Benthic algae

Hydrobiologia 522: 75–97, 2004. © 2004 Kluwer Academic Publishers. Printed in the Netherlands.

75

Empirical and dynamical models of production and biomass of benthic algae in lakes Lars Håkanson1 & Viktor V. Boulion2 1 Uppsla

University, Department of Earth Sciences, Villav. 16, 752 36 Uppsala, Sweden of RAS, Universitskaja emb., 1, 199034 St. Petersburg, Russia

2 Zoological Institute

Received 19 October 2001; in revised form 13 October 2003; accepted 6 December 2003

Key words: lakes, dynamic model, empirical model, benthic algae, biomass, production, zoobenthos, predation, environmental factors Abstract This work presents new empirical and dynamical models for benthic algae in lakes. The models were developed within the framework of a more comprehensive lake ecosystem model, LakeWeb, which also accounts for phytoplankton, bacterioplankton, two types of zooplankton (herbivorous and predatory), macrophytes, prey fish and predatory fish. The new dynamic model provides seasonal variations (the calculation time is 1 week). It is meant to account for all factors regulating the production and biomass of benthic algae for lakes in general. This work also presents and uses a new data-base established by us from published sources. Many of the lakes included in this study are situated in the former Soviet Union. They were investigated during the Soviet period and the data and results have up until now been largely unknown in the West. We present empirical models for benthic algae, and show that the biomass of benthic algae in whole lakes can be estimated from the ratio between the lake area above the Secchi depth to the total lake area and the primary production of phytoplankton. We also present several critical tests of the dynamical model. The dynamical and empirical models give corresponding results over a wide limnological domain. We provide algorithms for (1) the production rate of benthic algae (2) the elimination rate (related to the turnover time of benthic algae), (3) the rate of benthic algae consumption by zoobenthos, and (4) the rate of physical erosion of benthic algae. Our results indicate that the production of benthic algae is highly dependent on lake morphometry and sediment character, as well as water clarity, and less dependent on nutrient (phosphorus) concentrations in water and sediments. This work provides new quantitative support to such conclusions and also a useful model for predictions of production and biomass of benthic algae. Introduction and aim To predict the production and biomass of benthic alge is of great importance in lake management, ecology and in many types of studies concerned with the sediment habitat. Zoobenthos, benthic algae and macrophytes are the three categories of key functional organisms related to sediments incorporated in the LakeWeb-model (see Håkanson & Boulion, 2002a, for a thorough description of the LakeWeb-model). The dynamic model for macrophytes has already been presented (see Håkanson & Boulion, 2002b) and the aim of this work is to present, motivate and test the new model for benthic

algae. First, we will provide brief introductory sections on this group of organisms and also derive and define the empirical reference models used to calibrate the dynamic model. Figure 1 gives a broad compilation of the groups of organisms associated with lake sediments, benthic algae, macrophytes and zoobenthos. Evidently, all biological phenomena in aquatic ecosystems are immensely complex, and this is also valid for bottomliving communities. So, like always in lake modelling, simplifications are necessary. The following introduction is meant to explain the simplifications made for the dynamic model for benthic algae.

76

Figure 1. Compilation of concepts related to zoobenthos, benthic algae and macrophytes (see also Vollenweider, 1968; 1976; Cummings, 1973, Brinkhurst, 1974; Wetzel, 1983a).

Westlake (1980) distinguishes between three groups of periphyton communities. One is attached to different substrates and forms dense belts including young, old and dead cells. The second group consists of numerous filaments or lumps of gelatinous material. The third group includes communities whose members are not strongly attached to the substratum. They are not aggregated and move freely over the substratum, generally the bottom sediments. Microphytobenthos have often been included in this third group. Today, however, microphytobenthos are generally considered as a separate group of autotrophic organisms, and not included among periphyton. Such classification problems partially explain the differences in biomasses presented by different authors for various periphyton communities.

Obviously, the horizontal and vertical distributions of benthic algae strongly depend on the distribution of the illuminated substrates. In comparison with macrophytes and phytoplankton, benthic algae are confined to a relatively thin surficial sediment layer, within which the concentration of cells can be very high (Wetzel, 1983b). Organisms on underwater substrates form heterogeneous and complex associations and colonize almost all types of substratum in the littoral zone (see, e.g., Vollenweider, 1969; Nikulina, 1979; Makarevich, 1985; Lalonde & Downing, 1991; Anokhina, 1999). The terminology used for the various algae living on different substrates varies, it sometimes seems, with the number of researchers (Vollenweider, 1969; Wetzel, 1964, 1983b). Generally, the term ‘periphyton’ is applied for all forms of plants (with

77 Table 1. Biomass of periphyton (BMP er ) attached to different species of macrophytes. For periphyton 1 g ww = 0.003 g Chl (Vollenweider, 1969; Makarevich, 1985); for macrophytes 1 g ww = 0.16 g dw). Nr Lake

Region

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

Belarus

Naroch " " " " " " " " " " " " " " Sevan " Issyk Kul " " " 3 lakes 7 lakes 3 lakes 5 lakes 3 lakes 1 lake 1 lake Paajärvi

Substrate = macrophytes

Chara sp. Nitellopsis obtusa Fontinalis sp. Myriophyllum spicatum Ceratophyllum demersum Potamogeton lucens Potamogeton perfoliatus Potamogeton natans Sagittaria sagittifolia Phragmites australis Scripus lacustris Stratiotes aloides Elodea canadensis Equisetum fluviatile Eleocharis palustris Armenia Chara Potamogeton sp. Kirghizia Chara " " " Quebec Elodea canadensis " Myriophyllum spicatum " Potamogeton robbinsii " Potamogeton amplifolius " Valisneria americana " Potamogeton sp. " Potamogeton richardsonii Finland Equisetum fluviatle

BMPer (mg ww) BMPer (µg Chl) BMPer (g ww) References per 1 g dw of per 1 g dw of per 1 kg ww of macrophytes macrophytes macrophytes 269 73.5 6.7 253 144 27.7 9.17 13.2 43.2 7.4 18.8 41.7 54.7 271 26.7 733 820

494 487 267 200 147 89 63 MV SD Median

the exception of macrophytes) growing on submerged materials. The underwater substratum can be, for example, sediments, stones, boats, constructions, living organisms (see Fig. 1). Table 1 gives one example for algae of periphyton (= epiphyton) attached to macrophytes. From the data given in Table 1, it is possible to conclude that, as a first approximation, the epiphyton biomass is about 1–2% of the macrophyte biomass. In testing the dynamic model, it is essential to evaluate if the model yields adequate predictions along gradients, like TP-gradients (TP = total phosphorus), lake size gradients, colour and pH-gradients. We have

