2.8.1. 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.

Consider a predator school \(S_{pred}\).

2.8.1.1. Size predation

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

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

with \(R_{min}\) and \(R_{max}\) the maximum and minimum predator/prey size ratios. 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 2.26 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

\(R_{min} \gt R_{max}\)

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.

../../_images/size_ratio.svg

Fig. 2.4 Size-based predation in Osmose

2.8.1.2. Accessibility

First, the accessibility of all the preys to school \(S_{pred}\) 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 2.27 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%).

Table 2.28 Parameters for accessibility

predation.accessibility.stage.structure

Threshold type. Must be age or size.

predation.accessibility.stage.threshold.sp#

Array containing the stage thresholds for a given species.

predation.accessibility.file

CSV file containing the accessibility matrix

Warning

In versions <= 4.2.0, the order of the rows and columns must follow the indexing of species (focal, background and resource) and stages (e.g., species0; species1; species2 stage0; species2 stage1; species3). The threshold values provided in the CSV file are not used in this version

Since version 4.3.0, the predation.accessibility.stage.threshold.sp# parameter has been threshold has been deprecated, since the thresholds 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 what follows is the upper bound of the class.

Furthermore, the column and row order is no more important, since a match of the species name is performed.

Finally, since version 4.3.0, accessibility matrix can vary over time with the following parameters, which follow the parameterization of movements.

Table 2.29 Parameters for time varying accessibility

predation.accessibility.file.acc#

CSV file containing 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 map (instead of setting initial and final years)

predation.accessibility.steps.acc#

List of time steps when to use the map

Danger

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

2.8.1.3. Predation rate

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

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

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

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

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

\[P_{eaten} = min(P_{tot}, P_{eatable})\]

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

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

Finally, the success rate is computed as:

\[S_R = \frac{P_{eaten}} {P_{eatable}}\]
Table 2.30 Ingestion parameter

predation.ingestion.rate.max.sp#

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