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Lindbergia 35: 53–62, 2012ISSN 0105-0761

Accepted 14 August 2012

© 2012 The Authors. This is an Open Access article.

In the context of bryophyte physiological function, re-cent investigations have adopted the term ‘canopy’ or ‘mini-canopy’ (Rice et al. 2001, 2005, 2008, Zotz and Kahler 2007, Tobias and Niinemets 2010, Waite and Sack 2010) as a descriptor of the bryophyte functional unit. The knowledge that the structure and organization of stems, leaves, branches and branch systems affects the physiology and ecology of bryophytes has a long history in bryophyte ecology and traces its utility to the concepts of growth- and life-forms that have shown to correspond with variation in species’ distributions and performance in Antarctic, temperate and tropical systems (Gimingham and Birse 1957, Gimingham and Smith 1971, Mägdefrau 1982, During 1992, Bates 1998, Kürschner et al. 1999, Elumeeva et al. 2011).

Using the term canopy to describe bryophyte shoot systems implies that there is a significant functional ef-fect of the shoot system organization that is not caused

merely by the additive effects of structures at a lower-level of organization (e.g. leaves, stems or branches). This has been most fully explored within the vertical plane in bryo-phytes. In this dimension, variation in light dynamics is attributed to differences in the density and organization of canopy elements. Indeed, light attenuation follows similar exponential decay with shoot area in bryophytes as it does with leaf area in vascular plant canopies (van der Hoeven et al. 1993, Hirose 2005, Zotz and Kahler 2007, Tobias and Niinemets 2010). Also, variation in height among elements of the shoot system affects bryophyte function, particularly the dynamics of water loss mediated through the interaction between shoot systems and boundary-layer properties. Canopies with large variation in height (i.e. ‘rough’ canopies) show reduced boundary-layer thickness as shoots project into free-airstreams above the bryophyte surface, generate turbulent eddies, and have enhanced rates of water loss (Proctor 1980, Rice et al. 2001). Con-

The cost of capillary integration for bryophyte canopy water and carbon dynamics

Steven K. Rice

S. K. Rice (rices@union.edu), Dept of Biological Sciences, Union College, Schenectady, NY 12308, USA.

Due to their high shoot density and ability to store and transport water externally, ectohydric bryophytes may share water laterally among shoots. Given that rates of evaporation may be spatially variable across the canopy due to structural irregularities that cause surface roughness, lateral water transport via integrated capillary networks may affect shoot water status and influence carbon dynamics. The interaction between capillary integration and surface roughness was explored using simulation modeling. A shoot-level model of water and carbon dynamics and their interaction was developed to model acrocarpous or Sphagnum species. Shoots were distributed regularly in a 20 × 20 grid with the same mean height, but with different standard deviations to represent variation in surface roughness. Evaporation and light availability were modeled as a function of the shoot height relative to its neighbors. A drying cycle was simulated whereby canopies were fully recharged with water and allowed to dry during a 14-day period. Plants could either share water with their immediate neighbors or not. At low surface roughness, there was no dif-ference in canopy average water or carbon balance; however at high surface roughness, canopies without capillary integration experienced lower overall rates of evaporation and greater net carbon uptake. This was due to emergent shoots desiccating, but reducing the rate of water loss from lower shoots, which remained photosynthetically active. Consequently, there is a physiological cost to capillary integration in rough bryophyte canopies, a condition that differs from the benefits normally attributed to physiological integration in vascular plant colonies. The degree of capillary integration may be an important functional trait of bryophyte canopies.

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sequently, differences in the vertical structure or organiza-tion of bryophyte shoot systems affect energy and matter exchange of bryophyte shoot-systems and these factors alone qualify the use of the holistic term ‘canopy’ for bryophytes.

However, what is lacking in our knowledge of bryo-phyte canopy function is an understanding of the degree of physiological integration among canopy elements and how variation in this might affect overall function. In the examples provided above, elements within the canopy interact with one another through their effects on local environmental conditions within the canopy. In other words, the canopy effects are mediated through an extrin-sic factor. Canopy-level processes may also be influenced by intrinsic physiological activity that leads to functional integration among canopy elements. When this occurs, connectivity among elements within the canopy causes them to not behave independently or merely to respond to local environmental conditions. Coordinated responses could alter the dynamics of the whole canopy system. In vascular plant colonies, integration of this type occurs via efficient internal transport systems that cause coordinated leaf-level responses to drought, light or physical stress. Some of these are mediated through hormone action, oth-ers are due to connectivity of physiological systems driven by local light environments or water potentials (Ballaré et al. 1994, Hutchings and Wijesinghe 1997, Vermeulen et al. 2008). In both of these situations, individual leaf or branch responses within a shoot system are either coor-dinated or correlated due to underlying control or con-nectivity.

