1.7.5.1. Predation mortality

The central assumption in OSMOSE is that predation is an opportunistic process, which depends on:

• the overlap between predators and potential prey items in the horizontal dimension

• size adequacy between the predators and the potential prey (determined by predator/prey size ratios); and when the information is available

• 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.

During the predation mortality process, the predation success rate (predSuccessRate attribute) is updated.

1.7.5.1.1. Size predation

Size-predation matrix is controlled by two parameters. The predator school \(S_{pred}\) can only feed on prey schools whose length belongs to a given interval:

\[R_{max} < \frac{L_{pred}}{L_{prey}} \le R_{min}\]

with \(R_{min}\) and \(R_{max}\) the maximum and minimum predator/prey size ratios. Reorganizing this inequality, we obtain:

\[\frac{L_{pred}}{R_{min}} \le L_{prey} < \frac{L_{pred}}{R_{max}}\]

Therefore, the minimum and maximum sizes of a prey that a predator can eat is given by:

\[ \begin{align}\begin{aligned}L_{max} = \frac{L_{pred}}{R_{max}}\\L_{min} = \frac{L_{pred}}{R_{min}}\end{aligned}\end{align} \]

Table 1.15 Size-predation parameters

predation.predPrey.stage.structure	Structure to determine thresholds for predator/prey size ratios (age or size)
predation.predPrey.stage.threshold.sp#	Array of age or size thresholds
predation.predPrey.sizeRatio.max.sp#	Array of \(R_{max}\) values
predation.predPrey.sizeRatio.min.sp#	Array of \(R_{min}\) values

Danger

To make sure that \(L_{max} < L_{min}\), the predation.predPrey.sizeRatio.max.sp# and predation.predPrey.sizeRatio.min.sp# must verify \(R_{min} > R_{max}\)

Since resource groups are defined by a range of sizes, and not by a single sizes, the predator will feed on a given percentage of the resource:

\[R_{rsc} = \frac{min(L_{max_{rsc}}, L_{max}) - max(L_{min_{rsc}}, L_{min})} {L_{max_{rsc}} - L_{min_{rsc}}}\]

which is the overlapping range of the predator accessible range and of the resource size range.

Fig. 1.7 Size-based predation in Osmose

1.7.5.1.2. Accessibility

First, the accessibility of all the preys to a given school is determined from an accessibility matrix for every species and stages. This matrix must not be used to define diet preferences but rather to take into account for a difference of positions in the water column (meaning some schools might evolve around the same geographical area but never meet because they do not occur at the same depth).

Table 1.16 Example of a CSV predation accessibility file.

Prey / Predator	lesserSpotted < 0.45	lesserSpotted	redMullet < 0.25	redMullet
lesserSpottedDogfish < 0.45	0.05	0	0	0.05
lesserSpottedDogfish	0	0.8	0.4	0
redMullet < 0.25	0	0.4	0.8	0
redMullet	0.8	0.4	0	0.8
pouting < 0.25	0	0.4	0.8	0
pouting	0	0.8	0.4	0
whiting < 0.25	0	0.4	0.8	0
whiting	0	0.8	0.4	0
Dinoflagellates	0	0.5	1	0
Diatoms	0	0.5	1	0
Microzoo	0	0.5	1	0
Mesozoo	0	0.5	1	0
Macrozoo	0	0.5	1	0
VSBVerySmallBenthos	1	0.5	0	1
SmallBenthos	1	0.5	0	1
MediumBenthos	1	0.5	0	1
LargeBenthos	1	0.5	0	1
VLBVeryLargeBenthos	1	0.5	0	1
backgroundSpecies	0	0	0	0

Each line of the matrix corresponds to a prey (including plankton groups), and each column to a predator. The file must be understood as follow: lesserSpottedDogfish of age class less than 0.45 (line 1) are only accessible to young lesserSpottedDogfish (5%) and old redMullet (5%).

The class thresholds (age or size, defined with the predation.accessibility.stage.structure parameter) that are used to determine which row or column should be used are read directly from the CSV files by matching the < character. It is assumed that if there is no match, no threshold is provided. However, when < is matched, it is assumed that the number that follows is the upper bound of the class.

Furthermore, the column and row order is not important, since a match of the species name is performed.

Additionnally, accessibility matrix can vary over time. To do so, one set of parameters must be defined for each accessibility matrix, as done for the parameterization of movements. The keys of these parameters must end with .acc#, with # the number of the accessibility matrix.

Table 1.17 Parameters for accessibility matric

predation.accessibility.stage.structure	Threshold type. Must be age or size.
predation.accessibility.file	CSV file containing the accessibility matrix if constant over time
predation.accessibility.file.acc#	CSV file containing the accessibility matrix for the accessibility matrix #
predation.accessibility.initialYear.acc#	Start year when to use the accessibility matrix #
predation.accessibility.finalYear.acc#	Start year when to use the accessibility matrix #
predation.accessibility.years.acc#	List of years when to use the accessibility matrix # (instead of setting initial and final years)
predation.accessibility.steps.acc#	List of time steps when to use the accessibility matrix #

Danger

If the predation.accessibility.file (with no .acc suffix) is found, Osmose will assume constant predation accessibility matrix.

1.7.5.1.3. Predation rate

Finally, the predation rate is computed as follows. First, the total accessible biomass for the predator school is computed:

\[B_{avail} = \sum_{p=preys} A(pred, prey) \times B_{prey}\]

where \(B_{avail}\) is the total accessible biomass of preys, \(A(pred, prey)\) is the accessibility coefficient of the predator over the given prey (cf. Section 1.7.5.1.2) and \(B_{prey}\) is the biomass of the prey.

The total biomass that a predator can eat is also computed as follow:

\[B_{eatable} = \frac{B_{pred} \times I_{max}}{N_{mort}}\]

with \(N_{mort}\) the number of sub-step of mortality processes, \(B_{pred}\) the total biomass of predator and \(I_{max}\) the maximum ingestion rate for each species, expressed in grams of food per gram of fish and per year. It is assumed that predator eat as much as they can.

The effective biomass that will be eaten by the predator is

\[B_{eaten} = min(B_{avail}, B_{eatable})\]

The success rate for the given time-step (\(S_R(t)\)) is incremented by then the value computed for the given sub time-step as:

\[S_R(t) = S_R(t) + \frac{B_{eaten}} {B_{eatable}}\]

Finally, for each prey, the biomass eaten by the predator is given by:

\[B_{{lost}_{prey}} = B_{eaten} \times \frac{A(pred, prey) \times B_{prey}}{B_{avail}}\]

and used to increment the number of dead individuals by predation (nDead attribute).

Table 1.18 Ingestion parameter

predation.ingestion.rate.max.sp#

\(I_{max}\) (grams of food per gram of fish and per year)