Modelling the photosynthetic efficiency for Ulva rigida growth

Ecological Modelling, 67 (1993) 221-232 Elsevier Science Publishers B.V., Amsterdam

221

Modelling the photosynthetic efficiency for Ulva rigida growth G. Bendoricchio, G. Coffaro and M. Di Luzio Universitt~ di Padova, Facoltt~di lngegneria, Istituto di Chimica, Padoua, Italy (Received 2 March 1992; accepted 5 August 1992)

ABSTRACt Bendoricchio, G., Coffaro, G. and Di Luzio, M., 1993. Modelling the photosynthetic efficiency for Ulva rigida growth. Ecol. Modelling, 67: 221-232. The performance of Eilers' model, in a modified version, was analysed with reference to the photosynthetic efficiency of the seaweed UIL'a rigida growing in the Lagoon of Venice. The Eilers' formulation for the photosynthetic productivity, coupled with two functions presented in this application, represents a complete model calibrated on Ul~'a rigida, which for a given temperature and light intensity can give a reliable description of the photosynthetic behaviour of this seaweed. Further improvement is discussed, which includes the compensation point for light intensity in the model.

INTRODUCTION Ecosystem models simulate the system response to both natural and m a n - m a d e modifications. T h e y have b e e n applied as planning tools to abate pollution and to reduce the eutrophication of some water bodies (J0rgensen et al., 1973; C h e n and Orlob, 1975; J0rgensen, 1976; Straskraba, 1985; Riley and Stefan, 1988). Today, mathematical modelling is being used beyond the domain of pure research and is being applied m o r e and m o r e in ecological and environmental m a n a g e m e n t . Ecological models must be tailored to the particular aspects of the ecosystem u n d e r study. A small n u m b e r of variables and p a r a m e t e r s are n e e d e d to describe the most important mechanisms of the system. Models, by linking submodels of specific processes in a general Correspondence to: G. Bendoricchio, Universit~ di Padova, Facolt~t di Ingegneria, Istituto di Chimica, Industriale Via Marzolo 9, 35131 Padova, Italy.

Elsevier Science Publishers B.V.

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framework, should adapt themselves to the complex structure of ecosystems. Photosynthetic efficiency is one of the most important processes, its submodel always being present in the framework of a trophic model (Swartzman and Bentley, 1979). The influence of light intensity on the production and respiration of algae is the object of extensive research on processes. Unfortunately, only few of them concern the macroalgae and particularly the Ulva species which is the focus of the research carried out in the Lagoon of Venice. The traditional approach to photosynthetic efficiency models proposed for phytoplankton by Smith (1936), Steele (1962), Vollenweider (1965), Platt et al. (1980) and a more recent and complete one by Eilers and Peeters (1988), is considered and included in this paper. It focuses on the photosynthetic efficiency for Ulva rigida growth and is part of a more general model under development for Ulva rigida blooms in the Lagoon of Venice. CASE STUDY The Lagoon of Venice is a tidal embayment located in the north Adriatic Sea (Fig. 1). This relatively shallow (1 m average) water body has an area of 500 km:. The city of Venice is located on an archipelago of small islands that are located inside the lagoon.

Fig. 1. Spatial distribution of Ulva rigida (shaded areas) in the Lagoon of Venice, observed in April 1990. The dotted areas show the emerged lands. The lagoon is about 50 km long and about 10 km wide.

PHOTOSYNTHETIC

E F F I C I E N C Y FOR ULVA

223

The total surface area of the basin is ca. 1700 km 2, about two thirds of which are being used for agricultural purposes and the remaining portion for urban and residential uses. The watershed is a lowland, flat basin. Several centuries ago, two major rivers that drained into the lagoon were diverted to avoid the silting of the lagoon. Today freshwater flows into the lagoon mainly from small tributaries and drainage channels. Point and nonpoint pollution sources discharge a lot of nutrients in the lagoon, supporting wide and invasive algal blooms of Ulva rigida that reach values of 6-8 kg fresh w e i g h t / m E in June-July (Sfriso et al., 1988; Bernstein, 1991). The thick bed formed by macroalgae limits water circulation and light penetration and consumes nutrients. These factors and higher summer temperature reduce the productivity of the biomass and deplete the oxygen content of the water column. Anoxia occurs during the night, and redox potential of the sediment becomes as low as to induce sulfidric acid release in the water column and even in the air. In such an extreme situation the ecosystem crashes and the whole macroalgal biomass collapses on the bottom. Pollution removal, diversion of polluted waters and harvesting of macroalgae are being carried out to avoid such a critical situation in the Lagoon of Venice. All these activities need atrophic model of the Lagoon of Venice focusing on the macroalgae cycle for simulating the consequences of such dystrophic behaviour. MODEL DESCRIPTION

