Ecology of Biological Invasion - Spatial Spread by Stratified Diffusion

1.当一个物种在一个新地区定居时，它会以入侵浪潮的形式在该地区蔓延。这一波的速度不仅取决于随机移动到邻近地区，还取决于远距离扩散。利用分层扩散模型研究了入侵过程，模型中同时考虑了近距离扩散和长距离扩散。通过数值模拟计算了膨胀率，并与以前从解析模型得到的膨胀率进行了比较。结果表明，分层扩散模型应该为探索射程扩大的机制提供一个基本的框架。将模型应用于家雀的入侵，我们分别评估了长距离和短距离扩散对范围扩展的影响。我们在一个简单的随机元胞自动机模型中研究了单一物种在均匀地形上的入侵波速度。我们表明，与简单的确定性模型相比，随机性可以显著提高入侵波的速度。为了从数学上解释这一现象，我们发展了对随机模型的几种近似。这表明随机模型中波速的增加是由于波前形状的不规则性造成的，而在随机模型中并不存在。

1. When a species colonizes a new area, it spreads across that area in the form of an invasion wave. The speed of this wave is determined by not only by random movement into adjacent areas, but also by long-distance dispersal. We studied the invasion process by using a stratified diffusion model, in which both the short and long range dispersal are taken into account. Expansion rates are calculated from numerical simulations and compared with those previously obtained from the analytical model. The results suggest that the stratified diffusion model should provide a basic framework for exploring the mechanisms underlying range expansion. Applying models to the invasion of the House Finch, we evaluate the effects of long- and short-distance dispersals on the range expansion, separately.2. We investigated the speed of invasion waves in a simple stochastic cellular automaton model for a single species on a homogeneous landscape. We show that stochasticity can dramatically increase the speed of invasion waves compared to a simple deterministic version of the model. To explain this phenomenon mathematically, we developed several approximations to the stochastic model. These showed that the increased wave speed in the stochastic model is due to the irregularity in the shape of the wave front, which is present in the stochastic but not the deterministic model.