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Appendix D. A description of the estimation of post-settlement mortality function for kelp bass.

Due to logistical constraints, many of the annual benthic community surveys were performed before kelp bass (Paralabrax clathratus) settlement to SMURFs had tapered off. This situation precluded accurate estimation of the total initial size of the young-of-the-year (YOY) cohort, which in turn precluded consideration of factors affecting post-settlement mortality. However, post-settlement mortality tends to be quite high, and this period is thought to be quite important to the regulation of many benthic fish populations. As such, we attempted to simultaneously estimate both the initial YOY cohort size and its survivorship. This approach is admittedly crude, but nonetheless provides some information on this life history period to complement the analyses developed in the main body of the paper.

In the main text we reported a relationship between the the density of YOYs counted on transects in the benthic surveys and the number of settlers collected on SMURFs at each site prior to the benthic survey each year (Table 2, Fig. 2). We used the coefficients from this regression to predict the total number of YOYs settling in each cohort as a function of the total number of settlers collected on SMURFs in each site-year. We then examined the relationship between the predicted number of YOYs in year t and the number of one-year-old fish counted in the benthic surveys in year t + 1.

We considered regression models that included parameters for the density of giant kelp (Macrocystis pyrifera) stipes and adult (2+ year old) kelp bass and the interactions of those two variables with predicted YOY density (all models also contained a term for predicted YOY density). As in the analyses presented in the main text, fish densities were log(x + 0.01)-transformed for analysis.

In the initial round of model selection, adult kelp bass density emerged as a strong predictor, but this effect was entirely attributable to the influence of the two data points from Crook Point (San Miguel Island) where adult kelp bass densities were zero and the density of one-year-olds was also quite low. Adult density ceased to be a strong predictor when these two points were excluded, so we no longer considered adult density as a predictor and focused on the effects of predicted YOY density and kelp stipe density. The two most parsimonious models (combined w > 0.95) were those with predicted YOY density alone and both predicted YOY density and kelp stipe density. In both models, the term for YOY density had a slope < 1 in log space, indicating a saturating, density-dependent relationship (Table D1). In the model with terms for both predicted YOY density and kelp stipe density, the term for kelp was negative (Table D1, Fig. D1). The latter effect is somewhat hard to understand from a biological perspective, but may be an artifact of the strong positive relationship between kelp stipe density and predicted YOY density: initial densities may have been somewhat higher, and thus density-dependent mortality somewhat stronger, in site-years with high kelp stipe densities.

Because of the assumptions and uncertainties involved in this analysis we hesitate to make strong inferences or rely heavily on the resulting parameter values. Nonetheless, the results are suggestive of density-dependent survivorship for YOY kelp bass.

TABLE D1. Summary of relationship between predicted YOY density and one-year-old density. Multiple regressions were used to describe the relationship effect of young-of-the-year kelp bass density and giant kelp stipe density in year t on the density of one-year-old kelp bass in year t + 1 for 28 site–year combinations. The two most parsimonious regression models (selected by AIC_c) are shown. Both one-year-old density (the response variable) and YOY density were log(x + 0.01)-transformed for analysis. ΔAIC_c is the difference in AIC_c between each model and the model with lowest AIC_c.

FIG. D1. Partial regression plots showing effect of young-of-the-year kelp bass density (grand mean = 0.06 fish/transect) and giant kelp stipe density (grand mean = 121 stipes/transect) in year t on the density of one-year-old kelp bass (grand mean = 0.20 fish/transect) in year t + 1 for n = 28 site–year combinations. Each panel shows the effect of one regressor on one-year-old kelp bass density independent of the effect of the second regressor; this is achieved by obtaining the residuals of the relationship between the second regressor and both one-year-old kelp bass density and the first regressor.