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.

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

Probing ion specific effects on aqueous acetate solutions Ion pairing versus water structure modifications

The effect of monovalent cations (Li+, K+, NH4+, Na+) on the water structure in aqueous chloride and acetate solutions was characterized by oxygen K-edge X-ray absorption spectroscopy (XAS), X-ray emission spectroscopy, and resonant inelastic X-ray scattering (RIXS) of a liquid microjet. We show ion- and counterion dependent effects on the emission spectra of the oxygen K-edge, which we attribute to modifications of the hydrogen bond network of water. For acetates, ion pairing with carboxylates was also probed selectively by XAS and RIXS. We correlate our experimental results to speciation data and to the salting-out properties of the cations