# 1.2. Entities, state variables, and scales

## 1.2.1. Entities

In the current section, the different types of entities of the Osmose model are described.

• The Configuration entity describes the parameters and entities that will be shared among the different simulations.

• The Simulation entity describes a given simulation. Simulations differ from each other if stochasticity is enabled.

• The Cell entity describes the individual cells of the Osmose computation 2D grid (longitude, latitude, cell index, etc.)

• The Species entity represents the species whose life-cycle is fully represented. This entity contain fixed parameters, which are not modified during the simulation.

• The BackgroundSpecies entity represents the species whose life-cycle is not represented. These species can feed on and be eaten by Species, and can be fished. This entity contain fixed parameters, which are not modified during the simulation.

• The ResourceSpecies entity represents the low-trophic level species. These species cannot predatate Species or BackgroundSpecies but can be eaten by them. This entity contain fixed parameters, which are not modified during the simulation.

• The School entity describes a group of Species individuals, whose life cycle is fully considered and which all share the same characteristics (age, weight, species, location, etc, trophic level).

• The BackgroundSchool entity describes a group of BackgroundSpecies individuals, whose biomass is provided as input and whose life-cycle is not simulated and which all share the same characteristics (age, weight, species, location, etc, trophic level).

• The Resource entity describes a swarm of ResourceSpecies, whose biomass is provided as input.

## 1.2.2. State variables

### 1.2.2.1. Simulation

The Simulation entity contains the following state variables:

Table 1.1 Simulation state variables

Variable

Description

Type

Units

i_step_simu

Times step of the simulation

int, $$\in [0, N_{year} \times N_{step\_year}]$$

rank

Index of the simulation

int, $$\in[0, N_{simulation}]$$

schoolSet

List of the School inside the simulation

SchoolSet

backSchoolSet

List of the BackgroundSchool inside the simulation

BackgroundSchoolSet

### 1.2.2.2. Cell

The Cell entity contains the following state variables:

Table 1.2 Cell state variables

Variable

Description

Type

Units

i

i-index of the current cell on the 2D grid

int, $$\in [0, N_x - 1]$$

j

j-index of the current cell on the 2D grid

int, $$\in [0, N_y - 1]$$

land

true if the cell is on land

boolean

lat

latitude

float

Degrees North

lon

longitude

float

Degrees East

surf

surface

float, > 0

$$m^2$$

### 1.2.2.3. Species

The Species entities contain the following state variables:

Table 1.3 Species state variables

Variable

Description

Type

Units

name

name of the species

string

index

index of the species

int, $$\in[0, N_{species} - 1]$$

fileIndex

index of the species in the configuration file

int, $$>0$$

lifespan

species life span

int, $$>0$$

time-steps

c

allometric factor

float

bPower

allometric power

float

sizeMaturity

Size at maturity

float

cm

ageMaturity

Age at maturity

float

year

eggSize

Size of eggs

float

cm

eggWeight

Weight of eggs

float

g

firstFeedingAgeDt

First feeding age

int

time-step

Age at which the school is considered as adult

int

time-step

TL_EGG

egg trophic level

float, $$= 3.0$$

The BackgroundSpecies entities contain the following state variables:

Table 1.4 BackgroundSpecies state variables

Variable

Description

Type

Units

name

Species name

string

index

Species index.

int, $$\in [N_{species}, N_{species} + N_{bkgspecies}] - 1$$

fileindex

index of the species in the

int, $$>0$$

age

Age array

[float]

years

ageDt

Age array

[int]

time-step

c

allometric factor

float

bPower

allometric power

float float

classProportion

Proportion of biomass attributed to each size-class

float[]

%

length

Length array

float[]

cm

nClass

Number of size-classes

int, $$>1$$

trophicLevel

Array of trophic level

float[]

timeSeries

Time series of proportion of biomass attributed to each size-class

Table 1.5 ResourceSpecies state variables

Variable

Description

Units

accessMax

Maximum value for resource accessibility

0.99

accessibilityCoeff

Fraction of the resource biomass available to the fish

[0, 1]

fileindex

Species index in the configuration file

index

Resource species index

name

Resource species name

sizeMax

Maximum size of the plankton size

Cm

sizeMin

Maximum size of the plankton size

Cm

trophicLevel

Trophic level

### 1.2.2.4. School

The School entity contains the following state variables:

