# 1.1. Introduction¶

The present document contains all the necessary information and guidelines to help understand the principles and assumptions of the OSMOSE model, apply it to a specific case study and run simulations for addressing specific issues. The OSMOSE model aims at exploring fish community dynamics and the ecosystem effects of fishing and climate change. It is an Individual-based model (IBM) which focuses on fish species and their trophic interactions ([SC01][SC04]). The model description follows the ODD (“Overview”, “Design concept” and “Details”) protocol for describing individual- or agent-based models (Grimm et al. 2006, Grimm et al. 2010).

The Osmose model assumes opportunistic predation based on spatial co-occurrence and size adequacy between a predator and its prey (size-based opportunistic predation). It represents fish individuals grouped in schools, which are characterized by their size, weight, age, taxonomy and geographical location (2D model), and which undergo different processes of fish life cycle (growth, explicit predation, natural and starvation mortalities, reproduction and migration) and a fishing mortality distinct for each species and structured by age/size, space and season. The model needs basic biological parameters for growth and reproduction processes, that are often available for a wide range of species, and which can be found in FishBase for instance. It also needs to be forced by spatial distribution maps for each species, by age/size/stage and by season depending on data availability. In output, a variety of size-based and species-based ecological indicators can be produced and compared to in situ data (surveys and catch data) at different levels of aggregation: at the species level (e.g. mean size, mean size-at-age, maximum size, mean trophic level, within-species distribution of TL), and at the community level (e.g. slope and intercept of size spectrum, Shannon diversity index, mean TL of catch). The model can be fitted to observed biomass and catch data, using a dedicated evolutionary algorithm. Recent developments have focused on the coupling of OSMOSE to various hydrodynamic and biogeochemical models, allowing to build end-to-end models of marine ecosystems that explicit combined effects of climate and fishing on fish dynamics.

# 1.2. Purpose of the model¶

The OSMOSE model represents the dynamics of fish communities. It is a multispecies and spatial model which lies on size-based predation, traits-based life history, and individual-based processes. The model aims to explore the functioning of marine ecosystems, the ecosystem effects of fishing and climate changes, the impacts of management measures (changes in fishing pressure and fishing strategies, implementation of marine protected areas).

# 1.3. State variables and 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 (Table 1.1). 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 grid is a lattice of square cells of about 10 km resolution, and covers areas from $$10^4$$ to $$10^6 km^2$$. The model operates on a weekly to monthly time step, and runs up to 100 years or more depending on applications and simulations.

Table 1.1 List of state variables
Individual State variables Description Auxiliary state variables / indicators
abundance Number of fish (N) in the school at the beginning of the time step
biomass Biomass (B) of the school at the beginning of the time step (tons)
age Age of the fish (year) species N or B per age class
length Size of the fish (cm) fish N or B per size class (size spectrum), mean size of fish, large fish indicator
weight Weight of the fish (g)
trophicLevel Trophic level (TL) of the fish fish N or B per TL (trophic spectrum), TL of species, TL of catches
nDead[] Number of dead fish in the current time step for each mortality cause (predation, fishing, natural mortality, starvation) Catches per species, size class, age class
predSuccessRate Ingested biomass at current time step/maximum ingestion rate
preyedBiomass Biomass of prey ingested by the school at current time step (tons) fish diets per species, per size class, per age class
lat, lon location of the fish school in latitude and longitude coordinates

# 1.4. Input¶

There are two types of input to the model.

First, the spatial dynamics of OSMOSE focus species are driven by spatial distribution maps which can vary according to time (year, season or the age of fish). These maps are derived either from observational data (presence/absence data or density maps) or from climate niche models (see chapter X on integration of climate niches).

Secondly, the modelled system is driven by prey fields which are not explicitly represented as focus species in OSMOSE. For example, biomass fields of phytoplankton and zooplankton varying in space and time are typical input to OSMOSE. In the different OSMOSE applications, these prey fields were usually produced from coupled hydrodynamic and biogeochemical (BGC) models such as ROMS-NPZD ([TTSF14]), ROMS-PISCES ([OR14]), NEMOMed-ECO3M ([HLS+16]) or are derived from observational data ([GrussSC+15][FPS+13]). Benthic resources can also drive the dynamics of the system as in Halouani et al. (see chapter X on forcing OSMOSE with hydrodynamic-BGC models).

# 1.5. Process overview and scheduling¶

The life cycle of each focus species included in the OSMOSE model is modelled, starting with the egg stage. At the first time step, eggs are produced and split into a number of super-individuals called schools. At each time step, OSMOSE simulates the main life history processes for these schools, starting with the release of fish schools within their distribution area which is specified in input for each species and by age when presence/absence data are available. Then different sources of mortality are applied including predation, fishing, starvation and other natural mortality. In OSMOSE, predation is assumed to be opportunistic and based on predator and prey size adequation and spatio-temporal co-occurrence. Depending on the predation success, somatic growth is then implemented and mature individuals spawn at the end of the time step and produce new eggs for the next step.

