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Appendix 1: PCLake model description

(adapted from Janse 2005)

Structure

The model PCLake describes a completely mixed water body and comprises both the water column and the sediment top layer, with the most important biotic and abiotic components.

The model is thus meant for shallow, non-stratifying lakes. No further horizontal or vertical distinction within the lake is taken into account. The model offers the option to include a marsh zone with emergent vegetation, but that has not been used in this study.

Mathematically, the model is composed of a number of coupled differential equations, one for each state variable, as listed in Appendix 1 - Table 1. The model is numerically solved by the Runge-Kutta Cash-Karp method which has a variable time step. The structure of the lake model is shown in Figure 1. All biota are modeled as functional groups. Besides mass fluxes

(food relations, and so on), the model also contains some ‘empirical’ or indirect relations between components, such as the impact of fish and macrophytes on resuspension (see below). The overall nutrient cycles for N, P and Si are described as completely closed (except for external fluxes such as in- and outflow and denitrification). This was done by modeling most components in three elements, that is, dry weight (abbreviated as D), nitrogen (N) and

phosphorus (P), detritus also in silica (Si). Inorganic carbon (CO2) is not explicitly modeled.

The nutrient-to-dry-weight ratios are thus variable. As the nutrient ratios of organisms increase with their trophic level (that is, phytoplankton < zooplankton < fish), mechanisms are included to allow for those differences, such as a higher assimilation efficiency for nutrients than for carbon. The total mass balances per element are dynamically checked during the calculations. ‘Day’ was chosen as a uniform time unit for all processes (but the

1 simulation time can be chosen as variable); however, the relevant time scale for the output is about weeks to months. The main inputs to the model are: water inflow, infiltration or seepage rate (if any), nutrient (N, P) loading, particulate loading, temperature and light, dimensions (lake depth and fetch - determining indirectly wave intensity), sediment features and loading history (initial conditions). As output, the biomass and concentrations of all state variables, as well as a number of derived variables and fluxes, are calculated.

Processes

The processes in the model will be briefly described here; a complete description of the model is given by Janse (2005). a. Abiotic and microbial processes

At the base of the model are the transport processes: in- and outflow and external loading by nutrients and by organic and inorganic matter. Infiltration to, or seepage from, the groundwater can also be defined. The sediment top layer has a fixed thickness (default

0.1 m) and consists of inorganic matter (IM) (with a fixed fraction of clay particles), humus, detritus and pore water. Exchange of IM and detritus between water and sediment may take place via settling (described as a first-order process) and resuspension (zero-order process).

The settling rate decreases, and the resuspension increases, with the size of the lake. The resuspension also increases with the sediment porosity and with the amount of benthivorous fish (see below), while it decreases with the vegetation cover. A net increase of sediment material is met by an equal amount considered as buried to deeper layers.

Mineralization of detritus (degradable organic matter) is described as a first-order process, dependent on temperature assuming a maximum mineralization rate in the water of 1% d-1 and in the sediment of 0.2% d-1. Humus (refractory organic matter) is assumed to be

2 mineralized only very slowly. The released nutrients are dissolved in the pore water.

Inorganic P is subject to reversible adsorption to IM according to a Langmuir isotherm. It might also precipitate in case of a very high concentration. The relative adsorption increases with the sediment content of clay particles and with the aerobic proportion of the sediment.

The latter is modeled in a highly simplified way by defining a quasi-steady state oxygen penetration depth (or aerobic sediment fraction), which is a function of the oxygen concentration in the water, the potential sediment oxygen demand and the diffusion rate.

