MARINE PROGRESS SERIES Vol. 250: 13–28, 2003 Published March 26 Mar Ecol Prog Ser

Influence of model complexity on simulations of microbial communities in marine mesocosms

J. R. Dearman1, A. H. Taylor2, K. Davidson1,*

1Scottish Association for Marine Science, Dunstaffnage Marine Laboratory, Oban, Argyll PA37 1QA, Scotland, United 2Plymouth Marine Laboratory, Prospect Place, West Hoe, Plymouth PL1 3DH, United Kingdom

ABSTRACT: Marine mesocosm experiments were conducted using a natural assem- blage from the Tromsheim fjord, Norway, in June 2000. Replicate experiments were conducted at 2 inorganic nitrogen:silicon (N:Si) molar ratios, 4:1 and 1:1. Time course changes in the different groups that comprised the microplanktonic and inorganic concentrations were recorded. We sought to simulate these data using 3 alternative mathematical models based on a com- mon framework of functional groups and inter-group interactions following an earlier model. The functional groups incorporated within the model were , , , phyto- , picophytoplankton, heteroflagellates and larger microzooplankton along with inorganic , dissolved organic matter and . We modified the autotroph functional group sub- models to achieve different levels of model sophistication in terms of utilisation of nutrients (single [N] or dual [N:Si] inorganic nutrient models) and structure ( growth made a func- tion or extracellular or intracellular nutrient concentration). We tested the influence of different model formulations on simulations of particulate (C) biomass and its partitioning amongst the microbial groups in the 2 different experimental nutrient regimes. To achieve satisfactory global simulations (both nutrient regimes) with a single-parameter set, it was found necessary to include a dual currency of both inorganic N and Si in the model, and to relate C biomass growth to the intra- cellular rather than extracellular concentration of the nutrient in the least relative supply. Models lacking these 2 features were unable to simulate N and Si and C biomass dynamics of the microbial assemblage in alternative conditions of high and low N:Si ratio.

KEY WORDS: Microbial -web model · Nitrogen:silicon · Cell quota ·

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INTRODUCTION (e.g. Sherr et al. 1984, Suttle et al. 1986, Azam 1998). This, in combination with increasing computing power, In the of our ever-increasing understanding of has led to refinement of pelagic food-web model struc- marine , it is necessary to critically analyse ture, with various ‘new’ functional groups being intro- the fundamental building blocks and pathways in- duced into models as an ongoing process. The near- cluded within mathematical models, particularly of classic model of Fasham et al. (1990) is an excellent coastal regimes, where the influence of anthropogenic example of a model that incorporates some of our new nutrient loading is of concern. Traditionally, models of understanding of the complexity of the marine micro- marine ecosystems have relied on a simple nutrient- bial . Numerous refinements of this and simi- phytoplankton- (N-P-Z) structure (Steele lar models have occurred subsequently (Haney & Jack- 1974). The ‘discovery’ of the (Azam et al. son 1996, Fasham et al. 1999, Spitz et al. 2001). 1983) led the way towards an improvement in under- A common strategy when building biological ecosys- standing the interactions within microbial food webs tem models is to relate the specific rate of cell division

*Corresponding author. Email: [email protected] © Inter-Research 2003 · www.int-res.com 14 Mar Ecol Prog Ser 250: 13–28, 2003

or biomass increase to the local concentration of the dynamics. Hence, some representation of intracellular assumed least-abundant (limiting) nutrient based on nutrient concentration may be necessary to quantita- Monod-style kinetics (Monod 1942) incorporating a tively simulate the changes in biomass of different Michaelis-Menten style hyperbola or some modifica- microbial groups. tion thereof (Fasham et al. 1990, Taylor et al. 1993, If our goal is to produce global models capable of Baretta-Bekker et al. 1994). In many marine systems, simulating a range of environmental conditions, then it experimental evidence suggests that nitrogen (N) is may be necessary to routinely simulate both diatoms the limiting nutrient (Officer & Ryther 1980). and non-diatomous autotrophs and to include multiple In coastal marine systems, silicon (Si)-requiring dia- inorganic and organic nutrients within our formula- toms play a particularly important role within the tions (Flynn et al. 1997). In this paper we test this , forming the greater part of the spring phyto- hypothesis using a single-model framework in terms of plankton bloom in temperate latitudes. Si is also im- physical and biological interactions, microbial func- portant in the open ocean. Although variations exist, tional groups and species-species interactions, i.e. the diatoms require N and Si in approximately equal quan- model of Taylor et al. (1993). Using this framework, we tities (Schöllhorn & Granéli 1996). Hence, although assessed the predictive ability of microbial nutrient affinity is also important, should there be a models of varying levels of sophistication in terms of relative lack of Si, then Si- rather than N-limitation of nutrient currency and autotroph sub-model sophistica- the growth of the population may occur (Officer tion when applied to marine microbial mesocosm data & Ryther 1980, Conley et al. 1993, Conley 1997). sets under different N:Si nutrient regimes. In particu- The anthropogenic N loading that occurs in many lar, we determined the ability of models of different coastal waters may be increasing the inorganic N:Si levels of sophistication to simulate, using a single para- ratio (Jickells 1998, Egge & Asknes 1992, Sommer meter set, a single microbial assemblage that was sub- 1994), especially in regions of restricted exchange ject to alternative inorganic nutrient regimes. Hence, (Rahm et al. 1996, Aure et al. 1998) potentially result- we sought to gain an appreciation of the global appli- ing in a switch from N- to Si-limitation of diatoms. Si- cability of model structure, rather than the simple limitation may influence the species composition of a ability to fit a single data set. diatom assemblage (Sommer 1986, 1991) and change The model was formulated to simulate the produc- the species composition of the microbial assemblage as tion of organic C biomass as a function of inorganic a whole, producing a - rather than diatom- nutrient availability, and differentiated between 4 dif- dominated community (Officer & Ryther 1980, Smayda ferent autotroph groups (1 diatom and 3 non-diatom) 1990, Egge & Asknes 1992). Changes in the diatom along with various and other biological and autotrophic flagellate populations will influence state variables. Alternative versions of the model in- the quantity, type and quality of autotrophic food avail- cluded simulations of autotrophs at 3 levels of sophisti- able to both micro- and meso-heterotrophic grazers. cation: (1) single-nutrient (N) and Monod-style growth; Si-limitation of the diatom assemblage may therefore (2) dual nutrient (N,Si) and Monod-style growth; have significant implications for the dynamics of (3) dual nutrient (N,Si) and modified quota (Caperon microbial food webs and the flux of carbon (C) and N 1968, Droop 1968) style growth, in which C biomass in pelagic food webs in general. increase is related to the intracellular concentration of As noted by Davidson (1996), Haney & Jackson nutrient in the least relative supply. (1996) and Tett & Wilson (2000) the level of physio- To test the models, we simulated data collected from logical detail incorporated within models has varied a suite of mesocosm experiments conducted on a nat- markedly between different studies. Yet although ural microbial assemblage. The controlled conditions numerous different microbial food-web model formu- of mesocosms are increasingly being used to formulate lations exist, there is a surprising paucity of discussion and test mathematical models (Baretta-Bekker et al. regarding the implications of these different formula- 1998, Thingstad & Havskum 1999, Watts & Bigg 2001). tions (Tett & Wilson 2000). Should we choose to in- Here, experiments were conducted using 2 different corporate multiple nutrients in a model, the simplest supply ratios of inorganic N and Si to produce condi- approach is to relate biomass growth rate to the con- tions in which the diatom population was thought to be centration of extracellular nutrient in least relative N and Si yield-limited respectively. supply. However, as noted by Baretta-Bekker et al. We investigated the influence of changes in model (1998), the inclusion of luxury nutrient uptake of a sophistication on simulations of the biomass distribu- second, non-limiting nutrient and the decoupling of tion between different microbial groups and of the carbon (C) and nutrient dynamics (Lancelot & Billen food web as a whole to assess the benefits of increased 1985, Davidson 1996, Haney & Jackson 1996, Baretta- model sophistication set against the related problems Bekker et al. 1998) may influence microbial food-web of parameterisation of more physiologically detailed Dearman et al.: Microbial food-web model 15

