Progress 09/01/10 to 08/31/13
Outputs Target Audience: At a broader level: *Researchers and students in several disciplines that study the behavior of dynamic systems over space and time. *Researchers and students in several life sciences disciplines with an interest of spatiotemporal behavior. *Researchers and students studying the spread of invasive species as they interact with their environment. *Technical staff at the Federal government dealing with the monitoring, regulation and combat of invasive species. At a more local or institutional level: *Faculty members, researchers and students of the Departments of Biology, Mathematical Sciences, and Mechanical Engineering of the University of Puerto Rico with an interest in mathematical modeling of dynamic systems over space * Faculty members, researchers and students working in the fields of epidemiology, phytopathology, entomology, and weed science. * Technical staff and policymaking individuals in the Government of Puerto Rico dealing with the monitoring, regulation and combat of invasive species. * Students of the College of Agricultural Sciences at the University of Puerto Rico. * Nonprofit organizations interested in environmental issues. * Farmers with an interest on the impact of invasive species on their productive activities. Changes/Problems: * Less emphasis was given to Melaleuca quinquenervia because of insufficient data points to estimate the suitability map. * Long distance dispersion parameters for Mimosa pigra had to be estimated using data found in the literature. * We stopped using MDiG after the first year and began developing our own dispersal modeling environment in C++ but with a mind to making a more generaluse framework. What opportunities for training and professional development has the project provided? In 2013, graduate students taking the course on Mathematical Economics at the Department of Agricultural Economics and Rural Sociology were exposed to a module on the control of invasive species, where they were introduced to three different bioeconomic models of invasive species control: one where space is not considered, one with a onedimensional space, and one with a twodimensional space. *Mentoring2011. . Yetsabel Auccaille and Iván Henríquez, graduate students majoring in statistics and mathematics, respectively, were hired as RAs and are mentored by the project PI. *Mentoring2012. . Yetsabel Auccaille and Iván Henríquez, graduate students majoring in statistics and mathematics, respectively, were hired as RAs and are mentored by the project PI. *Mentoring2013. Yetsabel Auccaille and Iván Henríquez, graduate students majoring in agricultural economics and mathematics, respectively, were hired as RAs and are mentored by the project PI. The former is working on her thesis/dissertation with project data. How have the results been disseminated to communities of interest? Much of the dissemination to the broader scientific community is expected to be made through peerreviewed articles that are yet to be submitted. The local (Puerto Rico) scientific community was served by through oral or poster presentations at conferences and other gatherings (see listing below). The local modeling community was served with a oneonone approach (see section on Networks). **Dissemination2011. *For each abstract entry in the Abstracts section there corresponds here either an oral presentation or a poster here in the dissemination section. *Barragán, M.J. 2011. Oral presentation on the modeling of the spread of invasive species, made on 07/21/11 at UMSA, Bolivia. *Barragán, M.J.; Robles, W.; Camacho, W.; and Auccaille, Y. 2010. Modeling and controlling the spread of invasive species over heterogeneous landscapes. Oral presentation at the Eighth National Meeting on Remote Sensing and Geographical Information Systems (PRYSIG), Mayagüez, Puerto Rico. *Barragán, M.J. and Henríquez, I. 2011. Dispersal patterns of an invasive species with the use of MDiG: Exploring the sensibility of simulations to different parameter values in the case of Mimosa pigra in Puerto Rico. Oral presentation at SIDIM XXVI held in Humacao, Puerto Rico. *Barragán, M.J.; Robles, W.; Camacho, W.; and Auccaille, Y. 2011. A statistical suitability map for Mimosa pigra in Puerto Rico: Preliminary results based on presence/absence, temperature and precipitation data. Poster presented at SIDIM XXVI held at Humacao, Puerto Rico. *Barragán, M.J.; and Henríquez, I. 2011. Using sensibility analysis to optimize the calibration of mathematical models: An application to the study of the spread of Mimosa pigra in Puerto Rico. Oral presentation at the Anual SOPCA Scientific Meeting. Ponce, Puerto Rico. * We requested UPR a database on their server. We also requested that they download drupal. **Dissemination2012. * We created a basic website that is not yet open to the general public and started experimenting with format alternatives and content. *Barragán, M.J.; Robles, W.; Henríquez, I.; Auccaille, Y.; Alvarado, A. 2012 (May 23). Modeling the spread of invasive species over heterogeneous landscapes: Remarks on some modeling issues. Oral presentation made at the 48th Annual Meeting of the Caribbean Food Crops Society