A new general dynamic model to predict biomass and production of bacterioplankton in lakes

Ecological Modelling 160 (2003) 91 /114 www.elsevier.com/locate/ecolmodel

A new general dynamic model to predict biomass and production of bacterioplankton in lakes Viktor V. Boulion a, Lars Ha˚kanson b,
a

b

Zoological Institute of RAS, Universitskaja emb. 1, St. Petersburg 199034, Russia Department of Earth Sciences, Uppsala University, Villav. 16, Norbyv. 18B, Uppsala 75236, Sweden Received 13 February 2002; received in revised form 19 June 2002; accepted 2 October 2002

Abstract The main aim of this work is to present a new dynamic model to predict bacterioplankton production and biomass. This model has been developed as a submodel within the framework of a more comprehensive lake ecosystem model, LakeWeb, which is based on nine key functional groups of organisms. Beside bacterioplankton, LakeWeb accounts for phytoplankton, two types of zooplankton (herbivorous and predatory), two types of fish (prey and predatory), as well as zoobenthos, macrophytes and benthic algae. The model uses ordinary differential equations and gives seasonal (weekly) variations and accounts in a general way for all major abiotic/biotic interactions and feedbacks for entire lakes (the ecosystem approach). The new dynamic model has not been calibrated and tested in the traditional way using data from one or a few well-investigated lakes. Instead, it has been calibrated using empirical regressions based on data from many lakes. We have presented empirical reference models utilising data from a new database, which includes many lakes situated in the former Soviet Union. They were investigated during the Soviet period and those results have been largely unknown in the West. The basic aim of the dynamic model is that it should capture typical functional and structural patterns in many lakes. We have given algorithms for (1) bacterioplankton production, (2) elimination (related to the turnover time of bacterioplankton), (3) bacterioplankton consumption by herbivorous zooplankton, and the factors influencing these processes/rates. We have demonstrated that the new dynamic model gives predictions that agree well with the values given by the empirical reference models, and also expected and requested divergences from these regressions when they do not provide sufficient resolution. The new dynamic model is driven by data easily accessed from standard monitoring programs or maps and meant to be of practical use in lake management. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Lakes; Models; Bacterioplankton; Biomass; Production; Suspended particulate matter; Environmental factors

1. Introduction, background and aim


Corresponding author. Tel.: /46-18471-3897; fax: /4618471-2737 E-mail address: [email protected] (L. Ha˚kanson).

Many studies have shown that there exists a direct dependence between the biomass and/or growth of bacteria on the biomass and/or production of phytoplankton (Guseva, 1952; Kuznetsov,

0304-3800/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 0 0 ( 0 2 ) 0 0 3 2 6 - 5

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1952, 1970; Sorokin, 1964; Romanenko, 1965; Overbeck, 1972; Fursenko and Kuzmitskaja, 1975; Godlewska-Lipowa, 1976; Rai, 1978; Kuzmicheva, 1979; Potaenko, 1979; Aizaki et al., 1981; Bird and Kalff, 1984; Currie, 1990; Boulion, 1994; Boulion and Paveljeva, 1998; Conan et al., 1999). Nevertheless, there are few quantitative dynamic models capturing the most important factors and processes regulating bacterioplankton production and no such models have, as far as we know, yielded good predictive power over a wide limnological domain from just a few readily accessible driving variables. The basic aim of this work is to present such a dynamic model (as a submodel of a more comprehensive lake foodweb model, LakeWeb). The aim of this paper is not, however, to present the whole LakeWeb-model (see Ha˚kanson and Boulion, 2002). The new dynamic model uses ordinary differential equations and gives seasonal (weekly) variations. It is based on fundamental processes and factors regulating production and biomass of bacterioplankton in lakes. A very important demand for this model is that it should be driven by parameters readily available from standard monitoring programs and/or maps. This model only uses data on three standard limnological state variables (see Ha˚kanson and Peters, 1995), total phosphorus, pH, colour; the lake morphometric parameters, mean depth and area; and data on epilimnetic temperatures, which may come from measurements, climatological tables, or from a model (see Ottosson and Abrahamsson, 1998) which use data on latitude, altitude and continentality (distance from the ocean). The accessibility of the driving variables is a prerequisite for practical applicability. We will calibrate and test the dynamic model but not in the traditional way using data from one or a few well-investigated lakes. Instead, we have taken a more comprehensive approach and we will use data from empirical regressions based on data from many lakes as general reference values. This is done to highlight the fact that this dynamic model is meant to capture general structural and functional relationships. If such general relationships are known and quantified, divergences from these patterns attributed to other factors than

those included in the model (e.g. toxic contamination or differences among lakes in species composition) can also be identified and quantified. These empirical reference models concern the following parts of the model: . Bacterioplankton biomass: we will use an already available equation (see Table 1) to predict normal reference values of bacterioplankton biomass, and we will also present a new regression equation based not on total P (as in Table 1) but on chlorophyll data. This new regression is derived from data collected in the former Soviet Union, which have not been presented before in the West, and just like the equation in Table 1, it will give the number of bacterioplankton in million cells per millilitre (NB in million cells/ml). In order to transform this into bacterioplankton biomass in kg ww per week (the calculation unit in the LakeWeb model), one needs information on the relationship between number and biomass of bacterioplankton. We will present a comprehensive data set to address that question. A new empirical equation to calculate biomass of bacterioplankton will also be presented. This means that we will use two empirical reference equations against which the dynamically modelled values of bacterioplankton biomass will be compared. . We will also use results from an experiment using 14C in the forms of mineral (bicarbonate) and organic substrates in a differential filtration set-up. This experiment was carried out to get information on the relationship between bacterioplankton and phytoplankton production. The results will be used in the calibration of the dynamic model to control that it does not produce unrealistic relationships between the two groups. It should be stressed that these empirical regressions capture characteristic patterns in many lakes. However, they are basically static and do not provide any seasonal patterns; only characteristic mean y -values based on the x variables used in the regressions. We have, however, in some cases included feedbacks also in the regressions to

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Table 1 Regressions to predict bacterioplankton y -Value

Equation

Range for x r2

Bacterioplankton (ColB/50) /0.90TP0.66 3 /100 Bacterioplankton (Col]/50) /(1/0.25(Col/50/1))0.90TP0.66

obtain more realistic reference values for the model calibrations. This is generally done by using the Secchi depth (/the effective depth of the photic zone, which is closely related to the amount of suspended particulate matter (SPM), seston, in lakes), which is influenced by modelled values of the autochthonous production. Also note that the following calibrations target on comparisons between values for the growing season since most of the empirical regressions are based on data from this period. This means that divergences between modelled values and data from the empirical regressions for other seasons of the year are of less interest. The dynamic model is, however, meant to provide the best possible estimates of bacterioplankton biomass and production for all seasons of the year. It is evident that the conditions during the growing season are generally more important for lake foodweb characteristics than the conditions during the rest of the year. The parts of the LakeWeb model presented here are meant to give more information than the empirical models used for the model calibrations. Divergences between the modelled values and the data given by the empirical regressions should be logical and supported by solid limnological theory.

