三种寄生物与一种寄主的系统模型研究

STUDIES ON SYSTEMS MODEL OF THREE PARASITOID ONE HOST INTERACTION

建立了红圆蚧（Ａｏｎｉｄｉｅｌａａｕｒａｎｔｉ）与３种寄生蜂：盾蚧长缨蚜小蜂（Ｅｎｃａｒｓｉａｃｉｔｒｉｎａ）、岭南蚜小蜂（Ａｐｈｙｔｉｓｌｉｎｇｎａｎｅｎｓｉｓ）和印巴黄蚜小蜂（Ａｐｈｙｔｉｓｍｅｌｉｎｕｓ）相互作用的系统模型：Ｈｎ＋１＝λＨｎ（ｓｆ１ｆ２＋ｔｆ２ｆ３＋ｕｆ３）Ｐｎ＋１＝Ｈｎｓ（１－ｆ１）Ｑｎ＋１＝Ｈｎ（ｓｆ１＋ｔ）（１－ｆ２）Ｒｎ＋１＝Ｈｎ（ｕ＋ｔｆ２）（１－ｆ３）ｆ１（Ｐｎ）＝ｅｘｐ（－ａＰｎ），ｆ２（Ｑｎ）＝ｅｘｐ（－ｂＱｎ），ｆ３（Ｒｎ）＝ｅｘｐ（－ｃＲｎ）按红圆蚧的面积大小分成３种类型：ｓ（０．５５ｍｍ２以上）、ｔ（０．３９～０．５５ｍｍ２）、ｕ（０．３９ｍｍ２以下），分析了三维系统（２种寄生物与１种寄主）和四维系统（３种寄生物与１种寄主）在不同红圆蚧大小分布（ｓ，ｔ，ｕ）条件下系统的动态变化，确定了寄生物相互排斥和共存的边界条件。

This paper established an interaction model of Aonidiella aurantii and its three parasitoids: Encarsia citrina, Aphytis melinus, Aphytis lingnanensis: H n+1 =λH n(sf 1f 2+tf 2f 3+uf 3) P n+1 =H ns(1-f 1) Q n+1 =H n(sf 1+t)(1-f 2) R n+1 =H n(u+tf 2)(1-f 3) f 1(P n)= exp (-aP n), f 2(Q n) =exp (-bQ n), f 3(R n)= exp (-cR n)The host is devided into 3 types according to scale area: s (above 0.55 mm 2), t (0.39～0.55 mm 2), u (below 0.39 mm 2); through changing the value of( s, t, u) and the attacking rate of parasitoids (a, b, c) , we analysed the dynamics of 3 dimension systems(two parasitoid one host)and 4 dimension system(three parasitoid one host), determined the boundary conditions for parasitoids to compet exclusively or to coexist. It provided a theoretical guidance to the strategy of biological control of Aonidiella aurantii .