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 (σ_{d}), and mean displacement of larvae between spawning and settlement locations (D_{d}), 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 σ_{u} = 1 km/day. (b) Gaussian probability density function of dispersal of larvae released at alongshore location 0, given σ_{u} = 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. |
LITERATURE CITED
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.