Management history can cause irreversible changes in agroecosystems: insights from an extended Carpenter model

History-dependence plays a significant role in understanding how ecosystems can shift dramatically in response to environmental changes. Hysteresis is a special case in which a shift from a desirable state to an undesirable state can only be reversed when an external driver of change (e.g. pollution) is brought down to a much lower level than at the level at which the unfavourable transition first occurred. Here, we ask whether hysteresis or a different form of history-dependence can be observed in plant--soil interactions owing to the changing agricultural management by extending the classic Carpenter model of nutrient cycling, which shows that correlation between nutrient loss rate and recycling rate is sufficient to cause irreversible shifts in the plant--soil system. We provide some initial empirical validation of theoretical results and suggest improvements for future empirical studies. Overall, our results show that complex history-dependence owing to past management occurs in an agricultural context and plant--soil interactions more broadly.