01_device Development of a Simple Biological Model 43 Development Of A Simple Biological Model Of Vertical Phytoplankton Distribution *Corresponding author Karlo Primavera*, Maria Lourdes San Diego-McGlone, Cesar Villanoy Marine Science Institute, University of the Philippines, 1101 Diliman, Quezon City, Philippines E-mail: bilbo@upmsi.ph, mcglone@upmsi.ph, cesarv@upmsi.ph ABSTRACT Science Diliman (January-June 2006) 18:1, 43-52 INTRODUCTION Phytoplankton is the base of the oceanic food web. These are consumed by bigger plankton, that are in turn eaten by organisms in the higher trophic levels. Phytoplankters, much like terrestrial plants, grow in biomass by utilizing carbon (in the form of carbon dioxide) through the process of photosynthesis. Although much smaller than their terrestrial counterparts, phytoplankton have greater surface area to volume ratios and much quicker turnover rates, making the amount of carbon dioxide that they consume quite significant. Thus they could play an important role in the sequestration of atmospheric carbon dioxide, the most significant greenhouse gas contributing to global warming. Phytoplankton in tropical waters aggregate and form a maxima below the surface where the common limiting materials for growth (light from the surface, nutrients from the depths) are at optimal levels. The location of optimum growth conditions is dependent on various physical, chemical and biological factors. The formation of phytoplankton maxima was simulated through a coupled physical and biological model for vertical chlorophyll distribution in Philippine waters. This paper evaluates biological models and the significance of 1) different forms of phytoplankton response to irradiance and nutrient uptake, 2) rate of nutrient uptake, and 3) light and/or nutrient limitation determining nutrient uptake. Phytoplankton response-to-irradiance form is less important than rate of light extinction in affecting the deep chlorophyll maximum (DCM) depth. The Michaelis-Menten form of nutrient uptake gives a bigger and deeper DCM but only under certain conditions. Temperature does not significantly affect nutrient uptake gives bigger and deeper DCMs. These findings will come in handy in future work of simulating empirical chlorophyll profiles. Light is used as energy source in photosynthesis through the chlorophyll pigments, with chlorophyll α as the principal photosynthetic pigment common to all phytoplankton. A high correlation of chlorophyll-a and phytoplankton biomass distributions (Akbulut, 2003) would then allow the use of chlorophyll α as a measure of phytoplankton biomass (Parsons & Strickland, 1963; Engelsen et al., 2004; Cloern & Dufford, 2005). Any difference in the distribution of chlorophyll and phytoplankton biomass may be attributed to sinking velocity and increasing chlorophyll to biomass ratios at low light levels (Fennel and Boss, 2003). Aside from light, nutrients are required in the photosynthetic reaction as shown by the equation below (Stumm & Morgan, 1995). Primavera, McGlone and Villanoy 44 Nutrients usually determine the rate of photosynthesis since their concentrations are found in limiting amounts (nitrogen for oceanic systems) compared to the abundance of light and carbon dioxide in surface waters (Falkowski, 1997). The amount of light available for photosynthesis decreases with depth due to attenuation (combined absorption and scattering) from particles in the water as well as the water itself. Inversely, nutrient gradients increase with depth. Somewhere in between is where a combination of both factors will be optimum for photosynthesis and phytoplankton growth. Phytoplankters tend to aggregate in this area giving rise to a phytoplankton maximum, commonly referred to as the deep chlorophyll maximum (DCM). Models have been developed to explain phytoplankton dynamics. The NPZ (nutrient-phytoplankton- zooplankton) model