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Almost necessary and sufficient conditions for survival of species

机译:物种生存的必要条件

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We consider a nonautonomous competitive Lotka-Volterra system of two species, satisfying two inequalities involving averages of the growth rates and the interaction coefficients, which imply persistence. We introduce a third species and give a third inequality, involving the average of the growth rate of the third species and solutions of a linear algebraic system, which guarantees persistence of the system. It is also shown that reversing this inequality implies non-persistence; more specifically, extinction of the third species with small positive initial values, in the autonomous case. Our conditions are simple and computable. (C) 2003 Elsevier Ltd. All rights reserved.
机译:我们考虑两个物种的非自治Lotka-Volterra竞争系统,满足两个不等式,这两个不等式涉及增长率和相互作用系数的平均值,这意味着持久性。我们引入第三种,并给出第三种不等式,其中涉及第三种的平均增长率和线性代数系统的解,这保证了系统的持久性。还表明,扭转这种不平等现象意味着非持久性。更具体地说,在自主情况下,具有较小的正初始值的第三物种的灭绝。我们的条件是简单且可计算的。 (C)2003 Elsevier Ltd.保留所有权利。

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