Toward an Optimal Control Strategy for Sweet Pepper Cultivation – 1. A Dynamic Crop Model

Sweet pepper production is characterized by large fluctuations in fruit yield per week. Synchronization of yield patterns between nurseries in response to weather conditions leads to variations in market supply and affects price formation. In order to improve supply chain efficiency, auctions and wholesalers require nurseries to supply production forecasts several weeks in advance. At the nursery level, yield prediction is helpful for efficient labour planning. Because the dynamics of sweet pepper production are complex, growers find it difficult to understand and effectively control the production process. A model can be useful to assist growers in making efficient decisions with regard to crop and climate management. It is hypothesized that a phase-shift in the feedback-regulation of fruit set by growing fruits could be the cause of the periodic yield pattern observed in practice. This paper describes a dynamic model of sweet pepper production based on this principle. Model output was compared with measurements of sweet pepper production obtained from a commercial nursery. The calibrated model was able to simulate the measured data fairly well, in particular the yield fluctuations. These results are consistent with the hypothesis and serve as a promising starting point for further research aiming at a better understanding of the underlying processes and, consequently, model improvement. INTRODUCTION The production process in sweet pepper shows large fluctuations in the number of ripe fruits per week (Kato and Tanaka, 1971; Hall, 1977; Marcelis and Baan HofmanEijer, 1995; Heuvelink et al., 2003). Yield may vary between 5-10 fruits m wk during production peaks and less than 2 fruits m wk in intermediate periods. The production peaks typically occur once every 4-5 weeks, although the regular pattern of fruit production can be disturbed by sudden changes in weather conditions (Kato and Tanaka, 1971; Aloni et al., 1991; Jafaar et al., 1994). Yield fluctuations can, to a large extent, be explained by the equally large variations in the rate of formation of new fruits. Since sweet pepper plants tend to produce ample amounts of new flower buds, the dominant factor determining the amount of new fruits formed is the abortion of buds, flowers and young fruits (Bakker, 1989; Wien et al., 1989). Abortion in sweet pepper is influenced by light and temperature (Wien et al., 1989; Marcelis et al., 2004) in a way which is consistent with instantaneous regulatory effects of the supply (source) and demand (sink) of assimilates, often observed in other glasshouse fruit species (Kinet, 1977; Ho, 1988; Marcelis, 1994). Experimental evidence in support of the influence of source and sink on fruit set was published by Heuvelink et al. (2003) and Marcelis et al. (2004), who studied the effects of variations in Proc. IIIrd IS on HORTIMODEL2006 Eds. L.F.M. Marcelis et al. Acta Hort. 718, ISHS 2006 368 light and temperature level, planting density and pruning of leaves and fruits. These authors showed that fruit set is strongly correlated with the source/sink ratio, but also found additional effects that indicate that position may also play a role. A more complex regulation mechanism is also suggested by the observation that in a sweet pepper crop with parthenocarpic fruits, a significantly more constant fraction of fruits aborted, and yield fluctuations did not occur (Heuvelink and Körner, 2001; Heuvelink et al., 2003). This suggests that the seeds play a key role in the expression of source/sink influences on fruit set and abortion. In view of the dynamic nature of the process, growers generally find it difficult to predict the behaviour of the crop and to correct disturbances as they occur. A model can be useful to understand the mechanism behind the fruit production pattern of sweet pepper, to advise the grower regarding the cultivation measures that help to maintain a regular production, and to predict the number of ripe fruits during the weeks to come. Model studies of sweet pepper production have been published by Gijzen et al. (1990), Rijsdijk and Houter (1993), Nederhoff and Vegter (1994), but none of these models was capable of predicting yield fluctuations. Marcelis et al. (1998) referred to unpublished results, indicating that the production process of sweet pepper can be simulated using a combination of a model for dry matter production and a source/sink based partitioning function. Marcelis et al. (2006) obtained realistic simulation results, applying a fruit set function previously developed for cucumber in their sweet pepper model. However, the first publications that specifically demonstrate that periodic behaviour in sweet pepper fruit production can emerge as a dynamic model property appear to be the article by Schepers et al. (2006) and the present paper. Both models treat fruit set as depending on assimilate availability and distribution of fruits in different classes, but many details differ. Many oscillating systems involve a counteracting response which is shifted in phase relative to the original signal. It can be envisaged that a source-sink dependent regulation of fruit set could result in such oscillating behaviour, as assimilate demand of growing fruits depends on their developmental stage (Marcelis and Baan Hofman Eijer, 1995; Opara, 2000). Potential growth rates of young fruit are relatively low. Maximum sink strength is often reached somewhere halfway the course of fruit development, to diminish again at more advanced stages of maturity. Therefore, the change in fruit assimilate demand (sink strength) as a result of new fruit formation is shifted in phase relative to the surplus in assimilate availability for fruit growth (net source strength) which originally promoted fruit set. The same principle would apply for a source-sink related hormonal regulation of fruit set as suggested by Marcelis et al. (2004), provided that the evolution of a feedback signal from the fruits is again shifted in phase relative to the original event of fruit formation. In this paper, it is hypothesized that a dynamic crop model, constructed on the basis of these principles, should be capable of showing periodic behavior. The outlines of the dynamic model of sweet pepper production are described together with a comparison of simulations and measurements of sweet pepper production obtained in a commercial nursery in the Netherlands. Results of dynamic optimization using this production model are presented in a companion paper (van Henten et al., 2006). MATERIALS AND METHODS A Dynamic Model of Sweet Pepper Production The model of sweet pepper production is a discrete time model, describing the evolution of the sweet pepper crop in time steps of one day. A simple dynamic photosynthesis/growth model is used to describe crop growth and biomass partitioning between fruits, vegetative plant parts and a carbon buffer as illustrated in Fig. 1. The treatment of photosynthesis, respiration, source/sink dependent assimilate partitioning and growth is similar to that in many other dynamic crop models (Marcelis et al., 1998). Since the model calculates in daily steps, carbon fluxes and other rates are expressed as discrete