models. In particular we sought to determine (PNAN), heterotrophic nanoflagellates (HNAN), auto- (1) whether we could model a coastal planktonic trophic and heterotrophic dinoflagellates, and larger ecosystem under 2 alternative nutrient (N:Si) regimes, microzooplankton. Extracellular inorganic nutrient con- using a single model and a single parameterisation centrations NH4, NO3, PO4, SiO4 were assessed. Total thereof, and (2) the minimum level of complexity in particulate C and N contents were determined, and C terms of nutrient currency and modelled autotroph biomass of the different microbial groups was estimated functional-group physiology required to achieve this. from each experiment based on mean cell volume, MCV (Montagnes et al. 1994, Davidson et al. 2002). Modelling methods and framework. The model MATERIALS AND METHODS structure used for all our simulations was the single mixed-layer model developed by Taylor et al. (1993). Mesocosm experiments were conducted on a natural The model makes autotroph growth a combined func- planktonic assemblage from Tromsheim Fjord, Nor- tion of light and nutrient availability, with vertical way, in June 2000. An outline of the methodology is changes in light intensity being calculated using the given below. 2-waveband approximation of Taylor et al. (1991) Experiments were conducted in 1.5 m3 mesocosm based on Carr (1986). The physical framework of the bags (1.5 m depth and 1 m2 surface area) suspended in model was adapted to account for the conditions within an outdoor seawater basin within the Trondheim the mesocosms. These were a restricted depth of 1.5 m, Marine systems large-scale facility. Natural surface no loss of cells from the enclosure due to sinking or seawater (with a mean nutrient concentration of 4 µM mixing, and a semi-continuous removal of cells and nitrate and 1.5 µM silicate) was diluted with plankton- water and replacement with new water and nutrients. free deep water (~180 m, mean nutrient concentration The physical conditions are outlined in Table 1. of 13 µM nitrate, 5.3 µM silicate) and enriched by the Within this physical framework the time-dependent addition of inorganic nutrients (nitrate, silicate and biological , also of Taylor et al. (1993), excess ) to obtain different inoculum nutri- was incorporated, the structure of which is shown ent (N:Si) concentration ratios of approximately 4:1 in Fig. 1. The trophic relationships of this model are (28 µM:7 µM) and 1:1 (12 µM:12 µM) respectively, based on those in the of Azam et henceforth referred to as ‘high N:Si’ and ‘low N:Si’ al. (1983). The model is composed of 4 classes of auto- respectively. A total of 8 bags were studied, 4 for each trophs: diatoms (Pd), dinoflagellates (Pn), phytoflagel- nutrient regime. lates (Pf), picophytoplankton (Pc); and 3 classes of het- The Si requirements of diatoms are quite variable erotrophs: free bacteria (B), heteroflagellates (Hf), and (Paasche 1973, Olsen & Paasche 1986, Sommer 1986, larger microzooplankton (Z). Autotrophs take up inor- 1991, Schöllhorn & Granéli 1996), but on average a ganic nutrients, and loss terms are included to account diatom community may be expected to require N and for the production of non-living organic matter as Si in an approximately equal molar ratio (Redfield metabolisable dissolved organic carbon (D); and detri-

1963, Brzezinski 1985, Schöllhorn & Granéli 1996). tus (DT). Hence, the different N:Si nutrient regimes studied pro- In this study, only the equations simulating auto- duced fundamentally different forms of diatom nutri- trophs and inorganic nutrient concentrations have ent limitation with Si-limitation being induced at the been changed from those of Taylor et al. (1993), and high N:Si ratio (L. C. Gilpin et al. unpubl. data). these will be presented in full below. In all versions of The mesocosms ran in ‘batch’ mode until Day 6 to allow the populations to become established. Follow- Table 1. Measured physical and initial chemical conditions ing this, every 2 d a fraction, k, of 20% of the total vol- used in the operation of the models. Water renewal of 20% of ume was removed by pumping and replaced with a total volume was employed semi-continuously every 2 d from combination of fjord surface and deep water (in the Day 6 onwards, giving a mean renewal of 10% per day same volume ratio and manipulated to achieve the same nutrient concentrations as were apparent in the Parameter N:Si mesocosms at time zero). The mesocosms therefore ran High Low as semi-continuous cultures, such methodology allow- Nitrate conc. (mmol m–3)2612 ing prolonged duration of active cell growth (Williams Silicate conc. (mmol m–3)612 & Egge 1998) and better simulating the conditions that conc. (mmol m–3) 0.1 0.1 may be encountered by coastal microplankton. Temperature (°C) 10.5 10.5 Depth (m) 1.5 1.5 Samples were collected every 2 d to determine the Water renewal (k) 0.2 0.2 cell densities of the various groups within the meso- No. of days 16 16 cosms: bacteria, diatoms, photosynthetic nanoflagellates 16 Mar Ecol Prog Ser 250: 13–28, 2003

