The canonical equation of adaptive dynamics for life histories: from fitness-returns to selection gradients and Pontryagin's maximum principle.
The canonical equation of adaptive dynamics for life histories: from fitness-returns to selection gradients and Pontryagin's maximum principle.
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DOI：
10.1007/s00285-015-0938-4
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发表时间：
2016-03
影响因子：
1.9
通讯作者：
Johansson J
中科院分区：
文献类型：
--
作者：
Metz JAJ;Staňková K;Johansson J
本文件应作为Dieckmann等人的附录阅读。(J Theor Biol 241：370-389)和Parvinen等人。(J数学生物67：509-533，)。我们的目标是，利用高中微积分，(1)展示经典生活史问题的适应动力学正则方程的形式，其中Dieckmann等人的例子。(J Theor Biol 241：370-389)和Parvinen等人。(J Math Biol 67：509-533)被选择使得它们避免了人们在这一最相关的应用中遇到的许多问题，(2)从简单的适应度返回变元导出CE中发生的适应度梯度，(3)明确地示出将所述适应度梯度设置为零导致来自进化生态学的经典边际值原理中的结果，(4)示出后者又等同于庞特里亚金最大值原理，该公知的等价性然而在文献中给出了证明或用更高级的工具证明，(5)将生活史理论的经典最优化论点更好地与现实生物学(孟德尔种群性别不同，受环境反馈环路制约)联系起来；(6)以Dieckmann等人为例，对CE的形式进行了微小的改进。和Parvinen等人。
This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370–389,) and Parvinen et al. (J Math Biol 67: 509–533,). Our goal is, using little more than high-school calculus, to (1) exhibit the form of the canonical equation of adaptive dynamics for classical life history problems, where the examples in Dieckmann et al. (J Theor Biol 241:370–389,) and Parvinen et al. (J Math Biol 67: 509–533,) are chosen such that they avoid a number of the problems that one gets in this most relevant of applications, (2) derive the fitness gradient occurring in the CE from simple fitness return arguments, (3) show explicitly that setting said fitness gradient equal to zero results in the classical marginal value principle from evolutionary ecology, (4) show that the latter in turn is equivalent to Pontryagin’s maximum principle, a well known equivalence that however in the literature is given either ex cathedra or is proven with more advanced tools, (5) connect the classical optimisation arguments of life history theory a little better to real biology (Mendelian populations with separate sexes subject to an environmental feedback loop), (6) make a minor improvement to the form of the CE for the examples in Dieckmann et al. and Parvinen et al.