Caswell Hal, Takada Takenori
Biology Department MS-34, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA.
Theor Popul Biol. 2004 Jun;65(4):401-11. doi: 10.1016/j.tpb.2003.09.007.
In density-independent models, the population growth rate lambda measures population performance, and the perturbation analysis of lambda (its sensitivity and elasticity) plays an important role in demography. In density-dependent models, the invasion exponent lambdaI replaces lambda as a measure of population performance. The perturbation analysis of lambdaI reveals the effects of environmental changes and management actions, gives the direction and intensity of density-dependent natural selection on life history traits, and permits calculation of the sampling variance of the invasion exponent. Because density-dependent models require more data than density-independent models, it is tempting to look for substitutes for the invasion exponent, the sensitivity and elasticity of which can be calculated from a density-independent model. Here we examine the accuracy of two such substitutes: the dominant eigenvalue of the projection matrix evaluated at equilibrium (An) and the dominant eigenvalue of the matrix averaged over the attractor (A). Using a two-stage model that represents a wide range of life history types, we find that the elasticities of An or A often agree to within less than 5% error with those of the invasion exponent, even when population dynamics are chaotic. The exceptions are for semelparous life histories, especially when density-dependence affects fertility. This suggests that the elasticity analysis of density-independent models near equilibrium, or averaged over the attractor, provides useful information about the elasticity of the invasion exponent in density-dependent models.
在非密度依赖模型中，种群增长率λ衡量种群表现，而对λ的扰动分析（其敏感性和弹性）在种群统计学中起着重要作用。在密度依赖模型中，入侵指数λI取代λ作为种群表现的衡量指标。对λI的扰动分析揭示了环境变化和管理行动的影响，给出了密度依赖自然选择对生活史特征的方向和强度，并允许计算入侵指数的抽样方差。由于密度依赖模型比非密度依赖模型需要更多数据，因此人们试图寻找入侵指数的替代指标，其敏感性和弹性可以从非密度依赖模型中计算得出。在这里，我们研究了两种此类替代指标的准确性：在平衡状态下评估的投影矩阵的主导特征值（An）和在吸引子上平均的矩阵的主导特征值（A）。使用一个代表广泛生活史类型的两阶段模型，我们发现即使种群动态是混沌的，An或A的弹性与入侵指数的弹性通常在误差小于5%的范围内一致。例外情况是单次生殖的生活史，特别是当密度依赖影响繁殖力时。这表明在平衡附近或在吸引子上平均的非密度依赖模型的弹性分析，提供了关于密度依赖模型中入侵指数弹性的有用信息。