by Franks (2002) is the simplest model that describes oceanic plankton dynamics. + biological (1) dynamics C is the concentration of the state variable (N, P or Z), KH and KV are the horizontal and vertical eddy diffusivities, u, v and w are the horizontal and vertical water velocities, and ws is the vertical sinking or swimming speed of the state variable. The biological dynamics of the NPZ model is shown as: ( ) ( ) ( ) ( )PPiZPhPNgIf dt dP −−= ( ) ( )ZZjZPh dt dZ −= γ ( ) ( ) ( ) ( ) ( ) ( )ZZjPPiZPhPNgIf dt dN ++−+−= γ1 f(I) is phytoplankton response to irradiance, g(N) is phytoplankton nutrient uptake, h(P) is zooplankton grazing, i(P) is phytoplankton loss, j(Z) is zooplankton loss, and the constant g is the grazing assimilation efficiency of zooplankton. The NPZ model is a very general form of ecosystem model and has been modified. Hadfield and Sharples (1996) and Sharples (1999) added an internal cell nutrient variable to account for chlorophyll to phytoplankton biomass ratio variations with depth. Zakardjian and Prieur (1994) included oxygen as to deal with oxidation of reduced forms of nitrogen. Fennel and Boss (2003) differentiated phytoplankton biomass maxima and chlorophyll maxima. Different parameterizations have also been added, such as effect of photoadaptation and sinking due to phytoplankton aggregation (Doney et al., 1996) and nutrient exudation during respiration (Bahamon and Cruzado, 2003). Varela et al. (1992) and Hodges and Rudnick (2004) focused on the DCM. Varela et al. (1992) used several variables in his DCM model, these are 2 phytoplankton, 2 nutrients, and 2 heterotrophs. Although the model results were consistent with empirical data, Hodges and Rudnick (2004) noted that the fundamental constraint of nitrogen conservation was not satisfied in Varela et al.'s (1992) model. They then suggested a simple nutrient- phytoplankton model, where zooplankton grazing was factored into phytoplankton loss. Model results of Hodges and Rudnick (2004) showed that removal of nitrogen from the surface through surface boundary conditions and sinking of phytoplankton are necessary conditions in the formation of the DCM, and that addition of more variables do not significantly affect phytoplankton distribution. Because of the advantage of having less variables and satisfying balance of nitrogen in the system, the model of Hodges and Rudnick (2004) was adapted in this study. The objective of the study is to examine the degree to which nutrients (specifically nitrate) determine the vertical distribution of chlorophyll a using a coupled physical-biological model, with { } 216110263106 138OPNOHC + (algal protoplasm) +−− ++++ HOHHPONOCO 1812216106 2 2 432 (+ trace elements and energy) ( ) z C sww y C v x C u z C VK y C x C HK t C ∂ ∂ +− ∂ ∂ − ∂ ∂ − ∂ ∂ + ∂ ∂ + ∂ ∂ = ∂ ∂       2 2 2 2 2 2 Development of a Simple Biological Model 45 emphasis on the biological model. This could enhance understanding of phytoplankton dynamics and provide insights on fisheries potential of Philippine waters. MATERIALS AND METHODS The biological model used in this study is based on the nutrient-phytoplankton model of Hodges and Rudnick (2004). The coupled physical-biological model is shown below. Um is the maximum nutrient uptake rate and Kz is the vertical eddy diffusion coefficient. The boundary conditions are: P = 0, N = constant, at the bottom Hodges and Rudnick (2004) used only basic mechanisms to demonstrate the formation of the DCM. In doing so, complex formulations of parameters and relationship of variables that may be necessary to reproduce empirical chlorophyll profiles were not considered. Since this study will eventually attempt to duplicate empirical chlorophyll data, related literature were reviewed to examine parameters for irradiance, nutrient uptake, and phytoplankton loss (Tables 1 and 2). In the model of Hodges and Rudnick (2004), the