.. _reproduction:

Reproduction
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Mature individuals spawn during the breeding season, which occurs when successive time steps :math:`t`  
have a spawning seasonality value :math:`sp(t)`  (expressed as a fraction of spawning activity per time step and summing to 1 over one year) above 0. 
At the first time step  of the breeding season, all the energy contained in the gonadic compartment :math:`g(i, t)`  of individuals in school :math:`i`  is used to produce eggs. The sex-ratio is assumed to be 1 for 1 for all species and the number of eggs produced by school :math:`i`  for the whole breeding season is defined as follows:

.. math::

   N_{eggs} (i, t) = N(i, t) \dfrac{g(i,t)}{ 2 w_{egg}}


with :math:`w_{egg}`  the weight of an egg. The pool :math:`g(i,t)`  is then set to 0 and can start growing again (equation :eq:`eq_gonad_growth`) at the next time steps in view of the next spawning season. Then, the total number of eggs produced by the species :math:`s(i)`  for the breeding season is obtained as

.. math::

   N_{eggs_{tot}} = \sum_{j \lor s(j) = s(i)} N_{eggs}(j, t)

At each time step :math:`t`  of the breeding season, :math:`N_s` new schools are produced by species :math:`s(i)`, with the number of eggs, and thus individuals, per new school :math:`i'`  calculated as follows: 

.. math::

    N(i', t) = sp(t) \times \dfrac{N_{eggs_{tot}}}{N_{s}}

with age of offspring set to 0 (:math:`a(i', t) = 0`), their somatic weight set to the weight of an egg (:math:`w(i', t) = w_{egg}`) and their gonadic weight set to 0 (:math:`g(i,t) = 0`). 
The new schools are released randomly depending on the specific larvae habitat map.