The correct option is A Develop an explanation for the existence of lepidoptera population cycles.
"Identification of that driving force, however, has proved surprisingly elusive despite considerable research. The common approach of studying causes of population cycles by measuring the mortality caused by different agents, such as predatory birds or parasites, has been unproductive in the case of Lepidoptera." These sentences from the passage support option A as the answer. The second sentence following the first lets us know that measuring mortality caused by predatory birds and parasites was just one way of studying the population cycles of Lepidoptera (in order to find an explanation for the mentioned life cycles) by researchers.