eroflagellates and microzooplankton (gov-

erned by the transfer coefficients axy where x is the predator and y the prey) were each made directly proportional to the concentra- tion of multiple food sources: picophyto- plankton, bacteria and detritus in the case of heteroflagellates, and phytoflagellates, het- eroflagellates and detritus in the case of microzooplankton. The coefficient (Cil in Table 3) defines the ratio of grazing rates of larger microzooplankton to heteroflagel- lates (see Taylor & Joint 1990 or Taylor et al. 1993 for a full description). Losses due to

cannibalistic (axx) grazing were included and formulated in an analogous way to graz- Fig. 1. Schematic diagram of model structure used as the basis of our 3 microbial models. Model also includes silicate, nitrate, ammonium, ing on other components. DOC and detritus Dissolved organic carbon (DOC) equation (Table 2, Eq. T8): DOC is produced as a byproduct of autotroph growth (defined by φ the model studied, heterotrophs and organic pools are the 4 xy terms). The remaining terms represent produc- treated in the same way and in an identical manner to tion of DOC during grazing ('sloppy feeding') and the that of Taylor et al. (1993), who has explained the breakdown of detritus. DOC is taken up by the bacteria. equations in detail. Hence, only a brief description of Detritus equation (Table 2, Eq. T11): Detritus (DT) is the equations in Table 2 relating to heterotrophs is pre- produced in the course of grazing by heteroflagellates sented here: (athc Pc , athb B, and athh Hf) and larger microzooplankton Bacterial equation (Table 2, Eq. T5): The model (atzp Pd , atzn Pn, atzf Pf, atzh Hf , atzt Dt , and atzz Z). See the assumes bacterial growth rate to be related to the legend to Table 2 for the definitino of ax terms. Detritus availability of DOC (D), governed by a rectangular concentrations decrease through grazing by hetero- φ hyperbolic equation, where d is the degree of limita- flagellates (athDt) and breakdown by attached hetero- tion and Dh the half-saturation constant. trophic bacteria (mtt). Heteroflagellate and microzooplankton equations All respiration rates were temperature-dependent (Table 2, Eqs. T6 & T7): The growth rates of the het- following the equations of Taylor et al. (1993).

Table 2. Main biological interactions within Taylor Monod Model-1 and Model-2 (TMM-1 and TMM-2). Each coefficient ax de- scribes a rate of transfer between state variables. Thus, adhb is the constant representing the rate of dissolved organic carbon (d) production resulting from heteroflagellates (h) grazing bacteria (b). The subscripts associated with the other state variables are di- atoms (p), dinoflagellates (n) phytoflagellates (f), picophytoplankton (c), larger microzooplankton (z), silicate (S), nitrate (N), am- monium (A) and detritus (t). In the same way, each coefficient mx is a loss associated with the natural mortality (there being no loss but to mesograzer mortality as these had been excluded from the experiments). For definitions of terms see ‘Materials and methods’; fuller explanation is given in Taylor et al. (1993)

φ dPd/dt = (ap p – mp – k)Pd (T1) φ dPn /dt = (an NAn – mn – k)Pn (T2) φ dPf /dt = (af NAf – mf – afz Z – k)Pf (T3) φ dPc /dt = (ac NAc – mc – ach Hf – k)Pc (T4) φ dB/dt = (ab d – mb – abh Hf – k)B (T5) dHf /dt = (ahc Pc + ahb B + aht DT – mh – ahhHf – ahz Z – k) Hf (T6) dZ/dt = (azf Pf + azh Hf + azt DT – mz – azz Z – k) Z (T7) dD/dt = (a φ + m )P + (a φ + m )P + (a φ + m )P + (a φ + m )P – a φ B + m H + m Z dp p dp d dn NA dn n df NA df f dc NA dc c db d dh f dz (T8) + (adzf Pf + adzh Hf + adzt DT + adzz Z)Z + (adhc Pc + adhb B + adht DT + adhh Hf)Hf + mdt DT + mdb B + (D0 – D) k φ φ φ φ φ φ dN/dt = (N0 – N)k – (anp p Nr Pd + aNAn N Pn + aNAf N Pf + aNAc N Pc + aNdb N B) (T9) φ φ φ φ φ φ dA/dt = (A0 – A) k – (aAp p Ar Pd + aNAn A Pn + aNAf A Pf + aNAc A Pc + aAdb d B) (T10) + mAp Pd + mAn Pn + mAf Pf + mAc Pc + mAh Hf + mAz Z + mAt Dt + mAb B dDT/dt = mtp Pd + mtn Pn + mtc Pc + mth Hf + mtzZ + mtb B – mtt Dt + (athc Pc + athb B – (ath – atht)DT + athh Hf)Hf + (atzp Pd + atzn Pn + atzf Pf + atzh Hf + atzt DT + atzz Z) Z (T11) Model TMM-2 only: (T12) φ dS/dt = (S0 – S)k – asp p Pd Dearman et al.: Microbial food-web model 17

φ We next outline the 3 versions of the biological The term x represents the influence of nutrient lim- model for autotrophs that were studied comparatively. itation. Autotrophs are assumed to be able to utilise Biological Model 1: Single-nutrient Monod kinetics, both nitrate, N, and ammonia, A, with nutrient limita- TMM-1. Our first model is identical in format to that of tion of growth rate expressed by: Taylor et al. (1993). The model assumes a single in- φ φ φ φ x = ΝΑx = Νx + Αx (3) organic nutrient (N), as either nitrate or ammonia and φ limits the growth of all autotrophic groups. (Hence- where: Νx = (N/Nhx)/(1 + N/Nhx + A/Ahx) (4) forth this model is referred to as the Taylor Monod φ Αx = (A/Ahx)/(1 + N/Nhx + A/Ahx) (5) Model-1, TMM-1). The model employs Monod-style kinetics to represent autotroph (Pd, Pn, Pf, Pc) growth on where x defines the appropriate autotroph group: this nutrient, i.e. the rate of C biomass growth is a func- diatoms (p), dinoflagellates (n), phytoflagellates (f) and tion of extracellular rather than intracellular nutrient picophytoplankton (c). Nhx and Ahx are the half- concentration; C biomass increase is related to nutrient saturation constants for nitrate and ammonium uptake. uptake by a constant yield. The full set of equations The value of Ahx and Nhx were initially set to the same describing TMM-1 are included in Table 2. This model value for all autotroph groups (Table 3). was formulated with the specific intention of minimis- Inorganic nutrients. Equations for nitrate and ing the physiological differences between the auto- ammonium uptake were as follows: trophic phytoplankton populations included in the Nitrate equation (Table 2, Eq. T9): Nitrate concentra- simulation. The phytoplankton groups therefore differ tions change through uptake by the 4 groups of auto- φ φ φ φ only in their growth rates and their trophic relation- trophic phytoplankton (aNp p Nr , aNAn N , aNAf N , and φ φ ships. aNAc N) and by bacteria (aNdb N), and water renewal (k). Autotroph growth (Table 2, Eqs. T1–T4): The growth Ammonium equation (Table 2, Eq. T10): Uptake of φφ rate of autotrophs, is defined by the maximum growth ammonium by the 4 groups of autotrophs (aAp A , φ φ φ φ rate and the influence of both light and nutrient limita- aNAi A, aNAf A, and aNAc A) and by bacteria (aAdb d) are tion, following an equation of the form treated analogously to the nitrate equation as are φ changes due to water renewal (k). The remaining ax x (1) terms (mAp , mAi , mAf , mAc , mAh , mAz , mAt , and mAb)

