1
Appendix S1: Additional information on model parameterization and goodness-of-fit criteria
2
Initialization. Initial biomasses (Table 1) for the 24 guilds were the same in all models and given values
3
derived from a 10-year average of spring values. For fish inital biomasses, we used sonar and catch data
4
(Appenzeller 1998). For APP, we used lower initial values (20 μgC/m3, see Table 1) than observed to give
5
eukaryotic algae a head start in spring, mimicking slower onset of APP’s spring growth (Weisse
6
1988;Padisak et al. 1997) which is not appropriately reflected in allometric relationships.
7
Allometric parameterization. To achieve generality, we mostly applied allometric algorithms to estimate
8
parameter values (Tables 1 and S1) following Williams (Williams 2008) from the average body sizes of the
9
organisms of the 24 guilds (Lang 1997). These estimates involved normalization; the growth rate ri of
10
producer i is normalized to the growth rate of a chosen reference producer species k (Eq.1) by the
11
relationship
12
producer k, and the allometric constant
13
(Brose et al. 2006). Following (de Castro & Gaedke 2008), we set the allometric scaling exponent A to 0.15
14
for all species except fishes for which A=0.11 (Killen et al. 2010;Killen et al. 2007;Killen et al. 2007).
15
Consumers'
16
2006), we set
17
The allometrically estimated ri of APP and xi of Bac were reduced by a factor of 4 and 25, respectively, to
18
mimic the relatively slow metabolic rates of their populations (Makarieva et al. 2005;Chen & Liu 2010;Cole
19
et al. 1988;Joint 1990;Nielsen 2006) (Gaedke&Straile 1994, Simon 1998). Although individual bacterial cells
20
may achieve maximal growth rates based on allometric scaling under favorable conditions, the majority is
21
strongly resource-limited and partly in a state of metabolic inertia under natural conditions, resulting in an
22
overall low metabolic rate of the population. The ri of Alg3 which comprises several thermophilic species
23
was reduced by 75% in the LC-specific models M2-M4 to mimic its relative rarity before summer.
24
Diet-specific parameters. Following (Brose et al. 2006;Yodzis & Innes 1992), we set yij = 10. Placing
25
planktivore assimilation efficiency intermediate between herbivores and carnivores, we set eij to the
26
empirically supported value of 0.66 (Bierman & McIlroy 1986;Nielsen & Olsen 1989). Bacteria were assigned
27
eij =1 because they are osmotrophs.
1
, where
is the body mass of species i,
(massA/time) and
the body mass of the reference
(massA/time) which is 1 for all producers
is also normalized by reference producer k. Following Brose et al. (Brose et al.
= 0.314 (massA/time) for all plankton species i and
= 0.88 (massA/time) for all fishes i.
1
Functional response. We set the functional response F to a weak Holling type III response with q= 1.2
2
(Williams & Martinez 2004) to account for minimal refuges in pelagic freshwater systems q > 1 (Sarnelle
3
2003). We set
4
(
5
abundances (Williams 2008). We varied dkj of the functional response (Eq. 5) to mimic observed increases in
6
grazing resistance due to increased grazer density in 55 (37 for zooplankton, 1 for bacteria, and 17 for fish
7
predation) of the 107 feeding links in LC (see below and Table S3). Given the uncertainties involved in
8
extrapolating half saturation constants from lab measures to field conditions, and to avoid too many free
9
parameters, we set the same, low half saturation constant B0ij (cf. Eq. 5) for all zooplankton guilds (Table
10
S1). For the fishes, the half saturation constants differed among links (Table S2) to balance allometry-
11
independent effects of varying predation pressure on the competing crustacean guilds Dap and Cyc (also see
12
“prey resistance” below).
