Lewis Mark A, Li Bingtuan, Weinberger Hans F
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA.
J Math Biol. 2002 Sep;45(3):219-33. doi: 10.1007/s002850200144.
One crucial measure of a species' invasiveness is the rate at which it spreads into a competitor's environment. A heuristic spread rate formula for a spatially explicit, two-species competition model relies on 'linear determinacy' which equates spread rate in the full nonlinear model with spread rate in the system linearized about the leading edge of the invasion. However, linear determinacy is not always valid for two-species competition; it has been shown numerically that the formula only works for certain values of model parameters when the model is diffusive Lotka-Volterra competition [2]. This paper derives a set of sufficient conditions for linear determinacy in spatially explicit two-species competition models. These conditions can be interpreted as requiring sufficiently large dispersal of the invader relative to dispersal of the out-competed resident and sufficiently weak interactions between the resident and the invader. When these conditions are not satisfied, spread rate may exceed linearly determined predictions. The mathematical methods rely on the application of results established in a companion paper [11].
衡量一个物种入侵性的一个关键指标是它扩散到竞争物种环境中的速度。一个用于空间明确的两物种竞争模型的启发式扩散率公式依赖于“线性确定性”，该确定性将完整非线性模型中的扩散率与围绕入侵前沿线性化的系统中的扩散率等同起来。然而，线性确定性对于两物种竞争并不总是有效的；数值结果表明，当模型是扩散型洛特卡 - 沃尔泰拉竞争时，该公式仅对模型参数的某些值有效[2]。本文推导了空间明确的两物种竞争模型中线性确定性的一组充分条件。这些条件可以解释为要求入侵者相对于被竞争的本地物种有足够大的扩散，并且本地物种与入侵者之间的相互作用足够弱。当这些条件不满足时，扩散率可能超过线性确定的预测值。数学方法依赖于在一篇配套论文[11]中建立的结果的应用。