The term ax represents maximum growth rate represent the excretion of ammonium associated with (µmax_x) of organism x, and a hyperbolic function (I) that respiration by diatoms, dinoflagellates, phytoflagel- accounts for the influence of light limitation (this latter lates, picophytoplankton, heteroflagellates, larger function is more fully defined in Taylor et al. 1993) microzooplankton, detritus, and bacteria respectively. Hence: For a more complete description of the interactions described within these nitrate and ammonium equa- a = µ I (2) x max_x tions refer to Taylor et al. (1993).

Table 3. TMM parameter values. Original parameter values were taken from Taylor et al. (1993)

Name TMM parameter Units Original Tuned Tuned values TMM-1 TMM-2

–1 µmax_d Maximum specific growth rate of: Diatoms d 0.9 1.0 1.2 µmax_n Dinoflagellates 0.3 0.5 0.5 µmax_f Phytoflagellates 1.5 1.7 1.2 µmax_c Picophytoplankton 1.5 2.0 1.3 –3 Nhd Nitrate half-saturation constant of: Diatoms mmol m 0.3 0.1 0.4 Nhn Dinoflagellates 0.3 0.5 Nhf Phytoflagellates 0.5 0.5 Nhc Picophytoplankton 0.7 0.3 –3 × –3 × –2 × –3 Ahd Ammonia half-saturation constant of: Diatoms mmol m 5 10 1 10 7 10 × –3 × –3 Ahn Dinoflagellates 6 10 4 10 × –3 × –3 Ahf Phytoflagellates 9 10 4 10 × –3 × –3 Ahc Picophytoplankton 4 10 4 10 Cil Ratio of grazing rates of larger micro- Dimensionless 0.3 0.11 0.18 zooplankton to heteroflagellates Gams Carbon yield per unit Si mg C mg Si–1 28 4.25 4.05 –3 Sh Silicate half-saturation constant mmol m 0.3 – 0.25 18 Mar Ecol Prog Ser 250: 13–28, 2003

Biological Model 2: Dual-nutrient Monod kinetics, tures of diatom growth observed in the experiments of TMM-2. Our second version of the biological model Davidson et al. (1999), i.e. finite threshold Si concen- includes a second nutrient, Si. Nutrient uptake and trations and observed reduced growth rates when both nutrient-limited growth by dinoflagellates, phytofla- N and Si concentrations were low, it was necessary to gellates and picoflagellates is modelled in an identical derive and employ a modified version of the cell quota manner to TMM-1, utilising only N. However, diatoms model, the co-nutrient model. Davidson & Gurney now take up both N and Si, with growth limited by the (1999) parameterised the model using cell numbers as nutrient in least relative supply. This 2-nutrient, an index of biomass, but noted that using an identical threshold style model will be referred to as the Taylor structure the model was also capable of simulating C Monod Model-2 (TMM-2) it is represented schemati- biomass. Here we have parameterised the co-nutrient cally in Figs. 2 & 3. model structure to simulate C biomass of diatoms, The nutrient limitation of Si-limited diatom growth is dinoflagellates and phytoflagellates. This quota-style governed by the relation: model will henceforth be referred to as the Davidson Taylor Quota Model (DTQM); it is represented φ = S/(S + S ) (6) Sp h schematically in Figs. 2 & 3. The set of equations where S is the Si concentration and Sh is the half- describing the DTQM within the biological model are saturation constant for Si uptake. outlined in Table 4. Parameter values based on cell For TMM-2, the nutrient limitation of diatom growth, numbers and taken from Davidson & Gurney (1999) or φ p (Eq. T1, Table 2), is therefore defined by: elsewhere were converted to C biomass-specific val-

φ Table 4. Davidson Taylor Quota Model (DTQM) equations. DTQM model uses Eqs. (T4) φ Sp P = min φ (7) to (T8) and (T11) from Table 2 together with Eqs. (T13) to (T24) from this table. Eqs. (T1) { NAp to (T3), (T9) to (T10) and (T12) from Table 2 are replaced with (T13) to (T18). For de- tailed explanation of the underpinning rationale of the co-nutrient model see The rate of change of inorganic Si Davidson & Gurney (1999) in TMM-2 is described by Eq. (T12). Si concentrations are governed by β dPd /dt = (aP P – mP – k) Pd (T13) β diatom uptake and water renewal. dPn/dt = (an n – mn – k) Pn (T14) dP /dt = (a β – m – a Z – k) P (T15) Within the ap term of the model, a f f f f fz f further parameter (Gams; Table 3), dS/dt = (S0 – S)k – AmaxS [S/(S + kS)]qF Pd (T16) defines the yield of particulate C per   unit of silicate taken up under Si- AmaxNp[N/(N + kNp)]qF Pd + AmaxNn[N/(N + kNn)]qF Pn dN/dt = (N0 – N)k –  (T17)  φ φ  limited conditions. ()+ AmaxNf [ N/(N + kNf)]qF Pf + aNAc N Pc + aNdb B Biological Model 3: Quota-based growth functions, Davidson Taylor dA/dt = (A0 – A) k + mAp Pd + mAn Pn + mAf Pf + mAc Pc + mAh Hf + mAz Z + mAt DT Quota Model (DTMQ). In this third   AmaxNp[A/(A + kNp)]qF Pd + AmaxNn[A/(A + kNn)]qF Pn version of the model we choose to in- + mAbB –   (T18)  φ  troduce quota (Caperon 1968, Droop ()+ AmaxNf(A/(A + kNf))qF Pf + aNAc N B 1968)-based growth functions for 3 of the 4 autotrophic groups, namely dQNx β ————— = AmaxNx[(N + A) /(kNx + N + A)]qF – ax xQNx (T19) diatoms, dinoflagellates and phyto- dt flagellates (Table 4, with parameter values presented in Table 5). Nutrient dQS β ————— = AmaxS [S/(kS + S)]qF – ap p QS (T20) uptake occurs as a rectangular hyper- dt bolic function of extracellular nutrient β γ x = (Qg – Qg0) [kQg + (Qg – Qg0)] x (T21) concentration moderated by a feed- back mechanism related to intracellu- Np if (QN /QN0) < (QS/QS0) and if simulating Pd lar nutrient:C (the cell quota, Q) pre-  g = Nn when simulating Pn (T22) venting abnormally high intracellular Nf when simulating Pf nutrient:C ratios. The specific rate of { S otherwise biomass increase is then calculated θ [(Qmaxθ – Qθ) (Qmaxθ – Qθ 0)] where = N,S when simulating Pd using a rectangular hyperbolic func- qF =  (T23) {1 otherwise tion of the ratio of Q above a minimum threshold (Q ). ε ε ε o γ Q /(Q + k ) if (Q /Q ) > (Q /Q ), ε = 10 Previously, Davidson & Gurney x =  N N 3 N N0 S S0 (T24) { 1 otherwise (1999) found that to simulate the fea- Dearman et al.: Microbial food-web model 19