2. Regressions used for model calibrations 2.1. Primary production versus number of bacteria The direct connection between phytoplankton and bacterioplankton biomasses has been observed in, e.g. reservoirs in the former USSR (Guseva, 1952), Lake Plussee (Overbeck, 1972) and Central American lakes (Rai, 1978). In the following, we will give a compilation of some regression models expressing the relationship between chlorophyll (Chl in mg/l) and number of

n

Units

Reference

0.83 12 million/ml Peters (1986) Ha˚kanson and Boulion (2002)

bacteria (NB in million cells/ml) and we will also, as already stressed, introduce a rather comprehensive data set (from Boulion and Paveljeva, 1998). The basic aim of this compilation of data, and the following regressions, is to establish typical, general patterns for the relationship between phytoplankton biomass (Chl) and number of bacterioplankton (NB). The data are given in Table 2. This database includes 163 samples from lakes covering a wide range of limnological characteristics. The samples from two small lakes of the Luga area, St. Petersburg region, were taken during three growing seasons from 1986 to 1988. Lake Big Okunenok was used for breeding of carp. Lake Little Okunenok was practically without fish. From 1963 to 1982, mineral fertilisers and lime were added to both lakes. The lakes were eutrophic with obvious signs of hypertrophy. The Secchi depths varied from 0.6 to 1.1 m, and pH from 6.1 to 7.4. Both lakes have soft water. The six lakes of Southern Karelia (Elisenvara area) were sampled during the growing seasons of 1989/1993. Three lakes had quick water turnover times. They were relatively humic with colour values from 50 to 100 mg Pt/l and Secchi depths between 1.5 and 3.2 m. The pH values were close to neutral. The three other Karelian lakes were acidic (pH 5.2 /5.9) with clear water and colour values of 5/7 mg Pt/l, and Secchi depths between 4 and 7 m. During two trips in June and August 1995, samples were taken from 13 lakes of the Karelian isthmus (Vyborg area). The lakes differ in water colour (from 5 to 300 mg Pt/l), pH (from 4.6 to 8.0), Secchi depth (from 0.5 to 7.5 m) and chlorophyll-a concentration (from 1.2 to 35 mg/l). The chlorophyll samples were collected and analysed in a standard way (using membrane filters with a pore diameter of 1.5 mm). The chlorophyll-a concentrations were determined

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Table 2 Chlorophyll-a concentrations (Chl, mg/l) and total number of bacteria (NB, 106 cells/ml) Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

Region

Lake type

Lake

Date

Karelia

Humic

Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Kostomo-ja¨rvi Chernoe Chernoe Chernoe Chernoe Chernoe Chernoe Mollju-sochnoe Mollju-sochnoe Mollju-sochnoe Mollju-sochnoe Mollju-sochnoe Mollju-sochnoe Shkolnoe Shkolnoe Shkolnoe Shkolnoe Shkolnoe Shkolnoe Shkolnoe Goluboe 1 Goluboe 1 Goluboe 1 Goluboe 1 Goluboe 1 Goluboe 1 Goluboe 1 Goluboe 1 Goluboe 1 Goluboe 1 Goluboe 1 Goluboe 1 Goluboe 2 Goluboe 2 Goluboe 2 Goluboe 2 Goluboe 2

5 July 1993 16 July 1993 24 July 1993 3 August 1993 16 August 1993 25 August 1993 5 September 1993 16 September 1994 22 August 1994 12 September 1994 1 July 1994 23 June 1995 16 July 1995 4 August 1995 22 August 1995 21 September 1995 22 June 1993 18 July 1993 23 August 1993 17 June 1994 15 July 1994 13 September 1994 24 June 1993 19 July 1993 24 August 1993 17 June 1994 15 July 1994 13 September 1994 24 June 1993 19 July 1993 24 August 1993 16 June 1994 15 July 1994 24 August 1994 13 September 1994 22 June 1993 18 July 1993 23 August 1993 19 June 1994 13 July 1994 15 September 1994 2 June 1995 22 June 1995 17 July 1995 3 August 1995 19 August 1995 21 September 1995 2 July 1995 22 June 1995 17 July 1995 3 August 1995 19 August 1995

Clear-acidic

Chl 14.0 49.0 12.4 12.0 9.3 16.0 12.5 14.0 10.0 8.2 1.4 1.4 2.5 11.0 15.6 9.0 9.4 30.0 51.0 15.0 37.0 6.1 0.9 10.0 31.0 29.0 2.6 14.0 0.9 2.4 2.3 0.6 0.6 0.5 1.2 0.4 1.2 1.4 1.0 0.7 1.4 0.6 1.8 0.5 0.6 1.8 0.8 0.5 0.4 0.4 0.3 0.8

NB 1.20 1.50 2.00 2.75 3.30 3.00 1.70 2.40 2.40 1.75 2.35 1.85 2.25 5.60 3.90 2.60 1.95 4.20 3.45 3.20 4.95 2.40 1.85 3.60 3.00 6.60 6.20 3.55 1.45 1.15 1.00 1.15 3.00 3.10 3.20 1.35 1.45 0.70 1.42 0.67 1.70 1.05 1.25 1.25 1.10 0.88 1.75 0.86 1.15 2.15 1.20 0.92

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Table 2 (Continued ) Number 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 98 99 100 101 102 103 104 105

Region

Lake type

Leningrad

Fertilised fish nursery

Without fish

Lake

Date

Chl

Goluboe 2 Big Okunenok

21 September 1995 13 May 1990

0.7 202

Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Big Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok

