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.

生物半胚性是一种生命史适应，在这种适应中，个体生物繁殖一次，然后或之后不久死亡。这种繁殖策略在植物和动物王国中随处可见。长期以来，生殖与生存之间的权衡以及半产与非产生命周期之间的区别一直被认为是生命史策略研究的关键问题。我们感兴趣的主要主题是种群动态结果和半奇偶性与互偶性的进化优势（或劣势）。最近在半奇偶性数学建模方面的发展，利用非线性动力学和分岔理论的方法，建立了一个具有生物学和数学意义的基本动态二分法。从数学的观点来看，半胎种的动力学模型不在一般结构种群动力学的标准理论范围之内。具体来说，处理从种群灭绝到持久性过渡的基本分岔定理（因为新生儿产生的新生儿的预期寿命数量增加到临界值1）不成立。确定这一事实的动态后果的挑战仅在低维情况下（即，较短的成熟期）才得到满足，甚至在这种情况下也没有得到彻底解决。这些研究已经证实，在低维情况下，半胎生模型表现出一种动态二分法，粗略地说，这种二分法包括有重叠代的平衡和无重叠代的振荡之间的一种选择。后一种情况下的振荡可以是严格周期性的，但也可以是非周期性的。（它们源于一个结构为异斜循环的不变循环。）这两种动态结果中的哪一种（即，哪一种在数学上是稳定的）取决于当前阶段间竞争的程度（相对于阶段内竞争）。该项目的第一部分解决了这种动态二分法也存在于高维半胎模型中的猜想，以量化导致振荡动态的阶段间竞争的数量，并澄清这些振荡的性质。这些方法包括稳定性分析、分岔方法、微扰展开、单调半流理论、使用平均Lyapunov函数、持续理论和数值模拟。该项目的第二部分解决了关于半奇偶性的进化问题及其作为进化稳定策略（ESS）的可能性。所使用的方法是基于进化博弈论（被称为达尔文动力学），这是一种扩展种群动态模型的方法，包括进化（平均表型）特征的动态，这反过来影响种群动态（通过其对重要的出生、生长和死亡率的影响）。该方法主要是通过分岔理论，并将依赖于项目第一部分的动态研究。事实上，第2部分将获得第1部分的结果的一般化，并将其推广到一个进化的环境中。然后，在第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程序中。使用生物学上合理的权衡来建立作为进化特征功能的繁殖力和存活率的子模型，我们将研究在什么情况下半均等在进化上是有利的，什么情况下不是。达尔文动力学方法允许将非线性动力学和分岔理论的方法应用于这些进化问题。对生物科学中许多问题的研究基本上是基于对种群动态的理解。这包括气候变化对生态系统的影响、病虫害的传播和控制、濒危物种的保护、外来物种的入侵、农业系统的管理、渔业的运作、野生动物保护区的设计等许多其他问题。如果人们希望得到准确的描述和预测，为研究这类问题而建立的数学模型必须基于所涉及种群的准确动态模型。例如，目前正在进行大量的研究，以“缩小”全球气候数据的尺度，即将数据分解到更小的尺度，以便用于种群（生态系统）动态模型，最终目标是能够预测未来气候变化对特定动植物物种的影响。精确的种群动态模型必须在一定程度上考虑到有关物种生活史策略的细节，即通过优化适应度来实现的生长和繁殖计划。与具有不同生活史的物种相比，具有一种生活史的物种受到气候变化（或入侵物种、疾病或管理决策等）的影响可能会大不相同。生物学家将生命史分为两大类：一种是个体繁殖，然后或此后不久死亡（称为半胎性），另一种是个体在一生中反复繁殖（称为互胎性）。在植物界和一年生界中，有许多种是半胎生的（一年生植物、许多昆虫、一些鲑鱼等）。半胎种群动态模型在其许多重要方面还没有受到重视，而非双胎种群动态模型则受到重视。最近的初步研究表明，半胎种群表现出动态特征，在几个基本方面，与那些典型的无胎种群非常不同。除其他外，这些特征与半产种群表现出周期性崩溃和繁荣的倾向有关（例如，在臭名昭著的蝉周期或森林害虫的灾难性爆发中可以看到）。本研究项目的主要目标是：(1)发展基于广泛的半胎种群动态理论，了解种群振荡（周期性爆发）的特性，并确定它们发生和不发生的条件；(2)将种群动态理论扩展到进化的背景下，以提供对半胎种群如何适应和进化的理解；(3)将这些发现应用于理论生态学和应用生态学研究的特定的、重要的生活史类型的精心选择和推导的模型。在这项研究中使用的数学模型是一种特别适合那些在动力系统数学方面背景有限的人使用的类型。由于与这些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，向他们介绍动态系统数学理论中的复杂概念和方法，另一方面，允许他们进行有趣的应用，为生物学问题做出坚实的贡献。