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Keywords:

  • ammonium;
  • nitrate;
  • phytoplankton;
  • dark;
  • assimilation;
  • growth;
  • model

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Model Configuration
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • • 
    Alternative strategies for the dark assimilation of ammonium and nitrate into microalgae are explored using a mechanistic model of algal physiology.
  • • 
    The standard diatom strategy, continuation of N assimilation at high rates in darkness as long as reserve C remains, is the most advantageous. The flagellate strategy, incorporating ammonium but not nitrate at a reasonable rate in darkness, is best suited to organisms with high metabolic costs, inhabiting waters with relatively high concentrations of ammonium. The strategy of vertically migrating diatoms – accumulation of nitrate in internal pools for assimilation after return to the photic zone – is best suited to slow-growing cells in low-ammonium environments.
  • • 
    Differences between the strategies become less significant with increasing N-source limitation (the situation more typically encountered by flagellates and migratory species) because transport rather than post-transport assimilatory processes become most limiting.
  • • 
    It is suggested that optimization of dark N-assimilation is not a critical selective feature; organisms with contrasting abilities in this regard usually inhabit different water bodies and have other more fundamental phenotypic differences (e.g. motility or silicon requirements).

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Model Configuration
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

In a previous paper (Clark et al., 2002) we discussed the considerable variability expressed in microalgae for the capacity for dark N-assimilation. The ability to use ammonium is relatively unaffected by darkness provided that C is available to enable its incorporation. The ability to assimilate nitrate in darkness is, however, extremely variable, ranging from good to poor. One may expect that organisms capable of migration from low-nutrient surface waters down to nitrate-rich waters at the ergocline (energy discontinuity, typically a thermocline or pycnocline, often associated with a nutricline) would be well adapted to use nitrate in darkness. However, they do not appear to be capable of using nitrate at a high rate under these conditions and they appear no better adapted than nonmotile diatoms that typically inhabit mixed waters (Clark et al., 2002). So, is the ability to assimilate N in darkness an important adaptive feature or secondary to other physiological and behavioural traits? These different capabilities are expressed in organisms that are very different from each other (nonmotile rapidly growing diatoms to slow-growing vertically migrating dinoflagellates). As a consequence, it is difficult to determine the ecological significance of differences in single aspects of physiology.

One approach to this problem is to consider the behaviour of dynamic mathematical models that contain only the single difference in physiological behaviour. In this instance we have used a mechanistic model that describes algal growth and compare the performance of this model when endowed with contrasting abilities to use ammonium and nitrate in darkness.

We have previously developed a range of mechanistic models as aids to studies of the ecophysiology of phytoplankton (Flynn, 2001). These models contain components describing the interactions between ammonium, nitrate and photosynthesis. Within these models (Flynn et al., 1997), sigmoidal equations are employed for the differential control of nitrate reduction to ammonium, and of amino acid synthesis with incorporation into cell N, as functions of the cellular N : C ratio. Such controls may be used to regulate other processes; Flynn et al. (2001) used one to regulate the synthesis of chlorophyll in darkness. Here, with reference to the behaviour of phytoplankton with contrasting metabolic capabilities and the analysis of the output of mechanistic models, we consider the costs and benefits of different approaches for uncoupling N and C acquisition.

Model Configuration

  1. Top of page
  2. Summary
  3. Introduction
  4. Model Configuration
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Models have been developed from those of Flynn et al. (1997), using an updated form of the original ANIM (ammonium–nitrate interaction model) construction. Full details are available from the communicating author and only equations germane to this paper are given here. Only a brief overview of ANIM is given here. The model contains separate transporters for ammonium and nitrate, with the maximum rates controlled as functions of the cellular N : C ratio and the internal glutamine concentration. The nutrients enter internal pools of inorganic N. Nitrate is reduced (as functions of the operation of nitrate/nitrite reductase and the availability of reductant) and then enters the internal ammonium pool. For simplicity here, nitrate and nitrite reduction is handled as a single process supported by nitrate/nitrite reductase (NNiR). The ammonium pool is drained to support the synthesis of glutamine and then all other nitrogenous components of the cell as functions of the concentration of substrates and of the availability of C from photosynthesis or from reserves. The size of the glutamine pool (representing the first organic product of N assimilation) represses the synthesis of NNiR and the transport of ammonium and nitrate into the cell (Flynn et al., 1997).

