Nitrogen isotope discrimination in white spruce fed with low concentrations of ammonium and nitrate
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- Pritchard, E.S. & Guy, R.D. Trees (2005) 19: 89. doi:10.1007/s00468-004-0367-2
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Differences in δ15N among ten white spruce [Picea glauca (Moench) Voss] families were examined in hydroponic experiments testing (1) three N sources [100 μM N as (i) NH4+, (ii) NO3− or (iii) NH4NO3] and (2) two supply regimes [200 μM NH4+ (i) maintained steadily or (ii) recurrently drawn-down]. In the N-source experiment, the NH4+ treatment resulted in superior growth and lower C/N ratios. Whole plant δ15N was higher on NH4+ and NH4NO3, reflecting higher NH4+ removal rates from the media. Families expressed differences in biomass, C/N, δ15N and δ13C. Family δ15N and δ13C were positively correlated in the NH4NO3 treatment and the steady-state regime. Supply regime did not affect total biomass, but higher root/shoot ratios implied N was more limiting under the draw-down regime. Family rank changed with supply regime, but not with N source. Analysis of media isotope enrichment during substrate depletion revealed relationships between net discrimination and external N concentration. Discrimination against 15NH4+ was about twice that of 15NO3−. A simple model relating isotope discrimination to relative rates of ion efflux and influx predicted efflux/influx ratios consistent with published values for white spruce. We propose that genetic differences in discrimination are caused by different demands on assimilation and in uptake capacity which interact, influencing the balance between N influx and efflux.
KeywordsPicea glaucaStable isotopesFractionationNitrogen assimilationIon flux
Consistent relationships between the nitrogen isotope composition (δ15N value) of plants and N nutrition have recently emerged in the literature (Comstock 2001; Evans 2001; Robinson 2001). Similar to C isotope discrimination in photosynthesis, N isotope discrimination will only be expressed if there is opportunity for isotopically enriched N to return to the bulk medium. Fractionation of 14N and 15N could occur at uptake from the medium into root cells, or during subsequent enzymatic assimilation into other N forms. There is also opportunity for tissue to become enriched or depleted in 15N if biochemical components of varying isotopic composition are lost through translocation or exudation.
Uptake of inorganic nitrogen occurs by way of multiple transport systems. Uptake of NH4+ at low (μM) concentrations is primarily via a saturable high affinity transport system (HATS), whereas at higher (mM) concentrations most uptake occurs via an unsaturable low affinity transport system (LATS). Separate HATS and LATS are responsible for NO3− uptake over similar concentration ranges (King et al. 1993). If fractionation occurred during uptake, it might be expected to change with concentration during the transition from the LATS to the HATS as concentrations decrease (Hoch et al. 1992). Many studies have demonstrated this relationship (Högberg 1997), but separation between uptake and assimilation is necessary to ensure apparent discrimination is not an artifact of enzymatic discrimination associated with varying external concentrations (Högberg 1997). This separation was achieved with legume nodules which showed no fractionation during NH4+ transport across membranes from a bacteroid to plant cytoplasm (Shearer and Kohl 1989).
The next opportunity for 15N/14N fractionation occurs during nitrate assimilation by nitrate reductase (NR) or ammonium assimilation by glutamine synthetase (GS) (Evans 2001). In vivo estimates for discrimination by the two enzymes vary by over 9‰, depending on enzyme activity and experimental design (Robinson 2001). Few studies have directly measured discrimination by either NR or GS, but these enzymes appear to have similar discrimination factors. Using spinach extracts, Ledgard et al. (1985) found NR discrimination approaching 15‰. Yoneyama et al. (1993) reported in vitro GS discrimination values of 16.5±1.5‰.
If the assimilatory enzymes had free access to an infinite N source at a constant 15N/14N ratio, the resulting source-to-plant difference would approximate discrimination by the enzyme times negative 1 (i.e., −15 to −17‰). Most studies report much smaller differences in δ15N. In experiments with varying substrate concentration, increasing N concentration resulted in more negative whole plant δ15N values (Kolb and Evans 2003; Hoch et al. 1992; Högberg et al. 1999; Yoneyama et al. 1991, 2001). Conversely, fractionation decreased with increased (NR) enzyme activity. Mariotti et al. (1982) proposed that fractionation depends on the substrate to enzyme ratio: when enzyme levels are low relative to N supply, discrimination is high; in contrast, higher enzyme levels or lower N supply reduce discrimination. This trend also occurred in diatoms: when N demand was high following N starvation, less N effluxed from cells, reducing fractionation (Waser et al. 1999).
