LAUSR

Simple Summary Two beetles that are serious pests of maize, Diabrotica virgifera virgifera and Diabrotica barberi, have caused problems for farmers in the USA and Europe for many years. Because both species have developed resistance to several management tactics, including insecticides and crop rotation, mathematical modeling has been used to evaluate their life cycles for weaknesses and new tactics for value. This review highlights lessons learned from the past 35 years. Some models have focused on the probability of the beetles spreading across regions. Other models have been developed to estimate the risk of the evolution of resistance. These models are thoroughly reviewed with respect to the biological attributes incorporated in these models and the impact of those attributes on the evolution of resistance. Abstract Both Diabrotica virgifera virgifera LeConte and D. barberi Smith and Lawrence are among the most damaging insects impacting corn in North America. D. virgifera virgifera has also invaded Europe and has become an important pest in that region. Computer models have become an important tool for understanding the impact and spread of these important pests. Over the past 30 years, over 40 models have been published related to these pests. The focus of these models range from occupancy models (particularly for Europe), impact of climate change, range expansion, economics of pest management, phenology, to the evolution of resistance to toxins and crop rotation. All of these models share characteristics. We elaborate on the methods in which modelers have incorporated the biology of these pests, including density-dependence, movement, fecundity and overwintering mortality. We discuss the utility of both spatially-explicit, complex models and spatially-implicit, generational models and where each might be appropriate. We review resistance models that either explain past evolution to crop rotation, insecticides or insecticidal traits or attempt to predict the consequences of resistance management strategies.