AI 中文总结
研究格陵兰鲨长寿的繁殖窗口，应用进化熵理论，利用相关定理推导人口统计学情景，得出临界阈值等，其结果可用于未知人口统计学数据物种的繁殖窗口定量约束。
AI 中文摘要
格陵兰鲨是已知最长寿的脊椎动物之一，雌性成熟约156岁，最大年龄近四个世纪。我们应用年龄结构种群的进化熵理论，研究哪些繁殖窗口与这种极端人口统计学特征兼容。利用开放群体的齐次性和临界阈值定理，推导出生殖时间、繁殖分位数和熵最大化繁殖终点的人口统计学情景。临界阈值出现在\(q_c\approx0.9763\)，处于接近统一的持续状态。寿命校准情景跨越有限最大熵和渐近熵区域的边界。这些情景导致生殖时间接近或超过两个世纪，繁殖分位数延伸到生命的第三、第四和第五个世纪，涵盖了最古老格陵兰鲨的年龄范围。临界阈值方程有一个变分解释：其唯一解正是进化熵最大化时的\(q\)值。熵分解\(\log\lambda=H+\Phi\)将这些结果置于生命史的熵理论中，并给出了与校准生殖持续性兼容的佩龙增长率的简单上限。这些方法可用于在人口统计学数据 largely未知的物种中获得对繁殖窗口的定量约束。
英文摘要
The Greenland shark (Somniosus microcephalus) is among the longest-lived vertebrates known, with female maturity estimated at about 156 years and maximum ages approaching four centuries. We use the entropic theory of life histories and an open-group Leslie model to determine which reproductive windows are compatible with this extreme demographic profile. The model yields generation times, reproductive quantiles and entropy-maximizing reproductive endpoints. A critical value of reproductive persistence, approximately 0.9763, separates two regimes: below it, evolutionary entropy increases towards an asymptote; above it, entropy is maximized at a finite reproductive endpoint. Longevity-calibrated scenarios lie on both sides of this threshold and imply generation times near or above two centuries, with reproductive contributions extending into the third, fourth and fifth centuries of life. As an independent benchmark, an empirically parametrized Leslie model for the bowhead whale yields comparable entropy-based demographic quantities while allowing the reproductive and survivorship parameters to be calculated directly. The method provides quantitative constraints on reproductive organisation in exceptionally long-lived species for which detailed demographic data are unavailable.
Comments14 pages, 4 figures