27 June 1990 4 August 1990 14 August 1990 24 August 1990 16 September 1990 3 October 1990 2 November 1990 28 October 1990 21 May 1991 6 June 1991 11 June 1991 16 June 1991 2 July 1991 7 July 1991 12 July 1991 17 July 1991 29 July 1991 4 August 1991 10 August 1991 17 August 1991 23 August 1991 5 September 1991 23 September 1991 14 October 1991 28 October 1991 4 June 1992 9 June 1992 14 June 1992 19 June 1992 24 June 1992 29 June 1992 4 July 1992 9 July 1992 14 July 1992 10 August 1992 15 August 1992 20 August 1992 25 August 1992 31 August 1992 25 September 1992 5 September 1992 2 October 1992 27 June 1990 4 August 1990 14 August 1990 24 August 1990 16 September 1990 3 October 1990 2 November 1990 28 November 1990

60 99 64 141 123 94 119 102 52 47 24 18 31 20 21 48 46 32 26 15 15 34 23 23 21 3 5.6 7.4 11.4 16.5 20 27 19 17 30 27 36 35 38 52 83 41 112 33 66 25 21 14 57 26

NB 1.55 4.8 8.8 14.8 6.9 14 10.5 11.4 6.4 5.3 4.5 3.8 4.1 4.3 6.1 7.1 8.5 6.5 4.1 5.3 2.8 5.9 4.4 4.9 5 3.4 6 4.1 3.8 2.5 3 7 4.5 5.1 3.5 1.9 7.9 4.7 8.5 7.9 5.8 7.6 5 2.5 4.7 4.7 6 1.8 2.9 2.5 5 4.1

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96 Table 2 (Continued ) Number 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157

Region

Lake type

Karelian Isthmus (variables conditions Col/colour in mg Pt/l)

Clear if ColB/50 Humic if Col/100

Col/320 Col/150 Col/150 Col/110 Col/110 Col/28 Col/28 Col/215 Col/215 Col/80 Col/80 Col/8 Col/8 Col/17 Col/17 Col/16 Col/16 Col/34 Col/34

Lake

Date

Chl

Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Okunenok Lake N 1

21 May 1991 6 June 1991 11 June 1991 16 June 1991 2 July 1991 7 July 1991 12 July 1991 17 July 1991 29 July 1991 4 August 1991 10 August 1991 17 August 1991 23 August 1991 5 September 1991 23 September 1991 14 October 1991 28 October 1991 4 June 1992 9 June 1992 14 June 1992 24 June 1992 29 June 1992 9 July 1992 14 July 1992 10 August 1992 15 August 1992 20 August 1992 25 August 1992 31 August 1992 25 September 1992 5 October 1992 2 November 1992 June 1995

24 11 24 26 110 127 125 110 3.7 50 28 4.9 1.2 8.5 47 29 32 24 48 45 150 133 33 88 234 125 203 242 108 34 30 15 12.1

Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake

August 1995 June 1995 August 1995 June 1995 August 1995 June 1995 August 1995 June 1995 August 1995 June 1995 August 1995 June 1995 August 1995 June 1995 August 1995 June 1995 August 1995 June 1995 August 1995

N N N N N N N N N N N N N N N N N N N

1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10

22 6 4.47 2.7 10.4 4.1 4.78 25.3 27.1 2.58 8.15 1.94 1.41 2.35 2.74 1.18 1.82 2.13 5.73

NB 2.8 1.8 2.2 2.2 4.4 4.2 3.7 4.2 4.1 2.9 1.7 1.4 1.1 1.3 2.3 1.9 3 2.6 2.9 3.1 2.3 4.8 4 2.7 5.4 4.7 3.5 8.7 8.9 4.2 5.2 2.9 4.8 7.4 2.4 1.8 1.6 4.5 2.1 4.1 3.4 5.6 2.3 4.4 1 1.6 1.2 1.9 1.2 2 2.2 4.5

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Table 2 (Continued ) Number

Region

158 159 160 161 162 163

Lake type

Lake

Col/38 Col/38 Col/330 Col/330 Col/220 Col/220

Lake Lake Lake Lake Lake Lake

Date N N N N N N

11 11 12 12 13 13

June 1995 August 1995 June 1995 August 1995 June 1995 August 1995 Minimum Maximum Mean

Chl

NB

2.01 4.41 6.58 9.6 12.1 35.4

1.3 3 3.8 3.9 4.1 8.8

0.33 242 32.7

0.67 15 3.7

From Boulion and Paveljeva (1998).

from the optical density of acetone extracts at 663, 645 and 630 nm (Jeffrey and Humphrey, 1975). The total number of bacteria was determined by direct microscoping on membrane filters with a pore diameter of 0.23 mm. The filters were painted with erithrozine. To study the relationships between the data, we will use statistical methods (regressions, transformations, etc.) described by Ha˚kanson and Peters (1995). The aim is to quantify relationships among variables and these statistical methods will not be further elaborated in this section. To evaluate the results of the regression analyses based on empirical data, it is important to recognise that such data are always more or less certain due to problems related to sampling, transport, storage, analytical procedures, natural variations, etc. This will restrict the predictive or descriptive power of any empirical model (Ha˚kanson, 1999). It should be noted that many previous studies have addressed empirical NB /Chl relationships, and Table 3 gives a compilation of some important results based on data sets from defined regions. We will use the information in Table 2 only for comparative purposes. Fig. 1 illustrates the requested NB /Chl relationships based on the data in Table 2. If all data (n/ 163) are used, about 50% (r2 /0.51) of the variability in log(NB) can be statistically explained by variations in log(Chl). log(NB)0:27 log(Chl)0:19; r2 0:51; n163; P B0:0001;

(1)

or NB1:55Chl0:27 :

(2)