13
Fish mortality. A mortality term M(B) was used for fishes to maintain their total biomass at levels observed
14
in LC (Appenzeller 1998). For the generalizable models M0-M1, we set M ( B)  mBi 2 , with the mortality
15
coefficient m = 1.2 * 10-5. For the LC-specific models M2-M4, we replaced the quadratic term by a fisheries
16
model which simulates human exploitation of the two adult fish guilds that are commercially intensively
17
exploited in LC to a considerable extent. The fishery effort’s time derivative dF/dt is based on an equation by
18
Conrad (Conrad 1999):
19
dF
 n( pqBj  c ) F
dt
20
, with the economic openness n = 0.0055, the price per unit biomass p = 0.5, the catchability q = 0.00005, and
21
the exploitation cost per unit of fishery c = 0.03. The mortality of the exploited fish guild with biomass Bi then
22
becomes M ( B)  qBiF . We set F=500μgC/m3 as an initial value for the fisheries’ effort and the dynamics
23
of F were nearly constant during the simulation.
24
We excluded the fish from the evaluation of model fit because a.) there is no seasonal data on the four fish
25
guilds for validation comparable to the plankton community, and b.) we calibrated the mortality coefficient
2
making the relative inverse attack rates on prey range
add up to one
) and causing generalists to consume at lower feeding rates than specialists at similar prey
1
m and the economic coefficients n, p, q, and c in the way that the top predators would not surpass the coarse
2
biomass estimates available from LC catch and sonar data.
3
Activity and maintenance respiration. The approach to separate activity from maintenance costs (when
4
the animal is resting) is in agreement e.g. with Humphreys (Humphreys 1979), showing a rather constant
5
relationship between production (P) and respiration (R) of P/(P+R) ≤ 0.5. That is, in long-term sustainable
6
communities, production maximally equals respiration, but is often lower especially for highly active
7
animals (e.g. flying insects) or endotherms with higher maintenance costs (Begon et al. 2006). The idea to
8
separate activity and maintenance metabolic costs in plankton communities into a production-dependent
9
and a biomass-dependent part was elaborated in (Anderson 1992). Following previous studies (Humphreys
10
1979), we set fa = 0.4 describing the fraction of assimilated carbon gained for production and fm = 0.1 (Eq. 2)
11
describing the fraction lost by maintenance respiration. The fractions fa and fm (Eq.2) which determine the
12
relative balance of maintenance vs. activity costs depend on metabolic type because maintenance costs are
13
much higher (and transfer efficiencies lower) e.g. for endotherm vertebrate consumers.
14
Model time scale. All ordinary differential equations in the model describe the biomass change of species i
15
as
16
primary producer k (Alg1). Since Alg1 doubles every day (rk=1), one model time step equals one real-time
17
day.
18
Detritivores’ consumption. The detrital loop was closed for carbon in all models so that bacteria were
19
treated as consumers according to Eq. 2 with detritus as resource. The dead (particular and dissolved)
20
organic carbon pool (detritus) was made available to Bac with a time lag as a very coarse simulation of
21
photolysis. Following Davidson (Davidson 1996), we used an exponential decay function of the form
dBi
in model time t’=t/rk which is normalized by the mass-specific growth rate (rk) of the reference
dt '
N,
22
with
. = newly available detritus in each time step,
=
23
amount of detritus produced by the ATN model (Eq. 3), k=fragmentation rate, N=time lag constant. We set
24
k=0.45 and N=3500 for a time lag of approximately 1 week in the model.
25
Producer competition. There is strong evidence that competition for shared resources is generally lower
26
between than within LC phytoplankton guilds due to e.g. different nutrient requirements, resource uptake
3
1
capacities and other niche differentiation. We set cij = 1 for i ≠ j (neutral effect) and cii = 1.8 otherwise
2
(inhibitory effect) in the producer growth equation (Eq.4) for the LC-specific models M2-M4 to account for
3
moderately increased intra-guild competition within phytoplankton guilds. Using intra-guild producer
4
competition coefficients improved the biomass fit among the 6 phytoplankton groups which compete for a
5
common system capacity Ks in the model. The reason for the improved fit was that intra-guild producer
6
competition prevented the guild with the highest growth rate (Alg1) from dominating the others after the
7
CWP when predation pressure was temporarily lower than before and during the CWP.
