Wheat aphids are major wheat sap sucking pests found throughout the world. The analysis of wheat aphid population dynamics to develop aphid control strategies is therefore important. Even if all factors that control the size of aphid populations are known, several mathematical tools are needed to help us understand their combined effect. Based on the knowledge of population ecology and catastrophe theory, we proposed a generalized population dynamics model to describe variation of wheat aphid populations and obtained a dynamic threshold function for aphid control. Field survey data from 1997 to 2002 were used to validate this model. The results indicated the model could predict the results of practical measures against a pest if the factors of their immediate effects are known or could be estimated. By explaining and forecasting the size of an aphid outbreak and its probability of occurrence, this catastrophe model can provide a scientific basis for wheat aphid control.

小麦蚜虫是世界各地发现的主要吸食小麦汁液的害虫。因此，分析小麦蚜虫种群动态以制定蚜虫控制策略非常重要。即使控制蚜虫种群规模的所有因素都是已知的，也需要一些数学工具来帮助我们了解它们的综合影响。基于种群生态学和灾变理论的知识，我们提出了一个广义的种群动态模型来描述小麦蚜虫种群的变化，并获得了蚜虫控制的动态阈值函数。1997 年至 2002 年的实地调查数据用于验证该模型。结果表明，如果直接影响的因素是已知的或可以估计的，该模型可以预测针对有害生物的实际措施的结果。