Department of Botany, Stockholm University, Stockholm SE 10691, Sweden.
Ecology. 2011 May;92(5):1181-7. doi: 10.1890/10-1184.1.
To accurately estimate population dynamics and viability, structured population models account for among-individual differences in demographic parameters that are related to individual state. In the widely used matrix models, such differences are incorporated in terms of discrete state categories, whereas integral projection models (IPMs) use continuous state variables to avoid artificial classes. In IPMs, and sometimes also in matrix models, parameterization is based on regressions that do not always model nonlinear relationships between demographic parameters and state variables. We stress the importance of testing for nonlinearity and propose using restricted cubic splines in order to allow for a wide variety of relationships in regressions and demographic models. For the plant Borderea pyrenaica, we found that vital rate relationships with size and age were nonlinear and that the parameterization method had large effects on predicted population growth rates, X (linear IPM, 0.95; nonlinear IPMs, 1.00; matrix model, 0.96). Our results suggest that restricted cubic spline models are more reliable than linear or polynomial models. Because even weak nonlinearity in relationships between vital rates and state variables can have large effects on model predictions, we suggest that restricted cubic regression splines should be considered for parameterizing models of population dynamics whenever linearity cannot be assumed.
为了准确估计种群动态和生存能力，结构种群模型考虑了与个体状态相关的个体间人口参数差异。在广泛使用的矩阵模型中，这种差异以离散状态类别来体现，而积分预测模型（IPM）则使用连续状态变量来避免人为分类。在 IPM 中，有时也在矩阵模型中，参数化是基于回归的，这些回归并不总是对人口参数和状态变量之间的非线性关系进行建模。我们强调了检验非线性的重要性，并提出使用受限立方样条，以便在回归和人口模型中允许存在各种关系。对于植物 Borderea pyrenaica，我们发现与大小和年龄相关的生命率关系是非线性的，参数化方法对预测的种群增长率 X 有很大影响（线性 IPM，0.95；非线性 IPM，1.00；矩阵模型，0.96）。我们的结果表明，受限立方样条模型比线性或多项式模型更可靠。因为即使生命率与状态变量之间的关系存在较弱的非线性，也会对模型预测产生很大影响，所以我们建议，只要不能假设线性关系，就应该考虑使用受限立方回归样条来对种群动态模型进行参数化。
