Pure Bt-crop and mixed seed sowing strategies for optimal economic profit in the face of pest resistance to pesticides and Bt-corn

Highlights

• We developed a discrete pest growth model with evolution of Bt-corn resistance.

• The net present value with pure Bt-corn or mixed planting strategy is investigated.

• The effects of parameters on the net present values are studied.

• The optimal proportion of the field planted with non-Bt-corn has been discussed.

Abstract

With the evolution of pest resistance to Bt-corn, farmers’ economic losses are increasing. However, a planting strategy with Bt-corn mixed with non-Bt-corn to fight the development of pest resistance can be efficient. Nevertheless, this mixed strategy poses questions such as (1) what is the optimal ratio of Bt-corn to non-Bt-corn that should be planted in a field? And (2) what is the main factor affecting the farmers’ net present value? To address these questions, we propose and investigate a discrete pest growth model with pest resistance to Bt-corn. According to the model’s economic functions, the main factors affecting the farmers’ net present value are presented and discussed. By comparing the net present values of a pure Bt-corn planting strategy with the mixed planting strategy, an optimal planting strategy was devised. Moreover, the optimal ratio of Bt-corn to non-Bt-corn to be planted when the mixed planting strategy is implemented in the field was also investigated.

Introduction

Insects and other pests seriously affect crop yields, with consequent economic losses for farmers. Therefore, pest control is an issue for agricultural administrative departments. In the early stages of pest control, chemical control, generally the spraying of pesticides, had a very important role. However, due to the high frequency and regular use over the long term of pesticide sprays, some negative factors have resulted such as environmental pollution and pest resistance to pesticides.

The European Corn Borer (ECB) Ostrinia nubilalis is a major pest of cereal crops including corn (maize) Zea mays, which can cause serious losses to farmers. In order to control ECB and avoid the negative effects of high frequency spraying of pesticides, biotechnology companies have produced genetically modified corn grown from seeds with a toxin gene from the soil-dwelling bacterium Bacillus thuringiensis (Bt) inserted, which can withstand ECB attacks. The toxic gene in the plants produces delta endotoxins which are fatal to insects susceptible to them that feed on the crop [1], [2].

However, pest resistance, the adaptation of the pest population to some pesticides or to the toxin in Bt-corn thus decreasing its susceptibility, has emerged as a serious problem. With the evolution of pest resistance, farmers’ losses are increasing year by year. According to a survey, in the 1940s, farmers in the USA lost 7% of their crops to pests. Since the 1980s, the percentage lost has increased to 13%, even though more pesticides are being used, and more than 500 species of pests have developed resistance to pesticides since 1945 [3], [4], [5].

Scientists have responded by developing various insecticide resistance management (IRM) strategies, aimed at slowing down the build-up of pesticide resistance in pest populations and managing established resistant pest populations [6], [7]. These strategies may be implemented either at input level (Bt-corn seed and non-Bt-corn seed mixes, pesticide mixtures or gene stacking for pest-resistant transgenic varieties) or at farm level (refuges, alternation of pesticides, changes in cultural practices, integrated pest management (IPM)) [8], [9]. In economic terms, the stock of pest susceptibility to a given pesticide is a beneficial non-renewable resource, and IRM strategies delay the depletion of this stock [10], by methods such as mixed planting of Bt-corn with non-Bt-corn. The US Environmental Protection Agency (EPA) and US Department of Agriculture (DA) have required that in areas planted with Bt-corn, at least 20% of the area should be planted with non-Bt-corn as an IRM strategy [11], which we will refer to as the US EPA mixed strategy.

We will use mathematical models to answer the question what is the optimal strategy for pest control with economic benefits as the aim? Mathematical models have been used extensively in studies of pest control, including for IRM [12], [13], [14], [15], [16], [17], [18], [19], [20], [21]. Liang et al. used a mathematical model to study the switching of pesticides as an IRM strategy and estimated the optimal switching strategy and the optimal switching time with different pest control aims [17]. The balance of the number of natural enemies released and the evolution of pest resistance were studied, and the optimal numbers of natural enemies to be released were given [18], [19]. Considering the cost of pest control, yields of corn and so on, Liang and Tang modelled a benefit function with a pest control model, and the optimal pesticide spraying time and the optimal economic threshold were investigated [16]. In that study, they assumed that pest resistance was negligible. Linacre and Thompson considered four IRM strategies for Bt-corn plants and studied the net present value for four strategies with mathematical models [11]. Moreover, what farmers want to know are what are the main factors affecting the net present value, and what is the optimal planting ratio of Bt-corn and non-Bt-corn?

To answer the former questions, in this manuscript, we modelled a pest’s growth with evolution of pest resistance to Bt-corn. Under the pest growth model and considering the cost of pest control, yield of corn, price of corn, and so on, we investigated the net present values under two corn planting strategies: a pure Bt-corn strategy and the US EPA mixed strategy. The effects of Bt-corn on the mortality rate of the pest, the initial density of the pest population, the intrinsic growth rate and the carrying capacity of the pest on the net present value were analysed. Finally, we studied the optimal planting ratio of Bt-corn and non-Bt-corn under a mixed planting strategy. Whilst the above introduction has concentrated on Bt-corn as being genetically modified sweet corn or maize, our models are general and can refer to any genetically modified corn in the English rather than the American sense of corn, encompassing crops such as wheat Triticum spp., barley Hordeum vulgare, oats Avena sativa etc. as well as other varieties of genetically modified crop and their associated pests (resistant or not).