The dependence of discrimination by the plant (Dplant) on the balance between N supply and N demand can be understood in terms of the degree of isotopic coupling, or equilibrium, occurring between the site of N assimilation and the bulk medium. Net uptake of NO3− and NH4+ includes a substantial amount of efflux (Handley and Raven 1992 and citations therein). Isotopic equilibrium will only be achieved if efflux equals influx, a condition approached when external concentrations are high or when assimilation rates are low. Conversely, if external concentration is low or demand is high, most ions taken up will be immediately consumed and the efflux/influx ratio will approach zero. Isotope discrimination should vary in direct proportion to the change in efflux/influx ratio (Handley and Raven 1992). This concept is broadly analogous to the model of Farquhar et al. (1982) for CO2 uptake during photosynthesis where discrimination and plant water-use efficiency (WUE) are determined by the balance between supply (controlled by stomatal conductance) and demand (photosynthetic capacity).
Following assimilation, differences in δ15N values of plant constituents and organs can result from further enzymatic fractionation of organic N (Yoneyama and Kaneko 1989). This will not affect whole plant δ15N unless specific constituents with marked enrichment or depletion of 15N suffer significant losses at different rates (Bergersen et al. 1988; Evans et al. 1996; Comstock 2001). Genetic variation in components of N metabolism might also affect plant δ15N (Handley et al. 1997; Robinson et al. 2000). Hypothetically, genotypes with a high N demand, high N assimilation capacity or a low uptake capacity will all have a low substrate to enzyme ratio and therefore should discriminate less against 15N. These same variables influence plant nitrogen use efficiency (NUE), which varies between and within species (Patterson et al. 1997; Min et al. 1999). NUE also varies with fertilization in a genotype-specific manner (Li et al. 1991; Swiader et al. 1991; Eghball and Maranville 1993; Tirol-Padre et al. 1996; Livingston et al. 1999).
In practise three approaches can be used to measure N isotope discrimination: (1) analysis of product where the reaction or process under study has free access to an unlimited source, (2) analysis of the progressive isotope enrichment of product as it accumulates in a closed system, and (3) analysis of the progressive enrichment of substrate as it is consumed in a closed system. The first, most common approach requires that plants be grown for extended periods without substantial depletion of the nutrient medium or major changes in demand. These requirements can be challenging at the low concentrations typical of most soil environments. The second approach has been used extensively in phytoplankton (e.g., Needoba et al. 2003) but is not amenable to higher plants because of the requirement for repeated subsampling. The third approach, substrate depletion analysis, has only rarely been applied to the study of N isotope discrimination by plants (Kolb and Evans 2003). This method, which has the advantage of providing short-term data over a range of concentrations, is more often used to measure oxygen isotope discrimination in respiration (Guy et al. 1989; Henry et al. 1999).
Most studies on 15N discrimination have used fast-growing herbaceous plants. There are, however, some advantages to using gymnosperms for these types of investigations. White spruce (Picea glauca) has well characterized N acquisition physiology (Kronzucker et al. 1995a, b, 1997) and has available genotypes which have already been tested for growth, NUE, WUE, and carbon isotope composition (δ13C) under water and nitrogen stress (Sun et al. 1996; Livingston et al. 1999). Assimilation of both NH4+ and NO3− occurs strictly in the roots in this species, precluding the complications that can arise from only partial assimilation in roots and the consequent 15N enrichment of shoots (Evans et al. 1996). Like most gymnosperms, white spruce prefers NH4+-N. This is manifested primarily in greater biomass production on NH4+ nutrition, but also in higher capacities for accumulation and assimilation and higher rates of influx and efflux, indicating a more rapid N exchange between external and internal pools (Kronzucker et al. 1995a, b).
