Table 2
Stochastic matrix as mathematical representation of crop rotations — for examples a, b, c and d from Fig. 1; derived from Castellazzi et al. (2008).
a Current year
Sugar beet Fallow Wheat 1 Rapeseed Wheat 2
Previous year Sugar beet 0 1 0 0 0
Fallow 0 0 1 0 0
Wheat 1 0 0 0 1 0
Rapeseed 0 0 0 0 1
Wheat 2 1 0 0 0 0
b Current year
Sugar beet Fallow Spring barley 1 Wheat, late drilled Wheat 1 Spring barley 2 Beans Rapeseed Wheat 2
Previous year Sugar beet 0 0.3 0.35 0.35 0 0 0 0 0
Fallow 0 0 0 0 1 0 0 0 0
Spring barley 1 0 0 0 0 1 0 0 0 0
Wheat, late drilled 0 0 0 0 0 1 0 0 0
Wheat 1 0 0 0 0 0 0 0.5 0.5 0
Spring barley 2 0 0 0 0 0 0 0.5 0.5 0
Beans 0 0 0 0 0 0 0 0 1
Rapeseed 0 0 0 0 0 0 0 0 1
Wheat 2 1 0 0 0 0 0 0 0 0
c Current year
Sugar beet Fallow Spring barley 1 Wheat, late drilled Wheat 1 Spring barley 2 Beans Rapeseed Wheat 2
Previous year Sugar beet 0 0.3 0.35 0.35 0 0 0 0 0
Fallow 0 0 0 0 1 0 0 0 0
Spring barley 1 0 0 0 0 1 0 0 0 0
Wheat, late drilled 0 0 0 0 0 1 0 0 0
Wheat 1 0 0 0 0 0 0 0.5 0.5 0
Spring barley 2 0 0 0 0 0 0 0.5 0.5 0
Beans 0 0 0 0 0 0 0 0 1
Rapeseed 0 0 0 0 0 0 0 0 1
Wheat 2 0.5 0 0 0 0 0 0 0 0.5
d Current year
Wheat Rapeseed Beans Fallow
Previous year Wheat 0 0.2 0.5 0.3
Rapeseed 0.5 0 0.25 0.25
Beans 0.25 0.5 0 0.25
Fallow 0.2 0.3 0.5 0
Reading note: All crops, occurring in the rotation are listed within the first line and the first column of the table. The first line represents crops currently grown; the first column represents
crops previously grown. Within the cells of the table, one can read the probability for the current crop depending on the type of previous crop.
Reading example for crop rotation b: if sugar beet was the preceding crop in the previous year, with a probability of 35% late drilled wheat is to follow in the current year.