Sensitivity analysis of equilibrium in density-dependent matrix population models
Sensitivity analysis of equilibrium in density-dependent matrix population models
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DOI：
10.1111/j.1461-0248.2004.00595.x
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发表时间：
2004-05-01
期刊：
影响因子：
8.8
通讯作者：
Hunter, CM
中科院分区：
文献类型：
--
作者：
Caswell, H;Takada, T;Hunter, CM
我们考虑了参数扰动对平衡态下密度依赖种群的影响。这样的扰动改变了在平衡点处评估的投影矩阵的主特征值λ以及平衡点本身。我们表明，无论密度依赖的函数形式，λ的灵敏度等于有效平衡密度（N）的灵敏度在波浪线，这是一个平衡阶段的密度加权组合。权重衡量每个阶段对密度依赖的贡献及其对人口统计的影响。因此，波浪线上的（N）通常比总密度更相关，总密度只是简单地将所有阶段相加，而不管它们的生态特性如何。由于log lambda是入侵指数，我们的结果表明，成功的入侵将增加（N）的波浪号，和一个进化稳定的策略将最大化（N）的波浪号。我们的研究结果意味着，特征值敏感性分析的人口投影矩阵，在平衡附近进行评估，可以提供有用的信息的敏感性平衡人口，即使没有数据的密度依赖。
We consider the effects of parameter perturbations on a density-dependent population at equilibrium. Such perturbations change the dominant eigenvalue lambda of the projection matrix evaluated at the equilibrium as well as the equilibrium itself. We show that, regardless of the functional form of density dependence, the sensitivity of lambda is equal to the sensitivity of an effective equilibrium density (N) over tilde, which is a weighted combination of the equilibrium stage densities. The weights measure the contributions of each stage to density dependence and their effects on demography. Thus, (N) over tilde is in general more relevant than total density, which simply adds all stages regardless of their ecological properties. As log lambda is the invasion exponent, our results show that successful invasion will increase (N) over tilde, and that an evolutionary stable strategy will maximize (N) over tilde. Our results imply that eigenvalue sensitivity analysis of a population projection matrix that is evaluated near equilibrium can give useful information about the sensitivity of the equilibrium population, even if no data on density dependence are available.