| Based on a systemic review on the advances of community ecology theories,this paper demonstrated the application of modern mathematic methods,such as multivariable statistics,grey system theory,fuzzy,and geostatistics,and so on,in the pest management system.In the practice,these mathematic methods were used to evaluate the dominant natural enemies in peach orchards,plum orchards and jujube orchards.And the corresponding findings were showed as follows:1.The arthropod community was divided into four sub-communities:phytophages, predators,parasitorids and neutralities,according to the trophic and taxonomy relationship.Several community parameters were employed to analyse the structures and dynamics of arthropod community and the sub-communities.The results showed that there were 55 species of arthropod belonging to 37 families,including 28 species of phytophages representing 18 families;22 species of predators representing 14 families;3 species of parasitords representing 3 families;2 species of neutralities representing 2 families in peach orchards.In the whole,the relative abundance of phytophages and predators were 0.953367 and 0.046188 respectively,which indicated that the phytophages dominated the arthropod community in peach orchards.Whereas,these abundances exhibited a similar seasonal fluctuate which ranged from 0.38 to0.97 for the phytophages, and from 0.01 to 0.54 for the predators.The dominant concentration of phytophages was 0.980648,larger than that of predators(0.886292)and parasitoids(0.420000).The other parameters such as diversitv index(H)and diversity index(Hill)including N1,N2,revealed the same trends,and showed the following order:predators sub-community＞arthropod community＞phytophages sub-community.The dynamics of the relative abundance of predators was similar to that of the phytophages.Therefore,it could be found that the predators were dominant natural enemies which influenced phytophages in the peach growth stage.2.Investigations on the structure of arthropod community in peach orchards were conducted with the principal component analysis,the optimal sorting method and system clustering analysis.The results showed that more obvious main factors and temporal patterns exist in the community.Dealing with the population dynamics of 55 species of arthropod by system clustering analysis and takingλ=0.47,we divided the community into four stages.The number of pests and their natural enemies was grouped into three parts by the optimal sorting method.The dominant species of pests and their natural enemies were demonstrated by the principal component analysis.3.The correlation of the major pest insects and natural enemies in peach orchards was analysed,by the method of fuzzy-similitude-priority(FSP)and fuzzy-judgement(FJ).The results of FSP showed that the dominant natural enemy of Erythroneura sudra,,Myzus persicae,Chrysomelidae and Tortricidae were Thomisidae,Erigonidium graminicola, Chrysopidae,Chrysopidae respectively.And,the results of FJ showed that the dominant natural enemy of Erythroneura sudra was Erigonidium graminicola. 4.In order to evaluate the controlling rate of the various natural enemies on the dominant pest Myzus persicae in plum field,the relational grade between M.persicae and their various natural enemies was analyzed with the grey system theory.The results indicated that the relational grade between daily total predation of natural enemies and M.persicae population size was given as follows,from highly to lowly in proper order: Chrysopa septempunctata(0.7449),Propylaca japonica(0.7395),Therdion octomaculatum (0.7354),Tetragnathidae(0.7198)etc,and the one between daily total predation of ideal dominant natural enemies and natural enemies was Enigonidium graminicola(0.9672), Propylaca japonica(0.6706),Tetragnathidae(0.6505)respectively.The higher relational grade between the population size of natural enemies and that of Myzus persicae was Chrysopa septempunctata(0.7449),Propylaca japonica(0.7395),Therdion octomaculatum (0.7354)and Tetragnathidae(0.7198)respectively.Also the one between the population size of ideal dominant natural enemies and that of natural enemies was Enigonidium graminicola(0.9703),Propylaca japonica(0.6725)and Tetragnathidae(0.6482) respectively.Based on the results above,more influential natural enemies on M.persicae population were E.graminicola,Chrysopa septempunctata,Propylaca japonica, T.octomaculatum and Tetragnathidae from highly to lowly successively.5.The grey policy decision theory was used