43.0 11.8 1.07 40.5 23.0 4.43 1.47 2.11 6.91 1.18 3.01 6.67 8.75 43.4 4.27 39 44 10.3 9.33 5.00 4.45 26.3 25.9 14.2 10.7 7.83 4.74 3.36 13.1

Makarevich, 1985 " " " " " " " " " " " " " " Anokhina, 1999 " Nikulina, 1979 " " " Lalonde & Downing, 1991 " " " " " " Kairesalo, 1983

14.5 14.4 8.3

collected literature data to see if there are systematic changes in epiphyton biomass related to trophic gradients (see Table 2). From the results given in this table, one can see no significant tendency (r 2 = 0.03, n = 14) between TP-variations and changes of epiphyton biomass. The epiphyton biomass is generally about 1.5% of the total macrophyte biomass, so variations in lake TP-concentrations are not the main limiting factor for the production of benthic algae. Many epipelic (benthic) forms of algae display a daily migration pattern which creates additional variations in their distribution. The biomass of benthic

78 Table 2. Biomass of periphyton (BMPer ) attached to macrophytes (epiphyton) in lakes of different trophic state. D = sampling depth. Lake

Des Iles Orford Fournelle Quenouilles Echo D’Argent Memphremagog Champlain Massawippi Magog Waterloo Naroch Miastro Batorino

Quebec " " " " " " " " " " Belarus " "

TP µg/l

Chl µg/l

Chl of epiphyton, µg/g dw of macroph.

BMPer g ww/kg ww of macroph.

D m

Dominant macrophytes

References

5.8 6.9 7.0 11.2 12.8 13.2 17.5 23.3 23.9 57.5 72.8 20 32 68

1.5 1.5 2.6 1.6 8.3 7.5 3.3 3.5 15.9 19.8 41.7 4.3 20.9 64.7

480 235 466 217 142 209 114 120 995 414 122 639 276 123

25.6 12.5 24.8 11.6 7.6 11.1 6.1 6.4 53.0 22.1 6.5 33.3 14.4 6.4

1.6 2.0 1.6 1.3 1.6 1.5 2.2 2.0 2.2 1.6 1.1 3.0 1.2 1.4

Myriophyllum, Potamogeton Potamogeton, Elodea Potamogeton, Elodea Potamogeton, Juncus Chara, Potamogeton Myriophyllum, Nittella Myriophyllum, Vallisneria Vallisneria, Cladophora Myriophyllum Elodea, Myriophyllum Myriophyllum, Vallisneria" Chara Scripus, Phragmites Phragmites, Nymphaea

Lalonde & Downing, 1991 " " " " " " "

Mean SD Median

17.2 13.5 12.0

Figure 2. The relationship between empirical data from individual sampling sites for, on the y-axis, the ratio between production of benthic algae to total production (of benthic algae plus phytoplankton), and on the x-axis, the ratio between sampling depth (D in m) and Secchi depth (Sec in m).

Makarevich, 1985 "

algae in lakes (but not marine systems) is, however, generally expressed per unit of the water area, and not per unit of the substratum area (Loeb et al., 1983). The littoral primary production often dominates the total lake primary production in shallow lakes. Deep lakes usually only have a relatively small part of the total area within the littoral zone. A comparison of the littoral primary production in five oligotrophic lakes has indicated a large contribution of benthic algae (Loeb et al., 1983), but also, logically, a decreasing contribution of benthic algae to the total primary production with increasing water depth. Analysing data for lakes from different regions in the former Soviet Union, Boulion (2001) has shown that the contribution of benthic algae to the total littoral primary production depends on two important limiting factors, the morphometry of the littoral zone and the optical properties of the water. To calibrate the dynamic model, we need empirical regression models which are valid for entire lakes (and not just sites in lakes), preferably yielding high predictive power over a wide limnological domain from few and readily available driving variables. To our knowledge, no such models exist for benthic algae and we have collected data to derive such a model.

79

Figure 3. Illustration of Equation (1), showing the relationship between the production ratio, PRBA /PRtot versus the ratio D/Sec.

This new empirical model for benthic algae will be presented in the next section. Empirical model for production of benthic algae Tables 3 and 4 show the data used to derive the new empirical reference model for benthic algae. These are data from 9 lakes and 42 sampling sites. The information includes, lake name, region, latitude, longitude, altitude, Secchi depth, mean lake slope, lake area, mean depth, maximum depth, sampling depth, phytoplankton production, production of benthic algae, ‘total’ production (the sum of these two production values), literature references and the requested target variable, i.e., the production of benthic algae (PRBA ) relative to the defined total production (PRtot ). In the following statistical analyses, we have used methods presented by Håkanson & Peters (1995) including transformations to obtain normal frequency distributions, analyses of co-variations and internal correlations and stepwise multiple regressions. Those methods will not be elaborated here. First, it is interesting to note (see Fig. 2) that there is a highly significant relationship between the requested ratio, PRBA /PRtot , for the individual sampling sites and the ratio between the sampling depth (D in m) and the Secchi depth (Sec in m): (PRBA /PRtot ) = −85.7 · (D/Sec)0.5 + 115.7, (1) (n = 42; r 2 = 0.75).

As much as 75% (r 2 = 0.75) of the variability among these 42 sites can be statistically explained by variations in the D/Sec-ratio and there seems to be no significant differences between the lakes in this respect. The equation is evidently only valid for D/Sec-ratios yielding predictions of PRBA /PRtot smaller than 100%. So, Equation (1) may be generally applicable in its domain (as given by the range of the model variables in Tables 3 and 4). Equation (1) is valid for individual sampling sites and it demonstrates the logical relationship between the production of benthic algae in relation to lake primary production of benthic algae plus phytoplankton. The larger the sampling depth relative to the Secchi depth, the smaller the production of benthic algae compared to the phytoplankton production. We have tested two approaches for deriving a method to estimate the PRBA /PRtot -ratio for entire lakes: method 1 is based on Equation (1) and method 2 based on a statistical analysis of the data given in Tables 3 and 4. Method 1 Figure 3 provides a graphic illustration of Equation (1). It is evident that that the PRBA /PRtot -ratio attains maximum values at small sampling depths and that the ratio is zero if D/Sec is 1.82. The intense turbulence generally predominating in very shallow waters is not beneficial for benthic algae so the depthproduction curve given in Figure 3 in not linear but curved (see also Wetzel, 1983b). The integral is 70. The total production area in Figure 3 is 1.82·100 = 182. This means that, on average, the production of benthic algae in the littoral zone is 70/182 (= 38.5%) of the total production (= production of benthic algae plus phytoplankton), which is 182 units (see Fig. 3). It also means that the production of benthic algae is 63% of the phytoplankton production in the littoral zone. The area above the depth given by the Secchi depth in relation to the total lake area is ASec /A and might then be used as a first estimate of the total production of benthic algae: NPRBA = 0.63 · (ASec /A) · PRPH ,

(2)

ASec is calculated from the equation in Figure 4 and PRPH is the primary production of phytoplankton in the lake (in kg ww per week calculated according to Håkanson & Boulion, 2001a) and NPRBA is the requested empirical reference (or norm-value, called Norm bental), which will be used to get order of magnitude values for the following model calibrations.

