Background/Question/Methods Population irruptions and collapses are common occurrences in nature, consistent with theory that has characterized population dynamics as inherently non-linear.  For example, biological invasions frequently exhibit a boom-bust cycle and metapopulations often crash unexpectedly to extinction.  To explore the fundamental statistical dynamics of invasive species spread and declines in endangered species, a simple model was developed that determined the success or failure of a colonization episode based on the probability of establishment of an arriving individual (invasibility) and the number of individuals in the dispersal pool.

Results/Conclusions Consistent with prior theory, the model showed that spread of invasive species and colonization and extinction dynamics in metapopulations are likely fundamentally non-linear in their behavior.   In a three-dimensional graph of the three variables (number of propagules, invasibility, and probability of a successful colonization event), this sensitivity is illustrated by a cliff-like feature, which connects a lowland region (where colonization is unlikely) to a high plateau (where colonization is almost certain).  Specifically, the model shows that the existence of a threshold (the colonization cliff), where very small changes in invasibility and/or propagule number can increase the probability of a successful colonization event from near zero to near certainty, or vice-versa.  The fundamental non-linear dynamics associated with species spread and decline means that even as we continue to learn more about the underlying biotic and abiotic mechanism that control species spread and contraction, colonization episodes of invasive species and extinction episodes of threatened species will remain difficult to predict.  For managers trying to control the spread of an invasive species, or trying to sustain an endangered species in a fragmented landscape, this is not good news.  The threshold behavior of metapopulations and invasive species means that managers are vulnerable to serious decision-making traps.  Managers unaware of the colonization cliff are much more likely to be reactive, responding to a population only after it irrupts or collapses, at which point most any response will be too little too late.  An informed species manager will not be guided solely by the change, or lack of change, in the abundance of the target species.  Instead, the manager will recognize the importance of monitoring changes in patch quality and propagule pressure, realizing that persistent changes in these factors will often portend future changes in species abundance and spread, quite possibly very abrupt changes.  Such knowledge will enable the manager to respond proactively.