Models of Male and Mutual Mate Choice

了解动物选择配偶的方式有很多应用，包括确定保护脆弱物种所需的种群规模和结构，评估物种间杂交的机会，以及帮助预测基因在整个种群中的传播。绝大多数动物配偶选择的数学模型都是基于这样一个前提，即雄性不加选择地交配，而雌性是有选择性的。然而，越来越多的跨物种证据表明，雄性往往不是不分青红皂白的。这项拨款将用于发展雄性和雌性在择偶时的择偶基本数学模型。它将评估在什么条件下雄性会从配偶选择中获得遗传利益，并确定这是如何受到物种中个体是否形成伴侣关系的影响的。这些发展将使当前的择偶理论更加现实，适用范围更广。人们普遍认识到生物学家越来越需要数学训练和专业知识。在之前的NSF拨款的广泛影响下，PI一直在北卡罗来纳大学的生物学核心课程中开发数学轨道，致力于增加这种培训，特别是针对女性，这是一个在数学领域代表性不足的群体。这条赛道使用了各种各样的技巧来减少数学焦虑，这个问题对女性的影响比男性更大。这项拨款将通过增加一个模块来继续和扩大这种培训，在这个模块中，数学课程的学生可以参加数学生物学的辅导课，以扩大核心课程的范围。

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.