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Table 3. Geographic and morphometric data for the 9 lakes and the 42 sampling stations for phytobenthos production (see Table 4). Lake

Region

Lat (◦ N)

Long (◦ E)

Alt (m)

Secchi depth (Sec, m)

Slope (◦ )

Crater Lake

North America

42.9

122.1

1882

28

45

Lake Tahoe

"

39.1

120.0

1898

24.5

45

Fallen Leaf Lake

"

38.9

120.1

1939

16

35

Donner Lake

"

39.3

120.27

1809

13.5

Castle Lake

"

41.2

122.38

1706

Zelenetskoe

Kola Peninsula

60

36

6

Onega Lake ∗ 79-08-01

Karelia

61.5

35

?

Onega Lake ∗ 79-08-31

Issyk Kul ∗∗, St. 1 St. 2 St. 3

Area (km2 )

Mean depth (D m , m)

Max. depth (D max , m)

Sampling depth (D, m)

48

325

589

499

313

501

5.6

53

110

30

3.8

20

67

11.5

45

0.2

11

35

5.0

?

0.24

8.5

25

4.3

?

10340

29.5

120

?

6290

2 8 16 2 8 16 3 7 13 2 6.5 17.5 3 7.8 12 0.3 1 2 3 4 5 7 10 0.1 1 2 3 4 5 6 7 0.1 1 2 3 4 5 6 7 3.5 4 4

4.5

Kirghizia

42.5

77.1

1609

Note: ∗ Littoral zone of Lake Onega, Gulf of Gorskaja ∗∗ Littoral zone of Lake Issyk Kul, Gulf of Rybachinskiy

7 11.5 9

280

668

81

Table 4. Production data for the 9 lakes and the 42 sampling stations, and literature references. Lake

Phytoplankton production (mg C/m2 · d)

Benthic algae production (mg C/m2 ·d)

Total production (mg C/m2 ·d)

Benthic algae production (%)

References

Crater Lake " " Lake Tahoe " " Fallen Leaf Lake " " Donner Lake " " Castle Lake " " Zelenetskoe " " " " " " " Onega Lake ∗ 79-08-01 " " " " " " Onega Lake ∗ 79-08-31 " " " " " " Issyk Kul ∗∗, St. 1 St. 2 St. 3

3 11 29 16 71 133 25 60 121 41 146 308 129 328 489 3.08 9.74 16.9 21.1 23.3 24.6 26.1 26.9 4.5 42.4 79.5 111 138 160 176 187 4.0 37.8 71.1 100 124 144 160 171 66 64 50

84 62 126 49 96 147 19 44 22 78 171 5 202 156 153 195 118 87 12.6 3.75 11.5 15.1 0 600 800 500 100 60 10 0 0 2000 350 250 200 120 100 50 0 62 71 93

87 73 155 65 167 280 44 104 143 119 317 313 331 484 642 198 128 104 33.7 27.1 36.1 41.2 26.9 604 842 580 211 198 170 176 187 2004 388 321 300 244 244 210 171 128 135 143

97 85 81 75 57 53 43 42 15 66 54 2 61 32 24 98 92 84 37 14 32 37 0 99 95 86 47 30 6 0 0 100 90 78 67 49 41 24 0 48 53 65

Loeb & Reuter, 1981; Loeb et al., 1983 " " " " " " " " " " " " " Boulion, 1975 (phytoplankton) Nikulina, 1975 (phytobenthos) " " " " " " Nikulina, 1982 (phytobenthos) Umnova, 1982 (phytoplankton) " " " " " " " " " " " " " " Nikulina, 1979 " "

Note: ∗ Littoral zone of Lake Onega, Gulf of Gorskaja ∗∗ Littoral zone of Lake Issyk Kul, Gulf of Rybachinskiy

82 Method 2 Lacking well-tested empirical methods to calculate the production of benthic algae in whole lakes, we have also used the data given in Tables 3 and 4 to try to derive a statistical model for the target ratio, y = PRBA /PRtot . The y-variable can be defined in several ways: y1 : a simple mean value of the data given in Tables 3 and 4. This approach cannot be expected to give a very representative value since it is calculated from different depths in different lakes. For example, the mean value for the three data from Castle Lake is y1 = 0.39 or 39%. y2 : a weighted mean value where first the areas above of the different sampling depths are calculated using the method illustrated in Figure 4 (the hypsographic curve method yielding ADi/A-ratios, where ADi are the different areas for the different sampling depths, Di , and A is the lake area) and then we have calculated the y2 -values from these ratios, i.e., the weighted mean value is given by (PRBA /PRtot )· (ADi /A) for each lake. For example, in Castle Lake, the area above 3 m is calculated to be 144 400 m2 . The lake area is 200 000 m2 , and the ADi /A-ratio is 144400/200000 = 0.722. The weighted mean value y2 is obtained for all three depths in this lake. It is 47%. y3 : a normalized mean lake value related to the area of the lake above a water depth given by Sec/2. For Castle Lake, the Secchi depth is 11.5 m, so Sec/2 = 5.75 m. The requested lake-typical PRBA /PRtot -ratio, y3 , is 49% [61 − (61-32)·(5.75-3)/(7.8-3), where 61 is the value at D = 3 m sampling depth and 32 is the value at D = 7.8 m]. The following working hypotheses are put forward: • We assume that y2 or y3 are the most lake representative values but that there might be strong positive correlations among all three y-alternatives. • We assume that the y-value can be predicted well if D is replaced with the lake area of the photic zone above the Secchi depth (ASec ; as calculated from the equation in Fig. 4) and that Secchi depth can be replaced with lake area (A), i.e., D/Sec ≈ ASec /A. The ratio ASec /A is the fraction of the lake above the effective depth of the photic zone. • We also assume that predictive power will be lost when shifting from site-typical to lake-typical calculations using this data-set based on site-typical data.