held at the Barceló Maya Hotel, Quintana Roo, Mexico. *Barragán, M.J.; Henríquez, I.; Alvarado, A.; Robles, W. 2012 (March 23). Using a mathematical model of the spread of Mimosa pigra in Puerto Rico to estimate costeffectiveness of alternative control measures. Oral presentation at the XXVII SIDIM conference held at Mayagüez, Puerto Rico. *Barragán, M.J.; Auccaille, Y.; Robles, W. 2012 (March 23) Climate change implications on the suitability for Mimosa pigra in Puerto Rico. Poster presentation made at the XXVII SIDIM conference held at Mayagüez, Puerto Rico *Barragán, M.J.; Henríquez, I. 2012. Using sensibility analysis to optimize the calibration of matematical models: An application to the study of the spread of Mimosa pigra in Puerto Rico. Oral presentation made at the Ninth National Meeting on Remote Sensing and Geographical Information Systems (PRYSIG), Mayagüez, Puerto Rico. *Barragán, M.J.; Robles, W.; Auccaille, Y.; and Camacho, W. 2012. Climate change connotations of a suitability map for Mimosa pigra in Puerto Rico. Oral presentation made at the Ninth National Meeting on Remote Sensing and Geographical Information Systems (PRYSIG), held in Mayagüez, Puerto Rico. *Henríquez, I.; Barragán, J. 2012 (March 14) GRASS as an Open Source GIS alternative: Experiences and lessons from its use in a study of invasive plant species in Puerto Rico. Oral presentation made at the Simposio de GIS y Percepción Remota organized by the Escuela Graduada de Planificación of the UPR and held at San Juan, Puerto Rico. *Auccaille, Y.; Barragán, M.J. 2012 (March 14) Spatial economic models that can be implemented in a cellular automata framework. Oral presentation made at the Simposio de GIS y Percepción Remota organized by the Escuela Graduada de Planificación of the UPR and held at San Juan, Puerto Rico. *Barragán, M.J.; Robles, W.; Auccaille, Y.; Alvarado, D. 2012 (March 23). A suitability map for Mimosa pigra in Puerto Rico using an improved logistic regression approach that takes into account spatial autocorrelation. Poster presented at the First SACNAS Regional Meeting in Puerto Rico, Mayagüez, Puerto Rico. **Dissemination2013. * Barragán, J.; Robles, W.; Henríquez, I.; Auccaille, Y. "Mathematical modeling of natural resources and the environment: A selection of recent studies undertaken in at the PRAEE”. Poster presented in the “Reunión de Empresa Medio Ambiente y Recursos Naturales” held on March 5, 2013 at the PR Agricultural Experiment Station at Isabela. * Barragán, J.; Robles, W.; Henríquez, I.; Auccaille, Y. "Mathematical modeling of natural resources and the environment: A selection of recent studies undertaken in at the PRAEE”. Poster presented during the “Semana de Especies Invasivas” in an activity held on March 7th, 2013 in the lobby the Piñero Building. * Henríquez, I.; Auccaille, Y.; Barragán, M.J.; Robles, W. 2013. Optimal temporalspatial control of an invasive species over a heterogeneous landscape: Exploratory exercises for the case of Mimosa pigra in Puerto Rico. Oral presentation by Mrs. Auccuaille, Y. on the Tenth National Meeting on Remote Sensing and Geographical Information Systems (PRYSIC), Mayagüez, Puerto Rico. [A video of the oral presentation will be posted online on the PRYSIG] * Henríquez, I.; Barragán, M.J. 2013. A multispecies landscape model with dispersal, succession, competition and disturbance functions: Exploring determinants of succession paths and coexistence. Oral presentation by Mr. Henríquez, I. on the Tenth National Meeting on Remote Sensing and Geographical Information Systems (PRYSIC), Mayagüez, Puerto Rico[A video of the oral presentation will be posted online on the PRYSIG] * Barragán, M.J.; Henríquez, I.; Auccaille, Y.; Robles, W. 2013. A spatially explicit framework for modeling plant communities at the landscape level. Oral presentation at the Annual SOPCA Scientific Meeting, held in Hormigueros, Puerto Rico on November 15, 2013. *Seminars2011. Presenter: Barragán, J. Topic: Modeling the spread of invasive species over heterogeneous landscapes. Presented at the Department of Biology, UMSA, La Paz, Bolivia. Date: 07/14/11. *Seminars2013. Presenter: Auccaille, Y. Topic: The economics of the spatial control of invasive species. [Status: Accepted and scheduled. To be presented at the Applied Economics Seminar, Department of Agricultural Economics and Rural Sociology, UPR, Mayagüez, PR. Date: 12/04/13 ]. *Exhibitions2013.Two posters from our previous scientific presentations and a movie about promoting the Department of Agricultural Economics at the UPR with a brief section highlighting our bioeconomic modeling efforts through NIFA projects TSTAR132 and McIntire Stennis019. The exhibition was part of the Open House activities of the UPRM held on November1, 2013. *Exhibitions2014.Title: Mathematical modeling of invasive species and tropical forests. Place: Front entrance of the UPR General Library at Mayagüez. [Status: Accepted by library officials and scheduled for a monthlong term during the period 02/01/2014 to 02/28/2014. This exposition includes a movie and several posters, all of which have already been produced.] What do you plan to do during the next reporting period to accomplish the goals?