Table 1.6 School state variables

Variable

Description

Type

Units

abundance

Number of fish in the school at the beginning of the time-step

float

biomass

Biomass of the school at the beginning of the school

float

Tons

instantaneousAbundance

Instanteanous number of fish in the school

float

instantaneousBiomass

Instanteanous biomass of the school at the beginning of the school

float

Tons

Biomass of the school that has been discarded by each fishing gear

float[]

Tons

fishedBiomass

Biomass of the school that has been landed by each fishing gear

float[]

Tons

Number of dead fish in the current time nstep for each mortality cause (predation, fishing, natural mortality, starvation)

float

predSuccessRate

Predation success rate

float

%

preyedBiomass

Biomass of prey ingested by the school at current time step

float

Tons

preys

List of preys eaten by the school

HashMap<Integer

Prey>

uuid

Unique identifier of the individual

UUID

lat

Latitude of the individual

float

Degrees north

lon

Longitude of the individual

float

Degrees east

x

i-index of the individual in the 2D grid

int

y

j-index of the individual in the 2D grid

int

ageDt

Age of the school

int

Time-step

eggRetained

Buffer variable that will temporarily retain some eggs inside a time step

float

length

Length of the individuals in the school

float

cm

lengthi

Length of the individuals in the school at the beginning of the time-step

float

cm

out

True if the school is out of the computation domain

boolean

starvationRate

Starvation rate of the school

float

trophicLevel

Trophic level of the school

float

weight

Weight of the school

float

tons

species

School species

Species

abundanceHasChanged

True if abundance has changed in the current time-step

boolean

accessibility

Array of accessibility of the school to its preys

float[]

ageDeath

Age at which a school individuals die times the abundance

float[]

$$N\times years$$

Table 1.7 BackgroundSchool state variables

Variable

Description

Units

abundance

Number of fish in the school at the beginning of the time-step

biomass

Biomass of the school at the beginning of the school

Tons

Biomass of the school that has been discarded by each fishing gear

Tons

fishedBiomass

Biomass of the school that has been landed by each fishing gear

Tons

Number of dead fish in the current time nstep for each mortality cause (predation, fishing, natural mortality, starvation)

predSuccessRate

Predation success rate

%

preyedBiomass

Biomass of prey ingested by the school at current time step

Tons

preys

List of preys eaten by the school

uuid

Unique identifier of the individual

lat

Latitude of the individual

lon

Longitude of the individual

x

i-index of the individual in the 2D grid

y

j-index of the individual in the 2D grid

classIndex

Class index to which belongs the school

bkgSpecies

School background species

## 1.2.3. Scales

The basic units of OSMOSE are fish schools, which are composed of individuals that belong to the same species, and that have the same age, size (length, weight), food requirements and, at a given time step, the same geographical coordinates. From the school states (hereafter called individual states), biomass and abundance can be tracked at the population or community levels along with the size, age, and spatial dimensions.

Other variables can be reported such as the trophic level, the diets, the different sources of mortality, the catches from fishing operations. Because each school simulated in OSMOSE is represented from the egg stage to the terminal age, which necessitates high calculation and memory capacities, and because comprehensive information on entire life cycles needs to be parameterized, the selection of focus species is made parsimoniously, and usually between 10 and 20 high-trophic level species or functional groups are explicitly considered in OSMOSE applications.

The model operates on a weekly to monthly time step, and runs up to 100 years or more depending on applications and simulations.

For eggs (age 0), weight and sizes are provided as parameters. For the others, conversion from size to weight (and conversely) is obtained by using allometric relationships:

\begin{align}\begin{aligned}W = c \times L^b\\L = \left(\frac{W}{c}\right)^{\frac{1}{3}}\end{aligned}\end{align}

where the $$c$$ parameter is a condition factor, and $$b$$ the allometric power.

Biomass to abundance conversion for a school is made by using the mean weight of the school:

\begin{align}\begin{aligned}B = N \times W\\N = \frac{B}{W}\end{aligned}\end{align}
 species.length2weight.condition.factor.sp# Allometric factor ($$c$$) species.length2weight.allometric.power.sp# Allometric power ($$b$$) species.egg.size.sp# Egg size (cm) species.egg.weight.sp# Egg weight (g)