Modelling hake predation explicitly Andrea Ross-Gillespie and Doug Butterworth . MARAM

Key features Predator and prey species considered: Hake as predators and as prey “Other prey“ component, accounting for non-hake prey in the diet of hake as predators. No other predators of hake - instead a fixed basal mortality rate is included to account for all other sources of mortality. Holling Type II functional form. Input data for estimating predation-related parameters: Proportions of hake in the diet of hake predators Information on the predator-prey preference Daily ration: No estimates of daily rations available for hake - model is allowed to estimate these A lower bound of 0.1% of body mass is enforced, as well as a penalty on the slope of the daily ration with the predator mass. Estimates of the proportion of hake in the diet of hake predators, daily ration and predator-prey preference are time- varying model outputs.

Key features A gamma function models the preference exhibited by hake predators of a given age for hake prey of a given age. A function is incorporated that allows the extent to which hake prey on other hake to change with predator age. The model incorporates a “depth-availability” vector: Allows M. capensis preference to shift from M. capensis prey to M. paradoxus prey as the predators grow larger and move into deeper waters. A predator competition effect is mimicked by enforcing an upper bound on the predation mortality rates. A monthly time-step is implemented. Predation effect would likely be poorly approximated with a coarser time-step given that the predation dynamics are likely to be much faster than the hake dynamics.

Key factors to balance when fitting model Daily rations should not be too small, in particular those for M. paradoxus, which tended to become very low. A lower bound on daily ration of 0.1% was introduced. The slope of the log of the daily ration with the log of predator mass should lie close to -1/3. A penalty was added to enforce this. The biomass trajectories should not exhibit unrealistic oscillations, which result from a high predation mortality rate. A predator competition term was introduced to limit the predation mortality rate. The fit to the historical ICSEAF CPUE data should be adequate. Many runs were rejected on this basis.

Fit to CPUE data

Fit to diet data

Natural mortality Mortality rate at pre-exploitation equilibrium (will change as the population age structure changes over time). Natural mortality rates for hake of intermediate ages 4-6 are unusually high compared to other groundfish. However, the standard stock assessment does tend to prefer higher mortality rates – the high mortality rates arising from predation by other hake likely provides the explanation for this.

Population trajectories M. paradoxus exhibits some limited predation release when its M. capensis predators are reduced by the fishery prior to 1960. The estimate of current depletion of M. paradoxus is not affected substantially by this predation release.

OLRAC model The OLRAC predation model estimates a less heavily depleted M. paradoxus stock compared to the standard assessment model.

Current work Main feedback from panel for the 2016 International Stock Assessment Workshop: OLRAC and MARAM predation models Compare the MARAM and the OLRAC predation models with the predation “switched off”. Compare the full predation models only once the “predation-off” models match as closely as possible. MARAM predation model Adjust the way in which the predation constraint was implemented. The predation constraint should not come into play at equilibrium. Investigate the consumption of hake by the 14 and 15 year old hake predators. Investigate the proportions of hake in the diet of hake predators at equilibrium. Investigate convergence issues. Conduct a literature review of the mortality rate of 15 year old white fish. Other developments in the MARAM predation model: Update the model to incorporate data up to 2016. Update the model according to the latest standard stock assessment specifications.