It is evident, and it has been stressed before (see, e.g. Currie, 1990), that there is a large scatter around the regression line. This scatter can be explained by uncertainties in the given x- and y values, and by the fact that other factors than primary production, as given by chlorophyll data, influence the number of bacteria. It is well known (Wetzel, 1983) that also allochthonous carbon, related to the transport of humic matter from the catchment area, can significantly influence bacterial production. The LakeWeb model accounts for this, but this is evidently not included in the regressions in Fig. 1. From Fig. 1, it is interesting to note that the general NB /Chl relationship is probably not so different in clear-water and humic lakes. However, clear-water lakes generally have a lower primary production than more turbid lakes (often because of a lower phosphorus loading). For humic lakes, the Chl-values are higher and the relationship to NB is slightly less positive (the slope is 0.2, as compared with 0.3 for the clear-water lakes; the r2value is 0.16 compared with 0.34 for clear-water lakes; P /0.01 compared with B/0.001 for clearwater lakes). In Fig. 2, the models in Table 3 are directly compared with Eq. (1). One can see that if the actual NB-values are used (Fig. 2A), there seems to be great differences among the models based on data from different regions, and the model by Bird

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and Kalff (1984) gives much higher values for NB. However, if we look at the logarithms (Fig. 2B), one can see that all models actually show that (1) NB increases in a significant manner with Chl, but (2) differently in different lakes depending on trophic level, humic level, water chemistry (pH, etc.) and lake morphometry. The aim of the new LakeWeb model is to capture and explain a significant part of the variation among the models in Fig. 2 and around the regressions by accounting for the factors and processes causing such variations. It is important to emphasise that all equations in Fig. 2 have slopes smaller than 1. On average, the slope is 0.27. Our equation (Eq. (1)) agrees well also with a similar equation presented by Currie (1990) not for regional data but for data from many regions (NB /1.59Chl0.33; n/361; r2 / 0.16). From this, one can conclude that at lower trophic levels, lakes can generally be expected to have a relatively higher number of bacterial cells per unit of chlorophyll-a. Table 4 shows such relationships in a general way. It is meant to answer to the following question: how many bacterial cells can generally be expected in lakes of different trophic categories (using the trophic classes given by Ha˚kanson and Boulion (2001a)). 2.2. Number of bacteria versus bacterial biomass

Fig. 1. Three regressions between number of bacteria (NB in million cells/ml; log(NB)) and chlorophyll (Chl in mg/l; log(Chl)) for (1) all data given in Table 2, for (2) clear-water lakes and for (3) humic lakes.

number (NB in million cells/ml) and biomass of bacterioplankton (BMBP in mg ww/l) is very strong (r2 /0.78) and almost linear: log(BMBP )0:973 log(NB)0:438;

Does the bacterial biomass increases in a nonlinear way with the number of bacteria? By analysing data from the International Biological Program (IBP) and other literature data (see Table 5), we have tried to answer that question. The logarithmic relationship (see Fig. 3) between the

r2  0:78; n 72; PB0:001;

(3)

or BMBP 0:365NB0:973 :

(4)

The exponent is close to 1. It means that if the

Table 3 Four regressions illustrating the relationship between number of bacteria (NB in million cells/ml) and chlorophyll (Chl in mg/l) for lakes from different regions and limnological characteristics Number

Equation

n

r2

Range (Chl)

Area

Reference

1 2 3 4

NB/3.16Chl0.29 NB/1.59Chl0.22 NB/1.89Chl0.57 NB/0.24Chl0.76

23 26 13 23

0.45 0.17 0.66 0.91

1.5 /74 1.2 /70 1.3 /35 0.2 /190

USA, Canada Canada, New Zealand Quebec Japan

Currie (1990) Currie (1990) Bird and Kalff (1984) Aizaki et al. (1981)

n , number of lakes.

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number of bacteria increases two orders of magnitude, from 0.1 to 10 million cells/ml, the bacterial biomass is also likely to increase by two orders of magnitude (or rather by a factor of 89 and not by 100). From Table 4, where we have summarised the basic information in Eqs. (2) and (3), one can also see that the higher the lake productivity (as given by Chl), the lower the expected ratio between BMBP and Chl. This also implies that the ratio between bacterial production and biomass (the PR/BM ratio) would grow more progressively than the bacterial biomass. In other words, the production of bacteria (but not the number and biomass of bacteria) is proportional to the chlorophyll-a concentration and the phytoplankton production. Generalising extensive literature data, Billen et al. (1990) have presented the following empirical relationship between bacterial biomass (BMBP) and bacterioplankton production (PRBP): BMBP 46:8PR0:70 BP ; r2 0:91; n288; P B0:001;

(5)

where BMBP is given in mg C/l and PRBP in mg C/l h. One can also write Eq. (5) as

PRBP 0:71BM1:43 BP ;

99

(6)

where BMBP is in mg ww/l and PRBP in mg ww/l per day. To obtain Eq. (6), we set the wet biomass of bacteria to contain 10% carbon (from Ha˚kanson and Boulion, 2002). Then, from the compilation given in Table 4, one can see that the higher the lake productivity, the lower the ratio between PRBP and Chl. Thus, the number, biomass and production of bacteria are likely to increase relative to the phytoplankton biomass (or chlorophyll-a concentration) from hypertrophic to oligotrophic lakes (see Porter et al., 1988).

2.3. Phytoplankton production versus bacterioplankton production An essential element for bacterial production is dissolved carbon produced by phytoplankton (Fig. 4). The release of dissolved organic matter (DOM) by phytoplankton is confirmed by a number of experimental studies. The transformation of DOM to bacterial production is in fact a basic flow of organic carbon in fresh- and seawaters (Derenbach

Fig. 2. A comparison between five regressions between number of bacteria (NB in million cells/ml) and chlorophyll (Chl in mg/l) (A) using actual values and (B) logarithmic values.

