Methods from Kindinger and Albins (2016) "Consumptive and non-consumptive effects of an invasive marine predator on native coral-reef herbivores" doi: 10.1007/s10530-016-1268-1

Visual surveys of reef fishes were conducted by a pair of SCUBA divers throughout (seafloor to surface) two permanent square plots (10 9 10 m) and four permanent strip transects (2 9 25 m), for a total area of 400 m2 per reef (see Albins 2015 for detailed description). We positioned square plots to include areas of the reef with the highest apparent relief, and strip transects were placed randomly across the remaining hard substrate, with the intent of including all important high-relief habitat features. Divers conducted censuses of each sampling unit whereby each fish was identified to the species-level and total length (TL) was visually estimated to the nearest cm. Paired reefs (low- and high-lionfish-densities) were surveyed within 24 h by the same set of observers, and all reefs were surveyed by the author (M. Albins). Every 3–5 months thereafter, we resurveyed the fish community at all experimental reefs.

We quantified CEs of invasive lionfish on native herbivorous fish populations throughout the 2-year experiment by comparing the change in density and biomass of small and large herbivorous fishes between lionfish-density treatments. Small fish were B 10 cm TL, which encompasses the majority of prey fish sizes reported in invasive lionfish gut-content studies for the size range of lionfish (2–35 cm TL) observed on our experimental reefs (Morris and Akins 2009 ; Mun˜oz et al. 2011 ). Responses of fish [ 10 cm TL were consistent, regardless of whether individuals were binned into medium (11–20 cm TL) and large ([ 20 cm TL) size classes, so hereafter we refer to all fish[ 10 cm TL as large . To determine the relative response of different sub guilds of herbivorous fishes, we also calculated the change in small and large fish density and biomass by fish family: (1) parrotfishes (Labridae); (2) surgeonfishes (Acanthuridae); (3) angelfishes (Pomacanthidae); and (4) damselfishes (Pomacentridae). We used published length-weight conversions to calculate fish biomass; parameters of closely related species were used when conversions were not available (Online Resource 1). We calculated changes in fish density and biomass at every survey interval by subtracting the baseline value (prior to initial lionfish manipulation) for each sub-sample (plots and transects) from the corresponding value of each subsequent survey.

To test for an effect of invasive lionfish through time on changes in density and/or biomass of each group of native fishes (described above), we fitted linear mixed effects models (LMMs) with lionfish density treatment and time as categorical fixed effects, and sub -sample nested within reef as random effects (Pinheiro and Bates 2000 ; Bolker et al. 2009 ; Zuur et al. 2009 ). Time was a categorical variable because we had no a priori reason to assume any linear relationships with response variables. Full models included weighted terms allowing variances to differ among reefs and AR1 covariance structures to account for temporal autocorrelation (Zuur et al. 2009 ). We fitted full and reduced models (with vs. without weighted terms and/or AR1 structures) using restricted maximum likelihood (REML) and compared full and reduced models using Akaike’s Information Criterion (AIC) and likelihood ratio tests (LRTs, Online Resource 2). Visual examination of residuals of the best-fit models indicated that the assumptions of normality, homogeneity, and independence were all met.

To assess the significance of fixed effects, we refit each model using maximum likelihood estimation (ML) and applied LRTs (Zuur et al. 2009 ). Fixed effects that were not significant were sequentially dropped from models. The resulting best-fit models in terms of variance structure, temporal correlation, and fixed effects were refit using REML in order to estimate the fixed-effects parameters and associated effect sizes. If LRTs indicated the lionfish 9 time interaction was significant, we made simultaneous inferences about the marginal effects of the lionfish treatment at each survey period, and adjusted the associated p values to maintain an approximately 5 % family-wise error rate (Hothorn et al. 2008 ). Regardless of whether the lionfish 9 time interaction was significant, we estimated expected values and standard error of the means (SEMs) for all response variables from low- and high-lionfish-density treatments during each survey period. We also fit LMMs to compare the baseline levels of each response variable between lionfish-density treatments using a similar procedure to the one outlined above, but with density and biomass of each group of small and large fishes (described above) as the response (rather than the change in these variables). Additionally, we fit LMMs to assess whether small (B 10 cm) and large ([ 10 cm) native mesopredators (Online Resource 1) that are potentially ecologically-similar to invasive lionfish differed between the reefs assigned to each lionfish density treatment at the baseline survey (mesopredator density and biomass) and at each subsequent survey period (change in mesopredator density and biomass).