Fiona T.-Y. Francis 1,2 *, Karen Filbee-Dexter 1 , Robert E. Scheibling 1

1. Stalked tunicates Bolteniaoviferaform biogenic habitat in the rocky subtidal zone of Nova ScotiaOnline Resource Fig. S2 Fiona T.-Y. Francis1,2 *, Karen Filbee-Dexter1, Robert E. Scheibling1 1Department of Biology, Dalhousie University, Halifax, Nova Scotia B3H 4J1, Canada 2Present address:Department of Biological Sciences, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada *Corresponding author email: ftyfrancis@gmail.com

2. Fig. S2 Graph showing observed autocorrelation function (ACF) of residuals from the GAM procedure up to a lag of 250, along with a smoothed approximation to the data estimated using a two-part log-linear regression of the structure a*blag fitted separately to values from 1 to 10 [green line: ACF = 0.644625*(0.859756Lag)] and from 11 to 250 [purple line: ACF = 0.131098*(0.993635Lag)]. A two part regression was used because it fitted the data quite well, unlike any first-order autocorrelation function which fitted very poorly (William Link, Patuxent Wildlife Research Centre, perscomm). The effective sample size is given by N2 / ∑ rij where N is the total uncorrected sample size and rij is the correlation between point i and point j for all points (if there is no autocorrelation among samples, this reduces to N). For this two-part regression, the variance inflation factor ĉ = ∑ rij / N is given by the equation: ĉ=+ 2*a1­* b1111- b1+ 2*a2­*b2 (1-b210)1- b2 where a1 and b1 refer to the coefficients of the equation from lag 1 to 10, and a2 and b2 refer to the coefficients of the equation from lag 11 to 250. This gives a value of ĉ = 45 implying that the effective sample size of independent values was N / 45. This value of ĉ = 45 was used to calculate the QAIC, and all standard errors and confidence intervals of all coefficients and other parameter estimates were multiplied by 45