Fig. 2. Schematic diagram of format of the diatom model Fig. 3. Schematic diagram of format of autotrophic dinoflagel- within (a) Taylor Monod Model-2 (TMM-2) and (b) Davidson lates and phytoflagellates within (a) Taylor Monad Model-2 Taylor Quota Model (DTQM) (TMM-2) and (b) Davidson Taylor Quota Model (DTQM) ues using the experimentally observed values of car- g (Eqs. 10 & T22) defines the limiting nutrient and is bon per cell for each functional group (Davidson et al. defined by 2002) from our mesocosms. The functional behaviour NQQ if (/NN00 )(/)< QQ SS of equations of particular interest to our study are g =  (11) S otherwise described below for a single organism, assuming 2 potentially limiting nutrients N and Si. The rate of growth of an organism (Eqs. T13 to T15) is The rate of nutrient uptake is governed by a rectan- therefore defined by: β gular hyperbolic function of the extracellular nutrient ax (12) concentration:  Z  where, as for Models TMM-1 and TMM-2, the term a A q x max Z  +  F (8) defines the maximum growth rate and the influence of Zkz light limitation. where Amax is the maximum uptake of Z, where Z = Z γ, the degree of reduction in uptake and growth rate N,S and k is the half-saturation constant. Z due to low concentrations of a non-limiting nutrient, is q (Eqs. 8 & T23) is a feedback mechanism prevent- F defined (Eq. T24) as ing abnormally high intracellular nutrient:C ratios:

 QQθθ−  εεε = max QQ/(+> k ) if ( QQ / ) ( QQ / ) qF   (9) γ = NN300 NN SS (13) QQθθ−  max 0 1 otherwise where Qθ is the cell quota per unit C (θ = N or S), where ε is a shape parameter that determines the minimum Qθ 0, maximum Qmax_θ. The influence of nutrient limitation on growth rate is degree of inflection of the curve and k3 is analogous governed (Eq. T21) by a parameter β related to the to the half-saturation constant in a Michaelis-Menten internal cell quota and γ (the degree of reduction in hyperbola. growth rate due to low concentrations of a non-limiting Finally, to prevent unreasonably large luxury stor- nutrient, see Eq. 13 below): age of Si when diatoms are N-limited we relate Qmax_S to Q thus: β γ N = (Qg – Qg0)/[kQg + (Qg – Qg0)] (10) QmaxS = Y·QN (14) where kQg is the half-saturation constant. where Y is a constant. 20 Mar Ecol Prog Ser 250: 13–28, 2003

Table 5. DTQM parameter values. Baseline values (not shown) around which tuning was conducted were taken or estimated from Conway et al. (1976), Davidson & Gurney (1999), Paasche (1973), and Taylor et al. (1993)

Name DTQM Parameter Units Tuned values

–1 –1 –1 AmaxS Maximum diatom uptake rate of Si d mgSi mgC d 0.41 –1 –1 –1 AmaxNp Maximum uptake rate of N d of: Diatoms mgN mgC d 0.21 –1 –1 AmaxNn Dinoflagellates mgN mgC d 0.10 –1 –1 AmaxNf Phytoflagellates mgN mgC d 0.06 –3 kS half-saturation constant for diatom Si uptake: mmol Si m 0.8 –3 kNp Half-saturation constant for N uptake: Diatoms mmol N m 0.3 –3 kNn Dinoflagellates mmol N m 0.4 –3 kNf Phytoflagellates mmol N m 0.4 –3 Nhc Picophytoplankton mmol N m 0.2 –1 µmax_d Maximum specific growth rate of: Diatoms d 1.4 –1 µmax_n Dinoflagellates d 0.3 –1 µmax_f Phytoflagellates d 0.9 –1 µmax_c Picophytoplankton d 1.8 –1 kQS Half-saturation constant for growth: Diatoms (Si is yield-limiting) mgSi mgC 0.3 –1 kQNp Diatoms (N is yield-limiting) mgN mgC 0.4 –1 kQnn Dinoflagellates mgN mgC 0.2 –1 kQNf Phytoflagellate mgN mgC 0.1 –1 QS0 Minimum cell quota for: Diatom Si mgSi mgC 0.04 –1 QNp0 Diatom N mgN mgC 0.12 –1 QNn0 N mgN mgC 0.04 –1 QNf0 Phytoflagellate N mgN mgC 0.10 –1 × QmaxS Maximum cell quota for: Diatom Si mgSi mgC 5 QN –1 QmaxN Diatom N mgN mgC 2.4 –1 k3 Half-saturation constant in function γ mg N mgC 0.62

