Schematic compartment model illustrating how ecosystems may be classified into four invasion states (Susceptible, Exposed, Infectious and Resistant) linked by transitions relating transmission of non-native species amongst ecosystems, exposure and recovery. The characteristic dynamics within a receptor will exhibit three phases: a period prior to colonisation; growth as the local population increases; followed by fluctuations around the steady state. These phases can be identified with the epidemiological categorisations of Susceptible (no non-natives present), Exposed (low numbers of non-natives with essentially no dispersal) and Infectious (a viable population of non-native species contributing to dispersal). Termination of the Infectious state corresponds to the collapse of the meta-stable population due to stochastic events or some externally driven change (e.g. in the birth or death rates) or intervention which removes the local population and results in the receptor returning to either being Susceptible again or Resistant. Transitions between the four different states are: λ = the force of infection between Infectious and Susceptible ecosystems; θ = the rate at which an Exposed receptor reverts to become Susceptible; σ = the latency between initial exposure and infectivity; ξ = the rate of natural recovery of Infectious ecosystems to the Susceptible state; γ = the rate recovery of Infectious ecosystems following management to the Resistant state; ν = the rate which Resistant ecosystems enter the Susceptible state; μ = the rate which Susceptible ecosystems become Resistant. The total number of ecosystems (N) is given by the sum of the number of ecosystems in each state. Different weights for each arrow are for illustration only to highlight that transition rates between compartments differ and illustrate the probable importance of different transitions in biological invasions.