growth term (last term) for phytoplankton utilizes both nutrient and light influence at the same time. An alternative is Liebig's law, which uses either nutrient or light, or whichever is more limiting at a given time. Also, the maximum nutrient uptake rate can be either constant or variable. Eppley (1972) suggested a temperature-dependent maximum phytoplankton growth rate: Um(T) and Um(T0) are the maximum uptake rate at reference temperature T and reference temperature T0, respectively. q10 is the factor by which the uptake rate changes with every 10ºC change in temperature. ( ) ( ) 10/)(100 0 TT mm qTUTU −= ( ) ( ) ( )PNgIfUPPi z P w z P K t P msZ +−      ∂ ∂ −      ∂ ∂ = ∂ ∂ 2 2 ( ) ( ) ( )PNgIfUPPi z P K t N mZ −+      ∂ ∂ = ∂ ∂ 2 2 0=      ∂ ∂ −= ∂ ∂ z P KPw z N Zs , at the surface Response-to- irradiance, f(I) Terms Remarks Source 1. f(I)=I/I0 Linear; Edwards et al. (2000), Not dependent on Franks (2002), surface irradiance Hodges & Rudnick (2004) 2. f(I)=I/(I0+I) Saturating Franks (2002) 3. f(I)=1-exp(-I/ I0) Saturating; Franks (2002) When photo-inhibition is insignificant 4. f(I)=tanh(I/ I0) Saturating Franks (2002) 5. f(I)= (I/Io)(exp(1-I/ I0) Saturating; Franks (2002), When photoinhibition Steele (1962) is significant 6. f(I)=I/(kI+I) kI=irradiance Michaelis-Menten form; Varela et al. (1992), half-satn constant For multiple nutrients Zakardjian & Prieur (1994), & phytoplankton models Gecek & Legovic (2001), Bahamon & Cruzado (2003) 7. f(I)=qchl(αI-rB) α=slope of photo- Hadfield & Sharples (1996), synthesis-irradiance Sharples (1999) curve; qchl=chlorophyll: biomass ratio; rB=respiration Table 1. List of functional forms for phytoplankton response-to-irradiance Primavera, McGlone and Villanoy 46 0.0 0.2 0.4 0.6 0.8 1.0 response to irradiance 0 50 100 150 200 de pt h (m ) form 1 form 2 form 3 form 4 form 5 form 6 Figure 1. Phytoplankton profiles when nutrient uptake rate is constant (identical with profiles when nutrient uptake rate is variable). Table 2. List of functional forms for nutrient uptake and phytoplankton loss Nutrient uptake, g(N) Terms Remarks Source 1. g(N)=N N=nutrient concentration Edwards et al. (2000), Hodges & Rudnick (2004) 2. g(N)=N/(ks+N) ks=nutrient uptake Michaelis-Menten uptake Varela et al. (1992), Zakardjian half-saturation constant & Prieur (1994), Gecek & Legovic (2001), Bahamon & Cruzado (2003) 3. g(N)=1-(kQ/Q) Q=N/chl=internal Droop's internal cell Hadfield & Sharples (1996), nutrient pool; quota model Sharples (1999), Franks (2002) kQ=minimum Q required by cell Phytoplankton loss, i(P) Terms Remarks Source 1. i(P)=D/P D=loss rate, constant linear Franks (2002) 2. i(P)=D Non-linear; Doney et al. (1996), Edwards et density-dependent al. (2000), Franks (2002), Hodges & Rudnick (2004) Development of a Simple Biological Model 47 The parameter forms in Tables 1 and 2 were tested on the model using the parameter values given in Table 3. Irradiance was calculated using Beer's law, where I is irradiance at depth z, I0 irradiance at the surface, and χ the extinction coefficient. The first phytoplankton response-to-irradiance form in Table 1 is often used in very simple biological models where the magnitude of surface irradiance is not important. Forms # 2 - 4 are forms that have photosynthetically saturating response to irradiance. Form # 5 is also saturating but takes into account possible photo- inhibition by phytoplankton. The Michaelis-Menten response-to-irradiance form is often used in multiple nutrient and variable models. The profiles of these response-to-irradiance forms are shown in Figure 1. The last response-to-irradiance form was not used because it distinguishes phytoplankton chlorophyll and biomass. Only two of the three forms of phytoplankton nutrient uptake in Table 2 were used since there was no empirical data available on internal nutrient pool that is required for the third form. The first form