An outbreak species exhibits extreme, rapid population fluctuations that can be qualified as discrete events within a continuous dynamic. When outbreaks occur they may appear novel and disconcerting because the limiting factors of their dynamics are not readily identifiable. We present the first population hybrid dynamic model that combines continuous and discrete processes, designed to simulate marine species outbreaks. The deterministic framework was tested using the case of an unexploited benthic invertebrate species: the small, serpulid polychaete Ditrupa arietina. This species is distributed throughout the northeast Atlantic Ocean and Mediterranean Sea; it has a life cycle characterised by a pelagic dispersive larval stage, while juveniles and adults are sedentary. Sporadic reports of extremely high, variable densities (from <10 to >10,000 ind.m−2) have attracted attention from marine ecologists for a century. However, except for one decade-long field study from the Bay of Banyuls (France, Gulf of Lions, Mediterranean Sea), observations are sparse. Minimal formulations quantified the processes governing the population dynamics. Local population continuous dynamics were simulated from a size-structured model with a null immigration–emigration flux balance. The mathematical properties, based on the derived hybrid model, demonstrated the possibilities of reaching an equilibrium for the population using a single number of recruits per reproducer. Two extrapolations were made: (1) local population dynamics were simulated over 180 years using North Atlantic Oscillation indices to force recruitment variability and (2) steady-state population densities over the Gulf of Lions were calculated from a connectivity matrix in a metapopulation. The dynamics reach a macroscopic stability in both extrapolations, despite the absence of density regulating mechanisms. This ensures the persistence of D. arietina, even when strong, irregular oscillations characteristic of an outbreak species are observed. The hybrid model suggests that a macroscopic equilibrium for a population with variable recruitment conditions can only be characterised for time periods which contain several outbreak occurrences distributed over a regional scale.