In bryophyte canopies, shoot systems often occur at high densities and many species hold and transport water externally (i.e. ectohydric) with external conduction ac-counting for greater than 90% of water transport (Glime 2007). Externally held water can also be shared by adjacent shoots within the canopy forming an integrated capillary network. This has been well described in Sphagnum (Hay-ward and Clymo 1982, Andrus et al. 1983, Rydin 1985, 1993, Li et al. 1992, Robroek et al. 2007), but also in other bryophytes (Proctor 1982). The ecological importance of this effect has been identified in Sphagnum where hollow species with reduced ability to transport water may persist in hummock environments due to lateral water transport (Andrus et al. 1983, Rydin 1985, Robroek et al. 2007) and also for other bryophyte growth forms (Elumeeva et al. 2011, Michel et al. 2012). However, bryophyte spe-cies differ in their ability to share water within capillary networks due to differences in 1) resistance to transport within networks, which can be a function of leaf and stem characteristics that create connected capillary spaces at ap-propriate scales (Dilks and Proctor 1979, Schofield 1981, Proctor 1982, 1984) or also be affected by the degree of external versus internal transport, and 2) the degree of lat-eral conductance between adjacent networks, which can be enhanced by physical contact.

I investigate the functional significance of lateral shar-ing of capillary water within bryophyte canopies using computational modeling. Critical features that control water and carbon balance are known for bryophytes; in particular, the effect of surface roughness on bound-ary layer resistance to water loss (Proctor 1980, Rice et al. 2001) and the effects of plant water content on net carbon gain (Proctor 1982, Williams and Flanagan 1996, Rice et al. 2008) have been quantified for a number of bryophyte species. Using these relationships, I develop a computer simulation model to estimate bryophyte canopy water and carbon dynamics during a drying cycle. In this model, the degree of lateral connectivity in water trans-port can be modified to explore the interactions among rates of water loss, net photosynthesis and integration of plant water among neighboring plants across canopy types that differ in surface roughness. Generating and exploring a computational model can provide insights into factors that underlie complex, spatial dynamics. This investiga-tion is designed to address the following questions: 1) how does the presence of lateral capillary integration in water transport affect rates of evaporation from bryophyte cano-pies? 2) How is this affected by changes in surface rough-ness that would lead to enhanced and uneven drying from the canopy surface? And, 3) does the interaction between integration and surface roughness affect shoot and canopy rates of net photosynthesis and carbon accumulation?

Methods

In general, a difference equation approach (numerical changes to pools and fluxes are iteratively implemented) was used to simulate water and carbon dynamics in a bryophyte canopy. The model represents the canopy as regularly spaced individual shoots in a 20 × 20 grid, whose functioning in terms of water and carbon dynamics is af-fected by the eight neighboring shoots. For purposes of parameterizing the model, these are considered to be 1 cm2 vertical shoots and simulate various ectohydric, ac-rocarpous and Sphagnum species that are dense enough to physically touch. Within a canopy, shoots differ from one another only in their height, which through its lo-cal effects on evaporation and light attenuation, directly influences water and carbon budgets.

Each shoot maintains identical relationships that con-trol its water and carbon dynamics, and the presence or absence of lateral water sharing via capillary integration among neighbors. There are two main, interacting com-ponents of the model that represent the water and carbon pools and fluxes (Fig. 1, model adapted from Rice et al. 2011). Plant water content is determined by the balance of gain through recharge either from the environment (e.g. rainfall) or from lateral transport from neighbors. A drying event was simulated by beginning each modeling run with saturated shoots. Water loss occurred through

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evaporation where water gains and losses could occur among neighboring shoots. This transfer was accom-plished by allowing plants to simulate evaporation for one day and then water was allowed to equilibrate between each shoot and its immediate neighbors, accomplished by assigning an individual’s water content with the average water content of the group. This simulates recharge via lateral transfer that might occur during the night when water vapor deficits are low. Evaporation is controlled by environmental conditions: surface and air temperatures and relative humidity, which control the water vapor defi-cit; wind-speed; shoot water content; and boundary layer thickness. This latter term is modeled as a function of the height of the individual relative to its neighbors (Srel). The boundary layer thickness is reduced for individuals taller than the average of their neighbors and increased when shorter.