# 1.6. Design concepts¶

Following the ODD framework and terminology, we briefly present here some design concepts characterizing OSMOSE:

• Collectives. As the total number of fish (from eggs to adult fish) to be taken into account in the simulated system can reach a value of the order of 10^12, the model was not brought down to the fish level but to an aggregated level consisting of a group of fish having similar ecological attributes. The unit of action and interaction, i.e., the “super-individual” as defined by Scheffer et al. (1995), is a group of fish having the same size, the same spatial coordinates, requiring similar food, and belonging to the same species (therefore having similar physiological and morphological characteristics). For convenience, this super-individual is also called a “fish school” in the following sections.
• Interaction. Super-individuals/schools interact locally through predation events.
• Emergence. From these local interactions, population and community dynamics emerge. In particular, the whole food web structure emerges from size-based local predation interactions.
• Sensing. Schools are assumed to know perfectly all the potential prey which are located in its vicinity, i.e. in the same cell of the grid. They also know the limits of their habitat.
• Stochasticity. There are different sources of stochasticity in the model. First, the order at which schools act and interact. There is a randomization of the precedence of schools crossed with a randomization of different sources of mortality (predation, fishing, other natural mortality). In addition, fish movements are also randomized within their habitats.
• Observation. For model testing and fitting, a variety of auxiliary state variables can be used in output of the model and compared with observations, data time series, and maps. Typically, species biomass and commercial catches, age or size distribution of abundance/biomass, diets can be confronted to observations.

# 1.7. Initialization¶

In previous versions of the model, the main way of initialising the system consisted in building age-structured populations from target biomass specified in input. Osmose would distribute fish biomass across age classes and schools according to a simple exponential decay of fish populations and applying the total annual mortality from one age to the next (sum of fishing and natural mortality parameters in input). Fish numbers were then calculated by using the length-weight parameters in input of the model and distributed evenly among the schools of a given age cohort. This initialisation method shows several drawbacks:

• it provides a fully structured population though, ideally, no assumption should be made about this structure which the model needs ot build up given some basic laws at individual level.
• it often initializes the system with an unstable state which can lead to premature and artificial species collapses or explosion in the first year of the simulation.
• it slows down the simulation because the initial population contains a big number of schools: though mortality rates are applied to build the age structure of the populations, fish schools do not disappear from the system but only their fish numbers are decreased.

We must first acknowledge that there is no ideal solution for initialising OSMOSE but it should be done by making as little assumptions as possible, keeping the spin-up time as short as possible and individual rules as much as possible. Therefore, OSMOSE 3 Update 2 proposes a new “seeding” mechanism for initialising the population. The system starts from a pristine state, with no schools in the domain. For a few years (user-defined), Osmose will release some eggs for every species. The eggs enter the different steps of the life cycle, and once the fish reach sexual maturity, the reproduction process takes over. Osmose stops the seeding, unless the spawning stock biomass gets depleted. In that case Osmose resumes the seeding by releasing some eggs until there are again mature individuals in the system for carrying on the reproduction process. Osmose completely ceases the seeding when the simulation reaches the maximal number of years for seeding (user-defined).

By following this approach:

• No assumption is made about the structure of the populations but it emerges from individual interactions
• it reduces computing requirements for the spin-up as the first years are the fastest to run
• it reduces the number of time steps for the spin-up
• it minimizes the amplitude of population oscillations

The initialisation process is controlled by two parameters, the seeding biomass (population.seeding.biomass.sp#) and the seeding duration (population.seeding.year.max).

population.seeding.year.max defined the number of years for running the seeding process (from year 0 to population.seeding.year.max), and during which Osmose ensures that some eggs will be released even though there are no mature individuals in the system. Then, the seeding ceases completely until the end of the simulation. If the parameter is not specified, Osmose will set it by default to the lifespan of the longest lived species of the system.

population.seeding.biomass.sp# defines the spawning stock biomass (SSB) that Osmose considers during the seeding period when there are no mature adults to ensure the reproduction process. The number of eggs to be released in the reproduction process are computed the following way:

$N_{eggs} = FRAC_{fem} * \alpha * season * SSB$

with $$\alpha$$ the number of eggs per gram of mature female, $$season$$ the seasonal fraction of spawning, $$FRAC_{fem}$$ the fraction of females and $$SSB$$ = sum(biomass of mature individuals) or population.seeding.biomass.sp# if the biomass of mature individuals is zero.

# 1.8. Submodels¶

## 1.8.1. Spatial distribution of schools¶

The spatial distribution of schools at each time step is driven by input maps that depend on the focus species, the size/age of the fish, the year and the season. The maps in input can be derived directly from presence/absence or density survey data. They can also be produced by statistical climate niche models which determine the probability of fish presence in a given cell of the grid according to a set of predefined environmental variables (sea surface temperature, phytoplankton concentration, sea surface height, O2, etc). The climate niche models can be run using in situ data (as in Gruss et al. 2015) or using output from coupled hydrodynamic-BGC models (as in Oliveros-Ramos 2014). At each time step, if fish schools are assigned a new distribution map (due to aging, season, year, growth) or when new eggs are released, schools are distributed uniformly over the distribution area corresponding to their age/size, species, season, year of simulation. When the maps do not change from one time step to the next (for example within a season, or the same map is used for several age/size classes of a species), schools can move to adjacent cells within their distribution area following a random walk. Random walk movements are meant to represent small-scale foraging movements and diffusion.

