基于生灭过程的多斑块毒杂草入侵模型及空间模拟

Multipatches Poisonous Weeds Invasion Model and Space Simulation Based on Birth and Death Process

到多斑块毒杂草入侵问题中，研究毒杂草与周围有限数量斑块的可食牧草之间的入侵关系．借助生灭过程理论，利用全期望公式构建微分方程，计算出毒杂草的期望值．通过讨论极限期望，分析得出毒杂草成功入侵至周围斑块的条件．采用元胞自动机理论将入侵模型扩展到空间网格进行模拟研究，分析毒杂草属的空间分布类型，为毒杂草的控制提供数据支持．研究结果表明：（1）若毒杂草的内禀增长率大于死亡率且内禀增长率和死亡率之差大于毒杂草的入侵率时，毒杂草成功入侵至可食牧草的概率变大，增加了可食牧草灭绝的风险，不利于可食牧草的续存；（2）若毒杂草的内禀增长率小于死亡率或内禀增长率和死亡率之差小于毒杂草的入侵率时，毒杂草没有足够的生物量向可食牧草入侵，毒杂草成功入侵至可食牧草的概率变小；（3）毒杂草的入侵作用影响了毒杂草种群的空间分布特征，加快了空间分布的聚集程度．

In this paper, the model of birth and death process is applied to the invasion model of multi-patches poisonous weeds to study the invasive relationship between poisonous weeds and the surrounding limited number of patches of edible pasture. With the theory of birth death process, the differential equation is constructed by using the total expectation formula,and the expectation of poisonous weeds is calculated. By calculating the limit expectation analysis,we got the conditions for successful invasion of poisonous weeds into surrounding patches. Using the cellular automata theory, the competition model is extended to the space lattice to sim-ulate and study the spatial distribution patterns of poisonous weeds, which will provide data supporting their control. The results showed that： （1） If the intrinsic growth rate of poisonous weeds is greater than the mortality rate, and the difference between the intrinsic growth rate and mortality rate is greater than the invasion rate of poisonous weeds,the probability of suc-cessful invasion of poisonous weeds into edible pasture increases, which increases the risk of the extinction of edible pasture and is harmful to the continued existence of edible pastu; （2） If the intrinsic growth rate of poisonous weeds is less than the mortality rate or the difference between the intrinsic growth rate and mortality rate is less than the invasion rate of poisonous weeds, the poisonous weeds do not have enough biomass to invade the edible pasture, and the probability of successful invasion of poisonous weeds to edible pasture becomes smaller; （3） The invasion of poisonous weeds affected the spatial distribution of poisonous weed populations, and accelerated the aggregation degree of spatial distribution.