Anatomy of the last days of a long transient spatial pattern: The ecological mechanism by which a traveling wave spatial patterns may end

A spatially explicit simulation model was developed to assess the effectiveness of a biocontrol agent (a weevil) in consuming and thus limiting an invasive floating aquatic macrophyte (FAV) competing with native submersed aquatic vegetation (SAV). The three interacting species form a hierarchically intransitive network, specifically, rock-scissors-paper (weevil-FAV-SAV). Time delays in the system facilitate the emergence of a two-dimensional traveling wave involving the three species. In numerous simulations the traveling wave persists for long time periods despite stochastic disturbances in the form of added adult weevils. However, at a time that depends on the random number initiator, an apparently insignificant spatial deviation in a small set of pixels triggers an instability that grows rapidly until the striped pattern has been replaced by a chaotic-appearing pattern. The precise way in which this instability develops was studied through simulations at the resolution of daily time steps. The investigation showed that the time lags in the weevil life cycle and in spatial movement can lead to the instability and cause the original traveling wave to suddenly degenerate. Because the model simulates a parameterized ecological system, the results contribute to understanding how apparently stable ecological patterns, such as the striped traveling wave modeled here, can rapidly end as long transients.