin tree ferns, palms, or Gunnera, and none ofthese groups achieve secondary growth bymeans of a vascular cambium (Batham 1943;Tomlinson 1990). It is possible that the ex-


treme complexity of the petiolar vascular sys-tem is dictated by the vulnerability of petiolexylem to cavitation in plants having large leafarea supported by a moderate amount of stemxylem. The physiological benefits inferred forMedullosa would apply to those plants, as well.

Embolism and Repair. Water requirementsimposed by large medullosan fronds musthave placed great demands on the petiolarand stem vascular system in the plant, and thehydraulic conductivity model predicts thatthe vascular system must have been embo-lized and refilled repeatedly. The networkstructure of the medullosan vascular systemsuggests that embolisms may have propagat-ed easily through the highly connected vas-cular system, as recent theoretical work sug-gests for angiosperm vessels (Loepfe et al.2007).

The medullosan vascular cambium pro-duced only a small amount of wood duringsecondary growth and could not grow newwood every season to replace tracheids thatcavitated during environmental stress. The re-sulting high cost of cavitation and embolismnecessitates the plant’s having had some wayto refill xylem cells rapidly. The close prox-imity of large rays to tracheids suggests thatmedullosans may have been able to reverseembolized xylem cells by using waterpumped in under positive pressure, as seen inmodern grape vines (Holbrook et al. 2001).The abundant parenchyma around each vas-cular segment, in addition to the wide raysseparating nearly every pair of xylem cells,may have aided in refilling embolized xylemcells within the vascular segments. Medullo-san leaf traces, like the vascular segments, arealso surrounded by parenchyma, which sug-gests a potential role for refilling in their de-velopment. In general, then, the distinctivevascular anatomy of Medullosa results in aclose spatial relationship between large tra-cheids vulnerable to cavitation and parenchy-ma tissues potentially capable of refilling em-bolized conducting cells.

Structural Support. The whole-plant archi-tecture and vasculature of Medullosa is adapt-ed to have a ‘‘viny’’ or angiosperm-like divi-sion of labor between vascular cells devoted toefficient, low-resistance transport of water

and poorly conducting or nonconducting sup-port tissue. This division of labor may extendto the chemistry of xylem cell walls: in livingplants, the presence of lignin within the pri-mary wall and the compound middle lamellais inversely correlated with the ability of theplant to adjust pit membrane resistance rap-idly in response to changes in sap ion concen-tration (Zwieniecki et al. 2001; Boyce et al.2004). The inability of medullosan tracheids tofunction as a source of structural support sug-gests that medullosans may have exhibited ahydrogel response to changes in sap ion con-centration, independent of any measure of lig-nin presence within the cells themselves.

To achieve an arborescent form analogousto one suggested model, the extant tree fernAngiopteris, Medullosa would have requiredlignified fibers in the cortex that developedinto a rigid band. Persistent leaf bases, alsowith lignified fibers, may also have helpedsupport the plant (Mosbrugger 1990). Semi-rigid cortex and compression fossils from theBernice Basin, Pennsylvania, suggest that thiswas the case for at least some species of med-ullosans (Wnuk and Pfefferkorn 1984), andour data support previous hypotheses basedon cantilever models and stress-strain rela-tionships from cell morphology (Mosbrugger1990; Rowe and Speck 2004). This hypothesiscan be tested with geochemical methods onpermineralized specimens of Medullosa: thepresence of lignin in the cortex would supportan interpretation of stems as arborescent. Itsabsence from the entire plant would suggest ascandent or climbing habit. Possible analogymay be found in extant ferns of the Blechna-ceae, such as the large-leaved climbing fernSalpichlaena volubilis, which has unusuallylarge tracheids (Veres 1990). Such a growthform has been suggested for at least one med-ullosan species, Medullosa endocentrica (Hamerand Rothwell 1988). Known medullosan spec-imens, however, lack unambiguous anatomi-cal specializations for climbing, such as thehooks and trichomes found in the fossil seedferns Pseudomariopteris and Blanzyopteris(Krings and Kerp 2000; Krings et al. 2003).

Evolution of the ‘‘Division of Labor’’ betweenTransport and Support Tissues. It has longbeen suggested that the global ecological


dominance of angiosperms between approxi-mately 40�N and 40�S is due to their ability todivide xylem function between high-through-put vessels and load-bearing fibers (Bailey1953; Esau 1977; Raven et al. 1999). In a furtherexplication of this hypothesis, Bond (1989)suggested that the ecological dominance ofangiosperms was caused by competitive ex-clusion of juvenile conifers due to their in-creased growth rate, facilitated by more effi-cient leaf venation and vasculature. Accordingto this hypothesis, more efficient transport ofwater allowed for greater carbon assimilationand more rapid growth of juvenile angio-sperms over juvenile conifers after distur-bance events, which pushed the latter from thedominant ecological position they heldthrough much of the Mesozoic.

