Institut für Pflanzenkrankheiten und Pflanzenschutz, Universität Hannover, Herrenhäuser Strasse 2, D-30419 Hannover, Germany

Background and objectives
Many investigations of the effects of diseases on yield of Phaseolus beans, for instance caused by angular leaf spot [1], have shown that yield is only weakly correlated with disease parameters such as the AUDPC. Yield can be better predicted using parameters of the host plant, e.g. the healthy leaf area duration (HLAD). Diseases do not only effect the yield formation directly, but also indirectly through the reduction of host growth and/or the acceleration of defoliation. The objective of our study was to quantify theses effects and to construct a mathematical model for the disease progression of simultaneously occurring bean diseases including their effects on leaf area growth and defoliation.

Materials and Methods
Five field experiments were carried out at Hannover (Germany) with cultivar Dufrix and at Piracicaba (Brazil) with cultivar Rosinha using the single plant approach. By marking each leaf, the leaf areas of 96 bean plants were determined in a weekly interval. Epidemics of the following diseases were created by artificial inoculations: bean rust (Uromyces appendiculatus), angular leaf spot (Phaeoisariopsis griseola) and anthracnose (Colletotrichum lindemuthianum). The disease severities of all leaves were estimated by means of diagrammatic scales.

Results and conclusions
For the development of the leaf area of a bean plant, the model of Richter et al. [2] was applied with a modification of the defoliation rate which could not be held constant, but increased exponentially. To account for the effect of diseases, the development rate was multiplied and the senescence rate divided by the disease-free proportion of the plant.

The progression of the diseases was modelled using Jeger’s [3] approach with coupled differential equations for the disease categories but given in area units. As the infectious periods of the three diseases were much longer than the life time of the leaves, only differential equations for the latent and the infectious disease categories were needed for each disease. An additional term was added to both equations to take into account the reduction due to defoliation. While the latent infected area decreased proportional to the total defoliation, the loss of infectious area was more than proportional. The parameter estimation of the five data sets was carried out using an iterative approach.

In all cases the observed disease progress curves including their decreases at the end of the season could be well described by the model. Similarly, the leaf area of a single plant could be simulated under the influence of the three diseases. The coupling of disease progression with host growth and defoliation decreased the leaf area available for infection and for yield formation. Based on the experiment 1995 in Piracicaba with a total maximum disease severity of less than 5%, the reduction in HLAD was estimated to be 2.7%. If the effects of the diseases on host growth would have been neglected, the reduction in HLAD would be only 1.9%. When higher disease severities were simulated, for instance for angular leaf spot an epidemic with a maximum severity of 11.2% which is in the range observed in [1], the reduction in HLAD would be 6.6%. Applying the model with the same parameter values but excluding the effects on leaf area growth and defoliation, HLAD would be reduced by 4.8% although the maximum disease severity would be slightly higher (13.3%).

In the model, the parameters are assumed to be constant during a season which leads to different parameter values in the experiments conducted. As disease progression and host development are influenced by external factors, like temperature and relative humidity, their effects on the rates have to be quantified in order to generalize the model for variable environments.

1. Bergamin Filho A, Carneiro SMTPG, Godoy CV, Amorim L, Berger RD, Hau B, 1997. Phytopathology 87, 506-15.
2. Richter O, Spickermann U, Lenz F,1991. Gartenbauwissenschaft 56, 99-106.
3. Jeger, MJ, 1982. Phytopathology 72, 1185-89.

The financial support of the European Commission (Project ERBIC18CT960037) is gratefully acknowledged.