When simulating dinoflagellates and phytoflagel- dominately Skeletonema costatum. Subsequent to the lates we need only consider 1 nutrient, N. Hence Z = peak of the diatom bloom, an increase in other micro- N and γ = 1, reducing the co-nutrient model to a stan- bial groups was noted. dard cell-quota formulation for these groups. The Mesocosms ran in parallel and therefore received an DTQM model presented here is identical to that pre- identical light field. Light was therefore treated identi- sented by Davidson & Gurney (1999) with the follow- cally, in terms of model structure and parameterisation ing modifications: the use of C rather than cell num- in all simulations, allowing us to compare the influence bers as the index of biomass (as discussed above), the of nutrient regime. inclusion of light limitation as a multiplicative term within Eq. (12), and the non-inclusion of γ in uptake Eq. (8), so that only growth (Eq. 10) rather than Model TMM-1 uptake and growth is moderated by the lack of a non- limiting nutrient. This model employed Monod-style growth kinetics and a single potentially yield-limiting nutrient (N) for all autotroph groups. The diatoms therefore do not RESULTS utilise Si and are yield-limited only by the exhaustion of extracellular N in both sets of simulations (high and In all the following simulations, models are com- low N:Si). Initially we parameterised the model using pared with the mean data from the 4 mesocosms in the parameter set of Taylor et al. (1993) (Table 3). Data each set of N:Si conditions. Comparison between and model are compared (symbols and dashed lines model and experiment was made for the following respectively) in Fig. 4 (high N:Si mesocosms) and Fig. 5 parameters: nitrate, silicate, diatoms, phytoflagellates, (low N:Si mesocosms) respectively. dinoflagellates, heteroflagellates and larger microzoo- In both simulations the model qualitatively predicted plankton. Initial conditions in the model simulations the uptake of extracellular N, with N exhaustion being were estimated from the mean of the experimental predicted within 2 d of that observed in both N:Si data at time zero. conditions. In both cases the model predicted an ap- In both of the nutrient regimes studied, the microbial proximately exponential increase of diatom C biomass biomass was dominated by a bloom of diatoms, pre- when N concentrations remained greater than zero. A Dearman et al.: Microbial food-web model 21

failure of the model was that, subsequent to N exhaus- In order to obtain a quantitative measure of the tion, the diatom biomass was predicted to continue goodness-of-fit of the model to the data sets, 2 alterna- increasing in a linear fashion and hence to overesti- tive measures were used. Correlation coefficients and mate the observed values. This increase was related to weighted mean-square residuals were calculated be- the N supplied within the renewal water. tween the model output and the mean observed data The model also significantly overpredicted the for each output parameter. As we wished to determine observed phytoflagellate biomass. A large peak of the overall fit of each version of the model (using a phytoflagellates was predicted, approximately 10 and single parameter set) to the complete data set, we 15 times that observed, at the same time-point in high pooled the results from the 2 scenarios (high and low and low N:Si mesocosms respectively. This peak N:Si data) for each variable when conducting these decreased rapidly through grazing by heterotrophs calculations for correlation and mean-squared residu- and washout following the depletion of N. In contrast, als. The correlation coefficients and mean-squared the simulation of autotrophic dinoflagellates was rela- residuals for Model TMM-1 are presented in Tables 6 tively good in terms of C biomass. However, the model & 7 respectively. For correlation, a low mean value of predicted a decrease in dinoflagellate biomass sub- 0.37 was obtained. Indeed only heterotrophic flagel- sequent to N exhaustion in both nutrient regimes, con- lates and nitrate showed significant correlation be- trary to the observed increase. tween model and experiment at the 95% level. The The simulation of heterotrophic flagellates showed a mean-squared residual values were high, also indicat- slow increase throughout. The model failed to predict ing a poor fit of the model to data. This was particularly the decrease in heteroflagellate biomass near the end true for larger microzooplankton, but diatoms, nitrate of the experiments. Larger microzooplankton biomass and phytoflagellates were also poorly simulated by the was significantly overpredicted by the model, showing model. We therefore revised the model parameterisa- a peak of 120 to 50 times that observed at the same tion by varying each of the relevant parameters of the time point in high and low N:Si conditions respectively, biological model (Table 3) in turn, using a numerical and a subsequent decrease. optimisation programme Powersim Solver® (Version 2.0,

Fig. 4. Fit of Taylor Monod Model-1 (TMM-1) to high N:Si data (d) using parameters of Taylor et al. (1993) (dashed lines) and optimised parameters (continuous lines) 22 Mar Ecol Prog Ser 250: 13–28, 2003

Fig. 5. Fit of Model TMM-1 to low N:Si data (d) using parame- ters of Taylor et al. (1993) (dashed lines) and revised optimised parameters (continu- ous lines)

Powersim AS, Norway), that applies a weighted least- Model TMM-2 squares minimisation technique. To prevent biologi- cally unrealistic solutions, parameters were allowed to The second version of the model included a dual vary only within biologically reasonable limits. nutrient currency of N and Si. The diatom population The model predictions following this re-parameter- was limited by the nutrient (N or Si) in the least relative isation are presented as continuous lines in Figs. 4 supply as defined by Eq. (7). Comparisons between the (high N:Si) & 5 (low N:Si). Calculated correlation data and Model TMM-2 are presented in Figs. 6 (high coefficients (Table 6) reflect the improvement in sim- N:Si) & 7 (low N:Si) respectively (dashed lines). The ulation quality, the average value increasing from optimised parameter set of Model TMM-1 was ex- 0.37 to 0.63, with all quantities except dinoflagellates tended to include the relevant parameter values (from and phytoflagellates showing a significant positive Taylor et al. 1993) for Si uptake and Si-limited C bio- correlation between data and experiment at the 95% mass growth (Table 3). The model parameterisation level. Least-squares residuals also indicated a sub- was optimised using the Solver software as above, stantial improvement in the quality of the simulation allowing the model to predict a larger diatom bloom with the sum of squared residuals reducing almost in the high N:Si mesocosms and a slower consumption 20-fold. of inorganic Si than was otherwise predicted. In spite of these changes, an obvious qualitative fail- TMM-2 reproduced the observed changes in the Si ing of the model was the continual increase in the pre- concentration reasonably well in both sets of mesocosm dicted diatom biomass throughout the simulations, conditions, however for the low N:Si conditions N and indicating that it was failing to capture the true dynam- Si uptake was slow. An important qualitative failure of ics of the system. A possible cause of this was the the model was the prediction of a high N threshold in absence of an Si-limitation function from the model; high N:Si conditions, with net uptake of N ceasing on hence Si-limitation of diatom C biomass increase could exhaustion of Si. Sensitivity analysis indicated that this not occur. was a feature of this model, and not just a function of Dearman et al.: Microbial food-web model 23

this particular parameterisation. Simulations of the bio- rectly predicted the C yield of diatoms in both nutrient mass of phytoflagellates and larger microzooplankton conditions. Notwithstanding these deficiencies, the were improved from previous versions. quantitative as well as qualitative indicators of simula- The simulation of observed diatom C biomass were tion quality were improved using Model TMM-2. greatly improved in both nutrient regimes, with a Correlation coefficients (Table 6) were considerably plateau and slight decrease being predicted rather greater than for the previous version of the model, with than the continual increase of TMM-1. However, the an average value of 0.83. All quantities except dino- model overestimated diatom C in low N:Si conditions flagellates exhibited a significant positive correlation accompanied by an underestimate in the biomass of between model and data at the 95% level. Although autotrophic phytoflagellates. In contrast, in high N:Si the sum of least-squares residuals actually increased conditions, the magnitude of predicted diatom C was (Table 7), this was due almost entirely to the N thresh- considerably lower that the observed peak. A para- old predicted in high N:Si conditions (as confirmed by meter-sensitivity analysis using both numerical and conducting the calculation up the point of N exhaus- manual fitting techniques indicated that we were tion only; Table 7). The quality of the simulation of all unable to obtain any single parameter set which cor- other quantities was found to increase using this index.

