Ecological Archives E094-168-A4
Chantal M. Huijbers, Ivan Nagelkerken, Adolphe O. Debrot, Eelke Jongejans. 2013. Geographic coupling of juvenile and adult habitat shapes spatial population dynamics of a coral reef fish. Ecology 94:1859–1870. http://dx.doi.org/10.1890/11-1759.1
Appendix D. Optimization of the size-dependent dispersal model, resulting in a median dispersal distance of 20–25 km/yr for larger (>45 cm) fish, and 2–3 km/yr for smaller (<20 cm) fish.
Because in the model age is used instead of size, size was calculated using the von Bertalanffy equation:
size = 50.25*(1-exp(-.139*(age-2+.955)))
We assume that dispersal parameter λ is a linear function of size: λ = b0 + size × b1
and then optimize b0 and b1 for the model to best fit (1) the observed population sizes and (2) the observed size structures.
Result:
fitted to observed population sizes (R² = 59.9%)
fitted to observed size structures (R² = 49.5%)
The resulting λ-functions can be translated into median dispersal distances:
And the same median dispersal distances plotted against age: