Fig 1. A hypothetical example of the population change in a cluster over five years.

The number of inhabitants in a cell is indicated for inhabited cells shown in gray. The bold lines indicate the boundary of cluster c observed in year 2005. This cluster has $n_c^{\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}}\left(2005\right)={\sum }_{i\in \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}c}{n}_i\left(2005\right)$ = 10 + 20 + 30 + 40 + 50 = 150 and ${\tilde{n}}_c^{\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}}\left(2010\right)={\sum }_{i\in \mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}c}{n}_i\left(2010\right)$ = 10 + 15 + 60 = 85 inhabitants in 2005 and 2010, respectively. Although cluster c is split into different clusters in 2010, each of which extends beyond the border of cluster c determined in 2005, we neglect the split to calculate the population change in cluster c. Therefore, cluster c has lost 150–85 = 65 inhabitants in the five years.