Figure 5 gives four scatter plots: (A) between y3 (MV from Sec/2) and y2 (Weighted MV); the correlation is high (r 2 = 0.86), which supports the working hypothesis. (B) between y3 and y1 (Mean value); the correlation is rather low (r 2 = 0.36), which indicates that y1 , as expected, is not a very representative lake mean value. (C) y3 and the same ratio based on data from individual sampling sites (PBBA /PBTot ); the correlation is rather high (r 2 = 0.65), which supports the idea that y3 is a characteristic lake measure, and (D) between y3 and the ratio ASec /A; the correlation is low (r 2 = 0.16), which contradicts the working hypothesis concerning the key role of the ASec /Aratio in predicting y3 . To test if it is possible to obtain a relevant and useful regression model for entire lakes, we have data from only 8 lakes. From the morphometric data given in Table 3, one can also determine several lake form variables that could influence the PBBA /PBTot -ratio, such as the form factor, Vd, the dynamic ratio, DR, the relative depth, Drel , and various expressions for littoral area, such as ASec /A, A1/A, A3/A (see Håkanson, 1981, for definitions of these standard morphometrical parameters). We have also tested to see if the parameters given in Table 3, i.e., latitude, longitude, altitude, Secchi depth, slope, area, mean depth and maximum depth can statistically explain the variability among these 8 lakes in the PBBA /PBTot -ratio, as given by y1 , y2 and y3 . Table 5 gives a correlation matrix for a selection of the tested variables and Figure 6 shows scatterplots for the four strongest correlations. One can note that in all these plots there are great variations around the regression lines and that no clear and highly significant relationships appear. It is, however, interesting to see that variations in latitude can statistically explain almost 40% (r 2 = 0.38) of the variability of the PBBA /PBTot -ratio among these 8 lakes. To conclude, it was not possible to find any useful equation to calculate normal reference values of the PBBA /PBTot -ratio using statistical methods. This actually supports the results from method 1, that there are no major differences among lakes in the PBBA /PBTot ratio, and that one can use a general calculation constant of 0.63 in Equation (2) between the production of benthic algae and phytoplankton. However, more data from more lakes may alter this conclusion which is only based on data from 8 lakes.

83

Figure 4. An illustration of how the form factor (= the volume development), Vd, can be used to express the form, here given by the relative hypsographic curve (= the depth-area curve) of lakes. Shallow lakes with a small Vd have relatively large areas above the wave base, where processes of wind/wave-induced resuspension will influence the bottom dynamic conditions. Deep, U-formed lakes generally have smaller areas above the wave base (ET-areas). Modified from Håkanson (2000).

One important aim of the following part is to present a dynamic model predicting weekly production values and biomass of benthic algae for entire lakes in a general manner. These values will then be compared to the values given by the empirical regressions (here called Norm bental). Dynamic model for production and biomass of benthic algae This section will introduce a dynamic model for benthic algae. Figure 7 gives an overview of the model. The following ordinary differential equation gives the fluxes (kg ww week−1 ) to and from the compartment ‘Benthic algae’ (BA), which includes all types of bottom-living algae, except macrophytes, which are treated separately in the LakeWeb-model.

The two target variables are biomass and production of benthic algae. BMBA (t) = BMBA (t − dt) + (IPRBA − CONBABE − ELBA − EROBA ) · dt,

(3)

where BMBA = biomass of benthic algae (kg ww); the initial BMBA -value is set equal to the normvalue, which is given by the normal production of benthic algae (from Equation 2) times the turnover time for benthic algae (TBA ; see Table 6), i.e.: NPRBA ·TBA ; IPRBA = initial production of benthic algae (kg ww week−1 ); note that the ‘production’ of benthic algae, PRBA , is given by the ratio between the calculated biomass, BMBA , and the turnover time, TBA ; CONBABE = consumption of benhic algae by zoobenthos (kg ww week−1 ); ELBA = Elimination (= turnover) of benthic algae (kg ww week−1 );

84 Table 5. Correlation matrix based on linear correlation coefficient (= r) for actual data for the parameters defined in the text. Statistically significant correlations at the 95%-level are bolded (r > 0.75).

y3 y2 y1 ASec /A Lat Long Alt Secchi Area Dm Dmax Vd DR Drel

y3

y2

y1

ASec/ A

Lat

Long

Alt

Secchi

Area

Dm

Dmax

Vd

DR

1 0.93 0.60 0.44 0.59 –0.51 –0.50 –0.05 0.61 0.29 0.40 –0.16 0.60 –0.23

0.76 0.38 0.43 –0.35 –0.35 0.13 0.35 0.45 0.53 0.00 0.34 –0.08

1 0.61 –0.12 0.20 0.22 0.70 –0.19 0.87 0.90 0.61 –0.21 0.37

1 –0.03 0.04 0.10 0.54 0.19 0.76 0.79 0.66 0.16 –0.22

1 –0.99 –0.99 –0.77 0.76 –0.42 –0.35 –0.63 0.77 –0.53

1 1.00 0.80 –0.74 0.46 0.41 0.63 –0.75 0.60

1 0.83 –0.74 0.49 0.44 0.67 –0.74 0.56

1 –0.60 0.89 0.86 0.90 –0.61 0.50

1 –0.29 –0.19 –0.58 1.00 –0.77

1 0.99 0.87 –0.32 0.25

1 0.81 –0.22 0.21

1 –0.61 0.37

1 –0.77

EROBA = Physical erosion of benthic algae due to, e.g, wind/wave action. The same erosion rate is used for benthic algae and macrophytes (see Håkanson & Boulion, 2002b). It is defined in Equation (4). Physical erosion is a complicated process (see, e.g., Leclerc et al., 2000) involving wind speed, duration, fetch, wave characteristics, slope processes, erosion related to boating (from propellers, waves), etc. This means that the erosion rate (RERO ; 1/week) is an important part of the model. Basically, erosion is given by: EROBA = BMBA · RERO ,

(4)

where RERO is given by:

RERO = 0.112–0.134 · log(Maccov) + 0.077 · Vd. (5) According to Håkanson & Boulion (2002b), sixty percent of the variability in the values for the erosion rates can be statistically explained by differences among lakes in macrophyte cover (Maccov ) and the form factor (Vd; Vd = 3·Dm /Dmax ; Dm = the mean depth in m; Dmax = the maximum depth in m; see Håkanson, 1981). The larger the macrophyte cover, the smaller the erosion rate. This is logical since the exposed parts of the macrophyte cover could be regarded as a wave protection for the sheltered, inner parts. The next most important factor is the form factor. Lakes with large shallow areas (V-shaped lakes) logically have higher erosion rates than U-shaped lakes

Drel

1

The initial production of benthic algae is given by: IPRBA = RBA · ASec · YSec · Ytemp · YTP .