The carbon component is based on a photosynthetic light response curve for shoots, with an input of ambient light intensity that is reduced depending on the degree of shading by neighbors. This is a function of the shoot height of the target shoot relative to its neighbors with light attenuation described by Beer’s law. The water and carbon components interact as plant water status directly affects rates of photosynthesis in poikilohydric plants. At high water contents, photosynthesis is depressed as exter-nal water films limit diffusion of CO2 to photosynthetic cells. As plants dry, they reach an optimum rate of photo-

synthesis and begin to slow again as tissues desiccate. The functions used to describe the model and the coefficients used are shown in Table 1 and 2. The form of some of these relationships is graphed and shown in Appendix 1.

The model was used to explore water and carbon dynamics during a simulated drying event. Shoots were initially saturated with water (10 g H2O g–1 dry mass) as they might be after a prolonged rain and then simulated to dry for 14 d under constant environmental conditions (air and surface temperature 20°C; relative humidity 50%; 0.8 m s–1 wind-speed). Boundary layer thickness was set at 0.12 mm for plants at average relative height based on empirical values obtained for Pleurozium schreberi (Rice 2006) and varied as a function of relative height (Table 1, Appendix 1) based on values reported by Rice et al. (2001) and Rice (2006). Surface roughness, which is caused by size asymmetry as observed in natural bryophyte popu-lations (van der Hoeven and During 1997), was modi-fied by randomly varying the standard deviation of shoot height measurements (Ssd), while keeping the mean shoot height constant (10 cm). Interpretations are based on rep-resentative runs.

Results

The water and carbon dynamics of simulated bryophyte canopies varied with the magnitude of height variation

Figure 1. Shoot-level model of water and carbon dynamics. The model structure showing the interaction of water and carbon dynam-ics is adapted from Rice et al. (2011) with the addition of neighborhood interactions that affect the light availability and water content of the target shoot. Equations for the fluxes are shown in Table 1 with selected ones illustrated in Appendix 1.

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among shoots (Ssd, a measure of surface roughness), with lateral capillary integration and there was an interaction between the two (Fig. 2, 3). At low Ssd (standard deviation = 0.5 cm of shoot height), canopies showed similar aver-age patterns of evaporation and carbon uptake, regardless of their degree of integration. In both cases, average evapo-ration rates showed slight increases until day 9, followed by decreases (Fig. 2a) due to the effects of plant water con-tent on rates of evaporation (Fig. 1, Table 1, Appendix 1). Water content showed a steady decline during the 14 d period (Fig. 2d). During this time, average rates of net photosynthesis showed a steady decline (Fig. 3a), whereas cumulative carbon exchange remained positive for 8 d, but decreased due to respiratory losses caused by desiccation of shoot tissue after that time (Fig. 3d). Again, as with water dynamics, there were no significant differences between canopies with and without lateral sharing of water.

Increases in surface roughness (Ssd = 2 or 3.5) enhanced initial rates of water loss, but this effect was temporary as low canopy water contents reduced evaporation rates (Fig. 2b, c, e, f ) later in the simulated drying event. Canopies without lateral capillary integration initially showed simi-

lar patterns of evaporation, but these canopies showed a dramatic reduction in rates of evaporation after the sec-ond day (Fig. 2b,c) and maintained elevated water con-tent compared with those that shared water. This led to enhanced net photosynthesis and cumulative carbon gain in canopies that did not share water (Fig. 3b, c, e, f ). This effect was caused by the desiccation of taller shoots that ex-hibited low rates of evaporation combined with the higher boundary-layer thicknesses of shorter shoots that retained water throughout the simulation. Those shoots retained positive net carbon gain throughout the simulated 14 d period and contributed to an overall higher carbon gain in non-integrated canopies by the end of the simulation. These effects were magnified in canopies with higher Ssd (Fig. 3c, f ).

In addition to differences in whole canopy function, differences in lateral integration of canopy water also af-fected the distribution of water among shoots within the canopy. At all values of canopy roughness, variance in plant water content was much higher in shoots that did not laterally share water and this caused differences in the distribution of net photosynthesis among shoots within

Table 1. Model parameters and their derivations.

