Discrete event simulation of Mediterranean fruit flies propagation

Discrete event simulation of Mediterranean fruit flies propagation Jean Baptiste Filippi Paul Bisgambiglia Julie Acquaviva Jean-François Santucci. UMR CNRS 6134, Université de Corse {filippi, bisgambi, jacquaviva, santucci}@univ-corse.fr INTRODUCTION Most simulation models in environmental science are built by ecologist. The evident advantages of this fact is that all processes are well identified and understood, but the bottom line is that the computer implementation of the model is often poorly designed and hardly reusable. This result is partly due to the fact that only a few environmental modeling and simulation tools exists and even fewer that are based on strong modeling and simulation theory concepts. The other cause of the lack of efficiency in some environmental simulation models is that domain specialists lacks metaphors to conceptualize the world in computerized forms Those metaphors are found in the form of modeling paradigms, such as multi-agent or cellular automata. Many of those paradigms are in use today and implemented in specific modeling and simulation software. Specialists often uses one of those paradigms but, what is becoming difficult is not only to formulate but also to conceive higher level problems, whose complexity is such that they escape definition through a single metaphor. To build effectively such models, one must couple different sub-models that might have been built using different paradigms. Those kind of models are called multi-models, and have been introduced by [Orën, 1991] later extended by [Fishwick, 1995]. To achieve reusability in Multi-modeling it is necessary to use of a formal framework that is sufficiently open and flexible to enable the integration of several distinct modeling techniques. We propose to base our formal framework on a methodology called DEVS introduced by [Zeigler, 2000]. DEVS is a set-theoretic formalism that includes a formal representation capable of mathematical manipulation just as differential equations serves this role for continuous systems. It is possible to perform formal verifications of a model using DEVS formal representation thus decreasing testing and implementation time. DEVS formalism also presents an explicit separation between the phases of modeling and simulation, DEVS models are directly simulable in a specific experimental frame. The Experimental Frame (EF) describes a limited set of circumstances under which a system (real or model) is to be observed or subjected to experimentation. As such, it reflects the objectives of the experimenter who performs experiments on a real system or, through simulation, on a model. DEVS needs to be adapted and extended when replaced in a domain-specific context. A wide set of techniques that derives from DEVS, such as Cell- DEVS [Wainer and Giambiasi, 2001] or JAMES [Schattenberg and Uhrmacher, 2001] have already been developed to serve some domain specific needs [Zeigler, 2000].. From a software engineering perspective, we propose to base our approach on Object Oriented design concepts [Hill, 1996]. Those concepts had led to various analysis methods, among those methods, UML (Unified modeling language) [Gamma et al.] which now became a standard. UML and the modeling and simulation field should be distinguished despite the name and strong similarities. We are also making the use of "design patterns" [Gamma et al.,] to reduce the overall complexity of the global classes architecture of the software framework. THE JAVA DEVS TOOLKIT JDEVS toolkit is composed of five independent modules. They can interact with other modules that are already developed and some elements, including the java simulation kernel, might be changed for better performance. Modeling and simulation kernel The modeling and simulation kernel is a java implementation of the DEVS formalism. Atomics and coupled models are described as follow. Atomic DEVS models definition The DEVS formalism is offering well defined interfaces for the description of systems. The concept of model abstraction permits to use models that are coded in various object oriented languages. Those models are then accessed thought a software interface specified in DEVS. 1

