The kernel function presently used in GR3D is only based on basin accessibility (linked to distance between basins) even if a generic formulation including basin attractivity (related to basin size) and fish ability (based on fish lenght) is proposed in @rougier2015.

The kernel function presently used in GR3D is only based on basin accessibility (linked to distance between basins) even if a generic formulation including basin attractivity (related to basin size) and fish ability (based on fish length) is proposed in @rougier2015.

The first step is to compute for a departure $j_1$ the weight of each destination basin $j_2$ using:

where $D_{j_1\rightarrow j_2}$ is the distance between the departure and destination basins, $\alpha_0$ and $\alpha_1$ are the kernel parameters, $\mu_D$ and $\sigma_D$ are the mean and standard deviation between inter basin distances.

The last two parameters were introduced to standardise distance when accessibility is combining with attractivity and ability. When only considering only accessibility, $\mu_D$ and $\sigma_D$ are simply linked to the distance a strayer can reach. There is no need to be changed when the basins network (number and location of basins) change. Definitively the definition as mean and standard deviation of distances is confusing.

The last two parameters were introduced to standardise distance when accessibility is combining with attractivity and ability. When only considering only accessibility, $\mu_D$ and $\sigma_D$ are simply linked to the distance a strayer can reach. There is no need to be changed when the basins network (number and location of basins) changes. Definitively, the definition as mean and standard deviation of distances is confusing.

The sum of weights for the departure basin $j_1$ is: $$w_{j_1} = \sum_{j_2 \neq j_1} {w_{j_1\rightarrow j_2}}$$