Natural Resources Institute, University of Greenwich, Central Avenue, Chatham Maritime, Kent ME4 4TB, UK

Background and objectives
In some tropical irrigated rice systems, two or three rice crops may be grown each year in close succession and rice monocultures may occupy large tracts of land. Planting can be described as asynchronous if there is much variability in crop age between fields. The incidence of rice tungro virus disease (RTVD) in such systems is thought to be affected by both the degree of asynchrony and the susceptibility to RTVD of the varieties grown. The extent to which marginal decreases in asynchrony or in the proportion of RTVD-susceptible varieties grown can be expected to reduce RTVD incidence within a locality is unknown. A mathematical model of the epidemiology of RTVD [1] was used to investigate some of the principles involved in the dynamics of this disease on a supra-field scale.

Materials and methods
The cropping system was represented by a rectangular lattice of fields in which crops were harvested and replanted sequentially, and virus disease persisted by spread of inoculum between crops. Disease progress in each field was assumed to be logistic and determined by incidence within the field and in neighbouring fields, depending on the gradient of dispersal of the leafhopper vectors and the infection rate. In each growing season, planting date followed a normal distribution and its variance provided a measure of cropping asynchrony. RTVD-resistant and susceptible fields were represented by a difference in infection rate and the proportion of each variety type in the lattice was varied.

Results and conclusions
Disease incidence within the lattice (i.e. mean incidence over all fields) depended upon the epidemiological parameters of the disease but endemicity depended mainly on planting date variance. Disease persisted in the lattice if this variance exceeded a threshold, above which the response of mean disease incidence to planting date variance was nonlinear with the region of greatest sensitivity being closest to the threshold. Thus, disease systems which show moderate rather than high cropping asynchrony are more likely to be influenced by marginal changes in the variance of planting date.

Previous studies on the effect of genotype mixtures on disease progress within a single crop have shown that both the rate of disease increase [2] and the rate of focus expansion [3] were proportional to the logarithm of the fraction of susceptible plants in the mixture. Here, for long-term disease incidence in a lattice of transient crops, a similar'iogarithmic rule' applied, provided that resistant crop deployment was spatially random. A relatively large proportion of fields had to be planted with resistant varieties in order to have sufficient area-wide impact on inoculum levels to reduce disease incidence in fields of susceptible varieties. A conflict existed between the reduction of disease incidence strategically and in the individual fields of a newly deployed RTVD-resistant variety. Small genotype units and random patterns gave maximum area-wide impact whereas large units and concentrated deployment gave best protection of individual fields.

1. Holt J, Chancellor TCB, 1997. Plant Pathology 46, 490-501.
2. Leonard KJ, 1969. Phytopathology 59, 1845-1850.
3. Van den Bosch F, Verhaar MA, Buiel AAM, Hoogkamer W Zadoks JC, 1990. Phytopathology 80, 598-602.