Six habitat patches sit in a hostile agricultural "matrix". Consecutive patches are linked by a vegetated wildlife corridor. Individuals periodically disperse from a source patch to a randomly chosen target patch, moving either along a corridor (if the pair is linked) or in a straight line through open matrix (if not).
Each dispersal attempt succeeds or fails as a Bernoulli trial with a distance-decay probability, the same negative-exponential form used in graph-based landscape connectivity metrics such as the Probability of Connectivity (PC) index:
p_ij = exp( -d_ij / (k · w_eff + ε) )
w_eff = corridorWidth (patches linked by a corridor)
w_eff = matrixPermeability · 0.6 (no corridor: cross-country)
k = 3, ε = 0.05 (small constant, avoids /0)
Connectivity index = mean(p_ij) over all 15 patch pairs, ×100
Every successful crossing moves one individual into the destination patch; every failure removes it as dispersal mortality. A patch that reaches zero population turns grey and is marked extinct — a direct demonstration of how fragmentation drives local extinction even when the total landscape area is unchanged.
- Corridor width — physical width of the green wildlife corridors; widens the safe path and raises p_ij for linked patches.
- Matrix permeability — quality of the land between unlinked patches (e.g. hedgerows vs. monoculture); raises p_ij for cross-matrix trips.
- Dispersal rate — how often individuals attempt to move, in attempts per second.
- Connected / Fragmented presets — snap the corridor network to realistic best/worst cases.
This mirrors real conservation planning: agencies use connectivity indices exactly like this one to prioritise which corridors to protect or restore so that metapopulations can persist across fragmented landscapes.