(6)

In the dynamic model, we calculate the initial production of benthic algae, IPRBA , based on the results of the previous discussion, i.e., the by accounting for variations among lakes in Secchi depth (YSec ), the morphometry of the lake (the area shallower than the Secchi depth, ASec , in m2 ), water temperature (as given by Ytemp ) and primary phytoplankton production, or here the supply of phosphorus (as given by YTP ). RBA is the initial production rate constant, which gives production (kg ww week−1 ) per sediment are unit (m2 ). The initial production of benthic algae, IPRBA , has the dimension kg ww week−1 (for the entire lake). The initial production is higher than the production (PR = BM/T; BM = biomass, T = turnover time) because production also accounts for elimination, physical erosion and grazing by zoobenthos. So, Equation (6) gives that: (1) There is a benthic algae production rate constant, RBA , which drives the production. (2) The morphometry of the lake will influence the production. This is expressed by the area of the photic zone shallower then the Secchi depth (ASec in m2 ; as calculated from Secchi depth and the hypsographic method; see Fig. 4). The larger the ASec -area, the higher the potential production of benthic algae, if all else is constant. We assume

85

Figure 5. The relationship between y3 , i.e., the mean lake value of the ratio between production of benthic algae to total production (benthic algae plus phytoplankton) as calculated using the Sec/2-approach, and: (A) the same thing using weighted mean values (the y2 -method), (B) the same thing using mean values of actual data (the y1 -method), (C) the same ratio as calculated not for entire lakes but for sampling sites, and (D) the ‘littoral-zone ratio’, ASec /A assumed to be highly related to y3 .

Table 6. Characteristic turnover times (or life span; T = BM/PR; where BM = biomass in kg ww PR = biomass production in kg ww/day). Based mainly on data from Winberg (1985). Group

Turnover time (days)

Phytoplankton Bacteria Benthic algae Herbivorous zooplankton Predatory zooplankton Prey fish Predatory fish Zoobenthos Macrophytes

3.2 2.8 4.0 6.0 11.0 300 450 128 300 (according to Raspopov, 1973)

that there is a linear relationship between IPRBA and the ASec -area. (3) Secchi depth (in m), the more transparent the water, the higher the production of benthic algae. We assume a linear relationship also in this case and YSec is simple set to Sec/3, where 3 is a reference Secchi depth. This gives the requested dimension for IPRBA (kg ww week−1 ). (4) Evidently, the production of benthic algae is also temperature dependent, and in this approach we use the same dimensionless moderator for temperature as in many other similar situations in the LakeWeb-model (see Håkanson & Boulion, 2002a). So, Ytemp is given by the ratio between EpiTemp (i.e., weekly epilimnetic temperatures

86

Figure 6. Four scatterplots and statistics illustrating the relationship between the PBBA /PBTot -ratio and (A) the dynamic ratio (DR), (B) Latitude, (C) Lake area and (D) Longitude.

in ◦ C) and the reference temperature of 9 ◦ C (related to the duration of the growing season, see Håkanson & Boulion, 2001b). (5) We also assume that the production of benthic algae depends on the availability of phosphorus, but, as already stressed, less so than phytoplankton and more so than macrophytes. This dependency is given by the following dimensionless moderator (see Håkanson & Peters, 1995, for more information on dimensionless moderators in lake modelling): YTP = (1 + 0.75 · (CTP /10 − 1))

(7)

where CTP is the lake TP-concentration (in µg l−1 ). The normal value is 10 µg l−1 . The amplitude value is set to 0.75, which means that YTP is 0.48 if CTP = 3 µg l−1 (for a very oligotrophic lake) and YTP = 23

for a lake with CTP = 300 (a hypertrophic lake), if all else is constant. This means that lake phosphorus influences the production of benthic algae but it is not the key factor. We will soon demonstrate how the model works along several gradients, including a TP-gradient. The consumption of benthic algae, CONBABE , by zoobenthos is calculated from: CONBABE = BMBA · CRBABE

(8)

where CRBABE is the actual consumption rate (dimension 1/week) describing zoobenthos feeding on benthic algae; BMBA is the biomass of benthic algae (kg ww). CRBABE is calculated from the LakeWeb-model (see Håkanson & Boulion, 2002a) and given by: CRBABE = (NCRBE + NCRBE ·

87

Figure 7. Illustration of the dynamic model for benthic algae (= bental).

(BMBE /NBMBE − 1)),

(9)

The normal biomass of zoobenthos is given by (from Peters, 1986 and Håkanson & Boulion, 2002a):

where NCRBE = the normal consumption rate for zoobenthos is defined by the ratio NRBE /TBE ; TBE is the turnover time of zoobenthos (= 128 days, see Table 6). The number of first order food choices for zoobenthos, NRBE , is 2 [sediments or (benthic algae plus macrophytes)]; BMBE = the actual biomass of zoobenthos (kg ww); the higher the actual biomass of zoobenthos relative to the normal biomass of zoobenthos (NBMBE ), the higher the grazing pressure exerted by zoobenthos on benthic algae.

If CTPMV < 100 µg l−1 then NBMBE = (10−6 )· 0.71 ) · Area else, 810 · (CTPMV (10) 0.71 ) · Area· NBMBE = (10−6 ) · 810 · (CTPMV (1 − 0.5 · (CTPMV /100 − 1)). 0.71 )) The basic empirical regression (810 · (CTPMV is derived for lakes with mean TP-concentrations (CTPMV ) lower than 100 µg l−1 . Note that very eutrophic lakes are likely to have anoxic sediments where zoobenthos cannot survive. The critical oxy-

88 Table 7. The conditions in the default lake are as follows. Lake area = 1 km2 ; mean depth = 10 m; maximum depth 20 m, Lake coulour = 50 mg Pt/l and pH = 7, Lake TP-concentration is generally set to 10 µg/l, if it is not predicted to about 10 µg/l by the mass-balance model for phosphorus when ADA = 10 km2 (ADA = area of drainage area), Prec = 650 mm/yr (Prec = mean annual precipitation) and Cin = 30 µg P/l (Cin = the mean tributary TP-concentration).

gen concentration is about 2 mg l−1 (see Håkanson & Jansson, 1983) and hypertrophic lakes with TPconcentration higher than 300 µg l−1 and values of gross sedimentation higher than 2000 µg cm−2 d−1 , are not likely to have much zoobenthos in the Asediments, only in the ET-sediments. The elimination of benthic algae in (kg ww week−1 ) is given by: ELBA = BMBA · 1.386/TBA,

(11)

where 1.386 is the halflife constant (1.386 = −ln(0.5)/0.5; see Håkanson & Peters, 1995) and TBA is the characteristic turnover time of benthic algae, set according to Table 6 at 4 days. With this, we have considered all processes regulating the production and biomass of benthic algae in the dynamic model. The most important part for the model calibration, and actually the only calibration constant in the model for benthic algae which is not mechanistically motivated, is the value used for the benthic algae production rate constant, RBA . It has been calibrated to be 0.027 kg ww m−2 week−1 (i.e., production per area unit of the sediments). In a following section, we will illustrate the correspondence between modelled values and norm-values (as calculated according to method 1) for the production of benthic algae. Model tests and simulations The aims of this section are: To illustrate how the new model behaves in situations where gradients are created in a systematic manner for all the given driving variables. • Tributary TP-concentrations will be changed from 10 to 1000 µg/l. This covers the entire range from ultraoligotrophic to hypertrophic conditions. • Lake colour values, i.e., allochthonous influences, will be changed from ultraoligohumic to hyperhumic by creating colour gradients from 3 to 300 mg Pt l−1 .

