The Catastrophe Region Identification, Parameter Estimation And Software Development On Swallowtail Catastrophe Model Of The Aphid Population Dynamics And Its Application

Aphids seriously damage wheat by feeding on the different parts of the crop and bytransporting some disease causative agents. Hence it is very crucial to control them in asustainable way. Although there are several controlling methods such as chemical, biological,IPM and yellow traps, etc., the current trend is focused on biological controlling and pestforecasting as it is eco-friendly sustainable measure. For this, a good understanding of theirpopulation dynamics which is been impacted by intrinsic or extrinsic factors is criticallyimportant. Population dynamics of wheat aphid frequently show catastrophic movements anddifficult to predict the changes (dynamics). Complexity of this phenomenon urges differentmodeling frameworks other than traditional methodologies (calculus or statistical methods) tounderstand the trajectories of their behavior. Situations like this can be best handled usingcatastrophe theory. Identifying catastrophe regions and boundaries of population dynamicscan be used to forecast outbreaks or attacks which are economically important. A fewnumbers of experiments have been conducted to develop pest forecasting models or expertsystems using catastrophe theory. However, many of them are limited to the theoretical lowerdimensional models but not to the practical systems or software. Since identifying catastropheregions is a difficult task, many existing models are failed to analyze catastrophe regions andboundaries. Therefore the research purpose of this study was to build a catastrophe theorymodel which is capable of identifying catastrophe regions and boundaries, and forecastingpopulation dynamics by analyzing actual survey data. The research methodology was basedon the integration of simulation modeling and analytical modeling (catastrophe theory).Hence the model framework was designed on the swallowtail catastrophe theory and logisticgrowth equation. Then we built the swallowtail model from the aphid population as afunction of three controlling factors; weather, crop and natural enemy. Model parameterswere estimated using grey system theory. Finally the model was implemented as computersoftware (APHIDSim) using enhanced computer technologies. The development platformand the programming language used were Visual Studio.NET and Visual Basic.NETrespectively. A database is run under the system constructed with SQL server compact, anembedded database engine which can easily be integrated for distribution.The results showed that:1The developed model has been verified using five actual survey data sets and thecatastrophe regions and boundaries have been identified. Simulated results were analyzedaccording to the explanation of Wei (2009) about catastrophe regions and location ofcritical points within the regions. 2The results are graphically interpreted using three dimensional control space diagramsindicating the data points located in different catastrophe regions. Results have provedthat identifying catastrophe regions is possible using catastrophe theory model and theidentified catastrophe regions can be used to explain that increasing of wheat aphidpopulation (population dynamics) is basically a catastrophic behavior and sudden jumpsmay occur from one state to another even though the control factors change smoothly.3The population changes in actual survey data are clearly explained by simulated datawhich are located in the catastrophe regions. Biological reasons caused to the populationchanges can also be explained because nutritive value of the plants is high especiallywhen the crop stage change from the jointing stage to the booting stage. Consequentlyduring the period of high nutrition, the population of aphids grows rapidly. On the otherhand, different growth pattern in actual survey data are still existed, and it could be due toseveral other reasons; survival rates of aphids could be changed under different weatherconditions and the actual behavior of aphids after applying controlling measures isunclear.4The model parameters, predator rate, carrying capacity and intrinsic growth rate of aphids,have been estimated using the estimation method which was developed by grey systemtheory.5It was able to develop, test and evaluate a fully user friendly software, APHIDSim, awheat aphid population dynamics analysis program successfully in order to achieve themain target as expected by the author, and the result showed that it is suitable to use as aresearch tool as well as a decision making tool in pest forecasting and management.From the literature review, further we found that aphid population dynamics have beenstudied using fold, cusp, swallowtail, butterfly and elliptic umbilici catastrophe models butmany of them have not been verified with field data. Although the initial findings of thosemodels have proved that catastrophe theory can be used to analyze aphid populationdynamics of aphids, disappointingly theoretical and experimental difficulties have restrictedfurther studies and practical applications. Major difficulties identified can be summarized ascomplexity of selecting control variables, difficulty of understanding catastrophe regions forhigher dimensional models, lack of theoretical base of parameter estimation, and unclearnessof explaining biological meanings.Since integrating analytical model and simulation model is a difficult task, and are oftenseparately used, this study is innovative and a new approach in the field of insect controlling.We were able to incorporate practical environmental factors into the simulation model,estimate model parameters and to verify the model against actual survey data. The essence of catastrophe theory has been used as the framework of the simulation system. The interestingmodel results and graphical interpretation of data locations in the catastrophe regions wouldbe a new approach for short-term prediction of wheat aphid population dynamics. Since lackof practical application of catastrophe theory models on aphid population dynamics andidentifying catastrophe regions, these results would also be a new approach for scientists tostudy more about catastrophe theory and encourage more application of catastrophe theorymodels on aphid population dynamics.