Parameter Meaning Derivation Units

Srel Height of shoot relative to the average of its neighbors Sht – (avg. Sht of neighbors) cm

Sht Shoot height, average height is set at 10 cm variable cm

Ssd Standard deviation of shoot height, a measure of surface roughness

variable cm

WC Water content of shoot variable g H2O g–1 dry mass

WCmax Maximum water content of shoot given g H2O g–1 dry mass

WCrel Relative water content of shoot compared with maxi-mum shoot water content

WC / WCmax no units

WCn Average water content of neighboring shoots average of eight neighboring shoots g H2O g–1 dry mass

E Evaporation rate of water after accounting for Ebase and Ewc

E = Ebase×Ewc g H2O shoot–1 d–1

Ebase Baseline evaporation rate, determined by environmental and boundary layer conditions. Assumes a relationship between boundary layer thickness (dbl, cm) and Shrel: dbl = 6961·(10+Shrel)–4.23

a×(10 + Srel)4.23 g H2O shoot–1 d–1

Ewc Fraction of evaporation modified by shoot water content relative to maximum shoot water content

Ewc = b×WCrel2 + c×WCrel no units

Io Incident light intensity in visible range, 400–700 nm Variable µmol photons m–2 s–1

Is Light on shoot, depends on the relative height of neigh-bors and decays according to Beer’s law. For shoots taller than neighbors, Is equals Io

Is = Io×e(d×Srel) µmol photons m–2 s–1

PSIs Light saturation relationship for net photosynthetic rate at light intensity of shoot (Is)

PSIs = e×(1 – exp(f×·Is+g)) µmol CO2 shoot–1 d–1

PSwc Fraction of net photosynthesis modified by shoot water content

PSwc = h×WC3 + i×WC2 +j×WC no units

netPS Rate of net photosynthesis accounting for Is and the shoot water content

netPS = PSIs× PSwc µmol CO2 shoot–1 d–1

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the canopy (Fig. 4). Even though whole canopy water and carbon dynamics were similar at low Ssd, samples that did not share water showed much higher variation (Fig. 4a, shown for day 7 of the simulation). This difference was amplified at higher values of Ssd. (Fig. 4b, c).

Discussion

In the simulations performed, canopy structural properties and lateral capillary integration interacted to affect water and carbon dynamics during a simulated drying event. In

Table 2. Coefficient values used in simulations.

Coefficient Value Notes

a 2.53 × 10–5 Parameterized for 50% relative humidity, surface and air temperatures of 20°C

b –1.50 Based on the form of the relationships presented in Williams and Flanagan (1996) that are similar for Pleurozium schreberi and Sphagnum species. Values reflect maximum water content and rates of evaporation scaled to a maximum of unity

c 2.44 See (b) above

d –0.788 This represents the apparent light extinction coefficient (Zotz and Kahler 2007) and was fit with empirical data for Sphagnum (unpubl.)

e 40.2 The photosynthetic light response curve was empirically fit using data from Sphagnum fallax (Rice et al. 2008)

f –0.00628 See (e) above

g 39.9 See (e) above

h –0.00461 Photosynthetic water content relationships were empirically derived using data from Sphagnum fallax (Rice et al. 2008). Values reflect maximum water content and net photosynthesis values scaled to a maximum of unity

i 0.102 See (h) above

j –0.472 See (h) above

Figure 2. Water dynamics. Whole canopy rates of evaporation (a, b, c) and resulting water contents (d, e, f ) are shown for a 14 d period simulating a drying event. Canopies with no lateral capillary integration (open diamonds) and with lateral sharing of water within their adjacent neighbors (filled circles) are shown across three values of surface roughness (Ssd): 0.5 cm (a, d), 2.0 cm (b, e) and 3.5 cm (c, f ). See text for interpretation.

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many habitats, poikilohydric bryophytes routinely cycle through different states of plant water status during drying and rehydrating and the simulated differences should be realized in natural conditions.

By itself, increases in surface roughness, here modeled as the standard deviation of shoot heights (Ssd), led to en-hanced rates of evaporation while plant water contents were sufficient to maintain it. In wind-tunnel measure-ments, this relationship has been observed (Proctor 1980, Rice et al. 2001) and similar predictions were made for Sphagnum in a modeling effort by Hayward and Clymo (1983). This formed the basis for the boundary-layer mod-el structure. There are no quantitative studies with similar magnitude of canopy roughness variation to compare (al-though see Rice and Schneider 2004 for a field study with Leucobryum glaucum, where this pattern was not observed for fine-scale differences in surface roughness).

