Matrix models and sensitivity analysis of populations classified by age and stage: a vec-permutation matrix approach
Matrix models and sensitivity analysis of populations classified by age and stage: a vec-permutation matrix approach
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DOI：
10.1007/s12080-011-0132-2
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发表时间：
2012-08-01
影响因子：
1.6
通讯作者：
Caswell, Hal
中科院分区：
文献类型：
--
作者：
Caswell, Hal
矩阵种群模型中的个体分类的年龄和阶段可以使用向量置换矩阵。由此产生的年龄阶段模型可以用来推导特定年龄阶段的生活史的特定后果，或描述人口的生命率响应年龄和阶段。我推导出一个通用公式的敏感性的任何输出（标量，矢量，或矩阵值）的模型，任何向量的参数，使用矩阵演算。描述年龄阶段动态的矩阵几乎总是可约的;我提出的结果给出了人口增长从任何初始条件都是各态历经的条件。作为一个例子，我分析了一个特定的阶段发表的模型苏格兰扫帚（金雀花），一种入侵的多年生灌木。种群增长率的敏感性分析发现，选择梯度对成年人的生存并不总是随着年龄的增长而下降，但可能会增加在一个范围内的年龄。这可能对阶段分类种群的衰老进化产生影响。我还推导并分析了年龄和死亡阶段的联合分布，并提出了这种分布和死亡年龄的边缘分布的敏感性分析。
Matrix population models in which individuals are classified by both age and stage can be constructed using the vec-permutation matrix. The resulting age-stage models can be used to derive the age-specific consequences of a stage-specific life history or to describe populations in which the vital rates respond to both age and stage. I derive a general formula for the sensitivity of any output (scalar, vector, or matrix-valued) of the model, to any vector of parameters, using matrix calculus. The matrices describing age-stage dynamics are almost always reducible; I present results giving conditions under which population growth is ergodic from any initial condition. As an example, I analyze a published stage-specific model of Scotch broom (Cytisus scoparius), an invasive perennial shrub. Sensitivity analysis of the population growth rate finds that the selection gradients on adult survival do not always decrease with age but may increase over a range of ages. This may have implications for the evolution of senescence in stage-classified populations. I also derive and analyze the joint distribution of age and stage at death and present a sensitivity analysis of this distribution and of the marginal distribution of age at death.