Simulation of the effect of rainfall on farm-level cocoa yield using a delayed differential equation model

Cocoa (Theobroma cacao) is an economically important crop grown by approximately six million of smallholder farmers throughout the tropics and sub-tropics. However, farm level yields are often very low, and sustainable intensification is urgently required. Assessing the impact of on-farm interventions of farm productivity and profitability requires an understanding of the contribution of inter-annual climate variability to cocoa yields. A Delayed Differential Equation model (DDE) was used to simulate the effect of rainfall on cocoa yields. A DDE model is an ordinary differential equation model that incorporates time lags, and is therefore able to incorporate the delay in yield response to rainfall due interactions with the cocoa flowering and the pod development processes. The DDE was constructed and based on regional rainfall and farm-level cocoa yield data from 96 farms across the main cocoa growing regions in Ghana. Model outputs indicate that a good likeness of seasonality in crop production was achieved. The potential to conduct a detailed parameterisation and extend this model to include other parameters such as agrochemical inputs and farm management practices are discussed. By further developing this model into a useful tool to predict and understand variability in cocoa yield, the sustainable intensification of small holder cocoa farming is supported.