• Lake pH-values will be altered from extremely acidic to extremely basic conditions; pH-values from 3 to 11 will be tested. • We will also create a latitude gradient and ‘place’ the default lake at 40, 45, 50, 60 and 70◦ N. • Morphometric influences will be tested by changing the mean depth from 1 to 100 m and the lake area from 0.1 to 1000 km2 . All these changes will be calculated for: (1) Lake TP-concentrations and the norm TPconcentration calculated from the empirical standard model (OECD, 1982). (2) Secchi depths and the norm Secchi depths, as calculated from the empirical reference equation (see Håkanson & Boulion, 2002a). (3) Modelled values of the production of benthic algae and comparisons with the corresponding empirical norm. (4) Biomass of benthic algae and the corresponding empirical norm-values. Eutrophication gradient Figure 8 gives the results related to the given TPgradient. The driving variable is given by curve 3 in Figure 8A. Cin was changed in 2-year steps from 10 to 1000 µg l−1 . How will this influence the six targets using data for the default lake (i.e., the reference lake; see Table 7)? • Figure 8A shows how the model predicts the changes in modelled TP-concentrations (curve 1) and TP-concentrations calculated with the OECDreference model (curve 2). The correspondence between these two curves is good, especially in the domain of the OECD-model, but outside this domain (if the TP-concentration is higher than 100 µg l−1 ), the LakeWeb-model would be likely to produce more reliable predictions. These changes in lake TP-concentration will influence many lake processes. • Figure 8B shows the predicted response for modelled Secchi depth (curve 1) and norm Secchi depth (curve 2). Note that the correspondence

89

Figure 8. Critical model testing (sensitivity analyses) for the following four variables under default conditions along a trophic state gradient. The driving variable is the tributary TP-concentration, which has been varied according to curve 3 in (A) (from 10 to 1000 µg l−1 ). (A) Gives predicted lake TP-concentrations (curve 1) and the norm TP-concentration calculated from the OECD-model (curve 2). (B) Gives modelled Secchi depths (curve 1) and the norm Secchi depths, as calculated from the empirical reference equation. (C) Gives modelled values of the production of benthic algae (curve 1), the production of benthic algae, as given by the empirical norm (curve 2), predicted initial phytoplankton production (curve 3) and predicted phytoplankton production (curve 4). (D) Gives modelled biomass of benthic algae (curve 1) and the corresponding empirical norm-values.

is excellent, and that the norm-values are given only for the summer season. Thus, when lake TP-concentrations increase, primary production increases and Secchi depth decreases. Concerning the production of benthic algae these two changes counteract one another. The more phosphorus in the lake, the higher the production of benthic algae, and the more transparent the water, the higher the production of benthic algae. So, it is not a simple and self-evident matter to predict the response for benthic algae production in a TP-gradient. The LakeWeb-model is meant to provide a mechanistically sound and empirically based solution to this problem, as shown in Figure 8C. • Figure 8C illustrates in curve 1 the modelled values of the production of benthic algae, curve 2 gives the corresponding norm-values, and curve 3, as an interesting reference, the phytoplankton

production. One can note that the two curves for benthic algae production are close, and the phytoplankton production is a little lower in the default lake under the given presuppositions. The norm production of benthic algae (curve 2) is calculated from the phytoplankton production (using ‘method 1’). • Figure 8D illustrates the changes in biomass of benthic algae, curve 1 gives the modelled values and curve 2 the norm-values. Note the very good correspondence between the two curves. So, the model gives a reasonable response in this TP-gradient and the co-variations between the modelled values and the empirical norms are good where they should be and the divergences from the norms are logical.

90

Figure 9. Critical model testing (sensitivity analyses) for the following four variables under default conditions along a lake pH-gradient. The driving variable, lake pH, has been varied according to curve 3 in (A) (from 3 to 11). (A) Gives predicted lake TP-concentrations (curve 1) and the norm TP-concentration calculated from the OECD-model (curve 2). (B) Gives modelled Secchi depths (curve 1) and the norm Secchi depths, as calculated from the empirical reference equation. (C) Gives modelled values of the production of benthic algae (curve 1), the production of benthic algae, as given by the empirical norm (curve 2), predicted initial phytoplankton production (curve 3) and predicted phytoplankton production (curve 4). (D) Gives modelled biomass of benthic algae (curve 1) and the corresponding empirical norm-values.

Acidification gradient Similar results for pH-changes are shown in Figure 9. The driving variable is given by curve 3 in Fig. 9A. Lake pH was changed in 2-year intervals from pH 3 to 11. Note that pH-values lower than 5 and higher than 9 are relatively rare in natural lakes. How will this influence the target variables using data for the default lake? • Figure 9A shows how the model predicts the corresponding TP-concentrations (curve 1) and the TP-concentrations calculated with the OECDreference model (curve 2). The correspondence between curves 1 and 2 is good in the domain of the OECD-model (pH < 9), but outside this domain, LakeWeb predicts lower values. We would argue that these values are more reliable than the ones given by the norm since pH actually influences many lake processes not accounted for in the norm, like phytoplankton production, aggrega-

tion of suspended particles and Secchi depth. The given increases in pH will also lower lake TPconcentrations and hence also increase the Secchi depth. Low lake pH will also increase aggregation and sedimentation and reduce suspended particles from the water mass so that the Secchi depth becomes even higher (Fig. 9B). A higher pH means a lower Secchi depth, and also an increased concentration of suspended particulate matter (SPM), which will increase the sedimentation of particulate phosphorus, so that lake TP-concentrations become lower (curve 1 in Fig. 9A). With decreasing lake TP-concentration AND a decreasing Secchi depth, it is interesting and certainly not trivial to see the response in production of benthic algae. • Figure 9B shows the predicted response for modelled Secchi depth (curve 1) and the norm Secchi depth (curve 2). Note that the correspondence is

91

Figure 10. Critical model testing for the following four variables under default conditions along a lake colour gradient. The driving variable has been varied according to curve 3 in (A) (from 3 to 300 mg Pt l−1 ). (A) Gives predicted lake TP-concentrations (curve 1) and the norm TP-concentration calculated from the OECD-model (curve 2). (B) Gives modelled Secchi depths (curve 1) and the norm Secchi depths, as calculated from the empirical reference equation. (C) Gives modelled values of the production of benthic algae (curve 1), the production of benthic algae, as given by the empirical norm (curve 2), predicted initial phytoplankton production (curve 3) and predicted phytoplankton production (curve 4). (D) Gives modelled biomass of benthic algae (curve 1) and the corresponding empirical norm-values.