Nothing Reported
Impacts What was accomplished under these goals?
Major activities completed * A statistical suitability map was estimated for M pigra taking into account spatial correlation. * We developed a cellular automata (CA) environment and used it to reproduce a simplified dispersal version of MDiG that is decoupled from GRASS. * The suitability map was used to include a survival module within the CA environment. * We simulated several dispersal scenarios. * We optimized spatiotemporal control using a mixedinteger programming (MIP) framework. * We presented our results in several scientific forums, and on oneonone interviews with key researchers. We also organized outreach and educational activities. * We used our models as a point of departure in other research projects. Specific objectives met 1. We constructed suitability and survival probability maps. 2. We modeled invasive species (IS) spread over time under alternative scenarios, among which are alternative control programs. 3. We improved public awareness mainly at the Island level. We will reach a broader audience next year when we publish our journal articles and when we include our research results and our outreach material on the internet along with our results from our McIntireStennis project on the modeling of forest succession. Significant results achieved, including major findings, developments, or conclusions (both positive and negative) *In our simulations, the long distance dispersal parameters of M pigra are key determinants of its high spreading rate. In a landscape such as PR’s, with a central mountain range and several small clearly disconnected watersheds, the bristles in their seedpods that adhere easily to clothing and fur, together with their high germination rate, may prove crucial to disperse seed from one watershed to another, and thus to achieving high long distance dispersal rates. The opposite is true of Melaleuca. Ineffective longdistance dispersal mechanisms and low germination rates may explain their low spreading rate in PR. This we observe in our simulations in the form of few upstream dispersal events. However, our model predicts greater Melaleuca population downstream than actually observed, which points to possible environmental factors also being important determinants in the spread of this invasive species in PR. * The dispersal modules developed turned out to be easily expandable (several species). They can be added to other parallel environmental and biological processes. The gridbased environment in which the dispersal modules were developed seems like a natural and easy framework to model more complex environmental and ecological systems. Key outcomes or other accomplishements realized **Change in knowledge2011 *Honing of the team’s modeling knowledge and skills. Greater knowledge on modeling using CA, stochastic, PDEs, and spatial analysis methods was acquired. We learned the use of mathematical modeling software such as MDiG, GIS software such as GRASS, statistical software such as R, and plant structure analysis software such as OpenAlea. *We found these methods are in high demand in several applied fields of study and the skills in short supply or disconnected from potential fields of applications. *Field trips to sample the presence/absence showed us, with one exception, that M quinquenervia was not actively invading the ecosystems. Not enough data points were found to make significant statistical analysis for this species. M pigra, on the other hand was found to be aggressively invading several ecosystems. *First regression analyses showed that max temp is an important variable in determining the survival probability of M pigra. *The predicted survival probabilities for all the Island allowed us to build a suitability map with geographic regions where M pigra is most likely to survive. *The statisticalbased suitability map predicted well the presence of M pigra. In contrast, the indexbased suitability map proved to be a poor predictor of the IS presence. *The sensitivity analysis with MDiG revealed that longdistance dispersal parameters are much more influential on model results than shortdistance diffusion parameters. *We identified some limitations in MDiG. *Explorations with OpenAlea software made us visualize the potential that the analysis of plant structuralfunctional models has for the modeling of spread of plants over space. **Change in knowledge2012 *The findings of the suitability map with a spatial logistic regression gave similar coefficients that those obtained with a nonspatial logistic regression. *Programming the dispersal modules in our CA framework