In ANIM, the ability to perform assimilatory processes in darkness is regulated by the cellular N : C mass ratio (NC) according to the sigmoidal function described in Eqn (1) (of a form described by Flynn et al., 1997).

  • image(Eqn 1)

The shape of this function is altered by varying constant Cres2 over the range 0.1 and 0.0001. Cres1 is the value of the N : C ratio at which there is no surplus C available to support the process in darkness. An offset scalar, r, regulates the maximum dark : light ratio of the process rate; this scalar is only used here for modifying nitrate reduction, although it was employed in Flynn et al. (2001) to also modulate chlorophyll synthesis in darkness. The default forms of this function for amino acid synthesis (quotient CAAs) and for nitrate reduction to ammonium (quotient Nreds) are given as Type II in Fig. 1; in this instance, nitrate reduction operates at 60% of the rate attainable for amino acid synthesis (i.e. Nred (= r) = 0.6). The net impact for the assimilation of nitrate N into cell N is thus the product of CAAs and Nreds. This configuration is that used in all previously used forms of the ANIM family from Flynn et al. (1997) to Flynn (2001).

image

Figure 1. Control of assimilation rates in darkness. The rate of nitrate reduction to ammonium (n) and rate of ammonium assimilation (a) for the four model Types (I, II, III and IV) tested. The control quotient (see Eqn 1) is the ratio of the rate processes in dark : light.

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In this work, the implications of having different capabilities for performing amino acid synthesis and nitrate/nitrite reduction in darkness are considered. In addition, as the model contains cellular ammonium and nitrate pools, the alternative of simply accumulating inorganic N for full incorporation during the following light phase is also considered. It should be noted that if that particular behavioural pattern (internal ‘storage’ of inorganic N) is not of interest then there is no need to employ the form of ANIM that contains the added complexity of internal inorganic-N pools and NNiR. Rather, one can use the simpler form, as described by Flynn & Fasham (1997) and developed by Flynn (2001); these still contain the sigmoidal functions for control of dark N-assimilation (Flynn et al., 2001).

The models run here were configured to compare the ability to assimilate ammonium and nitrate in darkness, and to consider the implications of accumulating (but not incorporating) a large pool of nitrate. These differences had no effect on growth rates, cellular mass ratios of N : C, or chlorophyll (Chl) : C, when the models were operated under continuous illumination at different dissolved inorganic N (DIN) concentrations. Four ‘types’ (configurations) of microalgae were simulated: Type I, capable of using both N-sources in darkness constrained only by the availability of C until very close to attaining their maximum N : C; Type II, capable of using ammonium at a high rate in darkness, but nitrate at only 60% of that rate (similar to the original ANIM construction); Type III, as Type II for ammonium but with a poorer capability for the assimilation of nitrate in darkness; and Type IV, as Type III but now nitrate may only be accumulated into the (enlarged) internal nitrate pool in darkness, with assimilation during the following light phase. The values of constants for the model are given in Table 1, with the forms of these different controls shown in Fig. 1 (cf. Figs 8 and 9 in Clark et al., 2002).

Table 1.  Values of constants used to differentiate between the model types
ConstantDescription and unitsModel
Type 1Type IIType IIIType IV
  1. See also Fig. 1. Model Type II is a similar configuration to that originally used in Flynn et al. (1997). dl, Dimensionless.

ApmMaximum internal ammonium pool size (N : C)0.00070.00070.00070.0007
Cres2Curve-fitting constant, see Equation (1) (dl)0.00010.010.010.01
NpmMaximum internal nitrate pool size (N : C)0.00140.00140.00140.014
NredRelative rate of nitrate reduction to ammonium in darkness (dl); value of constant r in Equation (1)0.990.60.10
McostAssimilation cost multiplier (dl)1 or 31 or 31 or 31 or 3
UmMaximum growth rate (d−1)0.4 or 1.20.4 or 1.20.4 or 1.20.4 or 1.2

Because the cost of N-assimilation and of respiration also varies between different algae (e.g. dinoflagellates have higher rates of respiration; Harris, 1978), and because such a difference will affect dark N-assimilation through consumption of C, the models were run with contrasting metabolic costs (Mcost in Table 1). A value of Mcost = 1 applies the default costs for assimilating nitrate and ammonium (at 1.71 g C g−1 N for nitrate reduction to ammonium, and 1.5 g C g−1 N for ammonium assimilation into cell N; see Flynn & Hipkin, 1999). However, these mathematical constants are not biological constants: the real cost of N assimilation in darkness varies within a single organism depending on the NC status of the cell when supplied with DIN (see Clark et al., 2002). Not wishing to further complicate the model structure, here we compare results with Mcost set at 1 or at 3. These alternatives were also operated with contrasting maximum growth rates (Um in Table 1) of either 1.2 d−1 or 0.4 d−1. Cells with high growth rates would be expected to be most competitive with low assimilatory (Mcost) costs. Slower-growing cells would not be expected to be affected so obviously by the value of Mcost because the rate of N-assimilation rather than the actual amount of C available to support it would be more limiting.

