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 objective is to find the kernel parameters which correspond to knowledge expert, i.e. 50 % of strayers settle before 19 km, 95% before 111 km.
Mathematically, that leads to find $\alpha_0$ and $\alpha_1$ that solve the 2 following equations:
With parameter values defined in Rougier et al 2015, `r scales::percent(dataTarget$pct[1])` of strayers settle before `r RougierReferenceDistance[1]` km, and respectively `r scales::percent(dataTarget$pct[2])` before `r RougierReferenceDistance[1]` km.
# Parameters corresponding to the reference distance defined by US experts
```{r optimisation}
# sum of square error for percentage of settlement
To have `r dataTarget$pct[1]` and `r dataTarget$pct[2]` of strayer settlement before `r dataTarget$dist[1]` and `r dataTarget$dist[2]`, kernel parameters $\alpha_0$ and $\alpha_1$ take values `r resDispersal_USExpert$par[1]` and `r resDispersal_USExpert$par[2]`.
With this parametrisation, the curve of settlement before a distance becomes