involved coding several GIS functionalities into the environment, but allowed faster simulations than those obtained using MDiG. *The surface water flow model showed how useful and versatile CA can be in modeling complex dynamic systems. The hydrologic model in particular has a lot of potential for modeling other environmental and natural resource phenomena such as waterbased contamination, erosion, and the sequestration of greenhouse gases. *A major problem of the CAbased hydrologic model is the occurrence of “sink spots” in the geography which act as “lake beds” and impede water flow. The actual geography does not have these closed depressions. They are the product of coarse DEMs. *Simulating the control seed dispersal proved not to be a straightforward task. **Change in knowledge2013. * The efforts to model forest ecosystems under the auspices of project McIntireStennis019 enabled us to confirm our initial belief that the dispersal module developed with our TSTAR132 project could be used for other species, that the dispersal of many species could be modeled simultaneously, and that this could be easily done as part of a more ambitious model aimed at capturing the behavior of more complex systems (the forest model includes, for example, succession, light competition, and disturbance processes). * Not able to model spatiotemporal control of IS using DP. MIP proved more practical and feasible, but only for very coarse grid. In addition, the dispersal mechanism using mixed integer programming emulates CA dispersal processes, but cannot reproduce longdistance dispersal. **Changes in actions2011. *As a result of importance of the modeling methods and skills acquired during the first year, we developed stepbystep tutorials of the software and procedures used to help us share this knowhow. *Due to limitations found in MDiG we decided to work on a library of our own that has greater independence from GRASS and is more efficient. *As a result of our explorations with OpenAlea, we decided to measure, digitalize and analyze spatial parameters of the structure of M pigra. **Changes in actions2012. *Revisit seed dispersal literature in greater detail. *Move away from MDiG and develop own IS CA framework loosely coupled to ArcGIS. *Use our hydrologic model as basis for future proposals on bioeconomic models. *We dealt with “sink holes” on an individual level, modifying DEMs so as to flatten them out. *Review the literature in search of productive ways to model the control of seed dispersal. **Changes in actions2013. *For the spatiotemporal part of the project we chose MIP over DP. * Further gridbased modeling efforts to include processes at the landscapelevel. Candidate processes include (1) plantlightatmosphere processes, (2) plantsoil processes, and (3) water related processes e.g., sediment and particle transport, leaching. * Use the modeling framework that we developed to study a problem that has become a highpriority area for the incoming government of PR: the control of citrus greening.
Publications
 Type:
Journal Articles
Status:
Other
Year Published:
2014
Citation:
Barrag�n, M.J.; Robles, W.; Auccaille, Y.; and Henr�quez, I.. A statistical suitability map for Mimosa pigra in Puerto Rico. Journal of Agriculture of the University of Puerto Rico.
 Type:
Journal Articles
Status:
Other
Year Published:
2014
Citation:
Barrag�n, M.J.; Henr�quez, I.; Auccaille, Y.; and Robles, W. Modeling the spread of invasive species over heterogeneous landscapes: An application to the case of Mimosa pigra in Puerto Rico. Journal of Agriculture of the University of Puerto Rico.
 Type:
Journal Articles
Status:
Other
Year Published:
2014
Citation:
Enr�quez, A.; Barrag�n, M.J.; Henr�quez, I. A gridbased model of superficial water runoff as a basis for ecological modeling and simulations. Journal of Agriculture of the University of Puerto Rico.
 Type:
Journal Articles
Status:
Other
Year Published:
2014
Citation:
Aucaille, Y.; Henr�quez, I.; Barrag�n, M.J.; Robles, W. The spatiotemporal control of invasive species: A mixed integer programming approach to the case of Mimosa pigra in Puerto Rico. Journal of Agriculture of the University of Puerto Rico.
 Type:
Journal Articles
Status:
Other
Year Published:
2014
Citation:
Henr�quez, I.; Barrag�n, M.J. A gridbased spatiotemporal model of forest disturbance and succession. Journal of Agriculture of the University of Puerto Rico.
 Type:
Other
Status:
Other
Year Published:
2011
Citation:
Barrag�n, M.J.; and Henr�quez, I. 2011. A basic GRASS tutorial. Working Paper 201103. Department of Agricultural Economics and Rural Sociology, UPRRUM. Mayag�ez, Puerto Rico.