A model for the macroalgal biomass growth can be written as follows: 0B a-t- = (lZ - A)B

(1)

where: B is the biomass, g dry weight/mE; t~ is the specific growth rate, day-l; and A is the specific loss rate, day -1. The specific growth rate, IZ, can be written as: /z =/.Lopt "f(Ei, E., Et) where: /~opt is the maximum growth rate (day-l), set to 0.4 as in Dion (1988) and Menesguen and Salomon (1988); E i, E , and E t are the efficiencies of the process due to light intensity, nutrients ahd temperature, respectively; f is a function of the previous efficiencies. In particular the photosynthetic efficiency, El, c a n be written as: 1 1 r24 r Z m Ei = 2"-4Z--'~/ / El(h, z) dh dz ~0 ~0

(2)

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G. BENDORICCHIO ET AL.

where: E i is the efficiency due to the photosynthetic activity, E i = P ( I ) / P m ; Z m is the maximum depth; h is the time expressed in hours; z is the depth. Several authors proposed different relations between light intensity and the rate of photosynthesis in phytoplankton. A recent formulation is suggested by Eilers and Peeters (1988). Their model for the photosynthetic productivity P ( I ) is: I e(I)=

a

.12

+b'I+c

(3)

where I is the intensity of incident light. This model describes the photosynthetic processes and those connected with photoinhibition but does not show many differences to the curves proposed by Steele (1962), Vollenweider (1965) and Platt et al. (1980). A clear discrimination is possible only at very high light intensity. Often measurements will not cover a range of intensities large enough to make the distinction clear. However, an important aspect of their results is that the model is quite simple and gives a dynamic description of photosynthesis and photoinhibition. The authors point out that the main advantage of this model for the steady state compared to empirical curves is its foundation on physiological mechanisms. This makes it possible to derive effects of temperature on photosynthetic activity in a mechanistic way. Another improvement is the use of a parametric curve: the description is compact, rate is easily calculated, integration of production in a column of water is analytically performed and the influence of random errors is reduced. A characteristic like maximal production rate (Pro) is easily derived from (3): 1 Pm = (b + 2vra. c )

(4)

RESULTS The experimental data of Arnold and Murray (1980) and Brocca and Felicini (1981) are measurements of the oxygen production for a wide range of light intensities at four different temperatures. They have been fitted by the Marquardt method, with reference to the parameters a, b and c. The results of this fitting are reported in Fig. 2 (left-hand side) and Table 1. The differential equations were numerically solved by a Runge-Kutta 4th order algorithm and the model was implemented in Fortran. As indicated by Eilers and Peeters (1988), the parameter c represents the inverse of the initial slope of the model for photosynthetic oxygen

225

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LIG-ITINTENSITY(L~ ' 1000) LIGHTINTENSITY(lux ' t000) Fig. 2. Comparison between experimental data (Brocca and Felicini, 1981) and fitted curves. Eilers' model on the left (see E q . 3) and Eilers' model shifted by compensation intensity on the right (see E q . 10).

production and therefore it depends on chlorophyll content. If the production is expressed on chlorophyll basis, c should be constant. The parameters a and b account for biophysical and biochemical reactions, but only the biochemical reactions are influenced by temperature (Eilers and Peeters, 1988). From the simple hypothesis of Eilers and Peeters, which assumes the same influence of temperature on biochemical reactions, follows that both characteristics Pm (maximum productivity) and I m (inten-

TABLE 1

Parameter values obtained from calibration of Eilers' model (Eq. 3) with experimental data as shown in Fig. 2 (left-hand side) Temperature

a

b

12°C 17°C 21°C 27"C

6.55 X 10 - 9 5.51 x 10 - 9 4.903 × 1 0 - 9 4.458 x 10 - 9

4.698 X 2.747 x 1.518 x 8.707 x

c 10 - 9 10 - 4 10 - 4 10 -5

3.44 5.3 3.06 3.36

226

G. BENDORICCHIO ET AL.

sity at which maximum productivity is reached) are functions of the same /(T):

lm=f(T)'W, (5) Pm=f(T)'Z, (6) where W and Z are expressions not influenced by temperature. As reported in Eilers and Peeters (1988), both Pm and I m appear in the inverse equations for a and b: 1 1 2 a b (7) =