Comparisons were made with models run to steady-state under a 12 h : 12 h light–dark cycle with N supplied either at an ammonium : nitrate ratio of 50 : 50 or 1 : 20 at a range of (total) DIN concentrations between 0.25 µm and 10 µm (i.e. N-limiting to N-saturated). In addition, in order to simulate a situation where cells migrate to a nutricline at night, thereby obtaining DIN, simulations were also run in which transport was disabled during the light period so that growth could only proceed using N obtained during darkness. All models were constructed and tested using Powersim Constructor and Solver v2 software (Powersim AS, Isdalstø, Norway).

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Model Configuration
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Nitrogen assimilation over the diel cycle vs assimilation only in darkness

A comparison of the four different types of configurations (Fig. 1, Table 1) shows that when N was available over the complete diel cycle of light and dark, differences between the types are most pronounced at high relative growth rates (i.e. with high substrate availability and hence cells having a high N : C ratio and low C-reserves), in cells with high metabolic costs and when subjected to low availability of ammonium (Figs 2–4). The performance of these configurations becomes similar as N-stress increases (and growth rate falls). The explanation is, in part at least, because under the conditions required to process inorganic N in darkness, namely a depressed N : C ratio resulting from N stress, the transport of N into the cell is already limiting. This factor overrides the markedly different modelled abilities to assimilate N in darkness. As the transport rate becomes more limiting, at lower substrate (DIN) concentrations, the rate of assimilation post-transport becomes increasingly less important.

image

Figure 2. Comparisons of the performance of the four model types. Models were configured as Types I (circles), II (triangles, apex up), III (squares) or IV (triangles, apex down) (see Fig. 1) and supplied with dissolved inorganic N (DIN) at different concentrations during growth in a 12 h : 12 h light–dark cycle. N transport was enabled throughout the cycle (unfilled symbols) or only in darkness (filled symbols). Models were configured with either a low or high metabolic cost for N-assimilation (constant Mcost in Table 1) and with either a high or low maximum growth rate (µ; constant Um in Table 1). This figure shows growth when using nitrate alone, with 0% ammonium.

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image

Figure 3. Comparisons of the performance of the four model types. Models were configured as Types I (circles), II (triangles, apex up), III (squares) or IV (triangles, apex down) (see Fig. 1) and supplied with dissolved inorganic N (DIN) at different concentrations during growth in a 12 h : 12 h light–dark cycle. N transport was enabled throughout the cycle (unfilled symbols) or only in darkness (filled symbols). Models were configured with either a low or high metabolic cost for N-assimilation (constant Mcost in Table 1) and with either a high or low maximum growth rate (µ; constant Um in Table 1). This figure shows growth with DIN supplied as 10% ammonium and 90% nitrate.

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image

Figure 4. Comparisons of the performance of the four model types. Models were configured as Types I (circles), II (triangles, apex up), III (squares) or IV (triangles, apex down) (see Fig. 1) and supplied with dissolved inorganic N (DIN) at different concentrations during growth in a 12 h : 12 h light–dark cycle. N transport was enabled throughout the cycle (unfilled symbols) or only in darkness (filled symbols). Models were configured with either a low or high metabolic cost for N-assimilation (constant Mcost in Table 1) and with either a high or low maximum growth rate (µ; constant Um in Table 1). This figure shows growth with DIN supplied as 50% ammonium and 50% nitrate.

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Availability of the N-source only during darkness results in lower daily growth rates but otherwise a similar series of trends as seen during light-dark availability (Figs 2–4). The use of a large pool to accumulate nitrate in darkness for subsequent assimilation (Type IV) has little clear merit except for slow-growing cells in a low-ammonium environment.

