Population genetics of biological invasions

尽管它们的重要性得到了公认，但一个种群在入侵新领土时可能经历的基因变化却很少受到建模者的关注。为了进一步了解入侵种群的遗传学，将开发和分析两种类型的数学模型。第一个是突变型和野生型种群密度空间矩的积分差分方程组。通过分析方程行波的稳定性，研究人员将确定所谓的“突变冲浪”（突变体占据人口密度推进波的前沿）的概率如何取决于生物学相关的模型参数。第二类模型是种群密度与数量性状均值和/或方差的系统反应扩散方程。为了模拟入侵期间数量性状的演化，将研究这种系统的行波解的存在性和稳定性。对这两类系统的严格分析将适当地辅以方程的数值解和随机种群模拟。最后，在该项目的一个独立但相关的部分，将开发对生物学家有用的统计测试，这些生物学家希望根据突变冲浪或细分群体中多样化选择的存在来推断等位基因的年龄和起源点。该项目将提供1名博士后和2名本科生的培训机会。人们普遍认为，外来物种正在对本地生态物种造成严重破坏，并造成经济损失（根据一项研究，仅在六个大国，每年就超过3000亿美元）。有效的环境管理需要评估本地物种退化的风险以及新引入的物种或品系带来的经济风险（例如对作物的风险）。拟议项目的所有三个部分都将有助于我们测量和预测生态系统变化的能力，包括人为变化，如非本地物种或杀虫剂抗性或工程基因型的传播。研究外来物种入侵时的适应性进化将有助于提高外来物种入侵率的预测。这些结果将有助于改进对拟议控制战略的效益和成本的估计。突变冲浪的研究对主要目的是推断种群迁移历史的生物学家也很有用——例如，人类从非洲向欧洲、亚洲和美洲的传播。特别是，它将表明在对人口迁移历史作出某些类型的推断时所涉及的不确定程度。

Despite their recognized importance, the genetic changes that a population may experience while it is invading new territory have received little attention from modelers. To advance understanding of the genetics of invading populations, two types of mathematical models will be developed and analyzed. The first is a system of integrodifference equations for the spatial moments of mutant and wild type population densities. By analyzing the stability of traveling waves for the equations, the researchers will determine how the probability of so-called "mutation surfing"--in which mutants take over the leading edge of an advancing wave of population density--depends on biologically relevant model parameters. The second type of model is a system reaction-diffusion equations for population density and trait mean and/or variance of a quantitative trait. The existence and stability of traveling wave solutions to such systems will be studied in order to model the evolution of a quantitative trait during an invasion. Rigorous analysis of both types of systems will be complemented both by numerical solution of the equations and stochastic population simulations as appropriate. Finally, in a separate but related part of the project, statistical tests useful to biologists who wish to infer the age and point of origin of an allele based on mutation surfing or the presence of diversifying selection in a subdivided population will be developed. The project will provide training opportunities for a postdoctoral fellow and two undergraduate students. It is widely acknowledged that nonnative species are causing heavy damage to native ecospecies as well as economic losses (over US $300 billion per year in six large countries alone, according to one study). Effective environmental management requires assessing the risk of degradation of native species as well as the economic risk (e.g. to crops) posed by a newly introduced species or strain. All three parts of the proposed project will contribute to our ability to measure and predict changes in ecosystems, including anthropogenic changes such as the spread of nonnative species or of pesticide-resistant or engineered genotypes. This study of adaptive evolution during invasions will contribute to improvements in prediction of the rates of invasion by nonnative species. These results will allow improved estimates of the benefits and costs of proposed control strategies. The study of mutation surfing will also be useful to biologists whose primary goal is to infer the migration histories of populations--for example, the spread of humans from Africa to Europe, Asia and the Americas. In particular, it will indicate the degree of uncertainty involved in making certain types of inferences the migration histories of populations.