8
Abiotic forcing. Abiotic forcing of autotrophs was modelled by continuously reducing KS from 100% to a
9
minimum of 50% until summer by multiplying KS with a coefficient k  1/ (1  e z (t t max) ) , with decay exponent
10
z = 0.1, t as the current simulation time and tmax = 110 time steps (beginning of summer). Increasing nutrient
11
limitation was further reflected by multiplying autotrophs' ri by a light coefficient (cl) equal to
12
cl 
13
extinction with epilimnion depth h, while λ2 is the degree of self-shading in presence of phytoplankton at
14
concentration CPhyt, h = depth, and I0 = the half-saturation irradiance for phytoplankton growth (Wallace et
15
al. 1996). Abiotic forcing of consumers was modelled by multiplying xi by a temperature coefficient (ct) equal
16
to ct=Q10(T-T0)/10 where T = temperature, T0= the standard temperature and Q10 = temperature-dependency
17
coefficient. Daily T and I values for the calculation of ct and cl were interpolated from weekly LC observations
18
in 1990 (Fig. S1).
19
Prey resistance to grazing pressure. Prey defense is very widespread in nature, embraces several
20
phenomena occurring in natural communities, and may change due to e.g. inducible defense, behavioural or
21
morphological changes, shifts in clonal or species composition , and microevolution. However, it comes at a
22
cost since defense structures and mechanisms require energy which could otherwise be invested in growth
23
and reproduction. Hence, undefended individuals or species generally dominate under low predation
24
pressure and are replaced by more resistant ones at high predator abundance. The outcome of such a
25
variable degree of prey resistance is that predators consume per capita less when they are at high density
26
which influences the shape of predator-prey cycles (Jones et al. 2009). An explicit modeling of the multiple
4


1
log 10  I 0I h  where I = irradiance, λ = light extinction = λ1λ2 CPhyt. The factor λ1 accounts for light
I
0

Ie

,
h
1
causal mechanisms underlying alterations in prey resistance was not appropriate in the present context to
2
maintain generality of the modeling approach.
3
Numerous studies confirmed the importance of changes in prey resistance in response to
4
altered predation pressure, e.g. for algal-ciliate or –rotifer systems (Tollrian & Harvell 1999;Yoshida
5
et al. 2003;Fussmann et al. 2003;Abrams & Matsuda 1997;Lass & Spaak 2003), bacterial strains
6
(Matz & Kjelleberg 2005;Corno 2006), crustacean zooplankton resisting and/or avoiding fish
7
predation (Geller 1989;Stich & Lampert 1981;Straile & Halbich 2000) and beyond (Abrams &
8
Matsuda 1997;Jones et al. 2009). Despite a rather constant overall algal biomass, the biomass of
9
different algal species exhibited fast and pronounced changes in LC during spring, indicating that
10
edible and less edible species or morphotypes alternated in response to changes in grazing pressure
11
(Tirok & Gaedke 2007;Tirok & Gaedke 2007;Tirok & Gaedke 2010). Such changes in trait values
12
within predator and prey communities may strongly dampen their overall dynamics (Tirok & Gaedke
13
2010; Tirok et al. 2011).
14
Based on this argumentation in our ATN model, the prey resistance coefficient dkj (cf. Eq. 5
15
and see (Beddington 1975;DeAngelis et al. 1975)) was fitted to links between predator k and prey
16
species j when the occurrence of variable prey resistance was supported by empirical evidence. We
17
applied dkj to all links involving fast growing, diverse prey groups with a high potential to adjust fast
18
to changing grazing pressure: 1. small grazers (ciliates and rotifers) and Cyc consuming eukaryotic
19
algae, 2. all bacterivorous links, 3. Dap's and Cyc's consumption of rotifers, 4. Asp's consumption of
20
ciliates and rotifers, and 5. Fish predation on crustaceans. The parameter dkj was further fitted to
21
Bac’s consumption of detritus to mimic interference competition of bacterial strains at high densities
22
(Hibbing et al. 2010).
23
We first fitted dkj manually to strong interactions that cause the CWP, e.g. the links from
24
daphnids and ciliates to phytoplankton groups. In addition, we fitted dkj to balance fish predation
25
pressure on the competing crustacean guilds Dap and Cyc. Adult Dap (mostly daphnids) are larger
26
than Cyc (cyclopoid copepods), but they are known to metabolize and reproduce faster (also by
27
parthenogenesis) than copepods. In addition, the dominant cyclopoid copepod species (Cyclops
28
vicinus included in Cyc) enters a diapause from the CWP onwards until autumn. We modeled its
5
1
absence in this time by higher predation pressure of fish larvae (Fish1) and juveniles (Fish2) on Cyc. In
2
summer and autumn, in line with empirical evidence, the adult fish (Fish3 and Fish4) prey more strongly on
3
daphnids (Dap) through lower B0ij and dkj than set on links to Cyc. As a result, Cyc are able to increase again,
4
mimicking their return from the diapause.