Nitrification of NH4 increases, denitrification of NO3 decreases with the aerobic proportion of the sediment. Exchange of dissolved P and N between pore water and water column is modeled according to the concentration differences. The combined result of the described

processes is that the PO4 release rate follows a seasonal cycle, dependent on the temperature and the amount of detritus in the system. Mineralization and nitrification are described in the water column as well. Oxygen in the water column is modeled dynamically, dependent on the biochemical oxygen demand and sediment oxygen demand, the reaeration from the atmosphere, and the oxygen production by phytoplankton and/or submerged plants.

b. Phytoplankton

The phytoplankton module describes the growth and loss of the three functional groups of phytoplankton, that is, cyanobacteria, diatoms and green algae. This distinction was made because of their different characteristics. The biomass of each group is described by the following differential equations: dx/dt = production – respiration – mortality – settling + resuspension – grazing + transport and by parallel equations for phytoplankton expressed in N and P units (here denoted by y):

3 dy/dt = uptake – excretion – mortality – settling + resuspension – grazing + transport

The production (carbon fixation, for simplicity taken as equivalent to growth) depends on the maximum growth rate, temperature, day length, under-water light, P and N, for diatoms also on silica. The temperature dependence is described using an optimum function. The light dependent growth of cyanobacteria and diatoms is described according to Di Toro and

Matystik (1980), using Steele’s equation integrated with respect to the depth. This equation implies growth inhibition at high light intensities. For green algae, a similar equation is based on a Monod-type equation, assuming no light inhibition. The available light, taken as

‘photosynthetically active radiation’ (PAR), is determined by the light intensity at the water surface and its extinction in the water column (Lambert-Beer’s law). The extinction coefficient is the sum of the background extinction of the water and the contributions of IM, detritus and phytoplankton (and submerged plants) to it, thus accounting for the self- shading effect that sets a limit to the maximum biomass. P and N affect the growth rate via the internal nutrient contents of the phytoplankton rather than the external concentrations.

Nutrient uptake is thus described separately from the production, to allow for this variable stoichiometry. The uptake rate increases with the external nutrient concentration up to a maximum that is determined by the actual ratio (‘cell quota’), the minimum cell quota giving the highest maximum rate (Riegman and Mur 1984). The biomass production is then dependent on the cell quota according to the Droop (1974) equation: the growth rate increases asymptotically with the cell quota provided it is above the minimum. For the silica- dependent growth of diatoms, the more simple Monod formulation was chosen based on

the external SiO2 concentration, with a fixed Si content of the diatoms. The actual growth rate is calculated by multiplying the maximum growth rate with the combined reduction functions for light and temperature and the one for nutrients. The latter is taken as the

4 minimum of the functions for N and P (and Si for diatoms), following Liebig’s law. The chlorophyll-a content of the phytoplankton, a derived variable in the model, is assumed to be variable, being higher in case of a more severe light limitation (Riegman 1985). Secchi depth is calculated as the Poole-Atkins coefficient divided by the extinction. The loss processes, maintenance respiration and natural mortality, are described as first-order processes, respiration as temperature-dependent. Excretion of nutrients parallel to respiration is assumed to decrease if the internal nutrient ratio is low. Settling is also described as first order, the rate being the settling velocity [m d-1] divided by the water depth. For ‘analogy’ reasons, the settled algae are included as separate state variables, which may re-enter the water column by resuspension, coupled to the resuspension of other particles (see above). It is assumed that the settled algae do not grow, but are subject to respiration and mortality and may be eaten by zoobenthos. The parameter values of the three algal groups in the model differ. The cyanobacteria have a higher light affinity (they are shade-adapted) as well as a higher phosphorus uptake rate than the other groups. On the other hand, they have a much lower maximum growth rate and a stronger sensitivity to temperature. The diatoms have a lower temperature optimum, while the green algae are not inhibited by high light intensities. Both these groups have higher growth rates, but also higher loss rates through settling and zooplankton grazing (see below). The diatoms are the only group that might be limited by silica.

c. Aquatic vegetation

The submerged vegetation is described as one lumped group by the following differential equation for the biomass: dx/dt = production - respiration – mortality

5 and for nutrients (N and P) stored in the plants: dy/dt = uptake - excretion - mortality

It is assumed that the biomass is divided in an under-ground part (roots) and an above- ground part (shoots), and that the latter is homogeneously divided over the water column.

