Atlantis operating model equations
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1.4 Vertebrate Consumers The following are the rates of change for a vertebrate group (FX).  (C.8)
 (C.9)
 (C.10)
Where the subscript s stands for structural weight (skeletal and other material that can not be reabsorbed), r for reserve weight (fats and other tissues that can be broken down when food is scarce), d for density and i represents age class i (or age class i if life phases not age classes are used – an age class may be a single year class or it may represent a proportion of the total life span of the animal, the terms age class can be used interchangeably with age class for the remainder of the document), there is one equation for each age class included. The T terms represent the movement of vertebrates in to (TIMM,Fxi) and out of (TEM,Fxi) the cell. In addition there are short-term spawning and recruitment events which effect the various FX pools. At the same point each year (the exact day dependent on the vertebrate and with a window of +/- 14 days) the vertebrates reproduce and the materials required to do this is removed from the reserve weight of FX. At this point the proportion of the age class aging into the next age class (if in a scenario with external adult stocks then the oldest age class in the system leaves the system at this time). Sometime later (the exact period dependent on the group) the recruits settle out and their weights and density are assigned to the youngest age class. The amount of reserve weight (mg N per individual) that is used up during spawning is given by:  (C.11)
where UFxi is the proportion of age class i that is reproductively mature, ZFX is the fraction of the weight of FX used in spawning, YFX is the spawning function constant and XRS is the ratio of structural to reserve weight in well fed vertebrates. The formulations for recruitment are given by either:  (C.12)
for constant recruitment where Jt is element t of the recruitment vector (constant spatially and temporally). More commonly a Beverton and Holt recruitment function was implemented using the following formulation:  (C.13)
is used, where is the Beverton-Holt for the vertebrate group; is the Beverton-Holt for the vertebrate group, tx is total length of recruit period; and the biomass of the offspring of vertebrate group FX in cell j at time t (Ltj) is determined as follows:  (C.14)
where sFXi is the spawn from age class I of FX, recruit is the scalar for episodic recruiment and [t] is an impulse function, which is only non-zero when time t is a multiple of the period of the recruitment pulses. Directory: content -> suppl -> 2013 suppl -> Torres-Miranda et al. American Journal of Botany suppl -> Assessment of the acoustic telemetry positioning system suppl -> Additional File 1 Text summary suppl -> Additional file 5, Table costs and ccdss process-related outcomes for trials of acute care management a suppl -> Supplementary Notes and Figures 2013 -> Metal Application 2013 -> Genomic erv make-ups used in phylogenetic analyses 2013 -> Table specimens used for dna sequencing Download 2.6 Mb. Share with your friends:
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