5
All link-specific values of dkj in the models M2-M4 are given in Table S3.
6
We used the same parameter values in M2-M4 to maintain comparability and assess how close the
7
ATN model fitted to the biomass patterns. Our conclusion is that the broad biomass patterns (A/H ratios or
8
the intermediate 8-groups resolution) could be reproduced without the manually calibrated parameter
9
values (cf. M1), whereas the full range of LC-specific seasonal biomass patterns for each guild could only be
10
reproduced using the LC-specific parameter set.
11
Size-abundance distribution. We calculated the slope of the size-abundance distribution equivalent to the
12
normalized biomass size spectrum (Sheldon et al. 1972) by binning biomass densities into 33 size classes of
13
log body mass of the 20 plankton guilds. Pelagic food webs are characterized by a continuum of organisms
14
along the size gradient and an often rather even biomass distribution (Sheldon et al. 1972) which also holds
15
for the LC food web (Gaedke 1992b;Gaedke 1992a). Pelagic food webs are highly size-structured
16
communities because body size and trophic level are positively correlated. From the relation B = NM =
17
constant, with biomass B, abundance N, and body mass M, follows that the size-abundance distribution has a
18
slope of approximately -1 when log(abundance per size class) is plotted against log(body mass). This slope
19
estimates the efficiency of the energy flow from smaller to larger organisms (Gaedke 1993). A steeper
20
(=more negative) slope indicates that small organisms are relatively more abundant and a lower transfer
21
efficiency, yielding lower biomass in larger size classes.
22
Impact of temporal resolution on the goodness-of-fit. The interannual variability in the empirical data is
23
largely caused by site-specific abiotic forcing and weather events that we deliberately intended to average
24
out in our construction of an average year. Hence, we calculated averages across years and within phases to
25
compare modeled and LC data (see Methods and Fig S2). This, however, may imply that we overlooked
26
misfits at a finer time scale, i.e. within phases. Hence, we tested whether the biomass similarity was sensitive
27
to the model’s and LC’s within-phase variability, . In each year, LC biomass data was sampled with maximal
28
weekly resolution which determines the maximal temporal resolution for calculating the biomass similarity.
6
1
. Since the longest phase (87 days) in summer provided the most empirical data points, we used this phase to
2
calculate the 20-guilds biomass similarity using a bi-weekly and weekly resolution. We found that using this
3
higher resolution to calculate the biomass similarity did not change the general results, but provided insights
4
into the dynamics of each model on a finer time scale (Table S5a).
5
When using a biweekly or weekly average instead of the phase mean, M0’s low 20-guilds biomass similarity
6
in summer (20-guilds avg. sim. = 0.25) decreased very slightly (avg. decrease -0.04). M1’s intermediate 20-
7
guilds biomass similarity in summer (20-guilds avg. sim. = 0.41) decreased more than in M0 (avg. decrease -
8
0.14), largely due to oscillations between bacteria and HNF (cf. Fig. S4b). M2’s intermediate 20-guilds
9
biomass similarity in summer (20-guilds avg. sim. = 0.71) only decreased very slightly (avg. decrease -0.05).
10
M3’s high biomass similarity in summer (20-guilds avg. sim. = 0.85) was also relatively insensitive to using
11
biweekly or weekly averages instead of the phase means (avg. decrease = -0.09, Table S5a). M4’s
12
intermediate 20-guilds biomass similarity in summer (20-guilds avg. sim. = 0.77) decreased the most (avg.
13
decrease -0.19), presumably because of the absence of weak, but stabilizing links (cf. Fig. S4e).
