Mortality Additional mortality Larva mortality

Additional larva mortality

The scenario of larva mortality is defined by one of the following parameters:

• If mortality.additional.larva.rate.spX is defined, the larva mortality rate is constant over the year
• If mortality.additional.neonate.rate.spX is defined, the larva mortality rate is constant over the year
• If mortality.additional.larva.rate.bytDt.file.spX is defined, the larva mortality rate varies over the year.

Constant larva mortality rate

In this case, larva mortality rate is provided using the mortality.additional.larva.rate.spX and mortality.additional.larva.rate.shift.spX parameters.

The first parameter defines the larva mortality rates, in $year^{-1}$, and the second parameter defines the years when the values change.

• If the mortality.additional.larva.rate.shift.spX is not defined, then mortality.additional.larva.rate.spX expects one value, which will be used for the whole simulation.
• If the mortality.additional.larva.rate.shift.spX is defined and contains $N$ values, then mortality.additional.larva.rate.spX expects $N+1$ values. For example, if the shift values are 2, 5 and the mortality rates are 0.01, 0.02 and 0.03, the first value will be used between year 0 and 2, the second value between years 2 and 5, and the third value will be used between years 5 and the last year of the simulation.

Additional parameters can be provided:

• mortality.additional.larva.rate.multiplier.spX provides a multiplier to the mortality rate. If not defined, then the multiplier value is 1.

• mortality.additional.larva.rate.seasonality.file.spX or mortality.additional.larva.rate.seasonality provides a CSV file or a time-series containing multipliers, for each time-step, to modulate the annual larva time-series. When none of these parameters are defined, the multiplier will be set to 0.

With all these parameters, the larva mortality rate for a given time-step is given by:

$$ L(t) = \frac{M \times S(t) \times F_{add}(y)}{N_{step/year}} $$

where $M$ is the multiplier, $S(t)$ the seasonal modulation of mortality, $t$ the time-step and $y$ the current year and $N_{step/year}$ the number of time steps in a year.

An additional parameter allows to consider density-dependent mortality rate:

• mortality.additional.larva.referencedensity.spX takes into account density dependance in the larval mortality. This parameter $K$ is the spawning stock biomass (SSB) used to define the strength of density-dependent larval mortality. At $SSB = K$, larval survival is reduced by 50% relative to the low-density survival. For the purpose of this calculation, SSB is the sum of biomass of all mature schools (male and female) of the species.

In this case, a correction is applied to the larval mortality:

$$ C(t) = L(t) \times a(t) \times \frac{SSB}{K} $$

where $a(t) = \log(2)/L(t)$

and the new larva mortality rate is given by

$$ L_{cor}(t) = L(t) + C(t) $$

Tip

For more details on density-dependence mortality, see issue #59.

Warning

In the following implementation, the value of $C(t)$ is independent of $L(t)$. However, the current implementation allows for future new parameterisations of $a(t)$

Constant neonate mortality rate

In this case, larva mortality rate is provided using the mortality.additional.neonate.rate.spX and mortality.additional.neonate.rate.shift.spX parameters.

The first parameter defines the neonate mortality rates, in $year^{-1}$, and the second parameter defines the years when the values change.

• If the mortality.additional.neonate.rate.shift.spX is not defined, then mortality.additional.neonate.rate.spX expects one value, which will be used for the whole simulation.
• If the mortality.additional.neonate.rate.shift.spX is defined and contains $N$ values, then mortality.additional.neonate.rate.spX expects $N+1$ values. For example, if the shift values are 2, 5 and the mortality rates are 0.01, 0.02 and 0.03, the first value will be used between year 0 and 2, the second value between years 2 and 5, and the third value will be used between years 5 and the last year of the simulation.

Additional parameters can be provided:

• mortality.additional.neonate.rate.multiplier.spX provides a multiplier to the mortality rate. If not defined, then the multiplier value is 1.

• mortality.additional.neonate.rate.seasonality.file.spX or mortality.additional.neonate.rate.seasonality provides a CSV file or a time-series containing multipliers, for each time-step, to modulate the annual neonate time-series. When none of these parameters are defined, the multiplier will be set to 0.

For each time-step, the neonate mortality rate that will be applied to a school is:

$$ F_{add}(t) = \frac{M \times S(t) \times F_add(y)}{N_{step/year}} $$

where $t$ is the time-step, $y$ the current year and $N_{step/year}$ the number of time steps in a year.

Warning

No density-dependence is possible with neonate mortality.

Time-varying larva mortality rate

If mortality.additional.larva.rate.bytDt.file.spX is defined, then annual larva mortality rates will be provided in a CSV file.

Warning

Using this method, no multiplier is provided.

Caution

This will be deprecated soon. It is strongly advised to use the constant larva mortality rate framework with the multiplier and the seasonality file.

Caution

Using this method, rates are still expected in $year^{-1}$, in order to facilitate a change in time-stepping.