A systematic representation of crop rotations

Crop rotations are allocations by growers of crop types to specific fields through time. This paper aims at presenting (i) a systematic and rigorous mathematical representation of crops rotations; and (ii) a concise mathematical framework to model crop rotations, which is useable on landscape scale modelling of agronomical practices. Rotations can be defined as temporal arrangements of crops and can be classified systematically according to their internal variability and cyclical pattern. Crop sequences in a rotation can be quantified as a transition matrix, with the Markovian property that the allocation in a given year depends on the crop allocated in the previous year. Such transition matrices can represent stochastic processes and thus facilitate modelling uncertainty in rotations, and forecasting of the long-term proportions of each crop in a rotation, such as changes in climate or economics. The matrices also permit modelling transitions between rotations due to external variables. Computer software was developed that incorporates these techniques and was used to simulate landscape scale agronomic processes over decadal periods.