JDEVS is a java toolkit. Modeling atomic models directly in the toolkit can be done directly in this language. To help the modeler in this task, the GUI generates a java skeleton, stores it in the models library and compiles it. A formal DEVS atomic model is described as: M = <X, S, Y, δint, δext, λ, ta> With X is the input events set, S is the state set, and Y is the output events set. There are also several functions: δint manages internal transitions, δext external transitions, λ the outputs, and ta the elapsed time. Coupled models description in JDEVS If the user wants to interact directly with the simulation engine, the coupling between models can be made directly in a java class. However, with the use of the GUI, it is possible to graphically construct the model structure that is saved in XML. A DEVS coupled model is defined as: CM = < X, Y, D, {Mi}, {Ii}, {Zij} > Here, X is the set of input events, and Y is the set of output events. D is an index of components, and for each i Є D, Mi is a basic DEVS model. Ii is the set of influences of model i. For each j Є Ii, Zij is the i to j translation function. Part of the resulted XML document type definition for a coupled model is: Generic models library A complete description of the library can be found in [Bernardi et al. 2001]. The implementation of the library description in JDEVS is resulting in a module in the GUI. This module presents models according to its domain and sub-domain, all classified in a tree like architecture. Geographical Information System (GiS) interconnection To perform the coupling, the user has to select a zone in a GIS, then rasterize the zone and export the resulting map in an ASCII file. During the initialization of the simulation the cellular simulation panels automatically instantiates each cell using the attribute from the file. The simulation output is a set of discrete events (containing the cell coordinates, the cell new state, and when the change has occurred). Those events are flattened during the run to recompose discrete time maps that can be imported back to the GIS. Cellular simulation panels This module allows the user to perform (and debug) simulation of a cellular model. The user can directly interact with the simulation, as he can send events using the mouse. The general architecture shown in Figure 1 has been adopted to model cellular systems. <!ELEMENT MODEL (TYPE, NAME, BOUNDS?, INPUT*, OUTPUT*, CHILD*, EIC?, EOC?, IC?)> With TYPE defining the kind of coupled model (Cellular, kernel, coupled...), NAME the name of the model, BOUNDS the position of the model on the screen (used only by the GUI), INPUT the set of input ports, OUTPUT the set of output ports, CHILD the index for the components of the coupled model (in the priority order), EIC is the external input coupling, EOC the external output coupling and IC the internal coupling. Each coupled model is stored in a different XML file, the parser automatically instantiates the models and creates the links during loading. Hierarchical block modeling and simulation interface The graphical user interface is the modeling frontend of the toolkit, using this front end, the user can graphically create, compile, link and store atomic and coupled models, debug the resulting model and perform the simulation. Distributed modeling is made using the GUI, if different modelers works on sub-coupled models and store them in the same library, it is possible to federate those models in another graphical modeling client. Figure 1 : Cellular models architecture. It is composed of a distributor and cells in a cellular coupled model. The general inputs are connected to the inputs of the distributor, then the distributor will send them to either all the cell or to the cell that would have been selected by an event in its Select port. All cells are connected to the general output. During the initialization, the cellular coupled model is loading the GIS generated file, calculates the number of cells needed (width*height) and then instantiates and performs the coupling for every cell. The modeling is a straight forward process, to describe a model the user only need to define the java class that implements the characteristic functions of a cell-model according to the DEVS formalism. The next section presents an application of multi-modeling, a model of bugs propagation in an orchard coupling cellular automata and an neural network model, both encapsulated in DEVS models. 2

EXPERIMENTS OF USE The section use a study of the geographic distribution of adult Mediterranean fruit fly, or medfly, to illustrate the main advantages of using JDEVS : coupling and reusability of models in a multi-paradigm framework. The purpose of this application is to illustrate the new modeling scenarios possible by the use of the formal framework to couple two different models in nature. With the first model we show an implementation of a cellular model in JDEVS and give an overview of the effort needed to implement such model in the framework. The second model, a hierarchical block of Feedback-DEVS model, illustrates the integration of a neural network in a DEVS basic model. One is a model of spatial organization, the second is a non spatial empirical model. Nevertheless, the last part of this section shows that the coupling of these models is greatly simplified because the models are sharing the same simulation engine and the same interfaces. The Mediterranean fruit fly The medfly is one of the most serious economic pests of the fruit and vegetables. If control methods are not used, medfly can infest 100 percent of susceptible fruit such as apricots, pomelos and peaches and