While increasing the cost of assimilation (tripling it; Mcost in Table 1 set at 3) does have an effect, it is not as profound as may be expected (Figs 2–4). Again, in part, this is because cells that need to accumulate N in darkness (because the availability of N in the light phase is growth limiting) have such an excess of C that any extra expenditure on N assimilation is secondary to the rate limitation of transporting the N source into the cells in the first instance. This factor is again most important in the simulations for fast growing cells where nitrate is the only available N source.

Light-dark coupling of N assimilation

An analysis of the behaviour of the different configurations of the model in each light and dark phase shows the expected increase in the importance of dark N-assimilation as growth becomes increasingly limited by the availability of external N (Figs 5 and 6). For fast-growing Type I cells with an excess of nutrient, ammonium assimilation is minor in darkness, while for nitrate it is significant because the maximum rate of nitrate assimilation during the preceding light phase is inadequate compared with the fixation of C. This process is accompanied with elevated rates of respiration and hence also requires higher rates of C fixation during the light phase to support the whole process. Type II gives a lower ratio (1 : 0.3) of nitrate assimilation rates in light : dark under optimal (nitrate-saturating) conditions. Type IV gives a reasonable accumulation of N (nitrate not assimilated but just ‘stored’) in darkness with minimal C respiration. When the simulation is run with high metabolic costs (Fig. 6), the respiratory costs for dark N-assimilation become more significant (especially for nitrate), as do the rates of C growth during the light phase (needed to supply the additional C for dark N-assimilation).

image

Figure 5. Decoupling of C and N assimilation in low metabolic cost simulations. Steady-state low metabolic cost model simulations of the specific rates of growth for N (triangles) and C (circles) during the light (open symbols) and dark (closed symbols) phases of growth during a 12 h : 12 h light–dark cycle rate limited by the concentration of either ammonium or nitrate. Four model types were used, of which Types II, III and IV share similar ammonium controls (see Fig. 1). The total (daily) growth rate (which is the same for both C and N) is also shown.

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image

Figure 6. Decoupling of C and N assimilation in high metabolic cost simulations. Steady-state low metabolic cost model simulations of the specific rates of growth for N (triangles) and C (circles) during the light (open symbols) and dark (closed symbols) phases of growth during a 12 h : 12 h light–dark cycle rate limited by the concentration of either ammonium or nitrate. Four model types were used, of which Types II, III and IV share similar ammonium controls (see Fig. 1). The total (daily) growth rate (which is the same for both C and N) is also shown.

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The relative rate of nitrate assimilation, as a proportion of total N-assimilation, is described by the f-ratio (Dugdale & Goering, 1967); here this is given by

  • image(Eqn 2)

When confronted with a mixture of ammonium and nitrate (Fig. 7) a diel variation in the f-ratio is seen (Fig. 8). With Type I, in which nitrate assimilation proceeds at a rate similar to that of ammonium in darkness, that difference is minor. For Type II and especially for Type III, where dark nitrate assimilation is slower, there is a pronounced change in the f-ratio. However, the total day-averaged f-ratio is similar to the light-phase value because the contribution of the N-assimilation process in darkness is relatively minor (Fig. 8). Type IV differs from Type III because the accumulation of nitrate into the internal pool (with no immediate assimilation) does not result in the formation of glutamine, which would normally (as in Type III) repress transport (Flynn et al., 1997).

image

Figure 7. Decoupling of C and N assimilation when N is supplied as a mixture of ammonium and nitrate. Steady-state low metabolic cost model simulations of the specific rates of growth for N (triangles) and C (circles) during the light (open symbols) and dark (closed symbols) phases of growth during a 12 h : 12 h light–dark cycle rate limited by the concentration of a dissolved inorganic N (DIN) mixture of 10% ammonium and 90% nitrate. Other details as for Fig. 5.

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image

Figure 8. Diel variation of the f-ratio. Variation in the f-ratio for the assimilation of dissolved inorganic N (DIN) (supplied at 10% ammonium) during the light (open symbols) and dark (closed symbols) phases of growth by models configured with four contrasting dark N-assimilation capabilities, as shown in Fig. 7. The line with no symbols shows the 24-h average f-ratio (Eqn 2).