 Type:
Other
Status:
Other
Year Published:
2011
Citation:
Barrag�n, M.J.; and Henr�quez, I. 2011. A basic MDiG tutorial. Working Paper 201104. Department of Agricultural Economics and Rural Sociology, UPRRUM. Mayag�ez, Puerto Rico.
 Type:
Other
Status:
Other
Year Published:
2011
Citation:
Barrag�n, M.J.; Camacho, W.; and Auccaille, Y. 2011. Handling and statistical analysis of geographically indexed data: A stepbystep example from Puerto Rico using ArcGIS and R. Working Paper 201105. Department of Agricultural Economics and Rural Sociology, UPRRUM. Mayag�ez, Puerto Rico.
 Type:
Conference Papers and Presentations
Status:
Published
Year Published:
2011
Citation:
Barrag�n, M.J. and Henr�quez, I. 2011. Dispersal patterns of an invasive species with the use of MDiG: Exploring the sensibility of simulations to different parameter values in the case of Mimosa pigra in Puerto Rico. SIDIM XXVI Abstract Book. Humacao, Puerto Rico. (Page 16). [http://sidim.uprh.edu/sidim2011/es/Libro_SIDIM_XXVI_v4.pdf].
 Type:
Conference Papers and Presentations
Status:
Published
Year Published:
2011
Citation:
Barrag�n, M.J.; Robles, W.; Camacho, W.; and Auccaille, Y. 2011. A statistical suitability map for Mimosa pigra in Puerto Rico: Preliminary results based on presence/absence, temperature and precipitation data. SIDIM XXVI Abstract Book. Humacao, Puerto Rico. (Page 27). [http://sidim.uprh.edu/sidim2011/es/Libro_SIDIM_XXVI_v4.pdf].
 Type:
Other
Status:
Other
Year Published:
2011
Citation:
Barrag�n, M.J.; and Henr�quez, I. 2011. A suitability map for Mimosa pigra in Puerto Rico based on a subjective index: Results and tutorial using ArcGIS and GRASS. Working Paper 201106. Department of Agricultural Economics and Rural Sociology, UPRRUM. Mayag�ez, Puerto Rico.
 Type:
Other
Status:
Other
Year Published:
2011
Citation:
Barrag�n, M.J.; and Henr�quez, I. 2011. Digitizing and analyzing plant structure: An OpenAlea tutorial and results of a case study with a Garcinia madruno seedling Working Paper 201107. Department of Agricultural Economics and Rural Sociology, UPRRUM. Mayag�ez, Puerto Rico.
 Type:
Theses/Dissertations
Status:
Other
Year Published:
2014
Citation:
Yetsabel, A. Optimal spatiotemporal control of an invasive species A mixedinteger programming framework applied to the case of Mimosa pigra in Puerto Rico. M.S. Dissertation.
 Type:
Conference Papers and Presentations
Status:
Published
Year Published:
2011
Citation:
Barrag�n, M.J.; Robles, W.; Camacho, W.; and Auccaille, Y. 2010. Modeling and controlling the spread of invasive species over heterogeneous landscapes. Proceedings of the Eighth National Meeting on Remote Sensing and Geographical Information Systems (PRYSIG), Mayag�ez, Puerto Rico. [http://cohemis.uprm.edu/prysig/pdfs/res_jbarragan10.pdf].
 Type:
Conference Papers and Presentations
Status:
Published
Year Published:
2011
Citation:
Barrag�n, M.J.; and Henr�quez, I. 2011. Using sensibility analysis to optimize the calibration of mathematical models: An application to the study of the spread of Mimosa pigra in Puerto Rico. Proceedings of the Anual SOPCA Scientific Meeting. Ponce, Puerto Rico.
 Type:
Conference Papers and Presentations
Status:
Published
Year Published:
2012
Citation:
Barrag�n, M.J.; Robles, W.; Henr�quez, I.; Auccaille, Y.; Alvarado, A. 2012 (May 23). Modeling the spread of invasive species over heterogeneous landscapes: Remarks on some modeling issues. Presentation made at the 48th Annual Meeting of the Caribbean Food Crops Society held at the Barcel� Maya Hotel, Quintana Roo, M�xico. (Pages 4546).
