1. A Spatial Box Model for SA Hake with Explicit Movement Rebecca Rademeyer and Doug Butterworth MARAM

2. Spatial strata and age groupings
west coast, 0-100m; south coast, 0-50m;
west coast, m; south coast, m;
west coast, m; south coast, m; and
west coast, m; south coast, 200m+.
west coast, 401m+;
4 age groupings:
Age 0 (recruits);
Age 1;
Ages 2 to 4; and
Ages 5+.

3. Data fitted
Total catch for each fleet and spatial strata (species disaggregated externally)
CPUE:
ICSEAF CPUE series (pre-1978, species-aggregated)
GLM-standardised CPUE (1978-present, disaggregated by species and coast)
Commercial catch-at-length by fleet (not disaggregated spatially further than coast)
Survey indices by spatial strata (4 series: WC summer, WC winter, SC spring, SC autumn; species disaggregated)
Survey catch-at-length by spatial strata (4 series as above; species disaggregated)
(GeoPop output (average ( ) abundance index and average ( ) proportion per length class for each spatial strata and species))

4. Movement proportions
They reflect the probability that a fish of a particular age in region r’ at the start of the year moves to region r at the end of the year.
Assumed to be constant over time.
Constrained by gravity model (single “attractiveness” parameter for each area, by age-group)
Constrained by expert opinion:
Constraints on recruitment (e.g. no recruitment of M. capensis allowed deeper than 200m)
Certain movements are “forbidden”, so that corresponding matrix cells are set to zero (e.g. no M. paradoxus below 100m)

5. Mixing matrix Example: M. paradoxus, age group 2-4
Depth strata shown are west followed by south coast

6. Fitting to GeoPop outputs
Average abundance index by region for each species: taken as a relative index, log-normally distributed about its expected value
Average proportions-at-length by region, for each species: assuming a Punt-Kennedy error distribution
Care is taken to avoid “double-counting” of information in the process of incorporating the GeoPop results, as essentially GeoPop is providing a refined version of the same information which is in the survey data

7. Biomass trajectories . Model A: without GeoPop Model C: with GeoPop

8. Conclusions
Addition of the GeoPop results does lead to differences which would be of importance
Nevertheless there are concerns about attempts to estimate movement parameters, with the model experiencing convergence difficulties
A key problem is that there are no data which measure movement explicitly (typically tag-recapture data play an important role is assisting reliable estimation from such models)
One possible way forward is to attempt to simplify the spatial structure which might improve estimation performance
Clearly quantifying the extent of any trans-boundary movement is of importance in terms of the interpretation of the results from any joint SA-Namibian assessment; but are attempts to estimate movement parameters in the manner attempted here the best way to go?