Models of Male and Mutual Mate Choice

了解动物选择配偶的方式具有应用价值，包括确定保护脆弱物种所需的种群规模和结构，评估物种之间杂交的机会，以及帮助预测基因在整个种群中的传播。大多数动物择偶的数学模型都是基于这样一个前提，即雄性不分青红皂白地交配，而雌性是挑剔的。然而，越来越多的跨物种证据表明，雄性通常不是不分青红皂白的。这笔赠款将开发基本的数学模型，当男性和女性在选择配偶时都是有选择性的。它将评估在什么条件下雄性将从配偶选择中获得遗传利益，并确定这一点如何受到物种中的个体是否形成配对纽带的影响。这些发展将使当前的配偶选择理论更加现实和更广泛地适用。人们普遍认识到，对生物学家越来越多的需要有数学培训和专业知识。在前一笔NSF赠款的更广泛影响下，国际数学联合会一直在北卡罗来纳大学的生物核心班级开发一个数学轨道，致力于增加这种培训，特别是针对女性，这是一个在数学方面代表性不足的群体。这条赛道使用了各种技术来降低数学焦虑，根据记录，这个问题对女性的影响比对男性的影响更大。这笔赠款将继续并扩大这一培训，增加一个模块，让数学学科的学生参与更广泛的核心课程的数学生物学教程。

Understanding the ways in which animals choose mates has applications that include determining the necessary population size and structure for conserving vulnerable species, assessing the chance of hybridization between species, and helping to predict the spread of genes throughout populations. The large majority of the mathematical models of mate choice in animals are based on the premise that males mate indiscriminately while females are choosy. A growing body of evidence across species suggests, however, that males often are not indiscriminate. This grant will develop basic mathematical models of mate choice when males, as well as females, are selective in choosing mates. It will assess under what conditions males would gain genetic benefits from mate choice and determine how this is affected by whether individuals in the species form pair bonds. These developments will render current theory of mate choice more realistic and more broadly applicable.There is wide recognition of the growing need for biologists to have mathematical training and expertise. Under the broader impacts of a previous NSF grant the PI has been developing a mathematical track in a biology core class at UNC that is dedicated to increasing this training especially for women, an under-represented group in mathematics. The track uses a variety of techniques to reduce math anxiety, a problem documented to affect women more than men. This grant will continue and broaden this training by adding a module in which students in the mathematical track participate in tutorials in mathematical biology for the broader core class.