to a lesser extent, fruits such as apples and clementines. To limit the population of the medfly, a specific and environmentally nonpolluting method of medfly control called SIT (sterile insect technique) is used increasingly. This technique consists in releasing a large number of sterile males over the sufficient period time at the best location. One of the main objective of the model is to estimate geographical distribution of adult medfly. This model is to be used for guidance in implementing eradication procedures and preventing the spread to other locations. The onset of medfly activity is temperature dependent. In southern France (Corsica island) medfly is active in late spring, summer and autumn, when temperatures exceed an average climatic condition. Medfly can over the winter as adults, as eggs and larvae (in fruit), or as pupae in the ground. As temperatures increase in spring, adults begin to emerge from the ground and flies become active. Cellular spread model To manage potential geographical distribution of the Mediterranean fruit fly, it is necessary to model the phenomenon that alter those phenomena in order to quantify and qualify them. Figure 2 shows a simulation of the model developed to quantify medfly population in specific area. Like any other basic model, this cellular spread model is described in one file, the atom cell description file. The behavior is described in programming code. The skeleton for the file is generated by the GUI, it contains the four functions of the basic model as well as the following state set : <X {N, S, E, W, in1, in2 }, Y {N, S, E, W, out }, S {host, ripe, Neggs, Nlarvae, Npupae, Nadults, Aeggs, Alarvae, Apupae, Aadults, Afood } > N, S, E, W corresponds to the North, South, East and West ports of their neighborhood ; in1, out corresponds to the temperature of the day and to the number of flies exchanged ; in2 corresponds to values of the population at each stage of the life cycle (eggs, larvae, pupae, adults) ; host : the species hosts trees { apricots, pomelos, peaches, apples, clementines, other}. other corresponds to a medfly insensitive cell ; ripe = {false, true} depends on the ripening period of the host tree ; Neggs, Nlarvae, Npupae, Nadults are values to the population at each stage ; Aeggs, Alarvae, Apupae, Aadults corresponds to the average oldest of the population at each stage ; Afood correspond to the average day of diet for adults population. Figure 2 : Fruit fly model in 2D panel. Two specials functions that the specialist (ecologist) has to implement in order to have his model working must be define : scattering( ) and development( ). The first function calculates the number of adults flies waste by the cell, the second function describe the biological model of the life cycle corresponding to interactions for each of the four types of stages. This two functions are adapted from CLIMEX model [Vera et al., 2002] In this model : The λ function (output) is sending to the neighboring cells a quantity of adults flies given by the scattering() function and its 3

Aadults and Afood values. This function is called by the simulator in case of activation. The δext function (input) receives a number of adults from the neighboring cells, a temperature of the day or the values of the population at each stage and sends an activation message. The δint function (internal) is called when the cell receives an activation. It updates the states according to the function development() if the message is receives on the in1 port, initialise the Nvalue if the message is receives on the in2 port. In the other case the values Nadults, Aadults and Afood or changes taking into account the values received by the activation message. The ta function (time advance) defines the time to the next self-activation of the cell 1. <?xml version= 1.0 encoding= UTF-8?> 2. <Model key=27354 Name= cell[40-83] > 3. <Domain>JDEVS</Domain> 4. <InputPort Name= N >this</inputport> 5. <InputPort Name= in1 >this</inputport> 6. <InputPort Name= in2 >this</inputport> 7. <OutputPort Name= N >this</outputport> 8. <OutputPort Name= out >this</outputport> 9. <Variable Name= hots ></Variable> 10. <Variable Name= ripe ></Variable> 11. <Variable Name= Nadults ></Variable> 12. <Variable Name= Aoldadults ></Variable> 13. <Variable Name= Afood ></Variable> 14. <Method Name= cell[40-83] > 15. <ReturnType>public</ReturnType> 17. { super( cell[40-83] );... //export data from the GIS 18. states.setpropertiy( hots.));... //setting the variable 19. states.setpropertiy( Afood, 0 );} 20. </Code> 21. </Method> 22. <Method Name= extfunction > 23. <Parameter>Message m</parameter> 24. <ReturnType>EventVector</ReturnType> according to the number of adults (thus defining the propagation speed). The elapsed time is if there is no adult un the cell and is equal to the speed spread. Once the behavior of the basic cell model is described, the only work that has to be done is in the data preprocessing into the GIS (generation of ASCII raster maps of the initials stages : number of the flies at each stage, host type of the cell, choice of cell size). The 2d simulation panel serves as the experimental frame of the simulation of these phenomena. To interact with the model, it is possible to click on the map during the simulation run and add flies to a specific cell. The model can then be stored and retrieved from the library, it is serialized in the format shown in Figure 3. 