In this report we use product analysis to investigate family-level variation in δ15N as an indicator of genetic variation in the balance between N uptake and assimilation in white spruce, and to quantify relationships between growth, δ13C and δ15N. Because genotypes with inherently rapid growth should have high demand for both N and C, we predicted that δ15N might correlate positively with growth rate. On the other hand, in situations where N acquisition is limited by the capacity for ion uptake, rather than assimilation, a negative correlation should exist. A second major objective was to explore the use of the substrate depletion method to measure N isotope discrimination in the short-term. This method was used to assess the effect of N concentration and source on discrimination in a higher plant with a known NH4+ preference, i.e., white spruce. Our working hypothesis was that changes in discrimination would be consistent with published effects of N nutrition on efflux/influx ratio in this species.
Materials and methods
Plant material and germination
Regional provenances for full-sib family crosses, and parent tree British Columbia Ministry of Forests seedlot numbers. PG Prince George, EK East Kootenay, ENA Eastern North America. Family numbers correspond with Sun et al. (1996), except family 0, which replaces their cross 4 in this study
Once germinated, seedlings were watered with 100 μM N + 1/10 modified Johnson’s solution (Johnson et al. 1957) for 6 weeks followed by 1.5 mM N + 1/10 modified Johnson’s solution for 2 weeks before being transplanted into hydroponics. Seedlings were initially given 100 μM N to maintain treatment conditions in soil, but this concentration was too low in hydroponic medium and was increased for the last 2 weeks. Composition of the nutrient solution, excluding N, was: 200 μM KH2PO4, 200 μM K2S04, 100 μM MgSO4, 50 μM CaSO4, and micronutrients: 5 μM Cl, 2.5 μM B, 0.2 μM Mn, 0.2 μM Zn, 0.05 μM Cu, and 2 μM Fe. Seedlings were watered to the drip point every second day.
Plants in this experiment were grown hydroponically on 100 μM N as either (i) (NH4)2SO4, (ii) Ca(NO3)2 or (iii) NH4NO3. Eight seedlings from each family were transferred from Cone-tainers to plastic tubs (16 l, 46 cm ×33 cm ×11.5 cm) containing 14 l of 100 μM N + 1/10 modified Johnson’s solution. There were two tubs per treatment. Roots were first washed in tap water and then seedlings were suspended from black Plexiglas lids using foam rubber bungs for 60 days. Ambient air from within the chamber was pumped into the tubs to increase circulation and keep dissolved oxygen above 90% air saturation. Powdered CaCO3 was added as necessary to maintain pH near neutral (range: 5–7.8). Growth chamber conditions were identical to those for germination.
Nutrient concentrations were maintained by automatic pumps, fine tuned by daily manual adjustments. Six peristaltic pumps (FPU100 Series Omegaflex, Omega Engineering, Exton, Pennsylvania) interfaced to a computer and controlled by Labtech software continuously pumped concentrated modified Johnson’s solution into the tubs. Five times a week, media NH4+ and NO3− concentrations were assayed using the phenolhypochlorite (Solorzano 1969) and perchloric acid (Cawse 1967) methods, respectively. Ammonium levels were more difficult to maintain at the target concentration because uptake rate was higher and increased more rapidly than NO3− uptake. Addition of N changed the ratio of all other nutrients to N, but N always remained limiting. Nutrient solutions were replaced once a week when tubs were cleaned. The boxes were also rotated randomly within the growth chamber to prevent positional effects.
N supply regime experiment
Methods for supplying N were adapted to highlight genotypic differentiation in uptake affinity. Treatments were (i) a steady-state supply of 200 μM NH4+ and (ii) a recurrently drawn-down supply where NH4+ was depleted by the plants until there was a negligible amount left in the tub. Pre-treatment and hydroponic conditions were identical to the N-source experiment.
Substrate depletion analysis
To measure the concentration dependence of isotope discrimination in the short-term, 15N enrichment during progressive depletion of hydroponic media was assessed in the final two draw-down cycles of the N supply regime experiment. These data were supplemented by additional experiments using nursery grown 4-month-old seedlings placed into hydroponics under similar conditions but at twice the initial NH4+ concentration (400 μM) or into media containing NO3− (300 μM) instead of NH4+. NO3− treatment media were sampled at intervals as concentrations fell to approximately 30 μM over 12 h, and NH4+ treatment media were sampled down to 20 μM over 7 h. The concentration and δ15N of unassimilated substrate remaining in the samples was determined by the membrane diffusion method (Holmes et al. 1998) which relies on the volatilization of NH3 out of solution and subsequent deposition on Teflon-encapsulated acidic glass fiber filters. The encapsulated filters were combusted on a Carlo Erba model 1106 CHN analyzer interfaced to a Fisons Na 1500 ratio mass spectrometer (University of British Columbia, Department of Earth and Ocean Sciences). NO3− samples were reduced using 0.2 g of Devarda’s alloy in diffusion bottles (Brooks et al. 1989).
