Cruywagen G C, Kareiva P, Lewis M A, Murray J D
Sea Fisheries Research Institute, Rogge Bay, Cape Town, , 8012, South Africa.
Theor Popul Biol. 1996 Feb;49(1):1-38. doi: 10.1006/tpbi.1996.0001.
In recent years regulations have been developed to address the risks of releasing genetically engineered organisms into the natural environment. These risks are generally considered to be proportional to the exposure multiplied by the hazard. Exposure is, in part, determined by the spatial spread of the organisms, a component of risk suited to mathematical analysis. In this paper we exampine a mathematical model describing the spread of organisms introduced into a hetereogeneous environment, focusing on the risk of spread and plausibility of containment strategies. Two competing populations are assumed, one the natural species and the other an engineered species or strain, both of which move randomly in a spatially heterogenous environment consisting of alternating favourable and unfavourable patches. The classical Lotka-Volterra competition model with diffusion is used. Analyses of the possible spread and invasion of engineered organisms are thus reduced to finding periodic travelling wave solutions to the model equations. We focus on whether a very small number of engineered organisms can spatially invade a natural population. Initially we investigate the problem for spatially periodic diffusion coefficients and demonstrate that, under the right circumstances and a large enough unfavourable patch, invasion does not succeed. However, if spatially periodic carrying capacities are assumed along with spatially varying diffusion rates, the situation is far more complex. In this case containment of the engineered species is no longer only a simple function of the unfavourable patch length. By using perturbation solutions to the nonuniform steady states, approximate invasion conditions are obtained.
近年来，已制定相关法规来应对将基因工程生物释放到自然环境中的风险。这些风险通常被认为与暴露程度乘以危害程度成正比。暴露程度部分取决于生物的空间扩散，这是一个适合进行数学分析的风险组成部分。在本文中，我们研究了一个描述引入异质环境中的生物扩散的数学模型，重点关注扩散风险和遏制策略的合理性。假设存在两个相互竞争的种群，一个是自然物种，另一个是工程物种或品系，它们都在由交替的有利和不利斑块组成的空间异质环境中随机移动。使用带有扩散项的经典洛特卡 - 沃尔泰拉竞争模型。因此，对工程生物可能的扩散和入侵的分析就简化为寻找模型方程的周期行波解。我们关注极少数工程生物是否能在空间上侵入自然种群。最初，我们研究具有空间周期性扩散系数的问题，并证明在适当的情况下以及有足够大的不利斑块时，入侵不会成功。然而，如果假设具有空间周期性的承载能力以及空间变化的扩散率，情况就会复杂得多。在这种情况下，对工程物种的遏制不再仅仅是不利斑块长度的简单函数。通过使用非均匀稳态的摄动解，得到了近似入侵条件。
