The Dynamics and Evolution of Semelparity

Semelparity的动态和演变

• 批准号: 0917435
• 负责人: Jim Cushing
• 金额: $ 30万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0917435&HistoricalAwards=false
• 关键词: Dynamics; Evolution; Semelparity

Biological semelparity is a life history adaptation in which an individual organism reproduces once and then, or shortly thereafter, dies. This reproductive strategy is found throughout the plant and animal kingdoms. The trade-offs between reproduction and survival and the distinctions between semelparous and iteroparous life cycles have long been recognized as key issues involved in the study of life history strategies. Major topics of interest are the population dynamic consequences and the evolutionary advantages (or disadvantages) of semelparity versus iteroparity. Recent developments in the mathematical modeling of semelparity, using methods of nonlinear dynamics and bifurcation theory, have established a fundamental dynamic dichotomy that is of both biological and mathematical interest. From a mathematical point of view, models for the dynamics of semelparous species lie outside the standard theory of general structured population dynamics. Specifically, the fundamental bifurcation theorem that deals with the passage from population extinction to persistence (as the expected lifetime number of newborns produced by a newborn increases through the critical value of one) fails to hold. The challenge of determining the dynamic consequences of this fact have been met only in low dimensional cases (i.e., short maturation periods) and even then not thoroughly. These studies have established that, in lower dimensional cases, semelparous models exhibit a dynamic dichotomy that consists, roughly speaking, of an alternative between equilibration with overlapping generations and oscillations with non-overlapping generations. The oscillations in the later case can be strictly periodic, but also might be aperiodic. (They result from an invariant loop whose structure is a heteroclinic cycle.) Which of the two dynamics results (i.e., which is mathematically stable) depends on the magnitude of inter-stage competition present (relative to intra-stage competition). The first part of this project addresses the conjecture that this dynamic dichotomy is also present in semelparous models of higher dimension, to quantify the amount of inter-stage competition that results in an oscillatory dynamic, and to clarify the nature of these oscillations. The methods involve stability analysis, bifurcation methods, perturbation expansions, monotone semi-flow theory, the use average Lyapunov functions, persistence theory, and numerical simulations. The second part of the project addresses questions about the evolution of semelparity and the possibility of its being an evolutionary stable strategy (ESS). The method to be used is based on evolutionary game theory (and is called Darwinian dynamics), a methodology that extends a population dynamic model to include the dynamics of an evolving (mean phenotypic) trait, which in turn affects the population dynamics (through its influence on vital birth, growth, and death rates). The approach is primarily by means of bifurcation theory and will depend on the dynamic studies in the first part of the project. Indeed, part 2 will obtain (among other things) generalizations of the results in part 1 to an evolutionary setting. The theoretical results and methodology developed in part 2 will then be used in applications that address specific evolutionary questions. Using biologically reasonable trade-offs to build sub-models for fecundity and survivorships as functions of an evolving trait, we will study the circumstances under which semelparity is evolutionarily favored and when it is not. The Darwinian dynamics approach allows the methods of nonlinear dynamics and bifurcation theory to be applied to these evolutionary questions.Investigations of many problems in biological sciences are based fundamentally on an understanding of population dynamics. This includes problems concerning the effects of climate change on ecosystems, the spread and control of diseases and pests, the protection of endangered species, the invasion of non-native species, the management of agricultural systems, the operation of fisheries, the design of wildlife refuges, and many others. Mathematical models derived to study problems such as these must, if one hopes to obtain accurate descriptions and predictions, be based on accurate dynamic models of the populations involved. For example, there is currently a great deal of research being carried out to "downscale" global climate data, i.e., to resolve the data to smaller scales, so that it can be used in population (ecosystem) dynamic models, the ultimate goal being an ability to predict the effects of future climate change on specific species of plants and animals. Accurate models of population dynamics must take into account, to some level of resolution, details concerning the life history strategy of species, i.e., the growth and reproduction schedule by means of they optimize fitness. Species with one type of life history will likely be quite differently affected by climate change (or by an invasive species or diseases or management decisions, etc.) than will be a species with a different life history. Biologists recognize two broad types of life histories: one in which individuals reproduce and then, or shortly thereafter, die (referred to as semelparity) and individuals who have repeated reproductive events throughout their life (referred to as iteroparity). There are numerous species throughout the plant and annual kingdoms that are semelparous (annual plants, a great many insects, some species of salmon, etc.). Models of semelparous population dynamics have not received the attention, with regard to many of their important aspects, as have those for iteroparous populations. Recent preliminary studies have shown that semelparous populations exhibit dynamic features that are, in several fundamental ways, very different from those typical iteroparous populations. These features, among others, have to do with the propensity of semelparous populations to exhibit periodic crashes and booms (as, for example, seen in the notorious cicada cycles or disastrous outbreaks of forest insect pests). The main goals of this research project are: (1) to develop a broad based theory of semelparous population dynamics and understand the properties of population oscillations (periodic outbreaks) and ascertain the conditions under which they do and do not occur; (2) extend the population dynamic theory to an evolutionary context so as to provide an understanding of how semelparous populations adapt and evolve; (3) to apply the findings to carefully selected and derived models of specific, important types of life histories studied in both theoretical and applied ecology. The mathematical models to be used in this research are of a type that is particularly accessible to those with limited backgrounds in the mathematics of dynamical systems. Because of the quick learning curve associated with these kinds of models, the project provides abundant research opportunities for students (both undergraduate and graduate) that, on the one hand, introduces them in an accessible context to sophisticated concepts and methods in the mathematical theory of dynamical systems and, on the other hand, permits them to carry out interesting applications that make solid contributions to biological problems.