14
Statistical significance of the goodness-of-fit. Moreover, we tested to what extent the modeled phase
15
means XATNi fell into the range of values observed over 10 years in the corresponding phase (Fig. S2). For
16
each guild i and phase p, we calculated the distance of the modeled phase-mean XATNi from the observed
17
phase-means XLCi  1/ k
k

xy , with x y as the phase-means observed over k=10 years. We used the
y  years
18
normalized distance   1/ m
m

p  phase
 p , with  p  1/ n
n

i  guilds
di / 2 LCi , m = number of phases, n = number of
19
guilds, and the distance di | XATNi  XLCi | between XATNi and XLCi in reference to the standard deviation
20
 LC around XLC calculated from the individual phase means x y observed over 10 years. If   1, the
21
modeled phase-averages stay within the natural variability of the LC data set.
22
Generally, M2 and M3 performed best because their phase means fell on average within 2 LCi around XLCi
23
(Table S5b-c).
24
In M0, only 17% of all XATNi fall within 2 LCi around XLCi (  = 4.93). The corresponding value for M1 is29%
25
(  = 5.01,). In M2 and M3, 74% of the modeled XATNi fall within 2 LCi around XLCi (  = 0.86 and  = 0.71,
i
7
i
1
respectively). In M4, the absence of weak links destabilizes the dynamics, reflected in the higher average
2
distance of XATNi from XLCi with only 37% of all XATNi falling within 2 LCi from XLCi and  = 2.5 (Table S5b-
3
c).
4
5
References
6
7
Abrams P.A. & Matsuda H. (1997). Prey adaptation as a cause of predator-prey cycles. Evolution, 51, 1748.
8
9
Anderson T.R. (1992). Modeling the Influence of Food Cn Ratio, and Respiration on Growth and NitrogenExcretion in Marine Zooplankton and Bacteria. Journal of Plankton Research, 14, 1645-1671.
10
11
12
Appenzeller A.R. (1998). Persistent large-scale heterogeneity of pelagic fish in Upper Lake Constance and its
possible causes. In: Arch. Hydrobiol. Spec. Issues Advanc. Limnol. International Association for Theoretical and
Applied Limnology, Schweizerbartsche Verlagsbuchhandlung, Ergebnisse der Limnologie, pp. 303-316.
13
14
Beddington J.R. (1975). Mutual Interference Between Parasites Or Predators and Its Effect on Searching
Efficiency. Journal of Animal Ecology, 44, 331-340.
15
16
Begon M., Townsend C.R. & Harper J.L. (2006). The flux of energy through ecosystems. In: Ecology: From
Individuals to Ecosystems Blackwell Publishing, Malden, MA, USA, pp. 499-524.
17
18
Bierman V.J. & McIlroy L.M. (1986). User Manual for Two-Dimensional Multi-Class Phytoplankton Model with
Internal Nutrient Pool Kinetics. EPA Office of Research and Development, Washington D.C., USA.
19
20
Brose U., Williams R.J. & Martinez N.D. (2006). Allometric scaling enhances stability in complex food webs.
Ecology Letters, 9, 1228-1236.
21
22
Chen B.Z. & Liu H.B. (2010). Relationships between phytoplankton growth and cell size in surface oceans:
Interactive effects of temperature, nutrients, and grazing. Limnology and Oceanography, 55, 965-972.
23
24
Cole J.J., Findlay S. & Pace M.L. (1988). Bacterial Production in Fresh and Saltwater Ecosystems - A CrossSystem Overview. Marine Ecology Progress Series, 43, 1-10.
25
26
Conrad J.M. (1999). The economics of fisheries. In: Resource Economics Cambridge University Press, pp. 3941.
27
28
Corno G. (2006). Are grazer-induced adaptations of bacterial abundance and morphology time-dependent?
Journal of Limnology, 65, 35-40.
29
30
Davidson K. (1996). Accounting for nutrient processing time in mathematical models of phytoplankton
growth. Limnology and Oceanography, 41, 779-783.
31
32
de Castro F. & Gaedke U. (2008). The metabolism of lake plankton does not support the metabolic theory of
ecology. OIKOS, 117, 1218-1226.
33
DeAngelis D.L., Goldstein R.A. & O'Neill R.V. (1975). A model for trophic interaction. Ecology, 56, 881-892.
