Appendix A. Estimating adult spillover and larval export.
|FIG. A1. Adapted from Kramer and Chapman (1999), a calculation of the proportion of an adult population that moves outside a TURF in relation to home range length of the species and TURF width: m = 1 / (4W) when W ≥ 0.5; m = 1 - W when W ≤ 0.5, where W is alongshore TURF width in units of home range length. For example, W =10 can represent spillover of a species with a home range length of 100 m from a TURF 1 km long. Kramer and Chapman’s geometrically-based calculation assumes home range area to be roughly circular and uniform use of the home range area. Inset: movement rate in relation to W ≤ 10.|
|FIG. A2. Calculation of larval dispersal and larval export. (a) Standard deviation in the larval dispersal probability density function (σd), and mean displacement of larvae between spawning and settlement locations (Dd), in relation to pelagic larval duration of the dispersal phase, based on Siegel et al.’s (2003) Gaussian larval dispersal probability density function and root mean square current velocity σu = 1 km/day. (b) Gaussian probability density function of dispersal of larvae released at alongshore location 0, given σu = 1 km/day and a pelagic larval duration = 30 days. Filled areas sum to c = 0.4146, the probability of larval dispersal > 10 km (i.e., larval export from a TURF 20 km wide). Unfilled area under the curve corresponds with probability of larval retention within the TURF, (1 - c) = 0.5854.|
Kramer, D. L., and M. R. Chapman. 1999. Implications of fish home range size and relocation for marine reserve function. Environmental Biology of Fishes 55:65–79.
Siegel, D. A., B. P. Kinlan, B. Gaylord, and S. D. Gaines. 2003. Lagrangian descriptions of marine larval dispersion. Marine Ecology-Progress Series 260:83–96.