~

s-,r2

=

em

S'tm

where s does not d e p e n d on temperature. The present model assumes a sigmoid formulation for f ( T ) as suggested by Marsili-Libelli (1990): Kl f ( T ) = 1 + K2" e (-K3"(r-2°)) ' (8) Since Pm and I m are in p a r a m e t e r expression (7), substituting (8) into I m (Eq. 5) and Jam (Eq. 6), it is possible to obtain new expressions for a (Eq. 9) and b (Eq. 10), accounting for their t e m p e r a t u r e d e p e n d e n c e :

a ( r ) = Ka I "(1 + Ka2"e-K""(T-20)) 2,

(9)

b(T) = Kb, "(1 + Kb 2 • e - r b " ( r - 2 ° ) ) .

(10)

The calibrated values for the coefficients were: Ka 1 = 3.77 × 10-9; Ka 2 = 0.156; Ka 3 = 0.088; Kbl = 1.506 x 10-5; /(b~ = 11.237; Kb 3 --0.131.

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10 12 14 16 18 20 22 24 26 28 30

Temperature~ )

Fig. 3. Comparison between the best fitting values of coefficients a and b in Eqs. 3 and 10 at different temperatures and curves (5) and (6) in the paper that link values of a and b to the temperature in Eilers' model (left-hand side) and Eilers' model shifted by Ic (right-hand side).

PHOTOSYNTHETIC

EFFICIENCY

227

ULVA

FOR

Figure 3 (left-hand side) shows the calculated and the experimental data and the good fitting of the functions. As shown in Table 1, the fitted value of c for the set of experimental data at 17°C is quite anomalous and probably determined more by a wrong experimental measurement than by the peculiar physiological behaviour of Ulva rigida. The values of the functions for the parameters a and b can be fully computed using the given temperature• Thus Eqs. (3), (9) and (10) completely describe the Ulva rigida photosynthetic oxygen production as a function of light intensity and temperature, particularly when high light intensity can constrain the production by photoinhibition effect. DISCUSSION A comparison of Eq. (3) with the classical Steele's (1962) formulation for photosynthetic efficiency was carried out using the same data. To obtain an efficiency term from the P(I) function (3), the latter should be divided by the related Pm value resulting from (4): I

Ei(h,z)--(b+2"vcd'c) • a.i2+b.i+c

(11)

where: (b + 2" ~/'~"c ) is the inverse of the maximum productivity (Pro); I is the hourly incident light intensity. The data for temperature and Ulva rigida biomass reported in Sfriso (1988) were used in this application. A daily light energy model (Fig. 4), based on the representative data reported by Ente Zona Industriale Porto

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Fig. 4. Daily energy distribution (solid line) simulated by fitting experimentaldata (points) recorded during 1988 in the Lagoon of Venice (Ente Zona Industriale Porto Marghera, 1988).

228

O. B E N D O R I C C H I O ET AL. 04.

Steele

low biomass

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Fig. 5. Comparison of the photosynthetic efficiencyreported by Steele's model (solid line), Eilers' model (dashed line) and Eilers' model shifted by Ic proposed in the paper (bold line). The figure shows the differences between the classical models for photosynthetic efficiencyand the proposed formulation which includes the respiration activityvaryingwith the photosynthetic activity. Marghera (1987-88) and distributed over the photoperiod, was used to compute the incident light intensity. The hourly light extinction in the water column was computed with Lambert-Beer relation: I ( h , z ) = I o ( h ) . e -kz

(12)

where: Io(h) is the hourly distribution of the incident light. The constant k in the above formulation can be written as: k = kw + kb

(13)

where: kw assumes the value 1.7/Ds, with D s - - 2 . 3 (Secchi Disc depth), accounting for the water turbidity; kb assumes the value 0.014 B ( B - biomass) computed by calibration, accounting for the biomass extinction. The results of the computed efficiencies, using the Steele's and the modified Eilers' model, are shown in Fig. 5. The two different equations have similar behaviour except at low biomass values (B < 200 g dw/m2), where Steele's equation overestimates the photoinhibition effect and decreases sharply compared to either modified Eilers' formulation and to data measured. Since both photochemical and enzymatic processes are influenced by high light intensity, the effects of photoinhibition on photosynthesis performance should display the interaction between light and temperature. The model (3) and the functions (9) and (10) link light and temperature effects to photoproduction, providing a better description of the condition of