In low roughness canopies, there were no differences in either average water or average carbon exchange between canopies with lateral capillary integration relative to those without. This result did not change even when rates of evaporation were increased by changing the vapor pressure deficit (unpubl.). However, the average values obscure the high variation in water and carbon budgets among shoots within the canopy. Low Ssd canopies that share water later-ally exhibit uniform rates of evaporation and net photo-

synthesis among shoots. In contrast, these properties are highly variable in canopies that lack lateral water sharing and both evaporation and net photosynthesis indirectly relate to shoot height (Fig. 4a). In this model, even small changes in relative shoot height have a significant effect. It is interesting that at low Ssd (0.5 cm) these differences are symmetrical about the mean as evidenced by the similarity of the average values. This is due to the almost linear ef-fect of shoot height on boundary layer properties at points near the mean. At higher Ssd, this relationship becomes non-linear and the average values for canopies that share or do not share water diverge as seen in the asymmetry about the mean in rougher canopies (Fig. 4b, c).

At higher roughness, however, the effects of capillary integration on average rates of evaporation and net pho-tosynthesis becomes apparent, leading to an increase in evaporation rates after less than two days, with the interval shortening at higher roughness values. This is due to the protective effect of emergent shoots that experience high rates of evaporation and desiccate; these shoots then expe-rience lower rates of evaporation as water loss is depressed at lower water contents. Although at a different scale, this effect is analogous to the reduced evaporation observed in bryophytes with leaf hair points, which increase the dif-fusional path length for wet shoots in the canopy interior (Proctor 1980).

Figure 3. Carbon dynamics. Whole canopy rates of net photosynthesis (a, b, c) and resulting cumulative net carbon gain (d, e, f ) are shown for a 14 d period simulating a drying event. Canopies with no lateral capillary integration (open diamonds) and with lateral sharing of water within their adjacent neighbors (filled circles) are shown across three values of surface roughness (Ssd): 0.5 cm (a, d), 2.0 cm (b, e) and 3.5 cm (c, f ). See text for interpretation.

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When there is sharing of capillary water among neigh-bors, differences in canopy water equilibrate once per day as they might at night in some species and emergent shoots remain moist and experience higher rates of water loss the following day. In non-integrated canopies, shoot water contents continue to differ as emergent shoots dry whereas interior shoots maintain stored water and con-tinue photosynthetic activity longer. This is seen in both short-term and cumulative carbon gain where non-inte-grated canopies show elevated rates of carbon uptake rela-tive to the ones that share water laterally (Fig. 3). Indeed at the highest roughness values, the non-integrated canopy continues with positive carbon gain through the entire simulated 14 d period, whereas the integrated canopy moves into a net loss of carbon gain after 8 d.

The results of the modeling presented here indicate a physiological cost associated with capillary integration, at least when water becomes limiting to photosynthesis. In-tegration creates a more homogenous distribution of wa-ter within the bryophyte colony and leads to more overall loss of this resource. This result apparently contrasts with that found in vascular plants where physiological integra-tion normally benefits colony growth through carbon, wa-ter or nutrient sharing among shoots (Stuefer et al. 1994, Wijesinghe and Handel 1994, Hutchings and Wijesin-ghe 1997). In such cases, integration allows effective wa-ter, nutrient or light foraging and local optimization of physiological activity when resources are heterogeneously distributed. The situation within the bryophyte canopies investigated here may be more alike to cases where there is cost as well as benefit that can result from physiological integration. For example, vascular plant canopies may not achieve a benefit due to resource sharing if there are suf-ficient costs associated with some resource patches, even if

benefits are achieved in contrasting ones as has been dem-onstrated in the giant bamboo, Phyllostachys pubescens (Li et al. 2000). Costs may also associate with spread of patho-gens among integrated colonies, thereby reducing benefits of integration (D’Hertefeldt and van der Putten 1998). However, bryophytes may differ from these cases in that physiological integration leads to increased total colony resource loss through enhanced average evaporation: in vascular plants, physiological integration only causes a re-distribution of resources within the colony, not a loss. Due to their unique water economy that includes desiccation tolerance, capillary sharing of water within canopies and their inability to control short-term water loss, bryophyte colonies may present a novel growth form that differs in the costs and benefits of physiological integration.