34
35
Fussmann G.F., Ellner S.P. & Hairston N.G. (2003). Evolution as a critical component of plankton dynamics.
Proc. R. Soc. Lond. B., 270, 1015-1022.
8
1
2
Gaedke U. (1992a). Identifying Ecosystem Properties - A Case-Study Using Plankton Biomass Size
Distributions. Ecological Modelling, 63, 277-298.
3
4
Gaedke U. (1992b). The Size Distribution of Plankton Biomass in A Large Lake and Its Seasonal Variability.
Limnology and Oceanography, 37, 1202-1220.
5
6
Gaedke U. (1993). Ecosystem Analysis Based on Biomass Size Distributions - A Case-Study of A Plankton
Community in A Large Lake. Limnology and Oceanography, 38, 112-127.
7
8
Geller W. (1989). The energy budget of two sympatric <i>Daphnia</i> species in Lake Constance:
productivity and energy residence times. Oecologia, 78, 242-250.
9
10
Hibbing M.E., Fuqua C., Parsek M.R. & Peterson S.B. (2010). Bacterial competition: surviving and thriving in
the microbial jungle. Nature Reviews Microbiology, 8, 15-25.
11
12
Humphreys W.F. (1979). Production and respiration in animal populations. Journal of Animal Ecology, 48,
427-453.
13
14
Joint I. (1990). The allometric determination of pelagic production rates. Journal of Plankton Research, 13,
69-81.
15
16
17
Jones L.E., Becks L., Ellner S.P., Hairston N.G., Yoshida T. & Fussmann G.F. (2009). Rapid contemporary
evolution and clonal food web dynamics. Philosophical Transactions of the Royal Society B-Biological Sciences,
364, 1579-1591.
18
19
Killen S.S., Atkinson D. & Glazier D.S. (2010). The intraspecific scaling of metabolic rate with body mass in
fishes depends on lifestyle and temperature. Ecology Letters, 13, 184-193.
20
21
Killen S.S., Costa I., Brown J.A. & Gamperl A. (2007). Little left in the tank: metabolic scaling in marine teleosts
and its implications for aerobic scope. Proceedings of the Royal Society B-Biological Sciences, 274, 431-438.
22
23
24
Lang M.M. (1997). The pelagic food web of Lake Constance: An analysis based on food web theory (Das
Nahrungsnetz im Pelagial des Bodensees: Eine Analyse auf Basis der Theorie der Nahrungsnetze). Konstanzer
Dissertationen 546, Hartung-Gorre Verlag, Constance, Germany.
25
26
Lass S. & Spaak P. (2003). Chemically induced anti-predator defences in plankton: a review. Hydrobiologia,
491, 221-239.
27
28
Makarieva A.M., Gorshkov V.G. & Li B.L. (2005). Energetics of the smallest: do bacteria breathe at the same
rate as whales? Proceedings of the Royal Society B-Biological Sciences, 272, 2219-2224.
29
30
Matz C. & Kjelleberg S. (2005). Off the hook - how bacteria survive protozoan grazing. Trends in Microbiology,
13, 302-307.
31
32
Nielsen M.V. & Olsen Y. (1989). The dependence of the assimilation efficiency in Daphnia magna on the 14Clabelling period of the food algae Scenedesmus acutus. Limnology and Oceanography, 34, 1311-1315.
33
34
35
Nielsen S.L. (2006). Size-dependent growth rates in eukaryotic and prokaryotic algae exemplified by green
algae and cyanobacteria: comparisons between unicells and colonial growth forms. Jour. of Plankton
Research, 28, 489-498.
36
37
38
Padisak J., Krienitz L., Koschel R. & Nedoma J. (1997). Deep-layer autotrophic picoplankton maximum in the
oligotrophic Lake Stechlin, Germany: origin, activity, development and erosion. European Journal of
Phycology, 32, 403-416.
39
40
Sarnelle O. (2003). Non-linear effects of an aquatic consumer: causes and consequences. American Naturalist,
161, 478-496.
9
1
2
Sheldon R.W., Prakash A. & Sutcliffe W.H. (1972). The size distribution of particles in the ocean. Limnology
and Oceanography, 17, 327-340.