## 1.8.2. Computation of mortalities¶

Within each time step, the total mortality of a given school i is comprised of predation mortality caused by various schools j (Mpredation i, j), starvation mortality (Mstarvation i), fishing mortality (Fi), and diverse other natural mortality rate (Mdiverse i). The four different mortalities are computed so as to represent quasi simultaneous processes, and we consider that there is competition and stochasticity in the predation process.

Within each time step, OSMOSE considers each pair of {school-source of mortality} in turn in a random order. To ensure that the random order of the mortality sources and the schools does not bias the resulting instantaneous mortality rates applied and effectively correspond to the mortality rates specified in input (for fishing and diverse natural mortality), all the mortality events are iterated within a time step, over a fixed number of sub-time steps (user-defined as nsubdt, by default set to 10).

### 1.8.2.1. Predation¶

The central assumption in OSMOSE is that predation is an opportunistic process, which depends on: (1) the overlap between predators and potential prey items in the horizontal dimension; (2) size adequacy between the predators and the potential prey (determined by ‘predator/prey size ratios’); and when the information is available (3) the accessibility of prey items to predators, which depends on their vertical distribution (this being determined by means of ‘accessibility coefficients’). Thus, in OSMOSE, the food web structure emerges from local predation and competition interactions.

### 1.8.2.3. Diverse natural mortality¶

An additional source of natural mortality other than predation and starvation is applied to all schools older than 1 month: Mdiverse, which is the mortality due to marine organisms (top predators) and events (e.g., red tide events, diseases) that are not explicitly considered in OSMOSE. Moreover, an additional source of natural mortality other than predation is applied to the first age class corresponding to eggs and larvae (0–1 month old individuals): Mdiverse0, which is due to different causes (e.g., non-fertilization of eggs, advection away from suitable habitat, sinking, mortality of first-feeding larvae). For recruited stages, the Mdiverse parameter can be estimated from the predation mortality rate by marine organisms that are considered in Ecopath model but not in OSMOSE. Mdiverse0 is unknown for almost all the HTL groups represented in OSMOSE. Therefore, this parameter is estimated during the calibration process of OSMOSE.

## 1.8.3. Growth¶

Individuals of a given school i are assumed to grow in size and weight at time t only when the amount of food they ingested fulfill maintenance requirements, i.e., only when their predation efficiency at t is greater than the predation efficiency ensuring body maintenance of school. In such a case, the growth in length of school i at time t ( ) varies between 0 and twice the mean length increase $$Delta L$$ calculated from a von Bertalanffy model ([SC01][SC04]):

$\Delta L_{max} = L_{\infty} \times \exp^{-K\left(age - t_0\right)} \left(1 - \exp^{-K}\right)$
$\Delta L = 0 \ if\ \zeta_i<\zeta_{crit}$
$\Delta L = 2 \Delta L_{max} \frac{\zeta_i - \zeta_{crit}}{1-\zeta_{crit}} \ if\ \zeta_i>\zeta_{crit}$

(B.1) A von Bertalanffy model is used to calculate mean length increase above a threshold age Athres determined for each HTL group from the literature (Table B1). Below Athres, a simple linear model is used. The rationale behind this is that von Bertalanffy parameters are usually estimated from data excluding youngs of the year or including only very few of them. Assuming a linear growth between age 0 day and Athres ensures a more realistic calculation of mean length increases for early ages of HTL groups ([TSJ+09]). The weight of school i at time t is evaluated from the allometric relationship:

$W = C \times L^b$

where $$b$$ and $$C$$ are allometric parameters for the HTL group to which school i belongs (Table B1).

## 1.8.4. Reproduction¶

Any school whose length is greater than the length at sexual maturity Lmat reproduces at the end of each time step, allowing for the generation of new schools at the eggs stage for the next time step. At the scale of the HTL group, the number of eggs produced at time t ( ) is calculated as:

(B.3) where SR is the female: male sex ratio of the HTL group; the relative annual fecundity of the group (number of eggs spawned per gram of mature female per year); the probability for the HTL group to spawn a given month relatively to the other months of the year (Table B1); and the spawning stock biomass of the group at time t. In the absence of information, we assumed no seasonality of reproduction for reef omnivores. The parameters of all other HTL groups were estimated from the literature (Fig. B2 and Table B2). The eggs of all HTL groups are allocated a size of 1 mm, which appears to be a representative average estimate for marine fish species regardless of the body size of the adults (Cury and Pauly, 2000), and a weight of 0.0005386 g, considering eggs as spheres with water density. It can be noted that, since the growth of schools is evaluated in relation to their predation efficiency, the number of eggs produced at each time step, which depends on biomass (Eq. B.3), also depends implicitly on the food intake of schools (Shin & Cury, 2001, 2004).