Invasion by extremes: Population spread with variation in dispersal and reproduction
Invasion by extremes: Population spread with variation in dispersal and reproduction
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DOI：
10.1086/319934
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发表时间：
2001-05-01
影响因子：
2.9
通讯作者：
Horvath, L
中科院分区：
文献类型：
--
作者：
Clark, JS;Lewis, M;Horvath, L
对于具有由肥尾核（具有非指数有界的尾部的核）描述的扩散的种群，渐近种群扩散率不能由传统模型估计，因为这些模型预测持续加速（渐近无限）的入侵。不可能的预测来自于这样一个事实，即适合分散数据的厚尾核具有一种永远不适用于数据的性质（非离散个体，因此没有矩生成函数）。真实的生物体产生有限数量的（随机的）后代;因此，总是可以确定一个经验矩生成函数。使用另一种方法来估计传播率的极端扩散事件，我们表明，有限的估计可以得出肥尾内核，我们演示了如何变量复制修改这些速率。传统模型将扩散率定义为描述个体预期密度的前进前沿的速度，而我们对扩散率的另一种定义是群体中最远个体位置的预期速度。对于恒定的净繁殖率R-0，渐近波速近似为（1/T）（π uR（0）/2）1/2 m yr（-1），其中T是世代时间，u是具有形状参数的Clark等人的2Dt模型的距离参数（m（2））。从拟合扩散核与胖尾巴p = 1和无穷的方差，我们得到有限的传播速度和一个简单的方法进行数值估计。拟合的内核，具有无穷大的方差，产生的传播率的分布是渐近正态的，因此，有有限的时刻。可变的繁殖可以深刻地影响传播速度。通过纳入变异的寿命导致的繁殖，我们估计的利率远低于预测的标准方法，它假设一个恒定的净繁殖率。使用树木的基本生活史数据，我们表明这些估计的比率低于之前分析模型的预期，并且根据更新世末森林蔓延的古记录进行了解释。我们的研究结果建议重新审视过去的传播速度和未来应对气候变化的潜力。
For populations having dispersal described by fat-tailed kernels (kernels with tails that are not exponentially bounded), asymptotic population spread rates cannot be estimated by traditional models because these models predict continually accelerating (asymptotically infinite) invasion. The impossible predictions come from the fact that the fat-tailed kernels fitted to dispersal data have a quality (nondiscrete individuals and, thus, no moment-generating function) that never applies to data. Real organisms produce finite (and random) numbers of offspring; thus, an empirical moment-generating function can always be determined. Using an alternative method to estimate spread rates in terms of extreme dispersal events, we show that finite estimates can be derived for fat-tailed kernels, and we demonstrate how variable reproduction modifies these rates. Whereas the traditional models define spread rate as the speed of an advancing front describing the expected density of individuals, our alternative definition for spread rate is the expected velocity for the location of the furthest-forward individual in the population. The asymptotic wave speed for a constant net reproductive rate R-0 is approximated as (1/T)(pi uR(0)/2)1/2 m yr(-1), where T is generation time, and u is a distance parameter (m(2)) of Clark et al. 's 2Dt model having shape parameter. From fitted dispersal kernels with fat tails p = 1 and infinite variance, we derive finite rates of spread and a simple method for numerical estimation. Fitted kernels, with infinite variance, yield distributions of rates of spread that are asymptotically normal and, thus, have finite moments. Variable reproduction can profoundly affect rates of spread. By incorporating the variance in reproduction that results from variable life span, we estimate much lower rates than predicted by the standard approach, which assumes a constant net reproductive rate. Using basic life-history data for trees, we show these estimated rates to be lower than expected from previous analytical models and as interpreted from paleorecords of forest spread at the end of the Pleistocene. Our results suggest reexamination of past rates of spread and the potential for future response to climate change.