100

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Table 4 The total number of bacteria (NB) and the ratio NB/Chl at different chlorophyll concentrations (Chl), as calculated using the regressions given in the text (the total biomass of bacterioplankton (BMBP) and the ratio BMBP/Chl at different chlorophyll concentrations, and the production of bacteria (PRBP) and the ratio PRBP/Chl at different chlorophyll concentrations (Chl) are also given) Trophic level

Chl (mg/l)

Limits

Average 6

5/0.1 5/1 5/10 5/100

0.3 /1.15 1.15 /2.1 2.10 /3.90 3.9 /13.5

NB/Chl (10 cells/mg) 0.8 1.55 2.9 5.5

BMBP (mg ww/l) Ultraoligotrophic Oligotrophic Mesotrophic Eutrophic

Ultraoligotrophic Oligotrophic Mesotrophic Eutrophic

5/0.1 5/1 5/10 5/100

5/0.1 5/1 5/10 5/100

0.11 /0.42 0.42 /0.75 0.75 /1.4 1.4 /4.6

Average 6

NB (10 cells/ml) Ultraoligotrophic Oligotrophic Mesotrophic Eutrophic

Limits

3000 /11500 1150 /2100 210 /390 39 /135

8000 1550 290 55

BMBP/Chl (mg ww/mg) 0.3 0.55 1.0 1.9

1100 /4200 420 /750 75 /140 14 /46

2940 560 100 20

PRBP (mg ww/l per day)

PRBP/Chl (mg ww/mg per day)

0.03 /0.2 0.2 /0.5 0.5 /1.1 1.1 /6.5

300 /2000 200 /500 50 /110 11 /65

et al., 1974; Harrison et al., 1977; Cole et al., 1982; Larson and Hagstro¨m, 1979; Wolter, 1982; Sondergaard et al., 1985; Baines and Pace, 1991). DOM production can vary from 1 to 50% of the total phytoplankton production. It has been argued that the percentage of DOM released by phytoplankton is reduced at higher phytoplankton production (Watt, 1966; Fogg, 1966; Anderson and Zeutschel, 1970; Thomas, 1971). However, a study by Baines and Pace (1991) did not confirm this, and they based their conclusions on 225 observations from fresh- and seawater systems. DOM may be released by living phytoplankton cells (e.g. Sadchikov and Frenkel, 1990; Sadchikov and Makarov, 1997), but also by dying cells (Marker, 1965; Cole et al., 1982). From this brief overview, one can ask: what is a typical relationship between phytoplankton production and/or biomass and bacterioplankton biomass and/or production? This question can be addressed experimentally using the radioactive 14C isotope, and below we will present results from such an experimental study. The results will also provide data for the calibration of the LakeWeb model.

0.12 0.3 0.75 1.8

1230 310 75 18

The standard radiocarbon method for estimating the photosynthesis rate is based on measurement of particulate organic matter (SteenmanNielsen, 1952). This does not take into account DOM released by phytoplankton. Hence, an important problem concerns the estimation of the share of DOM in the total primary production. Note that some researchers explain the losses of DOM by the destruction of labelled phytoplankton cells in the process of the membrane filtration (Arthur and Rigler, 1967; Schindler and Holmgren, 1971; Schindler et al., 1972; Sharp, 1977). It is evident that the consumption of DOM by heterotrophic microorganisms is closely connected to the production of DOM by phytoplankton (Waite and Duthie, 1975; Iturriaga and Hoppe, 1977; Weibe and Smith, 1977; Cole et al., 1982). But the turnover time of DOM in natural waters is very quick, only some hours. This has been confirmed by experiments with organic substrates, e.g. glucose, acetate and aminoacids (Wright and Hobbie, 1966; Hobbie and Grawford, 1969; Azam and Holm-Hansen, 1973). Therefore, one can safely assume that DOM released by phytoplank-

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Table 5 Bacterial number and biomass Number

Type of system

Name

Number (106 ml 1)

Biomass (mg ww/l)

Reference

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Reservoir Reservoir Reservoir Reservoir Reservoir Reservoir Reservoir Reservoir Reservoir Pond Pond Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake Lake

Zelenetskoe Zelenetskoe Krivoe Krivoe Akulkino Akulkino Krugloe Krugloe Krasnoe Dalnee Sevan Sevan Sevan Drivjaty Vyrtsjarvi Glubokoe Rybinskoe Bratskoe Kljazmenskoe Kievskoe Kievskoe Kremenchugskoe Kakhovskoe Dneprodzerzhinskoe Zaporozhskoe Kramet-Niyaz Kramet-Niyaz Naroch Naroch Naroch Naroch Naroch Naroch Naroch Naroch Naroch Naroch Naroch Miastro Miastro Miastro Miastro Miastro Miastro Miastro Miastro Miastro Miastro Miastro Batorino Batorino Batorino

0.09 0.26 0.84 0.50 0.12 0.34 0.87 0.87 0.70 1.50 0.32 0.29 0.56 1.84 4.40 1.20 1.70 0.85 0.70 3.50 4.70 3.50 4.00 3.40 3.60 4.00 12.5 1.14 1.52 1.36 1.09 1.6 2.17 1.05 1.27 2.93 1.55 1.95 1.87 3.05 2.97 3.43 2.55 3.34 1.89 2.31 5.35 2.3 3.34 3.93 8.58 7.44

0.03 0.09 0.26 0.16 0.03 0.09 0.33 0.33 0.30 1.00 0.31 0.35 0.64 1.40 1.80 0.97 1.00 0.77 0.65 3.30 3.40 2.10 1.90 2.20 1.90 4.00 15.0 0.34 0.29 0.26 0.28 0.23 0.33 0.27 0.32 0.65 0.35 0.4 0.73 0.89 0.86 1.31 0.79 1.06 0.61 0.7 1.96 0.93 1.24 1.78 2.86 2.46

Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Saunders (1980) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979)

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102 Table 5 (Continued ) Number

Type of system

Name

Number (106 ml 1)

Biomass (mg ww/l)

Reference

53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

Lake Lake Lake Lake Lake Lake Lake Lake Backwater Backwater Backwater Backwater Backwater Backwater Backwater Backwater Backwater Backwater Backwater Backwater

Batorino Batorino Batorino Batorino Batorino Batorino Batorino Batorino Alte Donau Alte Donau Alte Donau Alte Donau Alte Donau Alte Donau Alte Donau Alte Donau Alte Donau Alte Donau Alte Donau Alte Donau

11.39 11.58 10.57 7.04 7.53 14.89 7.17 9.43 4.71 2.81 4.42 3.55 2.03 1.3 1.72 2.05 2.04 3.33 2.39 3.1

3.51 4.3 3.79 2.69 2.87 5.85 2.98 3.7 0.793 0.545 0.655 0.545 0.34 0.31 0.29 0.47 0.485 0.605 0.687 0.695

Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Potaenko (1979) Wieltschning et al. Wieltschning et al. Wieltschning et al. Wieltschning et al. Wieltschning et al. Wieltschning et al. Wieltschning et al. Wieltschning et al. Wieltschning et al. Wieltschning et al. Wieltschning et al. Wieltschning et al.

