Integer-based modeling of population dynamics: Competition between attractors limits predictability

► We show that the discrete-state population dynamics are impacted by competition between non-chaotic attractors. ► The non-chaotic discrete-state attractors emerge as a result of splitting of a continuous-state chaotic attractor. ► Predictability of the discrete-state dynamics is limited by noise driven transitions between the non-chaotic attractors. ► Provided the noise can be neglected, predictability of the discrete-state dynamics is shown to be time-scale-dependent.