3
4
Stich H.B. & Lampert W. (1981). Predator Evasion As An Explanation of Diurnal Vertical Migration by
Zooplankton. Nature, 293, 396-398.
5
6
Straile D. & Halbich A. (2000). Life history and multiple antipredator defenses of an invertebrate pelagic
predator, Bythotrephes longimanus. Ecology, 81, 150-163.
7
8
Tirok K. & Gaedke U. (2007). Regulation of planktonic ciliate dynamics and functional composition during
spring in Lake Constance. Aquatic Microbial Ecology, 49, 87-100.
9
10
Tirok K. & Gaedke U. (2010). Internally driven alternation of functional traits in a multispecies predator-prey
system. Ecology, 91, 1748-1762.
11
12
Tollrian R. & Harvell C.D. (1999). The Ecology and Evolution of Inducible Defences. Princeton University Press,
Princeton, NJ.
13
14
Wallace B.B., Hamilton D.P. & Patterson J.C. (1996). Response of photosynthesis models to light limitation.
Internationale Revue der Gesamten Hydrobiologie, 81, 315-324.
15
16
Weisse T. (1988). Dynamics of Autotrophic Picoplankton in Lake Constance. Journal of Plankton Research, 10,
1179-1188.
17
18
Williams R.J. (2008). Effects of network and dynamical model structure on species persistence in large model
food webs. Theoretical Ecology, 1, 141-151.
19
20
Williams R.J. & Martinez N.D. (2004). Stabilization of chaotic and non-permanent food-web dynamics.
European Physical Journal B, 38, 297-303.
21
22
Yodzis P. & Innes S. (1992). Body Size and Consumer-Resource Dynamics. American Naturalist, 139, 11511175.
23
24
25
26
Yoshida T., Jones L.E., Ellner S.P., Fussmann G.F. & Hairston N.G. (2003). Rapid evolution drives ecological
dynamics in a predator–prey system. Nature, 424, 303-306.
27
Figure Legends:
28
29
Figure S1 title: Temperature and irradiance curves from LC
30
Caption:
31
Figure S1. Interpolated temperature (solid line) and irradiance (dashed) curves from 1990 for the ATN models
32
with abiotic forcing (M1-M3, and M5) during the simulation period from early spring to autumn. Vertical dashed
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lines at phase begin.
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Figure S2 title: Constructing the time series of the average year
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Caption:
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Figure S2. Raw data (green dots) from 10 years (1987-1996) data on daphnids (Dap, blue line) biomass (µgC/m3) in
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LC were plotted on a normalized time axis. The days represent an average year from phase 2-6 (see Methods)
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indicated by the numbers between the dotted vertical lines. The dashed lines connect observations of three
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example years (1987, 1992, and 1996). Annual and within-phase variability ranges between 1-2 orders of
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magnitude for some guilds in highly dynamic phases, e.g. the second daphnid peak during summer (phase 5) in
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1987 and 1992 was not observed in 1996. We used the interval within two standard deviations  LC around the
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10-year LC phase-means XLCi (whiskers above and below the blue dots) to test whether the phase-means of the
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model simulation XATNi (red line, red squares) fell within LC’s natural variability.
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Figure S3 title: Comparison of relative biomass and production of models M0-M4
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Caption:
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Figure S3. Upper panel: Relative biomasses for LC data and models M0-M4. Lower panels: Relative production for
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models M0-M4.
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Figure S4 title: Relative biomass of 20-guilds in M0-M4 compared to LC data
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Caption:
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Figure S4. (a-c) Relative biomass for each guild in models M0-M4 compared to LC data. Arrows connect phases 2-
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6. Dashed line at x=y indicates perfect fit. Each reference line above (below) the x=y line indicates a 10%
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increase (decrease) of the model in reference to total biomass.
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Figure S5 title: Relative production in M0-M4 compared to LC data
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Caption:
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Figure S5. (a-c) Relative production for each major planktonic group in models M0-M4 compared to LC data.
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Arrows connect phases 2-6. Dashed line at x=y indicates perfect fit. Each reference line above (below) the x=y
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line indicates a 10% increase (decrease) of the model in reference to total production.
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