生物半质量是一种生活史的适应性，其中单个生物会曾经或之后不久或之后又一次再现。在整个动植物界都可以找到这种生殖策略。 长期以来，繁殖与生存之间的权衡以及半养生和迭代生命周期之间的区别已被认为是生活历史策略研究所涉及的关键问题。 感兴趣的主要主题是人口动态后果以及Semparity与迭代性的进化优势（或缺点）。 使用非线性动力学和分叉理论的方法，在半长度的数学模型中的最新发展已经建立了一种基本的动态二分法，既具有生物学和数学兴趣。 从数学的角度来看，半养子物种动力学的模型不在一般结构种群动力学的标准理论之外。 具体而言，涉及从人口灭绝到持久性的通过的基本分叉定理（因为新生儿产生的新生儿的预期寿命数量通过一个人的临界价值增加）。 确定这一事实的动态后果的挑战仅在低维情况（即短期成熟周期）中得到了应对，即使不是这样。 这些研究已经确定，在较低维度的情况下，半育模模型表现出动态二分法，该二分法大致说明了与重叠的世代平衡和与非重叠世代的振荡之间的替代方案。 后来情况下的振荡可能是严格周期性的，但也可能是至周期性的。 （它们是由一个不变的循环引起的，其结构是杂斜周期。）两个动态结果中的哪个（即，在数学上稳定）取决于存在的阶段间竞争的大小（相对于阶段内竞争）。 该项目的第一部分解决了以下猜想：这种动态二分法也存在于更高维度的半谱模型中，以量化导致振荡动态的阶段间竞争量，并阐明这些振荡的性质。 该方法涉及稳定性分析，分叉方法，扰动扩展，单调半流理论，使用平均Lyapunov函数，持久性理论和数值模拟。 该项目的第二部分涉及有关半超数演变及其作为进化稳定策略（ESS）的可能性的问题。 要使用的方法基于进化游戏理论（被称为达尔文动态），这种方法将人口动态模型扩展到包括不断发展的（平均表型）特征的动力学的方法，进而影响人群动态（通过对生命力，成长和死亡率的影响）。 该方法主要是通过分叉理论的方式，将取决于项目第一部分的动态研究。实际上，第2部分（除其他外）将在第1部分中对进化环境进行概括。 然后，第2部分中开发的理论结果和方法将用于解决特定进化问题的应用。 使用生物学合理的权衡取舍来建立用于繁殖力和生存的子模型，作为不断发展的特征的功能，我们将研究在进化中偏爱半偏长度以及何时不喜欢的情况下的情况。 达尔文动力学方法允许将非线性动力学和分叉理论的方法应用于这些进化问题。生物科学中许多问题的评估基本上是基于对人群动态的理解。 这包括有关气候变化对生态系统影响的问题，疾病和害虫的传播和控制，濒危物种的保护，非本地物种的入侵，农业系统的管理，渔业的运作，野生动物养殖的设计以及许多其他问题。 数学模型得出的数学模型必须基于所涉及的人群的准确动态模型，必须基于精确的描述和预测，必须进行研究。 例如，目前正在进行大量研究，以“降级”全球气候数据，即将数据解决到较小的尺度，以便可以在人群（生态系统）动态模型中使用，最终目标是预测未来气候变化对特定植物和动物物种的影响的能力。 准确的人口动态模型必须考虑到一定程度的解决方案，即有关物种生命历史策略的细节，即通过它们优化适应性的生长和繁殖时间表。 具有一种生命历史类型的物种可能会受到气候变化（或由侵入性物种或疾病或管理决策等）的影响，而不是具有不同生活史的物种。 生物学家认识到两种广泛的生活历史：一个人在其中繁殖，然后不久或之后死亡（称为半偏度），而个体在一生中重复生殖事件（称为迭代性）。 整个植物和年度王国都有许多物种，它们是半育种的（每年的植物，很多昆虫，某些种类的鲑鱼等）。 对于迭代人群的许多重要方面，半养生人群动态的模型尚未引起人们的关注。 最近的初步研究表明，半理性种群表现出动态特征，这些特征在几种基本的方式上与那些典型的迭代人群截然不同。 这些特征除其他外，与半理性人群的倾向有关（例如，在臭名昭著的CICADA循环中看到或灾难性的森林虫害爆发）。 该研究项目的主要目标是：（1）开发基于广泛的半理论人群动态理论，并了解人口振荡的特性（周期性爆发），并确定他们所做和不发生的条件； （2）将种群动态理论扩展到进化环境，以便对半占人群的适应和发展方式有所了解； （3）将发现应用于在理论和应用生态学中研究的特定重要类型的生命历史类型的精心选择的模型。 在本研究中要使用的数学模型是在动态系统数学中具有有限背景的人特别访问的类型。 由于与此类模型相关的快速学习曲线，该项目为学生（本科生和研究生）提供了丰富的研究机会，一方面，它们在动力学系统的数学理论中，在可访问的环境中介绍了它们，另一方面，这些概念和方法在一方面，另一方面，另一方面，它们允许他们对生物学问题进行良好的贡献。