Seasonality is modeled in a simplified way by assuming a high root fraction in the winter period and a low one during the growing season (default 0.6 and 0.1, resp.). The switch between both values in spring (triggered by water temperature) and autumn (triggered by season) mimics allocation and reallocation processes. The modeled vegetation thus stands for plants with overwintering parts. Biomass production by the shoot is modeled largely analogous to the phytoplankton production, that is, dependent on maximum growth rate, temperature, day length, under-water light, N and P. It is assumed that the macrophytes may extract nutrients from both the water and the sediment pore water, largely according to availability. In practice, sediment uptake is mostly higher. Respiration and nutrient excretion are modeled as for phytoplankton. Natural mortality is assumed to be low in the growing season and high at the end of it; a fixed fraction (default 0.3) is assumed to survive the winter. The description of the growth and mortality is combined with a density- dependent correction derived from the logistic growth equation, to account for other factors than the ones explicitly modeled, for instance space, that might be limiting for the plant density that could maximally be achieved, the ‘carrying capacity’. The vegetation is assumed to have some indirect impacts on other components of the system, that is, a hampering of resuspension, a slight negative impact on the feeding efficiency of benthivorous fish and a positive influence on the growth of predatory fish.

d. Food web

6 The food web module is kept as simple as possible and comprises zooplankton, zoobenthos, planktivorous, benthivorous and predatory fish. The general equation for the animal groups is: dx/dt = (feeding – egestion) – respiration – mortality - predation combined with a density-dependent correction derived from the logistic growth equation

(Hallam and others 1983; Traas 2004). The carrying capacities have been set to high values

(in the range of maximum observed biomasses). Zooplankton feeds on both phytoplankton and detritus. Grazing is described as a Monod-like function of the seston concentration, the specific filtering rate decreasing hyperbolically with increasing seston concentration (Gulati and others 1982; Gulati and others 1985). A selectivity constant is used for each food species to account for preference of the zooplankton: green algae > diatoms > detritus > cyanobacteria (for example, Gliwicz 1980). The assimilation efficiency for the consumed food is constant and quite low (0.3) for carbon (Gulati and others 1985), but variable (depending on the internal P ratio of the food) and, therefore, mostly higher for phosphorus. This is one of the mechanisms by means of which the differences in P content between the trophic levels are maintained. Zoobenthos is assumed to feed on sediment detritus and a bit on settled algae, also by a Monod-type (or ‘type II’) functional response. It is also assumed to be able to ‘accumulate’ P from its food comparable to zooplankton. All fish predation processes are modeled as a so-called ‘type III’ response (Holling 1965): the predation rate depends on prey density according to a sigmoid curve. Planktivorous fish feeds on zooplankton, benthivorous fish on zoobenthos, and predatory fish on planktivorous and benthivorous fish.

Planktivorous fish are considered as juvenile and benthivorous as adult fish. Spawning is simulated as the transfer, every May, of a small proportion of the adult biomass to the juvenile biomass. At the end of each year, half the juvenile biomass becomes ‘adult’. Also

7 planktivorous and benthivorous fish are assumed to have a relatively higher phosphorus assimilation efficiency, as the internal P content of fish is again much higher than that of its food organisms (Kitchell and others 1975). For predatory fish, this mechanism does not play a role any more. An indirect effect of benthivorous fish that is included in the model is its stirring up of the sediment during feeding, causing a flux of particles and nutrients to the water column (Breukelaar and others 1994). Predatory fish is assumed to be dependent on the presence of vegetation.

References belonging only to Appendix 1

Di Toro, DM and Matystik, WF. 1980. Mathematical models of water quality in large lakes Part 1: Lake Huron and Saginaw Bay. University of Delaware, USA.

Droop MR. 1974. Nutrient status of algal cells in continuous culture. Journal of the Marine Biological Association of the United Kingdom 54: 825-855.