Measures were taken to minimize and correct for organic or atmospheric N contamination. Samples containing NH4+ media were acidified to pH 2.0 to prevent NH4+ dissociation (Shearer and Kohl 1989). Samples were stored at 4°C prior to diffusion (Mulavaney and Khan 1999). A constant surface area to volume ratio inside diffusion flasks ensured standardized conditions for conversion of NH4+ to NH3 and gas transfer to the disc (Brooks et al. 1989). All samples were of approximately equal liquid volume (40 ml) and N quantity (∼8 μmol). Depending on concentration, samples were brought to this volume either by dilution or by rotary evaporation. The diffusion period was reduced to 6 days to allow complete recovery of inorganic N and minimize potential contamination from organic N.
Quantification of N contamination from water and Devarda’s alloy in the measurement of substrate δ15N. Each value is the mean of two replicate tests
Apparent [NH4+] (μM)
(1) 1 l ddH2O
(2) 1 l NH4+-free ddH2O
(3) 40 ml ddH2O + 2.0 g Devarda’s alloya
Solution (3) corrected for (1)
Data were analyzed by one-way analysis of variance (ANOVA) [(SAS Institute, Cary, NC)] where each variable (biomass, R/S, C/N, δ13C and δ15N) was tested in a split-plot design. Each variable was tested for normality and homogeneity of variance prior to ANOVA. Variables that did not meet the criteria were log transformed prior to analysis to meet assumptions; raw data are depicted in figures. All data were combined within each experiment to determine environmental correlations. To calculate family Pearson correlation coefficients, treatments were separated and families were blocked within treatments and replicates. Trend lines showing correlations between two independent variables were calculated by geometric mean regression (Ricker 1984). Significance values were set at α=0.05.
N-source effects on measured traits
N supply regime effects on measured traits
A steady versus a recurrently drawn-down supply of NH4+ did not affect total biomass. Mean C/N ratio for the draw-down treatment (31.6) was significantly higher (P<0.02) than for the steady-state treatment (21.7) and was negatively correlated with biomass. Within each treatment, there were significant differences in biomass and C/N ratio among families (P<0.002 and 0.0002, respectively). Family ranks were similar to those in the N-source experiment. R/S ratio was higher in the draw-down treatment (P<0.001).
The pattern of NH4+ supply did not significantly affect mean seedling Δδ15N values, but the variances of the two treatments differed (2-tailed α=0.05, F=4.03). Genotypes displayed less variation in the draw-down treatment, and in most cases family Δδ15N values were higher than in the steady-state treatment. Family Δδ15N values were significantly different (P<0.0002) but correlated with biomass only in the steady-state treatment (r=0.449, P=0.047; data not shown). Treatments resulted in substantial family rank changes for both traits in families 3, 5, 9 and 10, but there was no significant family by treatment interaction overall. There was a positive environmental correlation (r=0.485, P=0.030; not shown) across treatments between C/N ratio and Δδ15N, where the steady-state treatment resulted in seedlings with higher N content and lower Δδ15N values.
Treatment significantly affected δ13C (P<0.05), with the mean for the draw-down treatment being marginally higher than for the steady-state treatment (−28.78‰ and 29.40‰, respectively). Family δ13C values were also significantly different (P<0.0002) with the treatment effect removed, and there was a family by treatment interaction (P<0.05). Family δ13C ranks among treatments differed, and also differed from ranks in the N-source experiment. As in the N-source experiment, δ13C did not correlate with biomass or C/N ratio within either treatment (not shown).
