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Figure S1. Hartigans' dip statistic as a function of sample size, generated from the strongly bimodal size distribution of generalist North American freshwater fish species listed by Griffiths (2012).

Figure S2. Examples of size-frequency distributions with kurtosis <-1 for fish species found in (a) Alder lake (Rahel 1984), (b) Griffin lake (Keller & Crisman, 1990), (c) Lake Erie (Tonn et al., 1990), (d) Conesus lake (Bloomfield, 1978).

Figure S3. Mean moments (±1 SE) of 100 samples taken at random from the lake species pool.

Table S1. Data sources used in the analyses.

Table S2. The dip statistic as a function of kurtosis (all values negative), species richness (N, range 15–88 species) and lake group (Great Lakes, Finger Lakes areas)(R2 = 0.78).

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