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Appendix S1 Derivation of the expectations for the lattice model equations presented in Table S5, Figures S1–S7 showing histogram of mean edge lengths and total network length (S1) and the performance of each model type (S2–S7).

File S1 Frequency distributions for edge lengths and edge diameters for all 353 leaves (combined into a single pdf).

Table S1 Species List including, image ID number, Family, Genus and Species for each leaf image.

Table S2 Individual leaf data, including: image ID number, image scale, leaf area (mm2), nodes, edges, edges/ nodes, mean edge length, total network length, network density (total network length/total leaf area), mean distance to the nearest edge, mean distance to the nearest edge/mean edge length.

Table S3 Edge length and diameter frequency distributions including: image ID number, exponential log likelihood, exponential AIC score, maximum likelihood estimate for the exponential rate parameter, power law log likelihood, power law AIC score, maximum likelihood estimate for the power law scaling exponent, maximum likelihood estimate for the power law scaling constant.

Table S4 Results of the honeycomb, square and equilateral triangular lattice model tests, including predicted edges per unit area, network density, mean distance to the nearest edge, total number of nodes, total number of edges and total network length.

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