Fig. 3. The relationship (regression line, r2 and n ) between bacterioplankton biomass and number.

ton is quickly assimilated by bacteria. It means that DOM can also be measured as bacterial production. The scheme in Fig. 4 illustrates the flow of carbon in a community with autotrophic and

(1999) (1999) (1999) (1999) (1999) (1999) (1999) (1999) (1999) (1999) (1999) (1999)

heterotrophic organisms. If 14C (in the form of bicarbonate which is assimilated by phytoplankton in the process of photosynthesis) is added to lake or seawater samples, the tracer will be detected in phytoplankton cells and in the output (DOM) from algal cells. Simultaneously, heterotrophic microorganisms utilise the labelled DOM. Hence, the methodical problem concerns how to differentiate the labelled phytoplankton and the labelled bacterioplankton in order to compare their levels of 14C and to estimate the share of the primary production transformed into bacterial production. The method uses 14C in combination with differential (or stepwise) filtration of water samples (see Derenbach et al., 1974; Larson and Hagstro¨m, 1979; Wolter, 1982; Jensen, 1985; Sondergaard et al., 1985; Boulion, 1988, 1993, 1994, for further methodological information). The differential filtration in itself does not give a satisfactory separation of phytoplankton and bacterioplankton. Therefore labelled organic substrates are often used as markers of bacterial cells. This type of differential filtration (see Fig. 5) has been used, e.g. on water samples from lakes in Mongolia, Russia (Pskov area and Karelia), and

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two targets, bacterioplankton biomass and production. The following ordinary differential equation gives the weekly production and biomass of bacterioplankton: BMBP (t)BMBP (tdt) (IPRBP CONBPZH ELBP ) dt;

Fig. 4. The scheme of carbon flow in the ‘‘phytoplankton / bacterioplankton’’ system.

seawater samples from the southwest part of the Pacific (see Boulion, 1993, 1994). These studies showed that the production of bacterioplankton, PRBP, varied from about 7 to 48% of the production of phytoplankton, PRPH. The mean value was 20% (see Fig. 6). Note also that these results were derived from experiments and they reflect the bacterial production only from the phytoplankton production. In natural lakes, especially in humic lakes, it is likely that the bacterioplankton production is significantly higher. In the following calibrations, we have used a value of 50% as a general reference value, which should apply for oligohumic lakes with colour values of about 20 mg Pt/l. It should also be noted that these results (Fig. 6) are in general agreement with previously published results addressing the same issue (Derenbach et al., 1974; Larson and Hagstro¨m, 1979; Sondergaard et al., 1985; Baines and Pace, 1991; Conan et al., 1999; Weiss and Simon, 1999). With this, we have presented the empirical reference models/values that will be used in the following testing of the dynamic model for bacterioplankton.

(7)

where BMBP is the bacterioplankton biomass (kg ww), IPRBP the initial bacterioplankton production (kg ww per week), CONBPZH the bacterioplankton consumption by herbivorous zooplankton (kg ww per week) and ELBP the bacterioplankton elimination (or turnover) (kg ww per week). The initial bacterioplankton biomass is set equal to the norm value (NBMBP in kg ww), which is calculated from the empirical TP model (see Table 1; giving number of bacteria in million cells/ml) and the given (Fig. 3) empirical adjustments to transform bacterial number to biomass (million/ml to mg ww/l), and dimensional adjustments (to obtain kg ww). Bacteria can generally be found in the entire water mass, although the highest bacterial biomasses often appear close to the bottom and near the water surface (see Wetzel, 1983). For example, Kuznetsov (1970) has shown that there may be significant differences among lakes, and seasonally within lakes, in this pattern. So, NBMBP is given by 0:66 0:973 NBMBP (TP)0:365(0:9CTP ) 0:001(Vol);

(8)

where CTP is the lake TP concentration (mg/l) and Vol is the entire lake volume (m3). A complementary NBMBP-value has also been calculated from Eqs. (1) and (3). That is



3. The phytoplankton /bacterioplankton model The new dynamic model and its panel of driving variables are illustrated in Fig. 7. The model has

Fig. 5. The scheme of differential filtration of water samples. 1.5 and 0.23 mm are pore sizes of membrane filters.

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NBMBP (Chl) 10

(0:973(0:27 log(Chl)0:19)0:438)

0:001(Vol):

(9)

Eq. (8) is called ‘‘norm bacterial biomass, TP’’ and Eq. (9) ‘‘norm bacterial biomass, Chl’’. The initial production of bacterioplankton (IPRBP) is related to the available amount of seston from all sources (SPM in mg/l), and hence also to DOM, the basic fuel for bacterioplankton production, and factors known to influence bacterioplankton production, such as temperature and stratification of the water mass. IPRBP is given by   1 ; (10) IPRBP  Ytemp RBP SPM Vol 1000 where Ytemp is a dimensionless moderator expressing the influence of water temperature variations on bacterioplankton production */the higher the temperature, the more bacterioplankton will be produced. Ytemp is defined by the ratio between epilimnetic temperature (EpiTemp in 8C; the default values for EpiTemp have already been presented by Ha˚kanson and Boulion (2002)) and a reference temperature of 9 8C (related to the duration of the growing season, see Ha˚kanson and Boulion, 2001b). That is Ytemp  19EpiTemp:

(11)

The 1/1000 term in Eq. (10) is a conversion constant from mg/l to kg/m3 and RBP is the rate of initial bacterioplankton production (in l per week). The question is: which RBP-value gives the best correspondence between modelled values and the empirical reference values, as given by the two previously discussed empirical models (Eqs. (8) and (9)). The aim of the following calibrations is to find a generic value for RBP. Fig. 8 gives results from a calibration to find a generic value for the bacterioplankton production rate for a lake with a colour value 20 mg Pt/l and Fig. 9A gives a similar calibration along a TP gradient (3 /300 mg/l, which covers ultraoligotrophic to hypertrophic conditions; note that the default lake used in Fig. 9A has a colour value of 50 mg Pt/l). From these figures, one can note that RBP /1 provides an excellent fit between the model-predicted values and the empirical values. Fig. 9B shows how three RBP-values (0.5, 1 and 2) influence modelled values of bacterioplankton biomass and the ratio between bacterioplankton biomass and phytoplankton biomass (100BMBP/ BMPH) if colour varies from 3 to 300 mg Pt/l. Note that in Fig. 9B, we have not used production values but biomasses for the ratio. The two ratios for production and biomasses are very close since the production is defined by the biomass divided by the turnover time (PR /BM/T ). The turnover

Fig. 6. The relationship between bacterial production derived from phytoplankton production and phytoplankton production using data from the radiocarbon experiment.