Substrate depletion analysis
Relating isotope discrimination to efflux/influx ratio
In a series of reactions or transport processes, isotope discrimination will be associated with the rate-limiting irreversible step (O’Leary 1993). If diffusion to the surface of root cells is not limiting in a well-mixed hydroponic medium, then the acquisition of N may be limited either by uptake at the plasma membrane or by enzymatic assimilation. When discrimination factors for N-assimilating enzymes are fully expressed, plant discrimination (Dplant) is expected to equal discrimination by the isolated enzyme (Denzyme). Given that Denzyme is 15‰ for NR (Ledgard et al. 1985) and 16.5‰ for GS (Yoneyama et al. 1993), this condition should yield Δδ15N values of approximately −15‰ for growth on NO3− and −16.5‰ for growth on NH4+. Both treatments, however, resulted in Δδ15N values ∼13‰ higher than expected based on published estimates of Denzyme. Furthermore, the apparent discrimination against 15NO3− exceeded that against 15NH4+ by 2.2‰. As discussed below, these discrepancies come about because of progressive isotopic enrichment of the hydroponic media as N is consumed, in both steady-state and draw-down conditions, and because enzymatic discrimination was likely only partially expressed at the substrate concentrations used.
Data from the substrate depletion experiments are consistent with this expression. In these experiments, the media became enriched in 15N as N was consumed. Enrichment was much more pronounced when N concentrations were high.
In principle, media enrichment during N consumption could originate from three sources: bacterial fractionation, organic N efflux and inorganic N efflux. It is unlikely the first two potential sources contaminated media δ15N. Significant nitrification by bacteria in the media did not occur because NH4+ and NO3− concentrations were monitored almost daily and were within the expected range of uptake for the biomass and the species. The NH4+ concentration of the NO3− media and the NO3− concentration of the NH4+ media were assayed periodically and there was never a measurable accumulation of converted N. Organic N is a greater concern as there is potential for breakdown during sample preparation. Recovery of alkali labile organic N in distilled water using methods similar to ours showed that only 4.7% of added organic N was liberated as NH3 (Khan et al. 1997; Mulavaney and Khan 1999). This is not likely to be a problem unless effluxed organic N accumulates while inorganic N is depleted, as may occur towards the end of a draw-down experiment. However, if the rate of organic N efflux were no more than 5% the rate of inorganic N influx (Merbach et al. 1999), we calculate that the maximum error in D at low substrate concentrations (25–50 μM) would be less than ± 0.5‰ even if δ15N of the organic N were offset by as much 20‰.
Enrichment was more pronounced for NH4+ than for NO3− (Fig. 8). The highest Dplant observed was 20.2‰ over a concentration range of 219–336 μM NH4+, which, within measurement error, is close to the range of Denzyme reported for GS (Handley and Raven 1992). In contrast, the NO3− levels used did not permit full expression of discrimination by NR, where the highest Dplant obtained was 6.3‰ over a concentration range of 205–235 μM NO3−.
At 100 μM N, linear regressions through mid-points for data presented in Fig. 8 predict values for Dplant of 2.9‰ and 5.9‰ for NO3− and NH4+, respectively, corresponding to efflux/influx ratios of 0.193 and 0.356 (derived from Eq. 4). Kronzucker et al. (1995a, b), using 13N radioisotope as a tracer for compartmental analysis in white spruce, reported efflux/influx ratios of 0.056 and 0.281 at 100 μM NO3− and NH4+, respectively. Although these estimates are qualitatively similar, they differ in magnitude, especially for NO3−. There are several possible explanations for the discrepancy. First, the two approaches differ fundamentally in that compartmental analysis assumes steady-state conditions, unlike substrate depletion analysis. Second, we have assumed no discrimination in membrane transport. Third, discrimination factors for NR and GS have been measured only rarely and are poorly defined. Finally, differences in growing conditions and the genotypes used are likely to have affected N demand between the two studies.
Ammonium preference effects on Δδ15N
In white spruce, the greater proportional efflux of NH4+ relative to NO3− is more than compensated for by a much higher rate of gross uptake (Kronzucker et al. 1997). In our experiments, this “preference” for NH4+ was evident in its more rapid utilization and the negative correlation between biomass and C/N ratio across treatments (Fig. 1). Because net discrimination in NH4+ is about twice that for NO3−, at comparable concentrations, it might be expected that the NH4+ grown plants would have lower Δδ15N than NO3− grown plants. This was not the case (Fig. 2). The NH4NO3 treatment had even higher Δδ15N values. It must be emphasized, however, that it is inappropriate to draw inferences regarding treatment differences from such experiments unless the δ15N of the source is known and constant. We did not attempt to meet this condition. The Δδ15N values we report are relative to the source before it was partially consumed. We endeavored to maintain the hydroponic media at 100 μM N through incremental substrate additions. Spot checks revealed that this caused steady enrichment with effluxed 15N until media were completely replaced at the end of each week. Ammonium was consumed more rapidly than NO3− and therefore required a higher rate of addition resulting in a more rapid enrichment. The initial distribution of isotopes between the two N moieties was not known in the NH4NO3 treatment. Preferential consumption of NH4+ drove its relative concentration down and may have resulted in a greater change in the δ15N of this ion. Furthermore, although the total N concentration in this treatment was the same as in the other two treatments, the initial concentration of each ionic form was only 50 μM, which should reduce discrimination. These problems, which are common in the literature, do not impair comparisons between families within treatments.
