Online Supporting Information

1Online supporting Information

2Appendix S2

3Phytoplankton competition model

4To understand the mechanisms behind phytoplankton dynamics, we used a microscopic Lotka-Volterra

5competition (MLVC) model, with explicit recipes to compute its parameters (May 1973). Consider n

6phytoplankton species competing in the niche axis, here summarized by log2 (individual volume; V),

7which has proven to be highly related to several physiological and ecological aspects of phytoplankton

8dynamics (Follows et al. 2007; Kruk et al. 2010; Litchman & Klausmeier 2008; Litchman et al. 2007;

9Reynolds et al. 2001). Basic MLVC model considers the change in population biomass (Ni) in time of

10the n competing species:

 n  K i  αij N j  11 dN i  1  (1) = N i μi i = 1: n dt K i

12where i is the maximum growth rate and Ki is the carrying capacity of species i. The sum term

13represents the effect of competition of all species on species i (see calculations below). For a detailed

14list of model parameters and source data see Table S3.

16Size-dependent physiological constraints

17A literature search was carried out for the physiological traits of the species included in the current data

18set. Size-dependent growth rates and sinking velocities were compiled from 55 culture experiments

19(Kruk et al. 2010). All physiological data were obtained from laboratory experiments performed

20following a similar experimental design, including comparable temperature (18–25 °C) and saturating

21light conditions, but not from size calculations. Sinking velocities were obtained from both mesocosm

22and laboratory experiments. For each MBFG, relationships were fitted between the niche position X

-1 -1 23(log2 volume), maximum growth rate (; day ) and sinking velocity (s; m day ) using least squares. 24Non-significant parameters (P>0.05) were excluded from the final statistical model. If the slope of the

25relationship was not significant, mean values were used instead. If there were no statistical differences

26in physiological traits among MBFGs, overall mean values were used. MBFGs showed different

27behaviour in their growth and sinking parameters with respect to individual volume (Table S1).

-1 29Table S1. Allometric scaling (rate= a+ b log2V) of maximum growth (max; day ) and sinking rate (s; m

30day-1) with individual volume (V; m3) for the Laguna Rocha dominant morphology based functional

31groups (MBFGs). a is the intercept, b is the slope estimated by minimum least squares and R2 is the

32explained variance. Coefficients significance at the 0.05 and 0.01 level are marked with * and **,

33respectively, and non-significant coefficients are marked with ns. Number of data points (N) used is also

34given.

-1 2 -1 2 MBFG max (day ) R N P s (m day ) R N P a b a b

Group V 1.21* -0.054* 0.50 8 0.05 -0.258* 0.059** 0.89 7 0.001

Group VI 0.0* ns 0.097** 0.96 12 <0.001 Average= 0.563 0.015 28 0.53

36Fitness (R*) and carrying capacity (K) derivation

37To derive a proxi for phytoplankton species fitness (R*; e.g.Tilman 1982) and carrying capacity (Ki),

38we consider an explicit nutrient-phytoplankton model that has been tested and verified extensively

39using competition experiments (Huisman & Weissing 1999; Tilman 1982). The dynamics of the species

40biomass (N) depend on the availability of phosphate as the only limiting resource (R) and a mortality

41term, which can include being washed out from the system (f), sinking velocity (s) and predation by

42zooplankton (m). The resource concentration depends on the rate of resource supply (Ro), the

43remineralization of dead phytoplankton (assumed as instantaneous) and the amount of resource 44consumed by the phytoplankton species. For a particular species, basic equations governing population

45biomass (N) and ambient resources (R) dynamics are:

dN R = Nμ  Nf + s z 1 1 p+ m dt vol R + k vol 46 (2) dR  R 1  = Ro  R f  Q Nμ + Nf + svol z 1 p+ m dt  R + k 

47where the maximum growth rate (vol) and sinking velocity (s) are functions of individual volume and

48morphology based group membership (Table S2). We assumed the effect of ambient phosphate

49concentrations (R) on growth rate is represented by a Michaelis-Menton function, where k is the half-

50saturation constant (average k= 0.07 mg L-1; Kruk et al 2010). Q is the yield of nutrient per unit of

51phytoplankton (Q= 5.05x10-3; mg P mm-3; Reynolds 1984).According to equation 2, fitness (R*; as the

52break down resource level; mgL-1) and carrying capacities (K; in population biomass units; mm3L-1) for

53a single species can be calculated by evaluating functions at equilibrium. Some of the parameters are

54functions of individual volume and morphology based functional group membership of the species, so

55R* and K are also functions of them. We obtained functional forms of R* and K as:

1 f + svol z 1 p+ mk R *{Vol,MBFG}= 1 μvol  f + svol z 1 p+ m

56 (3) R  R * f K{Vol,MBFG}= o  R * 1  Q μvol  m+ svol z 1 p  R *+k 

58The two hydrological parameters (f and p) were randomly varied among simulations. First, flushing

59rate (f=rand[0.032–0.284]; day-1) varied in a range that captured the large variability observed in the

60lagoon, from a very low flushing rate when the lagoon is isolated from the sea for several months

61(when water inflow from tributaries is low) to a high flushing rate when the connection to the sea is re-

62established and the lagoon can wash out in a few days. The second important hydrological variable is 63the probability of resuspension (p=rand[0–1]) which is related to highly variable wind stress on a

64seasonal and daily timescale.