Fig. 6. Fit of Model TMM-2 (dashed lines) and DTQM (continuous lines) to high N:Si data (d), both using optimised parameters 24 Mar Ecol Prog Ser 250: 13–28, 2003

Fig. 7. Fit of Model TMM-2 (dashed lines) and DTQM (continuous lines) to the low N:Si data (d), both using optimised parameters

Model DTQM Application of this new version of the model involved further parameterisation. Initial estimates of the para- The remaining deficiencies in the simulations (N meters were obtained from literature using values threshold and inability to predict C biomass yield within the published range for our dominant diatom in 2 scenarios with a single parameterisation) led Skeletonema costatum (Paasche 1973, Conway et al. us to investigate the performance of the third and 1976) and for dinoflagellates and phytoflagellates from most physiologically complex version of the model, Taylor et al. (1993) and Davidson & Gurney (1999). Nu- DTQM, in which cell quota-type formulations are merically tuned parameters are presented in Table 5. applied to 3 groups of autotrophs: diatoms, dinofla- Simulations are presented (lines) in Figs. 6 (high gellates and phytoflagellates (Table 4; Eqs. T13 to N:Si) & 7 (low N:Si) respectively. Qualitatively this T24). As in Model TMM-2, diatoms utilised both N model performs considerably better than the previous and Si, but now the rate of C biomass growth was formulations. In contrast to TMM-2 and in agreement made a function of the intracellular concentration with the data, the model predicts exhaustion of the (WRT C biomass) of the nutrient in the least relative extracellular N in both nutrient regimes. Peak- supply. predicted diatom C is also in better agreement with Dearman et al.: Microbial food-web model 25

Table 6. Pearson correlation coefficient (r) values calculated for relationship between model and combined data (both N- and Si- limited) for each functional group. na: not applicable

Diatoms Dino- Larger micro- Phyto- Hetero- Nitrate Silicate Ave flagellates zooplankton flagellates flagellates

TMM-1 initial parameters 0.57 0.06 0.18 –0.22 0.74 0.88 na 0.37 TMM-1 fitted parameters 0.71 0.23 0.67 0.48 0.83 0.95 na 0.63 TMM-2 fitted parameters 0.90 0.51 0.75 0.80 0.91 0.97 0.96 0.83 DTQM fitted parameters 0.92 0.67 0.73 0.93 0.91 0.98 0.99 0.87

Table 7. Deviation of model from data as estimated by least-squares residuals, weighted to account for different magnitudes of the quantities within the model. Values in parentheses calculated using values only up to the time of N exhaustion

Diatoms Dino- Larger micro- Phyto- Hetero- Nitrate Silicate Total flagellates zooplankton flagellates flagellates

TMM-1 initial parameters 33.1 4.4 4730 131.2 10.7 242.5 na 5151.9 TMM-1 fitted parameters 41.0 7.9 64.0 51.8 47.3 64 na 276.0 TMM-2 fitted parameters 11.9 5.9 43.0 6.7 34.2 225.6 31.7 359.0 (33.4) (166.8) DTQM fitted parameters 7.8 4.4 42.5 7.5 21.8 35.8 12.5 132.3

observations in both nutrient regimes than was Recently, Tett & Wilson (2000) studied the effect of achieved in the runs of earlier models, while predic- changing the number of biological functional groups tions of the other variables are similar to the final run within a model. Here, we have taken a complementary of TMM-2. The exception to this is phytoflagellate approach of assuming a fixed number of functional biomass, which is improved in high N:Si conditions but groups but varying the number of potentially limiting is significantly poorer using this model in low N:Si nutrients and the method employed to predict the spe- conditions. However, the average correlation coeffi- cific rate of biomass growth for autotrophs (based on cient (Table 6) is increased from that in earlier runs, intracellular or extracellular nutrient concentration). and now all quantities show a significant positive cor- Although the sub-model of each biological group in relation between model and experiment at the 95% our ecosystem model is relatively parameter-sparse, level. The sum of least-squares residuals was also the total number of parameters within the model is markedly lower (Table 7). Individual values indicated quite large (over 100 parameters for DTQM). We that use of the DTQM improved the fit to each quantity therefore chose to explore different model formula- within the model. Hence a superior global simulation tions and parameterisations thereof by varying the (of both nutrient regimes) with a single parameter set parameter or parameters in question within biologi- is achieved using the DTQM. cally reasonable limits (set from the literature), while keeping other parameters at fixed values. Our aim was to produce the best overall fit to the combined data set DISCUSSION (both nutrient regimes) as a whole, but in particular to focus on quantities of particular interest and impor- The critical comparison of microbial models has been tance. With the large number of parameters in the hampered by difficulties in obtaining suitable test model, determining a global minimum as opposed to a data. We therefore chose to test our models on con- local minimum while keeping all the parameters in trolled mesocosm data that had been designed to sim- realistic ranges is a major problem. In addition, any ulate a coastal ecosystem with (high N:Si) and without solution obtained may well not be unique. We have (low N:Si) anthropogenic N loading. As noted by therefore used an objective numerical fitting routine, Baretta-Bekker et al. (1998), the use of mesocosm data Powersim Solver®, to optimise parameters, allowing us allows more detailed comparison between model and to explore the effects of changes in model structure data to be conducted than would be possible other- around our initial solution based on literature para- wise, field data being generally patchy in terms of tem- meters. To assess model performance we used 2 alter- poral and spatial coverage and in the parameters that native indices, least-squares residuals and correlation. have been measured and complicated by physical The former quantifies the sum of the magnitude of the mixing and exchange processes. deviation between data and model predictions at each 26 Mar Ecol Prog Ser 250: 13–28, 2003