 Type:
Conference Papers and Presentations
Status:
Published
Year Published:
2012
Citation:
Barrag�n, M.J.; Henr�quez, I.; Alvarado, A.; Robles, W. 2012 (March 23). Using a mathematical model of the spread of Mimosa pigra in Puerto Rico to estimate costeffectiveness of alternative control measures. SIDIM XXVII Abstract Book. Presentation made at the XXVII SIDIM conference held at Mayag�ez, Puerto Rico. (Pages 1213). [http://www.sidim.pr/programa.pdf].
 Type:
Conference Papers and Presentations
Status:
Published
Year Published:
2012
Citation:
Barrag�n, M.J.; Auccaille, Y.; Robles, W. 2012 (March 23) Climate change implications on the suitability for Mimosa pigra in Puerto Rico. SIDIM XXVII Abstract Book. Presentation made at the XXVII SIDIM conference held at Mayag�ez, Puerto Rico. (Page 27). [http://www.sidim.pr/programa.pdf].
 Type:
Conference Papers and Presentations
Status:
Published
Year Published:
2012
Citation:
Barrag�n, M.J.; Henr�quez, I. 2012. Using sensibility analysis to optimize the calibration of matematical models: An application to the study of the spread of Mimosa pigra in Puerto Rico. Oral presentation. Proceedings of the Ninth National Meeting on Remote Sensing and Geographical Information Systems (PRYSIG), Mayag�ez, Puerto Rico. [Abstract online: http://cohemis.uprm.edu/prysig/pdfs/res_ihenriquez11.pdf] [Slides: http://cohemis.uprm.edu/prysig/pdfs/pres_ihenriquez11.pdf]
 Type:
Conference Papers and Presentations
Status:
Published
Year Published:
2012
Citation:
Barrag�n, M.J.; Robles, W.; Auccaille, Y.; and Camacho, W. 2012. Climate change connotations of a suitability map for Mimosa pigra in Puerto Rico. Oral presentation. Proceedings of the Ninth National Meeting on Remote Sensing and Geographical Information Systems (PRYSIG), Mayag�ez, Puerto Rico. [Abstract online: http://cohemis.uprm.edu/prysig/pdfs/res_yauccaille11.pdf] [Slides: http://cohemis.uprm.edu/prysig/pdfs/pres_yauccaile11.pdf]
 Type:
Conference Papers and Presentations
Status:
Published
Year Published:
2013
Citation:
Henr�quez, I.; Auccaille, Y.; Barrag�n, M.J.; Robles, W. 2013. Optimal temporalspatial control of an invasive species over a heterogeneous landscape: Exploratory exercises for the case of Mimosa pigra in Puerto Rico. Proceedings of the Tenth National Meeting on Remote Sensing and Geographical Information Systems (PRYSIC), Mayag�ez, Puerto Rico. [Abstract online: http://cohemis.uprm.edu/prysig/pdfs/res_yauccaille13.pdf]
 Type:
Conference Papers and Presentations
Status:
Published
Year Published:
2013
Citation:
Henr�quez, I.; Barrag�n, M.J. 2013. A multispecies landscape model with dispersal, succession, competition and disturbance functions: Exploring determinants of succession paths and coexistence. Proceedings of the Tenth National Meeting on Remote Sensing and Geographical Information Systems (PRYSIC), Mayag�ez, Puerto Rico. [Abstract online: http://cohemis.uprm.edu/prysig/pdfs/res_ihenriquez13.pdf]
 Type:
Conference Papers and Presentations
Status:
Published
Year Published:
2013
Citation:
Barrag�n, M.J.; Henr�quez, I.; Auccaille, Y.; Robles, W. 2013. A spatially explicit framework for modeling plant communities at the landscape level. Proceedings of the Annual SOPCA Scientific Meeting, Hormigueros, Puerto Rico. November 15.

