Mathematical Theory and Biological Applications of Diversity

多样性是生物系统内部和之间的变化程度，包括从分子到雨林的变化。它的影响和评估对生命科学至关重要，例如：-遗传多样性对作物和牲畜的健康和生产力很重要-免疫多样性是保护宿主免受各种不断变化的病原体侵害的关键-病原体多样性为疫苗和药物开发提供信息-抗菌素耐药性的多样性是一个严重的临床和药物开发问题-物种多样性影响生态系统的健康和可持续性然而，衡量多样性受到一系列潜在措施的阻碍：物种丰富度、香农熵、期望杂合性、Gini-Simpson和Berger-Parker，仅举几例。它们的存在通常是为了捕捉多样性的不同方面-物种丰富度（其中“物种”可以是任何单位，例如抗原表型，受体转录）计算物种的数量，忽略丰度，而Berger-Parker评估优势物种的比例。但基本的数学问题仍然存在：不同的措施适用于同一方面的多样性可能会给出相互矛盾的答案。一个关键的测试，许多流行的措施失败，是一个措施是否直观的行为。假设一颗陨石毁灭了一个拥有100万同样丰富物种的大陆上50%的物种。香农熵下降了5%，而不是预期的50%，吉尼-辛普森指数仅下降了0.0001%。直观和合乎逻辑的衡量标准被称为“有效数字”。我们在多样性衡量中使用有效数字的能力在BBSRC资助的研讨会上得到了体现，并由共同研究者参加。使用有效数字，以及我们最近开发的一个重大理论进展，使我们能够包括个体之间的任何类型的相似性（例如遗传，系统发育，功能等）。在同样的多样性框架内，我们的长期目标是统一生命科学各重要战略领域多样性的衡量和解释。在这个FLIP奖期间，我们的目标是通过相互合作来了解理论及其应用如何连接的细节，从而为此奠定基础。我们将在多样性框架的数学和支持使用多样性的BBSRC资助的生物学应用的科学方面相互培训，分别弥合数学-生命科学接口的差距：-理论框架的开发者之一（Leinster）将被教导有关主要组织相容性复合体在家畜抗病性中的作用以及定量遗传学及其在动物育种中的应用，并致力于在这种情况下应用多样性框架。另一位数学家（Cobbold）将学习遗传和系统发育多样性的测量，及其在口蹄疫（FMD）流行病学中测量病毒循环的应用。在此基础上，她将探索抗原多样性测量如何帮助FMD控制的疫苗种子株选择。应用科学家（里夫）将学习支持多样性框架的纯数学，研究信息论，函数方程和范畴理论，然后确定这项工作将如何应用于正在进行的抗菌素耐药性（AMR）生态学研究，他与马修斯合作。然后，他将致力于确定该理论的发展，这将有助于研究AMR的来源和传播。除了加强现有的BBSRC资助的研究里夫，马修斯和他们的合作者，我们将调查这种方法的潜力，以团结研究领域，以前没有被认为是密切相关的，并培养一个强大的新的，多样性领域的跨学科研究领域。

Diversity is the extent of variation in and between biological systems and encompasses variation from the scale of the molecule to the rainforest. Its influence and therefore assessment is critical to the life sciences, for example:- Genetic diversity is important for the health and productivity of crops and livestock- Immunological diversity is key to host protection from diverse and evolving pathogens- Pathogen diversity informs vaccine and drug development- Diversity in antimicrobial resistance is a serious clinical and drug development problem- Species diversity influences the health and sustainability of ecosystemsHowever, measuring diversity is hampered by the range of potential measures: species richness, Shannon entropy, expected heterozygosity, Gini-Simpson, and Berger-Parker, to name just a few. Often they exist to capture different aspects of diversity - species richness (where 'species' may be any unit e.g. antigenic phenotype, receptor transcript) counts the number of species ignoring abundance, while Berger-Parker assesses the proportion of the dominant species. But fundamental mathematical problems remain: different measures applied to the same aspect of diversity can give conflicting answers. A key test, which many popular measures fail, is whether a measure behaves intuitively. Suppose a meteorite wipes out 50% of the species on a continent of a million equally abundant species. The Shannon entropy drops by 5%, not the expected 50%, and the Gini-Simpson index by just 0.0001%. The measures that do behave intuitively and logically are called 'effective numbers'.Our ability to use effective numbers across diversity measurement crystallised during a BBSRC-funded workshop run and attended by the co-investigators. Using effective numbers, and a major theoretical advance that we have recently developed that allows us to include any kind of similarity between individuals (e.g. genetic, phylogenetic, functional etc.) in the same diversity framework, our long-term goal is to unify the measurement and interpretation of diversity across strategically important areas of the life sciences. During this FLIP award, we aim to set the groundwork for this by working with each other to understand the detail of how the theory and its applications connect. We will train each other in the mathematics of the diversity framework and in the science underpinning the BBSRC-funded biological applications that use diversity, respectively, bridging the gap across the mathematics - life sciences interface:- One of the developers of the theoretical framework (Leinster) will be taught about the role of the major histocompatibility complex in livestock disease resistance and about quantitative genetics and its application to animal breeding, and work to apply the diversity framework in this context.- The other mathematician (Cobbold) will learn about the measurement of genetic and phylogenetic diversity, and its application to measuring viral circulation for foot-and-mouth disease (FMD) epidemiology. Building on this, she will explore how antigenic diversity measurement can help in vaccine seed strain selection for FMD control.- The applied scientist (Reeve) will learn the pure mathematics that underpins the diversity framework, working on information theory, functional equations and category theory, and then identify how this work will apply to ongoing research on the ecology of antimicrobial resistance (AMR) on which he collaborates with Matthews. He will then work on identifying developments to the theory that will help in the study of the sources and spread of AMR.As well as enhancing the existing BBSRC-funded research of Reeve, Matthews and their collaborators, we will investigate the potential for this approach to unite research areas that have not previously been considered to be closely related, and to foster a powerful new, interdisciplinary research area in the field of diversity.