Table 1 Model parameters.

u

Fraction of unsuitable patches

s

Fraction of suitable patches

ρ _i

Global patch occupancy of species i

ρ _{i, j}

Fraction of the suitable patches occupied by both species i and j with trophic interactions, or patch occupancy of the trophic link i → j, with “,” indicating the trophic link within a local patch

ρ _kl

Probability in a randomly chosen pair of neighbouring patches that one patch is k and the other is l (pair density; k, l∈ {s, u, 1, 2, 3})

q _k/l

Conditional probability that the neighbour of a l-patch is a k-patch (local density; k, l∈ {s, u, 1, 2, 3})

q _s/s

Clustering degree of suitable patches before species introduction (i.e., patch connectivity), indirectly indicating mean patch cluster size and configurational fragmentation

c _i

Species colonization rate

e _i

Species extinction rate

μ _ji

The top-down extinction rate of species i eaten by species j