Elasticity analysis of density-dependent matrix population models: the invasion exponent and its substitutes
Elasticity analysis of density-dependent matrix population models: the invasion exponent and its substitutes
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DOI：
10.1016/j.tpb.2003.09.007
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发表时间：
2004-06-01
影响因子：
1.4
通讯作者：
Takada, T
中科院分区：
文献类型：
--
作者：
Caswell, H;Takada, T
在非密度模型中，人口增长率lambda衡量人口表现，其敏感性和弹性的摄动分析在人口统计学中起着重要作用。在依赖密度的模型中，入侵指数log lambda(1)取代lambda作为种群表现的度量。λ(1)的摄动分析揭示了环境变化和管理行为的影响，给出了密度依赖性自然选择对生活史性状的方向和强度，并允许计算入侵指数的抽样方差。由于依赖密度的模型比不依赖密度的模型需要更多的数据，因此寻找入侵指数的替代品是很有诱惑力的，入侵指数的灵敏度和弹性可以从不依赖密度的模型中计算出来。在这里，我们检查两个这样的替代的准确性：在平衡（A((n) / cap)）处评估的投影矩阵的主要特征值和在吸引子（(A) / bar）上平均的矩阵的主要特征值。使用一个代表广泛生活史类型的两阶段模型，我们发现即使在种群动态是混乱的情况下，a （(n) / cap）或(a) / bar的弹性通常与入侵指数的误差小于5%。例外是半产的生活史，特别是当密度依赖影响生育时。这表明，对接近平衡的密度无关模型的弹性分析，或对吸引子的平均，提供了关于密度依赖模型中入侵指数弹性的有用信息。(C) 2004爱思唯尔公司版权所有。
In density-independent models, the population growth rate lambda measures population performance, and the perturbation analysis of (its sensitivity and elasticity) plays an important role in demography. In density-dependent models, the invasion exponent log lambda(1) replaces lambda as a measure of population performance. The perturbation analysis of lambda(1) 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 (A((n) over cap)) and the dominant eigenvalue of the matrix averaged over the attractor ((A) over bar). Using a two-stage model that represents a wide range of life history types, we find that the elasticities of A((n) over cap) or (A) over bar 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. (C) 2004 Elsevier Inc. All rights reserved.