is commonly used in simple coupled models that only have one nutrient variable while the Michaelis-Menten form is often used in more complex models with multiple nutrient variables. The constant phytoplankton loss form (#2) in Table 2 was not used because it does not conform to the closed system suggested by Hodges and Rudnick (2004). Thus the model runs for the study dealt primarily with 1) comparison of the different response-to-irradiance and nutrient uptake forms, 2) use of variable (temperature-dependent) nutrient uptake rate against a constant rate, and 3) application of Liebig's law compared to simultaneous light and nutrient influence in phytoplankton growth. RESULTS AND DISCUSSION The model was run to determine response of phytoplankton to light and nutrients separately, and with simultaneous influence of these two parameters. Different parameter forms of irradiance response and nutrient uptake were examined. Variable and constant nutrient uptake rates were also tested. The resultant phytoplankton profiles when nutrient uptake rate is constant are shown in Figure 2. As discussed below, Figure 2 can also represent phytoplankton profiles resulting from a variable nutrient uptake rate, making the figure representative of phytoplankton profiles for all runs. Comparison of parameter forms Response to irradiance Phytoplankton profiles using the different response to irradiance forms are differentiated among the columns in Figure 2. Model runs using the first four forms gave identical phytoplankton profiles (rows 1 - 4, Figure 1) even though response to irradiance profiles were different close to the surface (lines with solid blocks, Figure 1). The response to irradiance profiles converged at lower depths and could be the reason for the identical phytoplankton profiles. Profiles using response-to- irradiance forms # 5 and 6 have significantly slower light extinction rates thereby allowing for deeper light penetration (Figure 1) and thus the deeper DCM (rows 5 and 6, Figure 2). Nutrient uptake There is no significant difference in the phytoplankton profiles from the two nutrient uptake forms using Liebig's law (columns 3 and 4, Figure 2). In contrast, the DCM is bigger, deeper and more defined with the Michaelis-Menten nutrient uptake form when there is simultaneous nutrient and light influence on nutrient uptake (columns 1 and 2, Figure 2). Since nutrient concentration tends to be low (<1µM nitrogen) due to model constraints and the half saturation constant ks is small (0.05), nutrient uptake will increase when the Michaelis-Menten form is used. With the forms using Liebig's law, nutrient uptake increase occurs where light is limiting (below intersection of light factor and nutrient factor in Figure 3). Since the light factor (smaller than the nutrient factor) determines nutrient uptake in this region the increase in nutrient uptake is unable to influence the phytoplankton profile. When there is simultaneous influence of light and nutrients, the increase in nutrient uptake would result in a bigger, deeper and more defined DCM (columns 1 and 2, Figure 2). ( )zeII χ−= 0 Primavera, McGlone and Villanoy 48 0 1 nitrogen units (µM) 0 100 200 de pt h (m ) 0 100 200 de pt h (m ) 0 100 200 de pt h (m ) 0 100 200 de pt h (m ) 0 100 200 de pt h (m ) 0 100 200 de ot h (m ) 0 1 nitrogen units (µM) 0 1 nitrogen units (µM) 0 1 nitrogen units (µM) Simple nutrient uptake form Michaelis-Menten nutrient uptake form Nutrient and light influence Nutrient or light influence (Liebig's Law) re sp on se to ir ra di an ce fo rm 1 re sp on se to ir ra di an ce fo rm 2 re sp on se to ir ra di an ce fo rm 3 re sp on se to ir ra di an ce fo rm 4 re sp on se to ir ra di an ce fo rm 5 re sp on se to ir ra di an ce fo rm 6 Simple nutrient uptake form Michaelis-Menten nutrient uptake form Figure 2. Response-to-irradiance profiles. Development of a Simple Biological Model 