Many SS3 models include multiple fleets and include separate female and male stock dynamics. However, the openMSE OM object includes only a single stock and single fleet. When imported into openMSE, output from an SS3 model is first converted to an ‘MOM’ object which reproduces the predicted stock and fleet dynamics from the SS3 model in openMSE (see Importing MOM from SS3).
When an MOM object is converted by the SSMOM2OM function to an OM object, the overall fleet characteristics are calculated from the individual fleets within the MOM object, and the stock characteristics are calculated as averages from the sex-specific values in the SS3 model.
This page provides details on how the sex-structured, multi-fleet SS3 model is converted to a combined-sex, single-fleet OM object.
Biological Properties
Unfished Recruitment (R0)
The equilibrium recruitment to age-0 in the unfished state is calculated as the sum of the sex-specific R0s from the SS3 model.
Natural Mortality
Natural mortality for the combined sex model is calculated as the mean of the sex-specific M-at-age values in the SS3 model.
Weight-at-Age
Weight-at-age for the combined sex model is calculated as the mean of the sex-specific weight-at-age values in the SS3 model.
Length-at-Age
Length-at-age for the combined sex model is calculated as the mean of the sex-specific length-at-age values in the SS3 model.
Fecundity-at-Age
Fecundity-at-age in the combined model is taken from the female component of the sex-specific SS3 model.
Maturity-at-Age
Maturity-at-age in the combined model is taken from the female component of the sex-specific SS3 model.
Growth Parameters
Following above, the growth parameters for the von Bertalanffy growth model are calculated as averages of the sex-specific values in the SS3 model.
Length-Weight Parameters
The 2 parameters of the length-weight relationship are calculated as averages from the sex-specific values in the SS3 model.
Fleet Characteristics
Selectivity-at-Age
The overall sex-specific fishing mortality-at-age is calculated as:
\[F_{a,i,y} = \sum_n^N{S_{a,i,n,y} f_{y,n}} \] where \(F_{a,i,y}\) is fishing mortality for age \(a\), sex \(i\), in year \(y\), \(S_{a,i,n,y}\) is sex- and fleet-specific selectivity-at-age, and \(f_{y,n}\) is the apical fishing mortality for fleet \(n\) in year \(y\).
Overall selectivity-at-age for sex \(i\) then: \[V_{a,i,y} = \frac{F_a,i,y}{\max{F_a,i,y}}\] where \(\max\) represents the maximum value.
Finally, the combined selectivity-at-age is calculated as the average of the \(I\) sex-specific values: \[V_{a,y} = \frac{V_{a,i,y}}{\sum_i^I{V_{a,i,y}}}\]
Retention-at-Age
Overall retention-at-age is calculated with the same method described above, except using the sex- and fleet-specific retention-at-age values predicted by the SS3 model.
Fishing Mortality-at-Age
Overall fishing mortality-at-age is calculated by multiplying the apical fishing mortality in each year (calculated as the maximum of \(F_{a,i,y}\) across \(a\) and \(i\)) by the overall selectivity-at-age schedule.