65 Calculation of competition coefficients (  ) for the MLVC model

66We considered the niche axis as a gradient related to the log2 individual volume (V) of phytoplankton

67organisms. Each phytoplankton species i is represented by an average position on the niche axis Xi=

68 (where <> denotes mean values among the organisms of the i species), and a standard

69deviation σi, which measures the width of its niche. To reduce the number of model parameters, we

70searched for relationships among (X) and its standard deviation (σ). We checked model robustness

71against different types of relationships. Coexistence and abundance patterns stayed similar despite

72changes in the functional relationships (see below).

73 Relationship between empirical niche amplitude (  ) and niche position ( X )

74To calculate niche position, we measured several phytoplankton organisms of each registered species in

75Laguna de Rocha and calculated its average volume. The empirical set of data, although extensive,

76sometimes included only a few individuals of a particular species. Hence, to estimate standard

77deviations () we only used species with more than six measured individuals as we found that this was

78a compromise value between statistical reliability and the quality of the fitting accuracy). This left ~260

79measured individuals representing 16 species (Figure S1). The plot of the standard deviation  versus

80the position on the niche axis X shows a U- or V-shaped relationship (Figure S1). We fitted simple

81linear, parabolic and a piecewise linear regression to estimate statistical model parameters using R (R

82development Core Team 2009). For piecewise regression we used the segmented package (Muggeo

832008 ). Simple linear regression was not significant and presented significantly lower AIC (DAIC>2;

84Burnham & Anderson 2002) than parabolic and piecewise model parameters, which were significant

85and presented similar AIC (Table S2). The V-shaped relationship was robust to model assumptions, as

86non-linear quantile regression models fitted in the 10, 50 and 90 quantiles also showed a V shape (not 87shown).

89Figure S1. Relationship between niche position X [] and niche amplitude (). 90Parameters of fitted curves in Table S1. Dot size is proportional to the number of individuals measured 91to estimate standard deviation. 92

93Table S2. Equations and regression model parameters estimated for niche position [X; log2(Volume)]

94and niche amplitude (). AIC is the Akaike information criteria value for the estimated models.

95Significant model parameters are denoted by *= P≤ 0.05; **=P<<0.01, na: is not available; ns not

96significant at the 0.05 level.

Equation AIC Parameter

σ = a +blog 2 (V ) 33.75 a= 1.699** b=0.09ns a= 0.59** log (V )  b2 29.53 σ = a + 2 b=8.79** c c=4.40** S1= -0.247* S2= 0.28na σ = S1log 2 (V )+i1 if log 2 V < BP 31.22 i1= 2.73** σ = S2log 2 (V )+i2 if log 2 V  BP i2= -2.19na BP= 9.30** 97 98Algorithm for calculating competition matrix

99The competition coefficients ij were computed using a modified MacArthur and Levins overlap

100(MLO) formula (MacArthur & Levins 1967). In this particular case, assuming a niche of length Lmax

101and introducing a normalization term to account for heterogeneous sigmas (), the interaction matrix is

102given by:

2  X  X   2L max  X i  X j   X i + X j  i j erf  + erf   2 2  σ + σ   σ + σ  2σ i σ j 2σ i + σ j   i j   i j  103αij = 2 2 e σ i + σ j  Lmax  X i   X i  erf  + erf    σ i   σ i 

104where erf is the error function.

105 Model sensitivity to the functional form of the relationship of sigma (  with X

106To evaluate the robustness of the model to the functional form of with X, we run the model 1000

107times with three different functional forms:

108A) Piecewise segmented linear relationships (Table S2),

109B) Parabolic relationship (Table S2),

110C) No dependence of with X (constant; = 0.15 for all species).

111The model behavior showed moderate robustness against changes in functional form of X with 

112(Figure S2). The model run with functional forms A and B reproduced adequately the diversity patterns

113found in the empirical data. When using functional form (C), the model vaguely reproduced empirical

114patterns (Figure S2 C) only when assuming full resuspension (p=1). This suggests that the decrease in

115interaction strength at medium sizes is important in determining community structure. Future studies to

116test this hypothesis should be conducted with adequate sampling designs.

117 118

119Figure S2. Entropy as a function of size classes of X [log2(Volume)] for the average of 1000 model 120simulations with different functional relationships between niche position and niche amplitude (). A) 121Piecewise segmented relationship, B) Parabolic relationship and C) constant niche amplitude (= 0.15 122and p=1). See table S1 for parameters of functional relationships. 123Table S3. Parameters of the competition model

Parameter Symbol Dimensions Function Source Maximum growth This study; Table 1;  day-1 Volume, MBFG rate (Kruk et al. 2010) Carrying capacity K Volume, MBFG This study -1 -1 Nutrient supply Ro mg L day System property Empirical average value Flushing rate f day-1 System property Empirical average value Nutrient content of Q mg P mm-3 Constant (Reynolds 1984) phytoplankton This study; Table S1 Sinking rate s m day-1 Volume, MBFG (Kruk et al. 2010) Empirical average value; Depth of the system z m System property this study Probability of p adimensional System property - resuspension This study; Grazing mortality rate m day-1 Constant D. Calliari, unp. data. Empirical average value; Niche position X m3 2 this study Standard deviation Niche amplitude  m3 Empirical value; this study (log2(Volume)) 124 125REFERENCES

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