excellent for all pH-values in the range of the norm (i.e., if pH ≥ 5). • Figure 9C illustrates the production of benthic algae (curve 1), the corresponding norm-values (curve 2), and the phytoplankton production (curve 3). One can note that at very low pH-values (pH = 3), phytoplankton production (curve 3) is much lower than the production of benthic algae (curve 1); for pH-values in the ‘normal’ range (5 to 9), modelled values and norm-values for benthic algae production are very close; and for very high pHvalues, the modelled production of benthic algae is higher then the norm-values and phytoplankton production because the conditions in the benthic community are less dependent on water chemistry than phytoplankton living in the water. • Figure 9D illustrates the predicted changes in biomass of benthic algae, curve 1 gives the modelled values and curve 2 the norm-values. Note the very

good correspondence between the norm-values and the modelled for all ‘normal’ pH-values. So, also in this scenario, the model can capture the essential changes related to the pH-gradient and the relationships between modelled values and empirical norm-values are logical. Humification gradient Figure 10 gives the results along the colour-gradient. Lake colour values were changed in 2-year intervals from ultraoligohumic condition (3 mg Pt l−1 ) to very dystrophic conditions (300 mg Pt l−1 ). • Figure 10A shows that the model then predicts a successive lowering of TP-concentrations (curve 1). This can be explained by the following factors accounted for in the LakeWeb-model: low colour, i.e., a low concentration of humic and fulvic matter in the water, means a high Secchi depth (Fig. 10B), correspondingly low values of SPM, and low sed-

92

Figure 11. Sensitivity analyses for the following four variables under default conditions along a latitude gradient. The driving variable has been varied according to curve 3 in (A) (from lakes at latitude 40◦ N to 70◦ N). (A) Gives predicted lake TP-concentrations (curve 1) and the norm TP-concentration calculated from the OECD-model (curve 2). (B) Gives modelled Secchi depths (curve 1) and the norm Secchi depths, as calculated from the empirical reference equation. (C) Gives modelled values of the production of benthic algae (curve 1), the production of benthic algae, as given by the empirical norm (curve 2), predicted initial phytoplankton production (curve 3) and predicted phytoplankton production (curve 4). (D) Gives modelled biomass of benthic algae (curve 1) and the corresponding empirical norm-values.

imentation of particulate phosphorus and, hence relatively higher TP-concentrations in lake water. High colour values also increase the production of bacterioplankton. Note that by using the given scale for TP-concentrations (0 to 20 µg l−1 on the y-axis), it seems as though the difference between modelled lake TP-concentrations (curve 1) and the norm-values given by the OECD-model is large, but it is only about 2 µg l−1 for the initial lake colour conditions. • Figure 10B shows the predicted response for modelled Secchi depth (curve 1) and norm Secchi depth (curve 2). Note that the correspondence is very good (for the growing season). So, also in this scenario, we have a situation with decreasing TP-concentrations in the water AND decreasing Secchi depths, which should counteract one another with regard to the production of benthic algae. The more phosphorus in the lake, the higher the production of benthic algae, and the more

transparent the water, the higher the production of benthic algae. The predictions for benthic algae are given in Figure 10C. • Curve 1 in Figure 10C gives the modelled values of the production of benthic algae, curve 2 the corresponding norm-values, curve 3 the phytoplankton production. It is interesting to note that: (1) For all colour-values, there is a very good correspondence between the modelled values (curve 1) and the norm-values (curve 2). (2) Phytoplankton production (curve 3) is lower than the production of benthic algae. With increasing colour-values, and decreasing Secchi depth, the production of benthic algae becomes lower and lower, and so does the phytoplankton production because the TP-concentrations also get lower as well as the depth of the photic zone. • Figure 10D illustrates the changes in biomass of benthic algae. There is an excellent correspond-

93

Figure 12. Critical model testing (sensitivity analyses) for the following four variables under default conditions along a gradient created by variations in lake mean depth (curve 3 in (A); Dm has been set to 1, 3, 10, 30 and 1000 m). (A) Gives predicted lake TP-concentrations (curve 1) and the norm TP-concentration calculated from the OECD-model (curve 2). (B) Gives modelled Secchi depths (curve 1) and the norm Secchi depths, as calculated from the empirical reference equation. (C) Gives modelled values of the production of benthic algae (curve 1), the production of benthic algae, as given by the empirical norm (curve 2), predicted initial phytoplankton production (curve 3) and predicted phytoplankton production (curve 4). (D) Gives modelled biomass of benthic algae (curve 1) and the corresponding empirical norm-values.

ence between the empirical norm-values and the modelled values in the whole colour-range. We can conclude that also in this case, the model gives a logical representation of the target variables and the relationships to the given norms are good. Latitude (temperature) gradient The results along the latitude-gradient are given in Figure 11. The default lake has been ‘placed’ at latitudes, 40, 45, 50, 55, 60 and 70◦ N in 2-year steps. • Under these conditions, Figure 11A shows that the model predicts a successive but rather small decrease in TP-concentrations (curve 1) and there is a good correspondence between modelled values and the norm (curve 2, the OECD-model). The lower TP-concentrations are related to the changes in lake temperature, and hence the lower bio-uptake and the reduced retention of TP in the system. Lower epilimnetic temperatures reduce

primary and secondary production, as exemplified by the curves for phytoplankton production (curve 3 in Fig. 11C), benthic algae production (curve 1 in Fig. 11C) and benthic algae biomass (curve 1 in Fig. 11D). • The modelled Secchi depths (curve 1 in Fig. 11B) and the norm Secchi depths (curve 2) are in excellent agreement. • Figure 11C gives the modelled values of the production of benthic algae, the norm-values for benthic algae, and the phytoplankton production curve. All curves become lower with a lower temperature and higher latitude and this trend is supported by lower lake TP-concentrations, and it cannot be compensated by any significant changes in Secchi depth. • Figure 11D illustrates the changes in biomass of benthic algae and the good correspondence between the two curves.

94

Figure 13. Model testing for the following four variables under default conditions along a gradient created by variations in lake area (curve 3 in (A); Area has been set to 0.1, 1, 10, 100 and 1000 km2 and the catchment area is set to be 10 times the lake area. Note that this version of the LakeWeb-model is mainly tested for lakes smaller than 300 km2 . (A) Gives predicted lake TP-concentrations (curve 1) and the norm TP-concentration calculated from the OECD-model (curve 2). (B) Gives modelled Secchi depths (curve 1) and the norm Secchi depths, as calculated from the empirical reference equation. (C) Gives modelled values of the production of benthic algae (curve 1), the production of benthic algae, as given by the empirical norm (curve 2), predicted initial phytoplankton production (curve 3) and predicted phytoplankton production (curve 4). (D) Gives modelled biomass of benthic algae (curve 1) and the corresponding empirical norm-values.