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Model Configuration
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

There are several interesting results demonstrated in the simulations presented here. First, the great differences in the ability to assimilate ammonium and nitrate in darkness seen in different phytoplankters (Clark et al., 2002; Fig. 1) are not mirrored by differences in growth rates under N-limiting conditions. Second, while assimilation costs are important, again a significant difference (tripling) in these is not mirrored in growth rates. Both of these results (Figs 2–4) are explained by the fact that in order to be able to perform N assimilation in darkness cells need to contain an excess of C and thus must by definition be growth limited by the supply of N outside of the cell. Thus, transport into the cell rather than the rate of assimilation after transport is the critical factor. From a modelling point of view, the fact that model output is relatively insensitive to these factors is convenient because it means that we can use generic configurations (similar to the Types used here) without being overly concerned about minor differences in the value of model constants.

The greatest differences between the configurations (Types I–IV) tested are seen at high growth rates and high nutrient (especially nitrate) availability. This situation is typical for diatoms in the temperate spring bloom. Indeed, it appears that high growth rates in diatoms on nitrate may only be attained through the partial decoupling of C-fixation and nitrate assimilation because nitrate assimilation in the light phase alone may be rate limiting (Flynn et al., 2001; Clark et al., 2002). At least within the model, there also appears to be a positive feedback between the need to obtain N in darkness, consuming previously accumulated C, in order to be able to develop an enhanced photosynthetic system. The resultant elevated Chl : C ratio not only enhances the growth rate but also supplies excess C for the support of the next period of dark N assimilation. This process promotes the development of a pronounced diel cycle in Chl : C and N : C ratios, especially in cells growing at high irradiance. This is seen in the models developed in Flynn et al. (2001) run to simulate the growth of the diatom Skeletonema costatum described in Anning et al. (2000).

Some diatoms can accumulate significant pools of nitrate. This has been suggested to endow some species with a competitive advantage when nutrients are supplied in pulses (Stolte & Riegman, 1995), while some other diatoms engage in vertical migration from nutrient-depleted surface layers to the nutricline and thus obtain nitrate (Richardson et al., 1998). The accumulation of nitrate for subsequent reduction has an immediate cost advantage but is in totality rather wasteful. Relatively little nitrate can be accumulated; the configuration of the model for Type IV (Table 1) provides the organism with a maximum internal nitrate pool size equivalent to 200 mm (assuming a cell biomass of 200 g C l−1 cell volume). This value is at the upper extreme of nitrate pool sizes reported in the literature (Dortch, 1982; Villareal & Lipschultz, 1995). The absolute amount of nitrate that may be held in the pool is not very great compared with the requirements for cell doubling (assuming a mass ratio for C : N of 6 and 200 g C l−1 cell volume, cell N equates to c. 2.4 mol N l−1 so a pool of 200 mm would supply less than 10% of N for a cell doubling). Also, if the nitrate N is not actually assimilated until the next light phase then time is lost in the overall growth process. For example, the new N cannot contribute immediately to promoting photosynthesis, while N assimilated in darkness may already be within the photosystem apparatus by the following light phase. Further, if nitrate is to be accumulated rather than being reduced at least as far as nitrite, then either the enzyme nitrate reductase must be regulated in some way or not present at a high level. Nitrate reductase typically displays distinct diel cycles (Berges et al., 1995); this behaviour is also seen in migrating diatoms (Joseph & Villareal, 1998). In either instance, again a delay may be expected before N-assimilation is fully operational.

The development of the Type IV strategy would thus appear to cater for a situation where the distance between the illuminated surface and the nutricline are extreme and low growth rates are acceptable in competition. Diatoms that use this strategy are not active diel vertical migrators, lacking (as do all diatoms) flagella for locomotion, and indeed may take many days to complete the migration (Richardson et al., 1998). Under such conditions, where prolonged survival below the compensation depth becomes critical, an accumulation of nitrate (and/or other nutrients such as phosphate) with minimal expense is more likely to be important. Growth of these organisms is slow (Joseph & Villareal, 1998; Richardson et al., 1998), so the accumulation of nitrate from low concentrations under such conditions is plausible.

For organisms that inhabit low-ammonium, high-nitrate environments (such as diatoms in the spring temperate bloom) it is important to be able to assimilate nitrate rapidly in darkness, otherwise nitrate assimilation does indeed become rate limiting. For dinoflagellates, which grow slowly and inhabit waters that contain relatively more ammonium, that ability may be expected to be of less importance. Diel vertically migrating dinoflagellates are likely to use ammonium at least as much as nitrate (Prego, 1992), although most emphasis in laboratory experiments has been on nitrate utilization (MacIntyre et al., 1997) because the elevated levels of ammonium typically used in culture work are often toxic. These, and other flagellates that undertake diel vertical migrations may have evolved a metabolic strategy that conserves energy for survival at depth in light-limiting conditions.

