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Appendix I. Summary of model selection using alternative measures of predator abundance and settler density.

It is always possible that the poor performance of a particular explanatory variable in model selection is due to inaccurate estimation of that variable. In this study, we were concerned that our model-selection inferences were affected by the way we chose to estimate predator abundance (median density of serranids, carangids, and lutjanids) or the approximation we used to estimate small-scale settler density (Delaunay spokes connecting microsites to transect corners were used to approximate the influence of nearest-neighbors outside of the transect area). To address these concerns, we analyzed both the small-scale and large-scale mortality data using alternative measures of these variables.

For predator abundance, we compared models using (1) mean density of serranids, carangids, and lutjanids (in case the median is an inappropriate measure); (2) median density of serranids and carangids alone (these taxa are observed attacking juvenile bluehead wrasse more frequently than are lutjanids); (3) median density of serranids alone (serranids are the most common piscivore taxon and are observed attacking juvenile bluehead wrasse more frequently than are carangids); (4) median density of coneys (Cephalopholis fulva; the most common piscivore species and a confirmed (by gut content analysis) predator of juvenile bluehead wrasse).

For density, we compared models using (1) an estimate of mean spoke length calculated without including spokes extending to the corners of the transect and (2) an estimate of mean spoke length in which the lengths of spokes extending to transect corners were replaced by the grand mean length (within each site) of spokes connecting actual microsites. The first method ignores the problem of un-observed nearest neighbors outside the transect, and the second method uses the mean nearest-neighbor density to approximate the distance to un-observed nearest neighbors outside the transect.

In all cases, the AIC_cs of the models presented here were large enough so as not to affect the selection of the most parsimonious models identified in the primary analysis and discussed in the text.

TABLE I1. Site-scale mortality analysis using alternative predator abundance measures. Comparison of multiple regression models for large scale instantaneous mortality rate based on monthly surveys of recruit and subadult density in 2004. Covariates are settler density (D), predator abundance (P) and habitat rugosity (R). AIC difference () is the difference between the AIC_c of model i and the AIC_c for the most parsimonious model reported in the text, which only contained a term for settler density.

Model	Mean serranids, carangids, and lutjanids	Median serranids and carangids	Median serranids	Median coney
P	18.5	18.4	18.4	18.5
D, P	5.1	4.7	4.6	4.9
D, P, D × P	11.8	11.4	11.4	11.6
R, P	22.2	21.7	21.1	22.4
R, P, R × P	25.3	25.2	27.2	26.1
D, P, R	10.7	8.2	7.6	10.3
D, P, R, D × P	19.5	16.3	15.4	19.1
D, P, R, D × R	15.7	15.1	16.1	16.5
D, P, R, R × P	18.5	15.3	14.9	18.5
D, P, R, D × P, R × P	28.4	27.5	27.7	27.7
D, P, R, R × P, D × R	27.7	27.1	27.4	27.7
D, P, R, D × P, D × R	29.9	27.8	27.7	43.7
D, P, R, D × P, R × P, D × R	48.0	47.7	48.0	48.4

 

TABLE I2. Microsite-scale mortality analysis using alternative predator abundance measures. Comparison of models for small scale mortality rate based on daily observations of settlement and disappearance in 2005. Fitted parameters are a constant (C), fish age (A), group size (G), settler density (D), predator abundance (P), and habitat rugosity (R). AIC difference () is the difference between the AIC_c of model i and the AIC_c for the most parsimonious model reported in the text, which only had a constant term and a term for group size. Only low-dimensional models were considered in this additional analysis, since the primary model selection (given in Appendix G) indicated that high-dimensional models with many terms were extremely non-parsimonious.

Model	Mean serranids, carangids, and lutjanids	Median serranids and carangids	Median serranids	Median coney
C, G, P	10.5	52.5	55.1	53.5
C, G, P, R	39.9	82.3	34.9	58.3
C, G, P, P × G	2.9	76.9	77.1	78.9

 

TABLE I3. Microsite-scale mortality analysis using alternative settler density measures. Comparison of models for small scale mortality rate based on daily observations of settlement and disappearance in 2005. Fitted parameters are a constant (C), fish age (A), group size (G), and settler density (D). AIC difference () is the difference between the AIC_c of model i and the AIC_c for the most parsimonious model reported in the text. When calculating density without including corner points, seven fish that were always alone on transects had to be excluded from the analysis.

Model	Corners not included	Corner spokes = mean nearest-neighbor distance
C, D	29774.7	3391.2
C, D, A	24156.8	1643.5
C, G, D	17.2	60.1
C, G, D, A	30.2	40.3
C, G, D, G × D	30.5	96.5
C, G, D, G × D, A	29.8	86.4