Progress 09/01/11 to 08/31/12
Outputs OUTPUTS: ***Outputs **Activities: *Research conducted. Statistical suitability maps were estimated using logistic models that take into account special correlation in the data. The foundations of a cellular automata hydrologic model were programmed. This model was then used to construct the foundations of a model of seed dispersion through water (hydrochory). Some basic management scenarios were constructed. *Mentoring. Yetsabel Auccaille and Ivan Henriquez, graduate students majoring in statistics and mathematics, respectively, were hired as RAs and are mentored by the project PI. **Products: *Video. Several short videos (less than a minute) of cellular automata output using short and long distance dispersal modules, with alternative scenario managements, as well as a short video of the hydrochory model. *Networks. An explicit effort has been continued to be made to meet and interact with other faculty members at the UPR at Mayaguez, and sometimes abroad, who use similar mathematical tools or share an interest in the applications of our research project. *Software. We developed a cellular automata environment. We used this environment to reproduce a simplified version of MDiG that is loosely coupled to GRASS. We also used the cellular automata environment to build a program to simulate the surface flow of water in a watershed, and then we modified it to build a hydrochory model. ***Dissemination. Presentations include those listed in the Abstracts section below, as well as the following presentations: *Henriquez, I.; Barragan, J. 2012 (March 14) GRASS as an Open Source GIS alternative: Experiences and lessons from its use in a study of invasive plant species in Puerto Rico. Oral presentation made at the GIS and Remote Sensing Symposium organized by the Graduate School of Planning of the UPR and held in San Juan, Puerto Rico. *Auccaille, Y.; Barragan, M.J., March 14, 2012. Spatial economic models that can be implemented in a cellular automata framework. Oral presentation at the GIS and Remote Sensing Symposium by the Graduate School of Planning of the UPR and held in San Juan, Puerto Rico. *Barragan, M.J.; Robles, W.; Auccaille, Y.; Alvarado, D., 2012 (March 23). A suitability map for Mimosa pigra in Puerto Rico using an improved logistic regression approach that takes into account spatial autocorrelation. Poster presented at the First SACNAS Regional Meeting in Puerto Rico, Mayaguez. PARTICIPANTS: Barragan, M.J., Principal Investigator. In charge of the project at large. Robles, W., CoPI and weed science specialist. Yetsabel, A., Research Assistant working with secondarysource data collection, data manipulation in ArcGIS, and statistical analyses in R. Henriquez, I., Research Assistant working with data manipulation in GRASS, mathematical modeling in MDiG and with pdes, and data manipulation and visualization in OpenAlea. Gonzales, N., Research Assistant helping in the sampling presence/absence of invasive species under study, and implementing field experiments. Castillo, P., collaborating in several issues dealing with the design of the general framework needed to build a new cellular automata environment. TARGET AUDIENCES: *** At a broader level: Researchers and students in several disciplines that study the behavior of dynamic systems over space and time. Researchers and students in several lifescience disciplines with an interest in spatiotemporal behavior. Researchers and students studying the spread of invasive species as they interact with their environment. Technical staff of the federal government dealing with the monitoring, regulation and combat of invasive species. ***At a more local or institutional level: Faculty members, researchers and students of the Departments of Biology, Mathematical Sciences, and Mechanical Engineering of the University of Puerto Rico with an interest in mathematical modeling of dynamic systems over space Faculty members, researchers and students working in the fields of epidemiology, phytopathology, entomology, and weed science. Technical staff and policymaking individuals in the Government of Puerto Rico dealing with the monitoring, regulation and combat of invasive species. Students of the College of Agricultural Sciences at the University of Puerto Rico. Nonprofit organizations interested in environmental issues. Farmers with an interest in the impact of invasive species on their productive activities. PROJECT MODIFICATIONS: Because the data needed to estimate and calibrate longdistance dispersal of Mimosa pigra are unavailable, we decided to model instead some of the most important processes involved in longdistance dispersal. This is the case of hydrochory, or longdistance dispersal through water. The data needed to estimate and calibrate these models is more likely to be obtained either from the literature or from field measurements. MDiG will not be used in further simulations. From now on, we will continue to develop our own dispersal modeling environment.