data point, and the latter estimates the model’s ability ever, when Si is reduced to low concentrations it is less to follow trends in the data set. readily assimilated; its inclusion in the model therefore Our initial model (TMM-1) related the rate of growth reduced the tendency of the diatoms to overutilise of autotrophs to extracellular N concentration. Simula- extracellular N, and hence moderated predicted diatom tions of the individual microbial groups indicate that biomass increase and allowed the other autotroph although a qualitative representation of the early (pre- groups to become established in the model. nutrient exhaustion) growth of diatoms, dinoflagellates Our mesocosms simulate what is a fairly typical and heteroflagellates could be achieved, the simula- coastal scenario, high pre-bloom nutrient concentra- tion of phytoflagellates and larger microzooplankton tions and a continual nutrient input from riverine or was poor. These model runs were parameterised using other anthropogenic sources. The continued C biomass the data set published by Taylor et al. (1993) for the increase and resultant overestimate of total predicted North Atlantic bloom experiment of 1989. These para- C prior to the incorporation of the second nutrient indi- meters were in turn modified from those of Taylor & cated that a minimum level of sophistication required Joint (1990) for a model applied to the Celtic and by the model was a dual inorganic nutrient currency. Porcupine Sea Bight. Although we might hope that a Simple single-nutrient currency models may overesti- single parameter set would have global application, it mate microbial biomass subsequent to the onset of is not surprising that these parameters, which had nutrient limitation. As a consequence of the dual nutri- been optimised for the open ocean rather that coastal ent currency, the model predicted the behaviour (also , should not be directly applicable to our plank- observed by Egge & Aksnes 1992) of inhibition of tonic assemblage. However, we found that by numeri- diatom growth at low extracellular Si concentrations. cally optimising the parameters in Table 3, a more By varying parameter values (data not shown) we acceptable simulation was obtained. This indicates were able to achieve improved simulations of meso- that for bulk simulation purposes we might hope to cosms in either set of nutrient conditions using this assemble a generic parameter set that will require only dual N:Si model (TMM-2). However, we were still minor modification for the region or ecosystem to unable to achieve our goal of a global simulation of which it is applied. both nutrient regimes with a single-model parameteri- Following optimisation of the parameter set, many of sation. A particular failure was that simulations of high the characteristics of the mesocosm data in both sets of N:Si mesocosms underestimated observed diatom C nutrient conditions could be well reproduced by this biomass and did not reproduce the observed deple- single-nutrient (N) Monod-style model. Yet a major tion of inorganic N. Sensitivity-analysis indicated that discrepancy between data and model remained in that changes in parameter values that increased the diatom the diatom biomass was predicted to increase con- C yield in high N:Si conditions, and hence improved tinuously throughout the experiments. A parameter- this simulation, had a negative effect on the quality of sensitivity analysis indicated that this continued pro- the simulation in low N:Si conditions, with no single duction was fuelled by the addition of new, N-replete, parameter set giving an acceptable fit in both sets of water. The diatoms were always able to outcompete conditions. The inclusion of a dual nutrient currency of other autotrophs for this new N, and hence continually N and Si could therefore be regarded as a necessary increased in biomass over the timescale of the simula- but not sufficient step towards a model capable of tions. No modification of parameter values within bio- global simulations. logically reasonable limits was able to change these A feature of the data set was that the maximum yield general trends in TMM-1 prediction. of diatom C per unit N or unit Si was not constant Including a second nutrient, Si, within our Monod between different nutrient regimes. Monod-style mod- structure (as TMM-2) rectified the problem of the pre- els make the implicit assumption of a constant C pro- dicted continuous increase in diatom biomass. In high duced per unit limiting nutrient taken up. Our final N:Si mesocosms, the diatoms were thought to be Si- model (DTQM) introduced the concept of intracellular limited based on the accumulated evidence of increas- nutrient pools, cell quotas, on which autotroph biomass ing C:N ratio, change in cellular glucan content and growth was based. This allows variation in nutrient:C the concentration of inorganic nutrient in relation to its ratios and luxury consumption of non-limiting nutri- half-saturation constant (Escarvage et al. 1999, L. C. ents. Gilpin et al. unpubl.). The exhaustion of extracellular The inclusion of cell-quota methodology allowed the Si in the model led it to predict this Si-yield-limitation prediction of different cell silica and N content under of diatom biomass with the resultant cessation in different conditions. Hence the model predicted a net increase in accordance with the data. In low N:Si decline in cell silica content at low Si concentrations mesocosms, changes in the C:N ratio and intracellular and enabled higher diatom C concentrations to be glucan concentration suggested N limitation. How- reached in the high N:Si mesocosms, with almost all N Dearman et al.: Microbial food-web model 27

being taken up. A much-improved simulation of utilise it but, critically, the autotrophs that compete diatom C and extracellular nutrient concentrations was with diatoms for N and the heterotrophs that ingest therefore achieved. Small improvements or effectively both. The inclusion of Si moderated the diatom popula- no change in the quality of simulation of all other tion’s ability to utilise N subsequent to the peak of the quantities were obtained, with this model being able to bloom, making the N available for flagellates. achieve our criteria of a satisfactory global simulation In conclusion, we find that accurate simulation and (both nutrient regimes) with a single parameter set. the ability to respond to change (in our case to alter- The ability to model the growth of diatoms is of par- nate inorganic N:Si ratios) of quantities such as C flow, ticular importance due to the of diatoms in trophic exchange, and nutrient dynamics within our the spring phytoplankton bloom and their contribution microbial ecosystem requires a biogeochemical model- of the majority of new phytoplankton production (Dug- ling approach incorporating a specific representation dale & Goering 1967). Our simulations confirm the of different nutrients (C, N, Si) both extra- and intra- need for a multiple nutrient currency of N and Si and cellularly, and the representation of different func- variable nutrient:C ratios within the modelled diatoms, tional groups within a model. Employing a quota- suggested in a number of other studies. They also give based model allowed us to satisfactorily simulate the some (although far from conclusive) support for the system dynamics under 2 alternative nutrient regimes suggestion that smaller cells in general have smaller using only a single-model parameterisation. This indi- half-saturation constants for nutrient uptake. As noted cates the potential suitability of models structured in above, in order to model the microcosm data set of this way for predictive simulation rather than simple Davidson et al. (1999) which followed the interac- fitting of data. tion between the diatom Thalassiosira pseudonanna, a raphidophyte, and an autotrophic dinoflagellate, Acknowledgements. This work was funded by a small grant Davidson & Gurney (1999) found it necessary to derive from the Research Council, UK, and and employ a modified version of the cell quota model. SAMS research funds. It was also supported by the Improving Similarly, Haney & Jackson (1996) found that the in- Human Potential—Transnational Access to Research Infra- troduction of cell-quota-style growth equations for structures Programme of the European Commission. autotrophs within the model of Fasham et al. (1990) (which originally used Monod functions) significantly LITERATURE CITED changed model predictions, extending through to the heterotrophs to increase the zooplankton population Andersen V, Nival P (1989) Modelling of phytoplankton in an enclosed water column. J Mar and regenerated production. 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Editorial responsibility: Otto Kinne (Editor), Submitted: February 1, 2002; Accepted: November 12, 2002 Oldendorf/Luhe, Germany Proofs received from author(s): March 3, 2003