229

P H O T O S Y N T H E T I C EFFICIENCY FOR UL VA

photoinhibition. Thus the present modified version of Eilers' model is much more reliable to model Ulca sp. photoproduction. Generally photosynthesis models refer to gross oxygen production while the suitable oxygen measure in the photosynthetic tests often does not account for the respiration quote. Respiration is a significant contribution to death rate: it increases with temperature and depends upon the rates of basal and growth respiration. To avoid the use of an approximate respiration rate, included in the )t term of Eq. (1), Eilers' model was modified to represent the behaviour of the algae that adjust their respiration rate with the variations of their photosynthetic rate. The proposed equation is the Eilers' model shifted by Ic (the light compensation point, which increases with temperature):

(i-ic) P(1) =

a'(I-Ic)Z

+b.(I-Ic)

(14)

+c

Ic was estimated by fitting the temperature dependence of basal respira-

tion, measured as oxygen consumption at 0 light intensity, with Eq. 15 (see Fig. 6): Ko R ° ( T ) = 1 + K l • e (-g2"(r-21))

(15)

with K 0 = 298.17; K~ = 0.0627; K 2 = 0.231; and assuming a linear relationship between Ic and basal respiration rate R0: (16)

lc( Ro) = m R o + v

with m - - 3 . 6 4 and u = -312.7.

350 ^

300-

~ ~ 200150100 10 12 14 16 18 20 22 24

26

28

30

Tem0eratufe(*C) Fig. 6. Comparison between experimental data of basal respiration (Brocca and Felicini, 1981) and curve computed with Eq. 11, which accounts for temperature effect on dark respiration.

230

G. BENDORICCHIO ET AL.

TABLE 2 Parameter values obtained from calibration of Eilers' model shifted by Ic (Eq. 10). Ic values are computed using Eqs. 11 and 12 Temperature 12°C 17°C 21°C 27°C

a

b

"

5.751 X 10 -9 4.9 X 10 - 9 4.4 × 10-9 4.018 x 10-9

5.404 x 10-4 3.138 X 10 - 4 2.013 × 10-4 1.33 × 10-4

c

Ic

2.62 4.32 2.31 2.6

408.8 624.2 708.5 755.8

This assumption is supported by the theoretical and experimental observations concerning the constancy of c, which is the inverse of the" initial slope in the model (3). This parameter represents the photosynthetic capacity of the algae when the photosynthetic activity is expressed per unit of chlorophyll and the production is light-limited. Therefore, the data of Brocca and Felicini (1981) were fitted again by model (14) (see right-hand side of Fig. 2) and the values of the parameters a, b and c, computed with the modified version of Eilers' model, are shown in Table 2. It should be observed that the basal respiration rate is the intercept with the Y-axis, while the I c point is the intercept with the X-axis. The coefficients used in (9) and (10) (see right-hand side of Fig. 3) become: Ka~ = 3.414 x 10 -9, K a 2 = 0.1512, K a 3 = 0.0849 and Kb 1 = 6.81 × 10 - 5 , g b 2 = 2.34, Kb 3 = 0.13. Models (3) and (14) can be compared, computing the daily photosynthetic efficiencies in the water column (gross and net efficiencies). As expected the two models behave differently, particularly when the standing crop is high and consequently respiration is high. Particularly, Fig. 5 shows the reduction of springtime photosynthetic production when the highly stratified biomass in the water column induces a self-shading effect that could cause a negative balance of the oxygen production in the thick bed of macroalgae. For an overall balance of the dissolved oxygen in the water the reareation effect and the depletion due to the degradation of organic matter should be considered. Anyhow, the high standing crop for algae and their sometimes negative contribution to the oxygen concentration are the main causes of the periodic anoxic crises that occur in the shallow water of the Venice Lagoon. CONCLUSIONS The Eilers' model (14) coupled with the proposed relationships (9) and (10) represents a complete model, calibrated on U l v a rigida, which, for a given temperature and light intensity, gives a much more reliable descrip-