Gliwicz ZM. 1980. Filtering rates, food size selection, and feeding rates in cladocerans-another aspect of interspecific competition in filter-feeding zooplankton. American Society of Limnology and Oceanography Special Symposium 3: 282-291.

Gulati RD, Siewertsen K, Postema G. 1985. Zooplankton structure and grazing activities in relation to food quality and concentration in Dutch lakes. Archiv der Hydrobiologie: Beiheft, Ergebnisse der Limnologie 21: 91-102.

Hallam TG, Clark CE, Lassiter RR. 1983. Effects of toxicants on populations - a qualitative approach.1: Equilibrium environmental exposure. Ecological Modelling 18: 291-304.

Holling CS. 1965. The functional response of predators to prey density and its role in mimicry and population regulation. Memoirs of the Entomological Society of Canada 97: 5-60.

Kitchell JF, Koonce JF, Tennis PS. 1975. Phosphorous flux through fishes. Verhandlungen des Internationalen Verein Limnologie 19: 2478-2484.

Riegman, R. 1985. Phosphate - phytoplankton interactions. University of Amsterdam, Amsterdam.

Riegman R, Mur LR. 1984. Regulation of Phosphate-Uptake Kinetics in Oscillatoria agardhii. Archives of Microbiology 139: 28-32.

Traas, TP. 2004. Food web models in ecotoxicological risk assessment. Ch. 6: A mass-balance for the logistic population growth and implications for biomass turnover. Utrecht University, Utrecht.

8 Appendix 1 - Table 1: State Variables in PCLake

Component (state variable) In water column In sediment top layer Water water depth water -- (fixed)

Abiotic components inorganic matter (IM) D D

humus -- D

detritus D, P, N, Si D, P, N, Si

nutrients PO4, Pads, NH4, NO3, SiO2 PO4, Pads, NH4, NO3

oxygen O2 -- (aerobic fraction)

Phytoplankton diatoms D, P, N, (Si) D, P, N, (Si)

green algae D, P, N D, P, N

cyanobacteria D, P, N D, P, N

Vegetation submerged vegetation D, P, N

Animal groups zooplankton D, P, N

zoobenthos D, P, N

planktivorous fish D, P, N

benthivorous fish D, P, N

predatory fish D, (P, N)

Abbreviations: D = dry weight, P = phosphorus, N = nitrogen, Si =silica, O2 = oxygen.

9 Appendix 2: Changes in Biomasses and Process Rates Over Range of t-POM Loading for the Three Pathways

10 60 60 60

50 50 50

40 40 40

30 30 30

20 20 20

10 10 10

0 0 0 c h a n c c g h h 0 2 4 6 8 10 0 2 4 6 8 10 e 0 2 4 6 8 10 a a

i n n n g g

b e e t-POM loading t-POM loading t-POM loading i

o i i n n t u

b z r o b e o a n b t t h i o e i c n n

t f

16 25 [ 7 h i % s o h s ]

14

b 6 b

i 20 i o o m m 12 5 a a s s 10 15 s s

4

[ [ % % 8 ] ]

10 3 6 2 4 5 2 1 0 c 0 0 h a n g e c c 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 i h n h a a e n n x

t-POM loading g t-POM loading t-POM loading g t e i e n

c i i n n t i

o a i n n u o

t [ r h % g o

a -2 -1 c ] n

Appendix 2 – Figure 1: The percental changeh in variables belonging to the zoobenthos pathway over a range of t-POM loadings [g dw m d in autumn]. The percental change is i t c

h -2 -1 -2 -1

o m based on the lowest t-POM loading. Scenarios in the clear-water state (P load 0.7 mg P m d ) are presented as solid lines and in the turbid state (P load 3.3 mg P m d ) as n a o

t dotted lines. Consider the different scaling of the y-axes. Read figures from left to right and top to bottom to follow mechanistic sequence of t-POM effects. u t e s r

d

( e w t r a i t t u e s r )

[ [ % % ]

