Natural mortality
---------------------------------------------
.. Constant annual rate/catches by species
.. ############################################
.. Constant annual rate by species
.. ++++++++++++++++++++++++++++++++++++++
In a similar way to fishing, the parametrization of the natural mortality takes into account different levels of time variability.
Larval mortality
##################
The larval mortality rate is expressed in :math:`dt^{-1}`. This term represents sources of mortality for age class 0 (age class zero in OSMOSE lasts for one time step) such as the non-fecundation of eggs, a starvation more pronounced than at older ages (rel to CC), or predation by species that are not explicitly considered in OSMOSE:
.. math::
N_{dead_{0}}(t) = N(t) \times (1 – e^{-M})
Constant larval mortality is activated by setting the :samp:`mortality.natural.larva.rate.sp#` parameter, while
larval mortality by time-step is activated by setting the :samp:`mortality.natural.larva.rate.byDt.file.sp#` parameter.
The latter parameter is the path of a CSV file that contains a time series of larval mortality rates:
.. _table_paros_larmort:
.. table:: Example of larval mortality rate by time-step
.. csv-table::
:delim: ;
:header-rows: 1
:widths: 50, 50
Time step; Larval mortality rate
0;0.03
1;0.03
2;0.025
3;0.025
4;0.03
The time value does not matter. Osmose does not read it and assume that there is one line per time step.
The number of time steps in the CSV file must be a multiple of the number of time steps per year.
If the time series is shorter than the duration of the simulation, Osmose will loop over it.
If the time series is longer than the duration of the simulation, Osmose will ignore the exceeding steps.
Natural mortality
############################
The natural mortality rate includes all type of mortalities that are not explicitly represented in OSMOSE, such as mortality due to other predators (seals, seabirds).
Annual natural mortality is activated by setting the :samp:`mortality.natural.rate.sp#` parameter. It is expressed in :math:`year^{-1}`) such as :
.. math::
N_{dead_{natural}}(t) = N(t) \times (1 – e^{-D / n_{dt_{year}}})
Natural mortality rate by time-step is activated by setting the :samp:`mortality.natural.rate.byDt.file.sp#` parameter, which
is the path of a CSV file that contains a time series of natural mortality rates (expressed in :math:`dt^{-1}`, same as larval mortality rate by time-step).
Natural mortality rate by time step and by age/size class is activated by setting either the
:samp:`mortality.natural.rate.byDt.byAge.file.sp#` or :samp:`mortality.natural.rate.byDt.bySize.file.sp#` parameter, which contain the
path of the CSV file that contains time series of natural mortality rate (expressed in :math:`dt^{-1}`) per age/size class.
The CSV file has the format than the fishing mortality rates/catches per dt and per size/age class:
.. _table_paros_mnat_rate:
.. table:: Example of natural mortality rate by time-step and by age.
.. csv-table::
:delim: ;
:header-rows: 1
Time step / Age;0;2;3.5;5;7
0;0;0;0.05;0.08;0.08
1;0;0;0.05;0.08;0.07
2;0;0;0.04;0.07;0.06
3;0;0;0.04;0.07;0.07
Osmose scans the first line of the CSV file to define the age classes (expressed in year). In this example 5 classes have been defined :samp:`[0 2years[`, :samp:`[2years 3.5years[`, :samp:`[3.5years 5years[`, :samp:`[5years 7years[` and :samp:`[7years to lifespan[`. For size classes the first line would look like:
.. _table_paros_mnat_size:
.. table:: Example of natural mortality rate by time-step and by size.
.. csv-table::
:delim: ;
:header-rows: 1
Time step / Length;0;5;10;20;40
0;0;0;0.05;0.08;0.08
1;0;0;0.05;0.08;0.07
2;0;0;0.04;0.07;0.06
3;0;0;0.04;0.07;0.07
The five classes for this species are :samp:`[0cm 5cm[`, :samp:`[5cm 10cm[`, :samp:`[10cm 20cm[`, :samp:`[20cm 40cm[` and :samp:`[40cm Linf[`.
The value of the time step does not matter, Osmose assumes there is one line per time step.
The number of time steps in the CSV file must be a multiple of the number of time steps per year.
If the time series is shorter than the duration of the simulation, Osmose will loop over it. If the time series is longer than the duration of the simulation,
Osmose will ignore the exceeding steps.