Genetic variation in N isotope discrimination
Our study extends observations of genetic variation in δ15N in grasses, namely barley (Handley et al. 1997; Kolb and Evans 2003; Robinson et al. 2000) and rice (Yoneyama et al. 2001), to a gymnosperm tree species. The family by treatment interactions in both the N-source experiment (Fig. 2) and the N supply regime experiment suggest that genetic determination of discrimination and, presumably, efflux/influx ratio, varies with environment. This is not surprising since several components of nitrogen use are under genetic control (Li et al. 1991; Swiader et al. 1991; Tirol-Padre et al. 1996). Capacities for uptake and assimilation are two such components (Imsande and Touraine 1994), and efflux/influx ratios should reflect the balance between them (Evans 2001).
If assimilation (and ultimately, growth) tends to be limited by uptake, as it would be under NO3− nutrition, then efflux/influx ratios will be low and genetic variation in Δδ15N should reflect variation in uptake capacity. Family correlations between biomass and Δδ15N will then be negative. If assimilation is relatively non-limited by uptake, as it would be under NH4+ nutrition, then efflux/influx ratios should be higher and differences in Δδ15N will be determined more by variation in assimilation capacity and/or growth-driven N demand. In this case, family correlations between biomass and Δδ15N are expected to be positive. There was a positive correlation in the steady-state NH4+ treatments (both experiments) and a negative correlation in the NO3− treatment (N-source experiment), supporting this interpretation. In contrast, there was no correlation between biomass and Δδ15N in the recurrent draw-down treatment of the N supply regime experiment. No correlation is expected, because this treatment would have resulted in cycling between states of NH4+ uptake limitation and non-limitation.
Relationship to C isotope discrimination
Similar to published work on barley (Handley et al. 1997; Robinson et al. 2000), we found a positive family-level correlation between Δδ15N and δ13C in the NH4NO3 treatment of the N-source experiment (Fig. 5), and a comparable pattern in the supply regime experiment (Fig. 6). Such positive correlations might result from genotypic differences in photosynthetic capacity and attendant foliar N requirements, or from differences in N and C demand for direct incorporation into new organs. Certainly, improved N nutrition does increase the growth and photosynthetic capacity of white spruce, resulting in higher δ13C and enhanced WUE (Livingston et al. 1999). If genetic variation in 15N discrimination in this species is primarily due to variation in N-demand in NH4+ nutrition, and uptake capacity in NO3− nutrition, correlations between Δδ15N and δ13C would also be expected in the other treatments, but none were found.
Overall, our data are consistent with an interpretation of plant δ15N values whereby discrimination parallels efflux/influx, which varies with environment and genotype, as well as their interaction. The results provide strong evidence for a mechanistic basis for variation in plant δ15N based on a priori knowledge of the functional relationships between uptake, assimilation and concentration in white spruce. Net isotope discrimination in NH4+ was at least twice that in NO3− because of the increase in efflux relative to influx associated with the well-characterized NH4+ preference of this species. Genotypic determination of discrimination varied with the form of N supplied and supply regime. We propose that under NH4+ nutrition at sufficient levels, differences in discrimination are principally determined by demands on assimilation, whereas differences in uptake capacity are likely to be more important under NO3− nutrition or at low NH4+ levels. Genotypic and environmental variation in efflux/influx may be reflected by source-to-plant differences in δ15N, or assessed in the short term (over minutes or hours) using substrate depletion analysis. δ13C and δ15N may both be linked to growth when variation in water use efficiency is determined by inherent differences in photosynthetic capacity or production potential.
This research was supported by a Natural Sciences and Engineering Research Council (Canada) grant to R.D.G.