Although this modeling approach was based a matrix of vertical shoots that simulate acrocarpous or Sphagnum species, the results likely apply to pleurocarpous species that show spatial variation in shoot height and in lateral water transfer. In these cases, capillary water sharing may occur within individual stems as well as between adjacent stems, but this should not affect the expectations. Indeed, many species exhibit gaps in the capillary systems like dis-continuous paraphyllia (Dilks and Proctor 1979) or even within their internal conducting systems (Proctor 1982, Glime 2007) that may impede water movement. Further-more, the favorable water and carbon balance suggested by lateral capillary isolation may also be achieved by reduc-tions in vertical water movement. When upper portions of the canopy dry, whole canopy water loss would be re-duced, yet interior portions could remain photosyntheti-cally active. This could further improve carbon balance as shoots could reduce the time they spend with excess respiratory losses when at low water contents. In other

Figure 4. Variation in net photosynthesis. Each symbol represents the net photosynthetic rate of an individual shoot in the canopy (n = 400) at day seven during the simulation (Fig. 2, 3). Mean shoot height is 10 cm with the standard deviation (Ssd) increasing from 0.5 (a), 2.0 (b) and 3.5 cm (c). The arrow shows the points associated with neighborhood integration, which are shown as a horizontal group of points. Canopies without later capillary integration have higher among shoot variation in rates of net photosynthesis.

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words, branches would spend less time in the transitional state between wet and desiccated when respiratory carbon losses are high.

Unless the bryophyte canopies are either smooth or permanently saturated with water, the modeling sug-gests that there will be a benefit to carbon gain achieved by reducing lateral water integration, an expectation that should apply either within or among shoots. This result would suggest that endohydric species, which can con-duct up to 60% of water internally (Proctor 1982) and have limited ability to transfer water laterally may have a physiological advantage. Indeed, canopies of species in the Polytrichaceae are particularly successful in open habitats where they can experience high water vapor deficits. Of course there are many successful ectohydric species; under what conditions might that approach be favored? Ectohy-dry is associated with greater development of external wa-ter stores in leaf and branch cavities and many species have specialized structures like paraphyllia that further enhance external capillary volume. These features can increase the water holding capacity of shoots. Initial water content does not need to be adjusted much to achieve comparable carbon gain during the drying period simulated: with a Ssd of 2 cm, a 15% increase in initial water content makes up for the difference in net carbon gain over the two week period. The tradeoff between capillary independence and its efficient use of water as observed in endohydric spe-cies may be offset in ectohydric species by their ability to store water more abundantly and then share the resource among shoots.

Sharing of water laterally within bryophyte canopies also has implications for bryophyte community dynamics, a process that has been observed and investigated most thoroughly in Sphagnum. In open peatland systems, hol-low species normally have larger, rougher canopies that have elevated rates of evaporation and reduced rates of capillary transport compared with hummock species. Consequently, during periodic droughts, hollow species desiccate more quickly. However, hollow species are ob-served inhabiting hummocks where they are evidently supplied with water via later transport from hummock species that have high water holding capacities (Andrus et al. 1983, Rydin 1985, Robroek et al. 2007). In experimen-tal manipulations, Robroek et al. (2007) found that the persistence of hollow species on hummock was enhanced by lateral water transfer, but only following rainfall, indi-cating that differences in the water potentials achieved in capillary spaces in hummock and hollow species (Hay-ward and Clymo 1982) may be an important determinant of the magnitude of lateral water transfer.

In summary, the degree of capillary integration may be an important functional trait that affects water and car-bon dynamics of bryophyte canopies in ways that differ from those expressed in vascular plants. Progress could be made by applying more dynamic optimization modeling that would consider the interaction of shoot and canopy

properties during canopy development as suggested by Anten and During (2011). Like other canopy-level traits in bryophytes, there are likely many ways to achieve simi-lar functionality as water conductance is a complex func-tion of characteristics that span cell wall structure through shoot morphology and colony structure. Although lateral transfer was explored in this simulation study, patterns of variation in vertical transfer of water may be easier to treat experimentally and lead to an understanding of how limits to water conduction may be as important to a bryophyte as achieving rapid water transport.

Acknowledgements – This paper was developed as part of a sym-posium to honor Heinjo During – I have always admired his ability to combine the conceptual with the empirical and I ap-preciate the opportunity to undertake this study in his honor. I also thank M. Werger and N. Anten whose comments helped improve this manuscript.

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Appendix 1

Selected relationships. The mathematical relationships for the models shown are found in Table 1.

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This pdf has been updated.

The reference:

Pascale, M.P., Lee, W. G., During, H. J. et al. 2012. Species traits and their non-additive interactions control the water economy of bryophyte cushions. – J. Ecol. 100: 222–231.

has been changed to:

Michel, P., Lee, W. G., During, H. J. and Cornelissen, J. H. C. 2012. Species traits and their non-additive interactions control the water economy of bryophyte cushions. – J. Ecol. 100: 222–231.

/Ed.