25. <Code> 26. { if (m.getport()= in1 27. then development( m.getvalue( ) ); 28. elseif (m.getport()= in2 29. then //change the Nvalues 30. else //change adults informations 31. return new EventVector(); } 32. </Code> 33. </Method> 34. <Method Name= intfunction > 35. <Parameter>Message m</parameter>... //change adults informations 36. </Method> 37. <Method Name= outfunction > 38. <Parameter>Message m</parameter> 39. <ReturnType>EventVector e</returntype> 40. <Code> 41. { e = new EventVector(); 42. e.add(new Event(N, scattering( Nadults, N ), Aadults, Afood ); 43. e.add(new Event(E, scattering( Nadults, E ), Aadults, Afood ); 44. return e; } 45. </Code> 46. </Method> 47. <Method Name= timeavanced > 48.... 49. </Method> 50. </Model> Figure 3 : A generated context-out model for a cell. A neural network model of flies population The approach based on biological model integrate the effects of the climate and other environmental variables. Population evolution and geographical distributions all reflect this process. But, population abundance which is difficult to capture entirely in experiments, represent a principal limitation of the model. The model of flies population uses Feedback-DEVS [Filippi, 2003] for the implementation of an ANN (Artificial Neural Network) in a DEVS framework. Figure 4 presents the model in the JDEVS GUI. The neural network has been trained to provide distribution population at each stage of the life cycle (Neggs, Nlarvae, Npupae, Nadults) find in each part of land. The independent input variables for the models are : The host cultivate, HC, The period of the year, PY, The number of day degrees accumulated above the ripening period of the host, NDA, The percentage of cultivate area of the peach, PCA, 4

The percentage of infested fruit, PIF. Figure 4: A flies population ANN model in JDEVS, with neural network model (A) and quantizer (B). In Figure 4, the box A corresponds to the Feedback- DEVS model that encapsulates the pre-trained neural-network. In this model the variable HC, PY and PCA are parameters. The model is simulating the response in terms of number of medfly at each stage for a patch (population abundance) with a fixed host cultivate a period of the year and the percentage of cultivate area of the peach. This basic model has two input ports, NDA, the number of degrees accumulated, and PIF, the percentage of infested fruit. The number of eggs, larvae, pupae and adults are NE, NL, NP and NA. This model also have a Feedback input port FeedbackN when an external event is received on this port the model triggers the learning function to learn the new population abundance for the value of ports NDA and PIF. Box B corresponds to a basic model of a quantizer, with a parameter TH corresponding to the threshold of the host for medfly activity. This basic model has one input ports, AD the average daily temperature. The output of the quantizer model accumulate the day degrees (ADD) (AD-TH or 0 if AD<TH) from the date of the ripening period of the host and the current period of the year PY. For the simulation of this model, the daily data of average temperature for the patch is loaded as data series in the JDEVS GUI using the simulation panel. The outputs of the simulation are used to change the values of flies population at each stages. send certain quantity medfly at the different stages of the life cycle and at various time, while the cellular model is receipting on a port in2 values of the population at each stage of the life cycle. Then a cell must be chosen for study, and the temperature data for the cell extracted from a GIS. As of the subject of the experiment is be to test the impact of a new land use for the land patch represented by the cell, so the variables HC, PY, NDA, PCA, and PIF are given before the simulation by the user. Next, the modeler must define in a coupling parameter file to couple the two models. The XML parameter file created for the coupling of the flies population and spread model is : <?xml version="1.0" encoding="utf-8"?