Lifetime reproductive output: individual stochasticity, variance, and sensitivity analysis
Lifetime reproductive output: individual stochasticity, variance, and sensitivity analysis
复制标题
终生生殖输出：个体随机性、方差和敏感性分析
作者：
S. V. van Daalen;H. Caswell
终生生殖产出（LRO）决定了每一代的生长速率，建立了种群增长或下降的标准，是适应度的重要组成部分。LRO的实证测量显示个体之间存在很大的差异。这种差异可能来自个体属性的真正异质性，或者来自个体的随机性，即生命周期中概率人口统计事件的结果。为了评估个体随机性的程度，需要从人口统计学模型中计算LRO的统计量。通常计算平均LRO（作为净繁殖率），但方差的计算直到最近才受到重视。在这里，我们提出了一个完整的，精确的，分析的，封闭形式的解决方案的所有时刻的LRO，年龄和阶段分类的人口。以前的研究依赖于模拟、迭代解决方案或封闭形式的分析解决方案，这些解决方案只能捕获部分方差来源。我们还展示了LRO的所有统计数据对定义生存、阶段转变和（st）年龄特异性生育的参数的敏感性和弹性。在LRO中，只有当变异是由遗传异质性引起时，选择才能作用于变异。潜在的选择机会通过克罗指数Idocumentclass[12pt]{minimal} uspackage {amsmath} uspackage {wasysym} uspackage {amsfonts} uspackage {amssymb} uspackage {amssyb} uspackage {mathrsfs} uspackage {upgreek} setlength{oddsidemargin}{-69pt} egin{document}$mathcal {I}$end{document}，方差与均值的平方之比来量化。但是，由于个体随机性而产生的方差只是一个表面上的选择机会。在对一系列人口年龄分类模型的比较中，我们发现死亡率的比例增加对LRO的均值和方差的影响非常小，但对Idocumentclass[12pt]{minimal} uspackage {amsmath} uspackage {wasysym} uspackage {amsfonts} uspackage {amssymb} uspackage {amssfs} uspackage {upgreek} setlength{oddsidemargin}{-69pt} egin{document}$mathcal {I}$end{document}有很大的积极影响。随着生育率的增加，LRO的均值和方差均增加，但减少了Idocumentclass[12pt]{minimal} uspackage {amsmath} uspackage {wasysym} uspackage {amsfonts} uspackage {amssymb} uspackage {amssy} uspackage {mathrsfs} uspackage {upgreek} setlength{oddsidemargin}{-69pt} egin{document}$mathcal {I}$end{document}。对于大小分类的树木种群，LRO的均值和方差对阶段特异性死亡率的弹性均为负；对特定阶段生育的弹性是正的。
Lifetime reproductive output (LRO) determines per-generation growth rates, establishes criteria for population growth or decline, and is an important component of fitness. Empirical measurements of LRO reveal high variance among individuals. This variance may result from genuine heterogeneity in individual properties, or from individual stochasticity, the outcome of probabilistic demographic events during the life cycle. To evaluate the extent of individual stochasticity requires the calculation of the statistics of LRO from a demographic model. Mean LRO is routinely calculated (as the net reproductive rate), but the calculation of variances has only recently received attention. Here, we present a complete, exact, analytical, closed-form solution for all the moments of LRO, for age- and stage-classified populations. Previous studies have relied on simulation, iterative solutions, or closed-form analytical solutions that capture only part of the sources of variance. We also present the sensitivity and elasticity of all of the statistics of LRO to parameters defining survival, stage transitions, and (st)age-specific fertility. Selection can operate on variance in LRO only if the variance results from genetic heterogeneity. The potential opportunity for selection is quantified by Crow’s index Idocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$mathcal {I}$end{document}, the ratio of the variance to the square of the mean. But variance due to individual stochasticity is only an apparent opportunity for selection. In a comparison of a range of age-classified models for human populations, we find that proportional increases in mortality have very small effects on the mean and variance of LRO, but large positive effects on Idocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$mathcal {I}$end{document}. Proportional increases in fertility increase both the mean and variance of LRO, but reduce Idocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$mathcal {I}$end{document}. For a size-classified tree population, the elasticity of both mean and variance of LRO to stage-specific mortality are negative; the elasticities to stage-specific fertility are positive.