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Fig. 7. Illustration of the bacterioplankton submodel in LakeWeb. The panel of driving variables gives the obligatory driving variables, which should apply to a specific lake (total phosphorus, colour, pH, mean depth and lake area), and the default values used for these variables in many simulations in this work. To run the model, one also needs epilimnetic temperatures, which may be accessed from measurements, climatological tables or models. The panel also lists the four critical rates. These are meant to be general model constants applicable for all lakes.

time is 2.8 days for bacterioplankton and 3.1 days for phytoplankton (see Table 6). We have also included the reference line for the ratio (50%)*/ the bold line in Fig. 9B. Our conclusion from these tests, and many similar tests, is that one can use the RBP /1 as a general model constant. SPM (in mg/l) in Eq. (10) is the concentration of suspended particulate matter (/seston, i.e. dead and alive organic matter, humic matter and inorganic matter), as calculated in the lake web model from Secchi

depth (see Ha˚kanson and Boulion, 2002). Multiplication with Vol in Eq. (10) gives the requested dimension (values in kg ww per week). CONBPZH, i.e. bacterioplankton consumption by herbivorous zooplankton in Eq. (7), is given by CONBPZH BMBP CRBPZH ;

(12)

where BMBP is the bacterioplankton biomass (kg ww) and CRBPZH the actual consumption rate (l per week) expressing the loss of bacterioplankton from predation by herbivorous zooplankton (ZH).

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CRBPZH is defined from the turnover time of herbivorous zooplankton (TZH, in weeks, as explained by Ha˚kanson and Boulion (2002)), which is set to 6.0 days (see Table 6). That is  CRBPZH  NCRBPZH NCRBPZH



BM2H 1 NBM2H



(13)

where NCRBPZH is the normal consumption rate (bacterioplankton eaten by herbivorous zooplankton), as given by NRZH/TZH (1 per week) for NRZH /2 (NRZH is the number of first-order food choices for herbivorous zooplankton, i.e. phytoplankton and bacterioplankton). The characteristic composition of herbivorous zooplankton used in the LakeWeb model is shown in Table 7. CRBPZH is the actual consumption rate (1 per week). NBMZH is the normal biomass of herbivorous zooplankton (kg ww), when the actual biomass of herbivorous zooplankton (BMZH) is equal to the normal biomass of herbivorous zooplankton (NBMZH), the actual consumption rate (CRBPZH) is equal to the normal consumption rate (NCRBPZH). The last part of Eq. (7) concerns bacterioplankton elimination (or turnover). ELBP is given by

ELBP BMBP

1:386 ; TBP

(14)

where 1.386 is the half-life constant (/ln 0.5/0.5; see Ha˚kanson and Peters, 1995). TBP, the turnover time of bacterioplankton, which is set to 2.8 days (Table 6). This value is used as a general value for all types of bacterioplankton just like 6.0 days is used for all types of herbivorous zooplankton. The bacterioplankton production (in kg ww per week) is then given by PRBP /BMBP/TBP.

4. Model tests and model simulations

4.1. Set-up The aims of this section are: 1) To test the dynamic model using the general empirical regressions as references. So, we will study how the LakeWeb model predicts selected target variables compared with the empirical regressions, and we will specifically focus on the parts where the empirical models cannot, and should not, provide realistic predictions. This would be for situations outside the ranges of the empirical models and for

Fig. 8. Calibrations to find a generic value for the bacterioplankton production rate for a lake like the default lake but with clearer water (colour value 20 mg Pt/l). Three RBP-values, 0.5, 1 and 2 have been tested. The dynamic model has been run for 10 years (521 weeks).

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Fig. 9. Sensitivity tests along a gradient of TP concentrations (3, 10, 30, 100 and 300 mg/l) for the default lake to test if the default value of 1.0 for the bacterial production rate provides adequate predictions (curve 2). Curve 1 shows the results if the rate is set to 2 and curve 3 if the rate is 0.5. (A) Simulations for bacterioplankton biomass. The figure also gives the two empirical reference lines (Norm bact biomass TP and Norm bact biomass Chl). (B) Similar results for the ratio between bacterioplankton and phytoplankton biomass (100BMBP/BMPH). The figure also gives the reference line, 50%.

changes in variables not included in the regressions. 2) To illustrate how the model behaves in situations where gradients are created in a systematic manner for all pertinent driving variables. That is: . TP concentration will be changed from 3, 10, 30, 100 to 300 mg/l. This covers the entire range from ultraoligotrophic to hypertrophic conditions (see Ha˚kanson and Boulion, 2002; Fig. 10).

. Lake colour values, i.e. allochthonous influences, will be changed from ultraoligohumic to hyperhumic by creating colour gradients from 3, 10, 30, 100 to 300 mg Pt/l. . Lake pH-values will be altered from extremely acidic to extremely basic conditions; pH-values from 3 to 11 will be tested. . Morphometric influences will be tested by changing the mean depth from 1, 2, 4, 8 to 16 m and the lake area from 0.1, 0.5, 1, 10 to 100 km2.

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Table 6 Characteristic turnover times (or life span) Group

Turnover time (days)

Phytoplankton Bacteria Benthic algae Herbivorous zooplankton Predatory zooplankton Prey fish Predatory fish Zoobenthos Macrophytes (according to Raspopov (1973))

3.2 2.8 4.0 6.0 11.0 300 450 128 300

T /BM/PR, where BM/biomass in kg ww, PR/biomass production in kg ww per day. Based mainly on data from Winberg (1985).

. All these changes will be calculated for the following target variables for a hypothetical default lake. The characteristics of this lake are given by the insets in Figs. 11 and 12. . Bacterioplankton biomass (BMBP): the calculated values will be compared with the two empirical reference values, as given by Eqs. (8) and (9). . The ratio between bacterioplankton (BMBP) and phytoplankton biomasses (BMPH). We will use the already mentioned ratio of 50% as a general reference value for these simulations. This value should apply for clear-water lakes with colour values around 20 mg Pt/l (see Fig. 8).