49 Variable and constant nutrient uptake rate The phytoplankton profile resulting from use of a temperature-dependent nutrient uptake rate did not differ significantly from the profile resulting from the use of a constant nutrient uptake rate. Although nutrient uptake rate is higher at higher temperature especially for the upper 100 m of the water column, there was no significant change in the DCM. This indicates that temperature variation does not affect phytoplankton growth based on the biological model and the nutrient uptake rate formula of Eppley (1972). Parsons et al. (1984) stated that photosynthesis of phytoplankton in tropical/sub-tropical communities is more likely to be limited by nutrients rather than temperature. Valiela (1984) also suggests that temperature is not a primary limiting factor in primary production in the sea and may have an effect only under certain situations. Nutrient uptake based on Liebig's law and simultaneous nutrient-light influence The use of Liebig's law in phytoplankton nutrient uptake consistently gave bigger, deeper and more defined DCMs (columns 3 and 4, Figure 2) compared to using light and nutrient influence simultaneously (columns 1 and 2, Figure 2). This may be so because with Liebig's law nutrient available for uptake is situated deeper in the water column (Figure 4) and just below the nutricline nutrient availability is bigger, which could account for the bigger and deeper DCM. CONCLUSION The light extinction rate inversely affects the depth of the DCM and is more important than the form of phytoplankton response-to-irradiance. Compared to the 0 7 14 21 0 40 80 120 160 200 de pt h (m ) light factor nutrient factor (M-M) nutrient factor (simple) Figure 3. Nutrient and light factors when Liebig's law determines phytoplankton nutrient uptake. Primavera, McGlone and Villanoy 50 0 7 14 21 0 40 80 120 160 200 de pt h (m ) light factor nutrient factor (w/o Liebig's law) nutrient factor (w/ Liebig's law) Figure 4. Nutrient and light factors when light and nutrient factors simultaneously influence phytoplankton nutrient uptake. Parameter Symbol Value Unit Surface irradiance Io 100 µEm-2s-1 Irradiance half-saturation constant kS 12 µEm -2s-1 Light extinction coefficient c 0.05 m-1 Eddy diffusion coefficient KZ 1 x 10 -4 m2s-1 Maximum nutrient uptake rate Um 20 d -1 Sinking velocity ws 0.5 d -1 Phytoplankton loss rate D 0.1 d-1 Maximum uptake rate at reference temperature (20ºC) Um(20) 20 d -1 Uptake rate change factor q10 1.884 no units Table 3. Parameter constants used in all runs Development of a Simple Biological Model 51 simple nutrient uptake form the Michaelis-Menten form gives a bigger DCM depth and magnitude but only when there is simultaneous nutrient and light influence. Nutrient uptake rate does not seem to be temperature- dependent and might be due to temperature being less of a limiting factor in primary production especially in the tropics. The use of Liebig's law in phytoplankton nutrient uptake situates nutrients available for uptake deeper and results to deeper and bigger DCMs. These findings will be most useful when the study will try to duplicate unique chlorophyll profiles among the different basins in Philippine waters as reported by Cordero et al. (unpublished report). Rate of light extinction and application of Liebig's law will be considered in differences in DCM depth while the Michaelis-Menten nutrient uptake form and Liebig's law may be useful when there are differences in DCM magnitude. However, the need to increase the complexity of the biological model to include other nutrients, phytoplankton and zooplankton variables could arise. In which case the parameter forms used should be specific to such models (e.g. Greek and Legovic, 2001) and phytoplankton growth will follow Liebig's law, since this is typical of multiple-variable models (Varela et al., 1992; Zakardjian & Prieur, 