Analysing trade-offs in resource and labour allocation by smallholder farmers using inverse modelling techniques: a case-study from Kakamega district, western Kenya

Smallholder farms in sub-Saharan Africa face multiple trade-offs when deciding on the allocation of their financial, labour and nutrient resources. Day-to-day decisions have implications for the sustainability of their farming system, implying multiple trade-offs between short- and long-term objectives that have biophysical and socio-economic dimensions. We show that inverse modelling techniques can be used effectively for optimisation and trade-offs analysis of farming systems. By combining the multi-objective shuffled complex evolution metropolis algorithm and a crop/soil dynamic simulation model we were able to select farming strategies that resulted in the best possible trade-offs between different farming objectives. This integrated analytical tool allows optimisation of farmers' goals similar to linear programming, but an advantage over linear programming is that the proposed method takes into account a wider spectrum of biophysical processes including their interactions and feed backs. Tradeoffs between resource productivity, use efficiency and conservation in relation to different patterns of resource allocation were analysed for a maize-based, simplified case study farm from western Kenya (2.2 ha – comprising fields of poor, medium and high soil fertility), under three scenarios of financial liquidity to invest in labour and inputs (2000, 5000 and 10,000 KSh ha^-1; 75 KSh = 1 US$). The maximum farm-scale maize production achieved was larger when financial resources increased. However, increasing maize yields above a certain threshold by applying mineral fertilisers was associated with larger N losses by leaching, runoff and soil erosion; such threshold was 2.7 t grain ha^-1 for the scenario of no financial limitations (10,000 KSh ha^-1). N losses at farm scale fluctuated between 36 and 54 kg N ha^-1 season^-1, while the maximum maize yields achieved were around 3.4 t grain ha^-1. Soil losses by erosion increased abruptly beyond a certain maize yield (e.g. 1.8 t grain ha^-1 for the 2000 KSh ha^-1 scenario), while the minimum rate of soil loss differed between financial scenarios. Investments in hiring labour were prioritised over fertiliser use to obtain the greatest yields and the allocation of available resources favoured the more fertile fields. This inverse modelling exercise allowed us to analyse trade-offs between different farmers' objectives and to compare potential resource allocation strategies to achieve them. The set of strategies to achieve different goals was more numerous and variable when the conditions were less conducive for farming. This questions the validity of the prevailing model of extension/communication, based on generalised recommendations for resource-poor farmers in Africa.