Table 7 Composition of herbivorous zooplankton Composition

Total biomass (%)

Daily PR/BM at 20 8C

Copepods (diaptomides) Cladocerans Rotifers Protozoans

30

0.07

40 7 19

0.16 0.35 0.5

Based on data from Ivanova (1975), Kuzmich (1981), Krjuchkova (1985), Winberg (1985) and Ha˚kanson and Boulion (2002).

The results of all these tests will be summarised in the following multidiagram figures. The calculations have been done in 2 year steps for a period of 10 years (521 weeks).

4.2. Bacterioplankton biomass Fig. 11 gives the results for bacterioplankton biomass: . Fig. 11A shows how the model predicts bacterioplankton biomass (kg ww) along the given TP gradient and relative to the two empirical reference lines. Note that the correspondence between the three models is good, especially between model-predicted values and empirical values given by Eq. (9) (line 3). The empirical models may not give realistic seasonal patterns. . Fig. 11B shows the results along the colour gradient. Colour variations are not accounted for by the empirical models, and so one cannot expect a good correspondence between modelpredicted values and the empirical reference values in this case. However, one should expect a systematic departure from the reference lines so that the model should give higher bacterioplankton biomasses in humic lakes with high colour and lower biomasses in clear-water lakes, and this is exactly what the model does. . Fig. 11C demonstrates the correspondence between the model-predicted values of bacterioplankton biomass and the two references along the pH gradient. The model predicts a relatively large biomass of bacterioplankton at pH 11. . Fig. 11D illustrates bacterioplankton biomass along a gradient of mean depths. There is a fine and logical correspondence between the three curves, although the model predicts lower values than suggested by the two empirical models in deep lakes. We would argue that the model predictions are likely more reliable than the empirical reference values. . Fig. 11E shows bacterioplankton biomasses in lakes with different areas. Also in this case, there is a logical correspondence between the curves.

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Fig. 10. Calibrations to find a generic value for the bacterial production rate in a lake colour gradient (3, 10, 30, 100 and 300 mg Pt/l). Curve 1 shows the results if the rate is set to 2, curve 2 if the rate is 1 and curve 3 if the rate is 0.5. (A) Simulation results for bacterioplankton biomass. The figure also gives the two empirical reference lines (Norm bact biomass TP and Norm bact biomass Chl). (B) Similar results for the ratio between bacterioplankton and phytoplankton biomasses (100BMBP/BMPH). The figure also gives the reference line, 50%.

To conclude, the model seems to predict bacterioplankton biomass very well.

4.3. The ratio between phytoplankton and bacterioplankton biomasses Fig. 12 gives the results for the ratio between bacterioplankton and phytoplankton biomass (100BMBP/BMPH) relative to the reference value, 50%.

. Fig. 12A shows the results along the TP gradient. The model predicts ratios that vary in a logical manner. The departure from the reference value of 50% during the winter is partly related to the quicker turnover time for bacteria, and this also explains some of the faster increases in the modelled values during the peak of the production period. Note that the default lake has a colour of 50 mg Pt/l, so the bacterial production related to allochthonous carbon is significant.

110

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Fig. 11. Sensitivity analyses for bacterioplankton biomass under default conditions: (A) along a trophic state gradient (TP/3, 10, 30, 100 and 300 mg/l), (B) along a humic state gradient (lake colour/3, 10, 30, 100 and 300 mg Pt/l), (C) along an acid state gradient (pHs 3, 5, 7, 9 and 11), (D) along a gradient of mean depths (1, 2, 4, 8, 16 m) and (E) along a lake size gradient (area/0.1, 0.5, 1, 10 and 100 km2).

. This means that it is interesting to compare the results from Fig. 12A with the results given in Fig. 12B, the colour gradient. We can note that in ultraoligohumic lakes, the ratio is, as it should be, slightly below 20%. The ratio increases with increasing lake colour and attains a value of about 300% in hyperhumic lakes. This is, we would argue, realistic. . Fig. 12C demonstrates the relatively small impact of pH on this ratio for all realistic pH-

values (in the range from 5 to 9), but not for lakes with a pH of 11. . Fig. 12D and E show how changes in lake morphometry are likely to alter the ratio between bacterioplankton biomass and phytoplankton biomass. To conclude, under the given presuppositions, the model predicts phytoplankton biomass and bacterioplankton biomass well, and so it should

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Fig. 12. Sensitivity analyses for the ratio between bacterioplankton biomass and phytoplankton biomass, 100BMBP/BMPH, along gradients under default conditions: (A) along a trophic state gradient (TP/3, 9, 27, 81 and 243 mg/l), (B) along a humic state gradient (lake colour/3, 9, 27, 81 and 243 mg Pt/l), (C) along an acid state gradient (pHs 3, 5, 7, 9 and 11), (D) along a gradient of mean depths (1, 2, 4, 8, 16 m) and (E) along a lake size gradient (area/0.1, 0.5, 1, 10 and 100 km2).

also predict this ratio well, and this is shown in Fig. 12.

5. Concluding remarks This work has addressed several complex and interrelated topics concerning bacterioplankton

production and biomass. The basic aim has been to present the new dynamic model which is meant to capture the most important, general structural and functional characteristics relevant for this part of the lake foodweb. A very important demand for the model is that it must only be driven by readily accessible variables, otherwise it is likely that it will never be used. The dynamic model can be run if

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data are at hand on lake TP concentration, pH, colour, mean depth, lake area and epilimentic temperature. An important aspect of this work concerns the calibration and critical tests of the model. We have introduced extensive data sets not previously presented in the West and new empirical regression models and made compilations of previously presented regression models. This type of testing stresses the basic aim of the model. It is meant to quantitatively describe general and typical interrelationships regarding bacterioplankton in lakes. If these fundamental interrelationships are properly described, then divergences from these normal patterns can be quantified and related to factors not accounted for in the model, e.g. specific contamination situations.

Acknowledgements This work has also been carried out within the framework of the Russian Foundation for Basic Research (Projects 99-04-49614 and 00-15-97825).

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