Individuals differ in their life courses, but how this diversity is generated, how it has evolved and how it is maintained is less understood. However, this understanding is crucial to comprehend evolutionary and ecological population dynamics. In structured populations, individual life courses represent sequences of stages that end in death. These life course trajectories or sequences can be described by a Markov chain and individuals diversify over the course of their lives by transitioning through diverse discrete stages. The rate at which stage sequences diversify with age can be quantified by the population entropy of a Markov chain. Here, we derive sensitivities of the population entropy of a Markov chain to identify which stage transitions generate - or contribute - most to diversification in stage sequences, i.e. life courses. We then use these sensitivities to reveal potential selective forces on the dynamics of life courses. To do so we correlated the sensitivity of each matrix element (stage transition) with respect to the population entropy, to its sensitivity with respect to fitness λ, the population growth rate. Positive correlation between the two sensitivities would suggest that the stage transitions that selection has acted most strongly on (high sensitivities with respect to λ) are also those that contributed most to the diversification of life courses. Using an illustrative example on a seabird population, the Thick-billed Murres on Coats Island, that is structured by reproductive stages, we show that the most influential stage transitions for diversification of life courses are not correlated with the most influential transitions for population growth. Our finding suggests that observed diversification in life courses is neutral rather than adaptive, note this does not imply that the life histories themselves are not adaptive. We are at an early stage of understanding how individual level dynamics shape ecological and evolutionary dynamics, and many discoveries await.

中文翻译：

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个体生活过程中多样性的驱动因素：马尔可夫链的人口熵敏感性。

每个人的生活历程各有不同，但人们对这种多样性的产生方式，演变方式以及维护方式的了解却很少。但是，这种理解对于理解进化和生态种群动态至关重要。在有组织的人群中，个人生命历程代表着以死亡结束的各个阶段的序列。这些人生历程轨迹或序列可以通过马尔可夫链来描述，并且个人可以通过过渡到不同的离散阶段来实现其人生历程的多样化。阶段序列随年龄变化的速率可以通过马尔可夫链的总体熵来量化。在这里，我们得出马尔可夫链的总体熵的敏感度，以确定哪个阶段转换对阶段序列（即生命历程）的多样化产生或贡献最大。然后，我们使用这些敏感性来揭示生命过程动力学上的潜在选择性力。为此，我们将每个矩阵元素（阶段过渡）相对于种群熵的敏感度与它相对于适应度λ（人口增长率）的敏感度相关联。两种敏感性之间的正相关性表明，选择最主要作用的阶段转换（相对于λ的敏感性高）也是对人生过程多样化贡献最大的那些。使用一个以海鸟种群为例的实例，该种群是由生殖阶段构成的高士岛上的厚嘴穆尔雷斯，我们表明，生命周期多样化最有影响力的阶段转变与人口增长最有影响力的转变无关。我们的发现表明，在生活过程中观察到的多样化是中性的，而不是适应性的，请注意，这并不意味着生活史本身就不是适应性的。我们还处于了解个体水平动力学如何影响生态和进化动力学的早期阶段，还有许多发现在等待。