PHOTOSYNTHETIC EFFICIENCY FOR ULVA

231

tion of the photosynthetic performance of this seaweed than previous models. This is particularly true at low light intensities (under the self-shading conditions), when the results of (14) may be negative due to respiration, and at high intensities, when photoinhibition arises. Equation (14) includes the respiration that varies proportional to the photosynthetic activity (growth respiration) and avoids the use of an approximate rate of respiration included in the A term of Eq. (1). F u r t h e r investigations are required to link chlorophyll content to the light availability ( R a m u s et al., 1976; Lapointe and Tenore, 1981; Rosenberg and Ramus, 1982) in the thick bed often formed by Ulva rigida in the L a g o o n of Venice, in order to provide a dynamic description of the algae adaptation to the environmental variations. REFERENCES Arnold, K.E. and Murray, S.N., 1980. Relationships between irradiance and photosynthesis for marine benthic green algae (Chlorophyte) of differing morfologies. J. Exp. Mar. Biol. Ecol., 43: 183-192. Bernstein, A.G., 1991. Controllo del degrado ambientale della laguna di Venezia e raccolta selettiva delle macroalghe. Communications at Oltre l'Emergenza Alghe: Considerazioni Scientifiche e Possibilit~ di Intervento, Urbino, 21-22 February 1991. Brocca, M. and Felicini, G.P., 1981. Autoecologia di Ulva rigida 1. Influenza dell'intensitfi luminosa e della temperatura sulla produzione di ossigeno. Giorn. Bot. Ital., 115: 285-290. Chen, C.W. and Orlob, G.T., 1975. Ecologic simulation of aquatic environments. In: B.C. Patten (Editor), Systems Analysis and Simulation in Ecology. Academic Press, New York, NY, pp. 475-588. Dion, P., 1988. Etude prelimiaire a la dephosphation en Baie de St Brieuc. Rapport CEVA/Pleubian pour ie Conseil General des C6tes du Nord, 14 pp. Eilers, P.H.C. and Peeters, J.C.H., 1988. A model for the relationship between light intensity and the rate of photosynthesis in phytoplankton. Ecol. Modelling, 42: 199-215. Ente Zona Industriale, Porto Marghera, Venezia, 1988. Personal communication. J~argensen, S.E., 1976. A eutrophication model for a lake. Ecol. Modelling, 2: 147-165. Jorgensen, S.E., Jacobsen, O.S. and Hoi, I., 1973. A prognosis for a lake. Vatten, 29: 382-404. Lapointe, B.E. and Tenore, K.R., 1981. Experimental outdoor studies with Ulca fasciata Delile. I. Interaction of light and nitrogen on nutrient uptake, growth and biochemical composition. J. Exp. Mar. Biol. Ecol., 53: 135-152. Marsili-Libelli, S., 1990. Modelli Matematici in Ecologia. Pitagora, Italy, 457 pp. Menesguen, A. and Salomon, J.C., 1988. Eutrophication modelling as a tool for fighting against Ulva coastal mass blooms. In: B.A. Schrefler and O.C. Zienkiewicz (Editors), Computer Modeling in Ocean Engineering. Balkema, Rotterdam, pp. 443-450. Platt, T., Gallegos, C.L. and Harrison, W.G., 1980. Photoinhibition and photosynthesis in natural assemblages of marine phytoplankton. J. Mar. Res., 38: 687-701. Ramus, J., Beale, S.I. and Mauzerall, D., 1976. Correlation of changes in pigment content with the photosyntetic capacity of seaweeds as a function of water depth. Mar. Biol., 37: 231-238.

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Riley, M.J. and Stefan, H.G., 1988. MINLAKE: A dynamic lake water quality simulating model. Ecol. Modelling, 43: 155-182. Rosenberg, G. and Ramus, J., 1982. Ecological growth strategies in the seaweeds Gracilaria foliifera and Ulva sp.: photosynthesis and antenna composition. Mar. Ecol. Prog. Ser., 8: 233-241. Sfriso, A., Pavoni, B., Marcomini, A. and Orio, A.A., 1988. Annual Variations of nutrients in the Lagoon of Venice. Mar. Pollut. Bull., 19 (2): 54-60. Smith, E.L., 1936. Photosynthesis in relation to light and carbon dioxide. Proc. Natl. Acad. Sci. USA, 22: 504-511. Steele, J.H., 1962. Environmental control of photosynthesis in the sea. Limnol. Oceanogr., 7: 137-150. Straskraba M., 1985. Quantitative measurement of eutrophication in standing waters. In: M. Straskraba and A.H. Gnauck (Editors), Freshwater Ecosystems: Modelling and Simulation. Developments in Environmental Modelling, Vol. 8. Elsevier, Amsterdam, pp. 203-224. Swartzman, G.L. and Bentley, R., 1979. A review and comparison of plankton simulation models. ISEM J., 1: 31-82. Vollenweider, R.A., 1965. Calculation models of photosynthesis-depth curves and some implications regarding daily rate estimates in primary production measurements. Mem. Ist. Ital. Idrobiol., 18 (Suppl.): 425-457.