Although motility itself is likely to be of minor metabolic cost (Raven & Richardson, 1984), a saving in the expense of energy on nitrate reduction, or more specifically for nitrite reduction, may have been of importance in evolutionary selection. However, as discussed in Clark & Flynn (2002), the situation is not that simple because flagellates may take up and reduce nitrate and then expel nitrite, or indeed they may assimilate nitrate to organic N and then expel it. Thus, they expend the energy with no obvious gain. Indeed, Alexandrium minutum performs this action to extreme while simultaneously assimilating ammonium in darkness. Flynn & Flynn (1998) presented a model for simulating nitrite release by this organism. Presumably, energy is not a limiting factor initially during darkness, because an excess of C (and hence of ‘energy-reserve’) in the cell is likely to be the (or a main) factor triggering the migration activity.

Dinoflagellates have another problem: they are relatively N-rich, with a cellular N : C ratio typically between 0.1 and 0.2 (Flynn & Flynn, 1998), while most other eukaryotic algae have a range of 0.05–0.2 (the range used in all the simulations presented here). This narrow range has a negative impact on the availability of C to support dark metabolic activity. Allied to relatively high respiration rates (Harris, 1978), this may provide an additional selection factor explaining the apparent poor ability of certain dinoflagellate species to assimilate nitrate in darkness. However, because the assimilation of nitrate into these organisms (which have only a small internal nitrate pool; Flynn & Flynn, 1998) requires the presence of nitrate reductase it may be preferable for them to retain this enzyme activity and disable nitrite reduction in darkness. While this means that they may take up nitrate and expel nitrite in darkness, at least the cells are ready to make best use of any nitrate that becomes available in the following light phase without the delay for synthesis of nitrate reductase.

The determination of the f-ratio is important in oceanography because it is an index of the proportion of C fixed during primary production, which sinks to the seabed and hence may be locked into the sediments (Dugdale & Goering, 1967). The diel variability of the coupling of C- and N-assimilation complicates the estimation of the f-ratio using short-term incubations (Cochlan et al., 1991a,b; Probyn et al., 1996). Results from the simulations suggest that daylight incubations are likely to overestimate the daily integrated f-ratio by 0.1 (Fig. 8). While, the greatest diel variations in the f-ratio are likely to be seen in systems where N is not limiting, under such conditions the night contribution to the total N-assimilation is relatively low, except for Type I (diatom pattern). The model configurations presented here, when allied with other organism-types specific model details (for example, growth rate, silicon, P, light – see the model described in Flynn, 2001), enable simulations of the types of differences in diel N-assimilation (and hence the f-ratio) seen in mixed phytoplankton populations as described, for example, by Cochlan et al. (1991b).

One other important aspect of competition for these organisms is the form of the relationship between cellular N : C ratio (‘N-quota’) and growth rate. If this relationship is linear, rather than hyperbolic, then the formation of the C reserve needed to support N assimilation in darkness will be coupled strongly with a decrease in growth rate. The optimal strategy would be to have a distinctly hyperbolic relationship so that the growth rate was still high even when significant C reserves were present. Many models of algal growth contain components relating growth limitation to the cellular nutrient quota (Caperon, 1968; Droop, 1968); in this instance, relating the growth rate to the N : C ratio. ANIM and allies (Flynn, 2001) also use quota-linked controls. For simplicity, many models use the linear quota equation (e.g. Andersen, 1997), with the form

  • image(Eqn 3)

where NCm and NCo are the maximum and minimum cellular N : C values, NC the current N : C ratio, and NCu the resultant quota quotient. The recent versions of ANIM all use a normalized version of the full hyperbolic function (Flynn, 2001), thus

  • image(Eqn 4)

with the constant Kq enabling the form of the growth–N : C relationship to be altered. In the simulations run here, Kq was set to 0.4, giving a weak hyperbolic curve. Whether rapid growth is attainable when using N only in darkness (i.e. decoupling C- and N-acquisition completely), as discussed by Harrison (1976), MacIsaac (1978) and Sciandra (1991), depends critically on the form of this relationship. Quota-based models should not use the linear form (Eqn 4) by default, especially if they simulate diel processes.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Model Configuration
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

This work was supported by the Natural Environment Research Council, UK, and by the Leverhulme Trust/Royal Society through a Fellowship to KJF.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Model Configuration
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
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