New measures and tests of temporal and spatial pattern of crops in agricultural landscapes

Crops are allocated to their fields by growers according to rotational principles and such rotations may be defined and classified. Rotations evolve through the aggregate choices of crops by growers over time which create the characteristic agricultural landscapes for a given region. As agriculture becomes ever more competitive, growers increasingly should use such rotational principles to maximise efficiency. Their choices of crop allocations alter the observed temporal heterogeneity and spatial pattern of cropped landscapes. Within the European Union the forms of heterogeneity studied here are increasingly evident at the landscape scale. We present techniques to study these patterns of crops in time and space. This is essential in order to build realistic simulators of large-scale cropped landscapes within which farming practices may be studied across national boundaries. Simulation is required to provide realistic arenas to extend current models of gene flow from the field to the landscape scale, in furtherance of studies of coexistence between genetically modified and conventional and organic crops. We provide simple, empirical descriptors of cropped landscapes in terms of the degree of the non-randomness of the allocation. Non-randomness of fields is assessed in terms of (i) spatial pattern, (ii) temporal heterogeneity, and (iii) spatio-temporal heterogeneity. Four formal statistical tests of significance are presented: one of spatial pattern, two of temporal heterogeneity and one of spatio-temporal heterogeneity that may also be used to test for spatial pattern. The tests were exemplified using data taken from a study landscape of 72 arable fields farmed by 10 different growers in Burgundy, France, from 1994 to 1997. Two of the tests were based on simple χ2-statistics; two were randomisation tests. The χ2-test of spatial pattern demonstrated clustering in the distribution of set aside fields. The χ2-test of temporal heterogeneity demonstrated non-randomness for eight growers who employed 15 rotations. The randomisation test of temporal heterogeneity found significant non-randomness for one grower in three of the five crops examined. The common 3-year rotation of oilseed rape, wheat, winter barley was employed by one grower on 10 of their fields, for which significant spatio-temporal heterogeneity was shown by the proposed randomisation test. It is possible to extend the analysis of these test-statistics between -- and within -- units in a hierarchy, so that the methods could be used to study pattern at larger scales than landscapes, say at regional or national scales.