Once again, we can conclude that the model gives a very good and logical representation of the target variables and realistic relationship to the given norms. Lake mean depth gradient Figure 12 shows the results in relation to the given Dm -gradient. The mean depth (Dm ) was varied between 1 and 100 m. For lakes with mean depths larger than 15 m, the maximum depths have been set to 1.5·Dm in this test. How will this influence the targets using data for the default lake? • Figure 12A shows how the model predicts the changes in TP-concentrations (curve 1) and in norm TP-concentrations calculated with the OECD-model (curve 2). The correspondence between curves 1 and 2 is good. Generally, under these presuppositions, the LakeWeb-model predicts TP-concentrations about 2 µg l−1 lower

than the OECD-model. Note that the tributary TPconcentration has been kept constant at 30 µg l−1 , so that these changes in lake TP-concentrations are logical and partly a mathematical consequence of changing volumes related to changing mean depths. But changes in lake morphometry will influence many internal lake processes, such as the areal extent of the ET-areas and hence resuspension, and the amount of phosphorus on A-areas and hence also diffusion. So, Figure 12A does not just illustrate a simple decrease in lake TP-concentration from an increase in lake volume. • Figure 12B gives the predicted response for modelled Secchi depths (curve 1) and norm Secchi depths (curve 2). Note that the correspondence is very good for all ‘normal’ lakes. It must be stressed that it would be quite exceptional to have a lake with an area of 1 km2 and a mean depth of

95 100 m (and a max. depth of 150 m). The marked increases in Secchi depths for higher mean depths are related partly to the decreases in lake TPconcentrations (and hence primary production), but also to the changes in lake morphometry, and the fact that very deep and small lakes are U-shaped with smaller areas influenced by windinduced resuspension. So, this is a situation with decreasing lake TP-concentrations and increasing and Secchi depths. • Figure 12C gives the modelled values of the production of benthic algae (curve 1), the norm-values (curve 2), and the phytoplankton production curve (curve 3). The two curves for production of benthic algae are very close for all ‘normal’ lakes, i.e., as long as the mean depth is smaller than 30 m (area = 1 km2 ). The modelled values for the production of benthic algae increase markedly with increasing Secchi depth. This scenario clearly illustrates the close and interesting relationships between changes in morphometry, lake TP-concentrations, Secchi depth, phytoplankton production and production of benthic algae. Evidently, changes in morphometry do not concern individual lakes, it concerns the important general problem regarding ‘form and function’ of aquatic ecosystems and characteristic variations among lakes. • Figure 12D illustrates the changes in biomass of benthic alge and the good correspondence between modelled values and norm-values. The model also gives a logical response in this Dm -gradient and the co-variations between modelled values and the empirical norms are relevant. Lake area gradient Figure 13, finally, gives the results in relation to changes in lake area, which has been altered in a stepwise manner from 0.1 to 1000 km2 . Note that we basically intend the model to predict well for lakes smaller than 300 km2. Larger lakes may have to be divided into sub-areas where different water chemistry, hydrodynamical and sedimentological conditions prevail, and hence also different key functional organisms. Also note that totally unrealistic predictions would be obtained if in this scenario we had not also changed the catchment area of the lake. Normally, as a rule of the thumb, one can expect that a catchment area is 10 times larger than the lake area (see Håkanson & Peters, 1995). In the following simulations, we have used this simple calculation constant.

• The correspondence between modelled TP-values (curve 1) and the norm-values (curve 2) are shown in Figure 13A. Note that the scale is from 0 to 20 µg l−1 on the y-axis. At each step when the lake area has been altered, we can see a marked dip in curve 1, related to the sudden increase in lake volume. Also in this case, we have kept the tributary TP-concentration constant (30 µg l−1 ), so the changes in lake TP-concentrations are again partly a function of the change in lake volume from the given changes in lake area. But in this case there are no major changes in Secchi depths, as it was along the Dm -gradient, and there is a reasonable correspondence between modelled values and norm-values (Fig. 13B). The seemingly lower TPconcentrations with increasing area are balanced by increasing resuspension, so the net effects for the Secchi depths are small. Resuspension as such is not accounted for in the norm for Secchi depth (curve 2 in Fig. 13B), which is based on changes in lake TP-concentration (and colour and pH). It should be noted, however, that all measured lake TP-concentrations (if they are done correctly) account for all processes (including resuspension) influencing the given concentration, but this cannot be specified in the empirical model as it can in the dynamic model. • Figure 13C gives the modelled values of the production of benthic algae (curve 1), the norm-values (curve 2) and the phytoplankton production (curve 3). Note: (1) The logarithmic scale on the y-axis. (2) That the two curves for production of benthic algae are close (curve 1 and the norm, curve 2). (3) That the modelled values for the production of benthic algae by definition increase with lake area. The Secchi depths are fairly constant. (4) These production values for benthic algae are reflected in the increased biomass of benthic algae (Fig. 13D). So, the model gives logical responses also in the area-gradient and the relationships between the modelled values and the empirical norms are reasonable. Concluding comments An important aspect of these tests is that one does not need to speculate about the explanations to the various

96 observed phenomena. They are, in fact, mathematically defined. This is of course not the case for most observed phenomena in natural ecosystems. So, if the dynamic model can capture the essential interactions in natural ecosystems at the given scale, it is an excellent tool to gain understanding about often very complex and contradicting observations. This paper on benthic algae has presented a new empirically-based approach to estimate the production of benthic algae from phytoplankton production, and a new dynamic model for benthic algae. This dynamical model has been critically tested along six gradients which cover a very wide limnological domain. These critical tests have demonstrated that the dynamic model can capture essential mechanisms regulating production and biomass of benthic algae at the lake ecosystem scale from few and readily accessible driving variables. This work has also introduced extensive data-sets on benthic algae in lakes. When more and better empirical data become available from even more lakes covering an even wider limnological range for which one would also have data on the factors regulating the production and biomasses and benthic algae, many of the results and the values used for the model variables discussed here should be revised. There is still very much research needed on the role of, e.g., benthic algae in lake ecosystems, and the dynamic model presented here should be regarded as a first contribution. It should be noted that many of the processes and mechanisms accounted for in the dynamical model for lakes would also probably apply for brackish and marine areas. This modelling has focussed at the ecosystem scale (i.e., on entire lakes), on weekly predictions and on a functional group. Much work in aquatic ecology concerns finer temporal and spatial scales and species rather than functional groups. In the future, it might be possible to develop predictive models also for species. To achieve good predictions for species by generic models (based on driving variables that are easy to access) would, however, be much more complicated than for functional groups. But maybe these results can be seen as a step in that direction because it may be easier to model at those finer scales if the overall conditions for functional groups at the ecosystem scale are first sorted out.

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