to evaluate the dominant natural enemies of Myzus persicae.Three major natural enemies of Myzus persicae were in order of Chrysopa septempunctata(0.3646),Propylaea japonica(0.3202)and Theridonn octomacutatum(0.0445),by the predatory ability,in the whole sampling stage.6.Based on the principle of community ecology and by the method of fuzzy clustering,this paper studied the temporal and quantitative dynamics of the arthropod community and sub-community in jujube orchard(Feidong 2003),aimed to utilize natural enemy resources for pest control.There were 52 species of arthropod belonging to 47 families in the orchard.The relative abundances of arachnida and cecidomyidae were higher than other families in total community,i.e.,0.3465 and 0.2309 respectively.(The number of individuals of the arthropod community came to the peak on 8 June and 21 September.)The individuals of the arthropod community were the highest on 8 June and 21 September.The total community and pests -neutral insect sub -community could be clustered into 4 clusters,respectively.For total community,the clusters(T=0.92)were that on 22 March,on 6 April,on 22 November,and on other datas,and for pests -neutral insect sub -community,they(T=0.94)were that on 22 March,on 6 April,on 8 June,and on other datas.The natural enemy sub-community could be clustered into 3 clusters(T=0.94),i.e., that on 22 March,on 6 April,and on other datas.The results of cluster analysis partly reflected the seasonal differences of total community and sub-community,while the temporal overlaps of cluster results mirrored the complexity of community structure.7.Investigations on the spatial structure and distribution of Contarinia sp.and its natural enemy,Erigonidium graminicola,in Feidong at different period were conducted with geostatistics.The results indicated that the semivariogram of Contarinia sp.in 8 June, 27 August and 19 October could be described by the spherical models,showing an aggregated spatial distribution with the distances of spatial dependence which were 26.3m, 7.8m and 22.0m respectively.The degrees of its spatial dependence were 88.05%,85.77% and 87.58%respectively.As for Erigonidium graminicola,the corrrsponding models were also spherical ones,showing an aggregated distribution with the distances of spatial dependence which were 28.3m,22.5m and 22.2m respectively.The degrees of spatial dependence were 90.09%,87.96%,85.72%which revealed that Erigonidium graminicola was dominant natural enemies against population of Contarinia sp.in the Jujube orchard examined.8.Investigations on the spatial correlation of Contarinia sp.and its natural enemy, Erigonidium graminicola,in Feidong at different period were conducted with Cross-variogram.The results indicated that there is a significant spatial dependence between Erigonidium graminicola and Contarinia sp.from 21 May to 19 October except 27 August and 21 September,which showed strongly the following relationship of Erigonidium graminicola to Contarinia sp.in number and spatial especially on May 30 and October 19.It is demonstrated that Erigonidium graminicola is the dominant natural enemy again.9.Investigations on the spatial structure and correlation of Chactocnema ingenua and its natural enemy,Erigonidium graminicola,were conducted with geostatistics.The results indicated that the semivariogram of Chactocnema ingenua displayed as a spherical models, showing an aggregated spatial distribution with the distance of spatial dependence which was 18.82.The degrees of its spatial dependence were 49.39%.The estimating error of cross validation present normal distribution.The KRE equals to 0.0638,while the KRMSE is 0.9900.There are five aggregated patchs for Chactocnema ingenua in the survey area.As for Erigonidium graminicola,the corrrsponding models were also spherical ones, showing an aggregated distribution with the distances ranges of spatial dependence which was 22.45m.The degrees of spatial dependence were 33.8%.The KRE equals to 0.0185, while the KRMSE is 0.9902.In agree with the Chactocnema ingénue,Erigonidium graminicola also demonstrated five aggregated patchs.The consistence of Chactocnema ingénue with Erigonidium graminicola in the range,the spatial distribution and the degrees of spatial dependence supported the spatial following relationship of Erigonidium graminicola to Chactocnema ingénue.All of the results,gave the strong evidence that Erigonidium graminicola was the dominant natural enemy in the lawn.
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