] 11

5 50 5 2500

4 40 4 2000

3 30 3 1500

2 20 2 1000

1 10 1 500 c

0 0 0 h 0 a n c g c h t e h e -1 a -1 a n r c i n n r g h

0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 e 0 2 4 6 8 10

g e a s s e u n t i

r s n g i i n p a t-POM loading t-POM loading t-POM loading t-POM loading e a

e l

c

v i m n n o a d

n a i z l e s a o t t u d b o e m l p r e

e l

c a f d o o n

18 10 n o k f o s t d o u o

n

0 [ 16 m d %

b 8 e [ ] % i

14 d

o -2

m ] [

%

a 12 -4 6 s ]

s 10

[ -6 % 8 4 ]

-8 6 -10 2 4 -12 2 m 0 c c a

-14 h

h 0 t a t a n e n

-16 g r g

e c e c

o 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 i

h n i n n a

s e

n a u x

t-POM loading g t-POM loading t-POM loading u m t e i t n o e

c i c d n t h

i o a [ t % h n u o

t ] [ h n

% o o c

] -2 -1 u

h

s Appendix 2 – Figure 2: The percental change in variables belonging to the zooplankton pathway over a range of t-POM loadings [g dw m d in autumn]. The percental change t

h -2 -1 -2 -1 is based on the lowest t-POM loading.o Scenarios in the clear-water state (P load 0.7 mg P m d ) are presented as solid lines and in the turbid state (P load 3.3 mg P m d ) as n o

dotted lines. Consider the different scalingu of the y-axes. Read figures from left to right and top to bottom to follow mechanistic sequence of t-POM effects. s

m a t t e r

[ % ] 12 3000 14

2500 12

10 2000 8 1500 6 1000 4 500 2 c

0 h a 0 n g e

i 0 2 4 6 8 10n 0 2 4 6 8 10

e x t i c

t-POM loading n t-POM loading h c a t i n o g n e

[

% i n ]

s -2 -1 u Appendix 2 – Figure 3: The percental change in variables belonging to the extinction pathway over a range of t-POM loadings [g dw m d in autumn]. The percental change is s e -2 -1 -2 -1 p based on the lowest t-POM loading. Scenarios in the clear-water state (P load 0.7 mg P m d ) are presented as solid lines and in the turbid state (P load 3.3 mg P m d ) as e n d dotted lines. Consider the different scaling of the y-axes. Read figures from left to right to follow mechanistic sequence of t-POM effects. e d t e r r e s t r i a l m a t t e r

( w a t e r )

[ % ]

13 Appendix 3: Functional Response Zooplankton

The functional response for zooplankton is implemented in PCLake according to Gulati and others (1982) who found in a long-term study that an increased amount of an unpreferred food reduced the total amount of food consumption above a certain food concentration. To illuminate this type of functional response we compare it for a system with one prey (A - preferred) and with two prey (A, B - unpreferred). The predator has a certain preference for each prey, pA and pB with pA > pB. Without loss of generality we put pA=1. Both functional responses, and , have the same half-saturation constant h (Eq. 1). The presence of the additional food B enhances the overall food consumption per predator when A is relatively low and reduces it at high concentrations of A (Appendix 3 – Figure 1). The threshold value of A when the food consumption is equal with or without B can be determined in the following way:

(1)

This equation can be rearranged into:

(2)

14 Given that during most of the simulations done with PCLake the equivalent term is larger than

pB, the additional food B often reduces the overall food consumption (Appendix 3 – Figure 1).

1.0 without additional food 0.9 with additional food 0.8

0.7

0.6

0.5

0.4

0.3

0.2 c o n 0.1 s u m 0.0 e d

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 f o o

d concentration of preferred food p

e r p r e Appendix 3 - Figure 1: The consumed food per predator increases as a function of the concentration of the d a

t preferred food (A) less steep when an additional less preferred food (B) is available. (pB=0.5; B=1; h=1) o r

15