Atlantis operating model equations

where

with X_RS the maximum ratio of reserve to structural weight FX can have and X_pR,FX is the relative degree to which FX concentrates on replenishing reserves rather than undergoing structural growth when underweight.

where “prey” is the group being consumed by CX, k_cx is the clearance rate of CX and p_prey,CX is preference (or availability) of that prey for the predator CX. This last parameter is similar to the “vulnerability” parameters in ECOSIM (Christensen et al. 2000) and represents the fact that the entire prey population will not be available to the predators at any one time (some may be hiding for instance). The availability of the food is further modified by _refuge if the group is dependent on biogenic habitat refuges, or size refuges (if they are physically outside the gape range of their vertebrate predators) or if the spatial range of the predator and prey do not completely overlap (and so explicit spatial refuges exist). If the group is dependent on biogenic habitat then _refuge is given by:

where -_cover is the refuge magnitude coefficient, _cover is the habitat steepness coefficient and d_cover is the relative cover in the cell for the prey, which is calculated by:

where _{substrate,habdegrad} is degradation in the physical habitat due to coastal development (e.g. reefs broken up), _substrate is the proportion of the cell covered with suitable substrate types, _substrate,j is the proportion of the cell covered by biogenic habitat defining group j and _canyon is the proportion of the cell covered by canyons (which is treated as an enhancement factor here as they are known concentrate production but their absence does not prevent the establishment and growth of the groups (Alan Williams pers. com.)).

where _low,FY is the lower prey selection size limit for FY and _up,FY is the upper prey selection size limit. The _refuge for benthic prey (vertebrate and invertebrate alike) is calculated as follows:

and if anaerobic

where _CX is the depth in the sediment that the predator CX can forage down to and _top is set to zero (as there is only one sediment layer).