1994; Gecek and Legovic, 2001; Bahamon & Cruzado, 2003). Future work will be to find and develop a suitable physical model to couple with these biological models that will properly take into account the influence of hydrodynamics on the profiles of the variables studied. ACKNOWLEDGMENTS This study is partly funded by the thesis grant from the Office of the Vice-Chancellor for Research and Development. REFERENCES Akbulut, A., 2003. The relationship between phytoplanktonic organisms and chlorophyll a in Sultan Sazligi. Turk. J. Bot. 27: 421-425. Bahamon, N. & A. Cruzado, 2003. Modelling nitrogen fluxes in oligotrophic environments: NW Mediterranean and NE Atlantic. Ecological Modelling 163: 223-244. Cloern, J.E. & R. Dufford, 2005. Phytoplankton community ecology: principles applied in San Francisco Bay. Mar. Ecol. Prog. Ser. 285: 11-28. Cordero, K. S. A., C. L. Villanoy, & L. T. David. Comparison of chlorophyll distribution in the water basins around the Philippines. (unpublished report) Doney, S. C., D. M. Glover, & R. G. Najjar, 1996. A new coupled, one-dimensional biological-physical model for the upper ocean: Application to the JGOFS Bermuda Atlantic Time-series Study (BATS) site. Deep-Sea Research II 43(2- 3): 591-624. Engelsen, O., H. Hop, E.N., Hegseth, E. Hansen, & S. Falk- Petersen, 2004. Deriving phytoplankton biomass in the Marginal Ice Zone from satellite observable parameters. Int. J. Remote Sensing 25(7-8): 1453-1457. Eppley, R. W. 1972. Temperature and phytoplankton growth in the sea. Fishery Bulletin 17: 15-24. Fennel, K. & E. Boss, 2003. Subsurface maxima of phytoplankton and chlorophyll: Steady-state solutions from a simple model. Limnol. Oceanogr. 48(4): 1521-1534. Falkowski, P.G., 1997. Evolution of the nitrogen cycle and its influence on the biological sequestration of CO2 in the ocean. Nature 387:272-275. Franks, J., S., 2002. NPZ models of plankton dynamics: Their construction, coupling to physics, and application. Journal of Oceanography 58: 379-387. Franks, J. S., J. S. Wroblewski, & G. R. Flier, 1986. Behavior of a simple plankton model with food-level acclimation by herbivores. Marine Biology 91: 121-129. Gecek, S. & T. Legovic, 2001. Nutrients and grazing in modelling the deep chlorophyll maximum. Ecological Modelling 138: 143-152. Primavera, McGlone and Villanoy 52 Hadfield, M., J. & J. Sharples, 1996. Modelling mixed layer depth and plankton biomass off the west coast of South Island, New Zealand. Journal of Marine Systems 8: 1-29. Hodges B. A. & D. L. Rudnick, 2004. Simple models of steady deep maxima in chlorophyll and biomass. Deep-Sea Research I 51: 999-1015. Mann, K.H. & J.R.N. Lazier. 1996. Dynamics of marine ecosystems: Biological-Physical interactions in the oceans 2nd Edition. Massachusetts, Blackwell Science Inc.: 394 pp. Parsons, T.R. & J.D.H. Strickland, 1963. Discussion of spectrophotometric determination of marine plant pigments, with revised equations for ascertaining chlorophylls and carotenoids. J. Mar. Res. 21: 155-163. Sharples, J., 1999. Investigating the seasonal vertical structure of phytoplankton in shelf areas. Marine Models 1: 3-38. Steele, J.H., 1962. Environmental control of photosynthesis in the sea. Limnol. Oceanogr. 7: 137-150. Stumm, W. & J. J. Morgan, 1981. Aquatic Chemistry An Introduction Emphasizing Chemical Equilibria in Natural Waters 2nd Edition. New York, John Wiles & Sons: 780pp. Valiela, I. 1984. Marine ecological processes. New York, Springer-Verlag Inc.: 546 pp. Varela, R. A., A. Cruzado, J. Tintore, & E. G. Ladona, 1992. Modelling the deep-chlorophyll maximum: A coupled physical-biological approach. J. Mar. Res. 50: 441-463. Zakardjian, B. & L. Prieur, 1994. A numerical study of primary production related to vertical turbulent diffusion with special reference to vertical motions of the phytoplankton cells in nutrient and light fields. Journal of Marine Systems 5: 267-295.