This hypothesis has been criticized on manylevels (Becker 2000); the influence of watertransport on growth rate, especially the char-acterization of gymnosperm xylem as hydrau-lically less efficient than angiosperm xylem,has been refuted for conifers (Pittermann et al.2005, 2006; Pittermann and Sperry 2006), andwe suggest here that the cordaites had pit arearesistance values comparable to extant coni-fers. In Medullosa, the combination of extrax-ylary fibers, presumably used for structuralsupport (Delevoryas 1955; Mosbrugger 1990),and high-conductivity xylem is more similarto angiosperm lianas than to self-supportinggymnosperm trees. Medullosa’s angiosperm-like hydraulic system should be taken into ac-count in any attempt to relate the success offlowering plants to biomechanical division oflabor in their stems. Angiosperms have a di-vision of labor within tissues derived from thevascular cambium—fibers for structural sup-port and vessels for low-resistance transport.Stem seed plants, including Medullosa, mayhave derived a similar division of labor fromtwo different tissues in their stem: highly con-ductive large tracheids combined with struc-turally supportive fibers and cortex.

Medullosan Stomatal Behavior. Land plantscan resist damage from the drying power ofthe atmosphere by increasing conductivityand/or by regulating transpiration throughthe timing of stomatal opening and closure.The two are related via guard cell sensitivity

to water potential loss, which signals for sto-matal closure (Buckley et al. 2003), but thereare distinct developmental and evolutionaryhistories represented in each of these strate-gies. In contrast to xylem conductivity, whichis directly preserved in anatomy and chemis-try, the record of stomatal response to vaporpressure deficit is not preserved by fossil plantanatomy. It may, however, be indirectly pre-served chemically (Smith and Freeman 2006).Given the constraints that the medullosan vas-cular system places on whole plant function,we may be able to infer something of its sto-matal behavior by comparison with livingplants.

Recent work has shown that modern fernsand angiosperms in the Tropics have low leafcapacitances; leaf water potential can drop 1MPa in less than five minutes in ferns and inthree minutes for many angiosperms (Brod-ribb et al. 2005). Angiosperms allow cavitationto occur and leaf conductivity to drop 50% be-fore closing stomata, whereas ferns close theirstomata well before 50% loss of conductivity(Brodribb and Holbrook 2003); this may bedue to a reduced ability to refill cavitated xy-lem cells in ferns. Medullosa is phylogenetical-ly intermediate between ferns and crown seedplants, but in terms of stomatal behavior itsecophysiology may be more reminiscent offerns than of conifers or flowering plants.Medullosa’s large leaf area and stem vascularsystem, already operating near the thresholdof cavitation and implosion, suggest that itsstomata may have closed at modest leaf waterdeficits, even if the plant was able to refill cav-itated xylem rapidly, as postulated above. Fail-ure to close stomata early and rapidly mightwell have induced water stress damage be-yond the possibility of repair.

Environmental Limits on Medullosan Distri-bution. The ecophysiological interpretationadvocated here has implications for environ-mental distribution of medullosan fossils.Medullosan fronds required large amounts ofwater to permit carbon assimilation and pho-tosynthesis. These requirements, combinedwith the structural weakness (vulnerability toimplosion) of the vascular system, suggestthat Medullosa could not have survived in atemperate forest, any place that was season-


ally dry, or anywhere with hard frosts. Evenmodest levels of water stress, such as thoseseen in a temperate forest on a sunny day,would have induced cavitation and then per-manent tracheid implosion within its vascularsystem. Seasonal frost would have nucleatedice crystals within the large lumens of tra-cheids and ruptured cambial tissue. These cli-matic constraints suggest that tracheids with-in the stem and leaf traces of Medullosa prob-ably embolized repeatedly, depending on theavailability of water. Medullosan seed ferns,therefore, were dominant components of trop-ical floodplains (DiMichele et al. 2006) be-cause of environmental constraints on theirfunction; medullosans relied on a constantsupply of water to support their high evapo-transpirative demand. Their disappearancefrom tropical flora during the protracted lateCarboniferous to Permian regional-scale dry-ing may reflect their vulnerability to waterstress.

Conclusions

Water transport modeling provides insightsinto the ecology, biomechanics, and environ-mental distribution of extinct and extantplants. Medullosan seed fern tracheids wereadapted to provide a high-volume/low-resis-tance pathway for water to reach their largeleaves, but functioned with a high risk of per-manent failure. This stands in contrast tomodern gymnosperms, which use their xylemfor structural support and function withinmuch greater safety margins.

Aspects of medullosan anatomy heretoforeconsidered enigmatic, including anastomos-ing vascular segments and abundant leaf trac-es, may be adaptations for the irrigation oflarge leaf surfaces using modest amounts ofwater transport tissue.

Advances in modeling fluid flow in extantseed plants will allow us to understand thephysiology, ecology, and evolutionary historyof extinct plants, permitting new insights intothe evolution of terrestrial flora through time.

Acknowledgments

We thank S. Pruss, W. Fischer, F. Rockwell,and S. Costanza for comments on early draftsof this manuscript. Comments from two anon-

ymous reviewers improved this manuscript.J.P.W. is supported in part by the NASA As-trobiology Institute.

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Modeling ﬂuid ﬂow in Medullosa, an anatomically unusual...

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