> <IC><LINK> <PORT model="populationmodel.xml" > Population</PORT> <PORT model="cell[40-83]">in2</port> </LINK></IC> The file specifies an internal coupling between the port Population of the population model with the port in2 of a chosen cell (here the cell at line 40 and row 83). Nevertheless, those links must be duplicated for each cell of the study, so a population model is instantiated for every patch of studied patch. The linkage is done when the cellular spread model is loaded in the cellular panel with the coupling parameter file. The simulation being finally launched by the simulation panel of the GUI (Figure 2 and 5). This model is actually under test by the environmental and agriculture agency of Corsica. Coupling the flies population model with the cellular spread model Although the spread model is a cellular model, and the flies population model is a Neural Network model, once integrated in the framework they both share the same port based interfaces. Thus it is possible to couple these models and simulate the impact of a new land use for a patch of land. Before performing the coupling, the modeler has to verify that the data that will pass from the a model corresponds with the data required by the model it will be connected to. In this experiment the data are compatible, flies population model will Figure 5 : Flies propagation simulation. Results The simulations has been performed in a zone of 100 Km² divided in 178 cells (16 * 13). Figure 5 presents resulted maps of the simulation at different periods of a year. 5

Observation has been made of the quantity of infested fruits for three of those patches of land, one of peaches, one of pomelos, one of apples. The following table gives the results observed and simulated. Peaches Pomelos Apples Simulation 85.3% 91.4% 24.8% Observed 60% 80% 20 We can see from this table that the models gives an overestimation of the infestation. Nevertheless, is the observation is only on tree patches and the model is not well calibrated. This is not the purpose of this paper to discuss the actual results of the model but more the feasibility of such model in JDEVS. Limitations Thanks to the use of JDEVS and DEVS methodology it is possible to couple two models that uses different modeling paradigms in a single simulation frame without a strong effort of reengineering. Nevertheless, when it comes to the modeling of spatially distributed systems, it still exists strong limitations of using this toolkit. From a modeling perspective, it is not possible to specify a model that will share common spatial attributes with another in the forms of layers. The multi-layered representation is used in GIS to represent the data, thus it is probably the most convenient representation for a modeler to conceptualize the behavior of a system. In the bug propagation model, it is the same cell that simulates the growth of fruits and the behavior of the bugs. It is obvious that the two shall be separated, but the only possibility with the current toolkit and methodology will be to link a cell of a fruit model to a cell of a bug model one by one. From a simulation perspective, this limitation leads to the fact that it is only possible to simulate one layer at a time. CONCLUSION This paper has presented a bugs propagation model implemented in JDEVS. This multi-modeling example shows how models can be coupled together even if they are using different paradigms thanks to the use of a formalism : DEVS. The models enable to study the spread of fruit-flies with a cellular models driven by a neural network population model. Despite the model is still limited because of the poor geographic coupling possibilities of the toolkit, we are now working on the methodologies and software to facilitates this coupling and allow the study and development of spatially distributed systems. REFERENCES [Bernardi et al. 2001] Bernardi, F. and Filippi, J-B. and Santucci, J.F. XML Object-Oriented Models Libraries with Web-Based Access Capacities, conference ICSSEA, Genie logiciel et ingénierie de systèmes [Filippi, 2003] J.B. Filippi, PhD Thesis, Université de Corse, 2003. [Fishwick, 1995] Fishwick, P.A. Simulation Model Design and Execution: Building Digital Worlds, Prentice Hall, 1995 [Gamma et al., 2000] Gamma, E. and Helm, R. and Johnson, R. and Vlissides, J. Design Patterns : Elements of Reusable Object Oriented Software, Addison- Wesley [Hill, 1996] Hill, D.R.C. Objetct-Oriented Analysis and Simulation, Addison-Wesley Longmann, 1996 [Orën, 1991] Orën, T I. Dynamic Templates and Semantic Rules for Advisors and Certifiers, Knownledge Based Simulation: Methodology and application. Pp 53-76, 1991. [Schattenberg and Uhrmacher, 2001] Schattenberg, B. and Uhrmacher, A.M, Planning Agents in James, Conference IEEE transacions on modeling and computer simulation, 2001, v. 89, n. 2 pp 158-173. [Vera et al., 2002] T. Vera, R. Rodriguez, DF. Segura, JL Cladera, and RW. Sutherst. Potential Geographical Distribution of the Mediterranean Fruit Fly, Ceratitis capitata (Diptera: Tephritidae), with Emphasis on Argentina and Australia. Environmental Entomology, Vol. 31(6):1009-1032. 2002. [Wainer and Giambiasi, 2001] Wainer, G.A. and Giambiasi, N. Application of the Cell-DEVS paradigm for cell spaces modelling and simulation, Simulation, January 2001. [Zeigler, 2000] Zeigler, B.P. Theory of Modeling and Simulation, Academic Press, 2000. 6