性信息素诱捕下害虫Logistic增长及经济阈值数学模型

Abstract

The research on proper,accurate observation and monitoring pest population is of great significance in forecast and control pests based on sex pheromone trap.Construction of mathematical models by practical observation,measurement in fields and calculation is able to play an important role in the aspect concerned by many.Given this situation,in this study,occurrence and real-time monitoring of population dynamics of pests have been accomplished by application of production from sex pheromone of insects.According to the characteristics of sex pheromone trap of male insects,combined with the Logistic differential equation and based on the balanced point between sex pheromone trap and increase of population,relationships among several values were analyzed and compared with those under other common trappings.The values were as following: trapping intensity(E) at the time when a population was increasing under the condition of sex pheromone trap,the natural increasing rate of pests(r),the trapping amount(x(t)),the pest amount in fields(N).The maximal consistent trapping amount when the balanced point was reached was articulated [hmax*=rN 41-E*],and at this moment,the relationship between the best trapping intensity(E*) and the natural increasing rate of pest(r) were in accord with the formula of E*=r 1+r.At the same time,in terms of the characteristics of harms of pests,on the foundation of analysis of the substantial field pest amount coefficient α=SEF(SE meant the survival rate of larvae,F stood for the maximal reproductive vitality of each female pest,was the ratio between the maximal egg amount and the substantial egg amount),the expense of forecast and control utilizing sex pheromone trap and increasing output were analyzed.When λ[λ=2r1-c pαN+1]was assumed as the regulating coefficient(p meant the economic damage caused by larvae,its unit should be RMB Yuan),the following values were definite,the trapping intensity at the time of the highest profit was ER=λ-λ λ;the consistent trapping amount was hR==ERN r1-λ-1 2r the trapping intensity at the time when the economic threshold was reached was Es=λ-1 λ and it should be less than 2r 2r+1.After illustration and calculation,the necessary condition of existence of the economic threshold was pc αN,when c αNp2c αN,there was the relation EREs2E*,that meant Es2 was the economic threshold;whenp2c αN,there was the relation Es1E*,that meant Es1 was the ecological threshold.Taking the trap of Oriental Fruit Moth by sex pheromone as example,the model was verified.Furthermore,the amounts of adults of Oriental Fruit Moth Grapholitha molesta(Busck) in fields were investigated.By fitting Logistic model,the natural increasing rates of Oriental Fruit Month(r) under 3 sex pheromone trap intensities were measured.Subsequently,the trapping intensity(E) was acquired by the model established in this study;also,the largest consistent trapping amount when the value of economic threshold of Oriental Fruit Moth(Es) was reached,which was determined with the economic threshold model.On the ground of analysis and articulation mentioned above,in this paper,the mathematical model based on sex pheromone trap of insects was established in order to provide measurement of the trapping intensity E in fields and the natural increasing rate of pests r with theoretical guide,in addition,it also could offer theoretical foundation to forecast and control of pests by sex pheromone of insects.