Impacts ***Change in knowledge. *The findings of the suitability map with a spatial logistic regression gave coefficients similar to those obtained with a nonspatial logistic regression. *Programming the dispersal modules in our cellular automata framework involved coding several GIS functionalities into the environment, but allowed faster simulations than those obtained by using MDiG. *The surface water flow model showed how useful and versatile cellular automata can be in modeling complex dynamic systems. The hydrologic model in particular has a lot of potential for modeling other environmental and natural resource phenomena, such as waterbased contamination, erosion, and the sequestration of greenhouse gases. *A major problem of the cellular automatabased hydrologic model is the occurrence of "sink spots" in the geography which act as "lake beds" and impede water flow. The actual geography does not have these closed depressions. They are the product of coarse DEMs. *Simulating the control seed dispersal proved not to be a straightforward task. ***Changes in actions. *Because of the importance of spatial statistics in our future work on seed dispersal, we decided to revisit the topic, this time reviewing the literature in greater detail. *We decided to move away from the use of MDiG and instead further develop our own seed dispersal cellular automata framework loosely coupled to ArcGIS. Again, this measure was taken because MDiG was too slow with large simulation exercises, particularly those involving Monte Carlo simulations. *We decided to use our hydrologic model as a basis for a proposal to be submitted soon regarding carbon and nitrogenrelated greenhouse gases and organic agriculture. To this end, we would like to further explore how the model would have to be built if we allow for water movement in the soil. *So far we have dealt with "sink holes" on an individual level, modifying DEMs so as to flatten them out. Because they tend to be frequent, we would like to explore ways to solve this problem automatically. *We will review the literature in search of productive ways to model the control of seed dispersal.
Publications
 ***Abstracts: *Barragan, M.J.; Robles, W.; Henriquez, I.; Auccaille, Y.; Alvarado, A., 2012 (May 23). Modeling the spread of invasive species over heterogeneous landscapes: Remarks on some modeling issues. Presentation made at the 48th Annual Meeting of the Caribbean Food Crops Society held at the Barcelo Maya Hotel, Quintana Roo, Mexico. (Pages 4546).
 *Barragan, M.J.; Henriquez, I.; Alvarado, A.; Robles, W., 2012 (March 23). Using a mathematical model of the spread of Mimosa pigra in Puerto Rico to estimate costeffectiveness of alternative control measures. SIDIM XXVII Abstract Book. Presentation made at the XXVII SIDIM conference held at Mayaguez, Puerto Rico. (Pages 1213). [http://www.sidim.pr/programa.pdf]
 *Barragan, M.J.; Auccaille, Y.; Robles, W., 2012 (March 23) Climate change implications on the suitability for Mimosa pigra in Puerto Rico. SIDIM XXVII Abstract Book. Presentation made at the XXVII SIDIM conference held at Mayaguez, Puerto Rico. (Page 27). [http://www.sidim.pr/programa.pdf]
 *Barragan, M.J.; Henriquez, I., 2011. Using sensibility analysis to optimize the calibration of matematical models: An application to the study of the spread of Mimosa pigra in Puerto Rico. Oral presentation. Proceedings of the Ninth National Meeting on Remote Sensing and Geographical Information Systems (PRYSIG), Mayaguez, Puerto Rico. (In Press). [Abstract online: http://cohemis.uprm.edu/prysig/pdfs/res_ihenriquez11.pdf] [Slides: http://cohemis.uprm.edu/prysig/pdfs/pres_ihenriquez11.pdf]
 *Barragan, M.J.; Robles, W.; Auccaille, Y.; and Camacho, W., 2011. Climate change connotations of a suitability map for Mimosa pigra in Puerto Rico. Oral presentation. Proceedings of the Ninth National Meeting on Remote Sensing and Geographical Information Systems (PRYSIG), Mayaguez, Puerto Rico. (In Press). [Abstract online: http://cohemis.uprm.edu/prysig/pdfs/res_yauccaille11.pdf] [Slides: http://cohemis.uprm.edu/prysig/pdfs/pres_yauccaile11.pdf]

Progress 09/01/10 to 08/31/11
Outputs OUTPUTS: ***Outputs **Activities *Research conducted. A random sample of presence/absence data was collected. Databases of several georeferenced environmental and biotic variables were obtained. GRASS and MDiG were installed and linked to one another. Indexbased suitability maps were made by using ArcGIS and GRASS software. Statistical suitability maps were estimated by using ArcGIS and R. The suitability map was imported into GRASS. A computer code was written to facilitate MDiG simulations and their analysis after running Monte Carlo experiments. Elasticities were then computed to determine which parameters, when perturbed, had the greatest impact on the results of the simulation. In addition to the MDiG cellular automatabased stochastic simulation model, we worked on a partial differential equations model of the spread of Mimosa pigra. Finally, as part of a marginal but important effort to explore different venues to the analysis of spatiotemporal dynamic systems, we have collected, digitized, and analyzed the geometric and topological data of a plant using OpenAlea. *Mentoring. Yetsabel Auccaille and Ivan Henriquez, graduate students majoring in statistics and mathematics, respectively, were hired as RAs and are mentored by the project PI. **Events *Seminars. On invasive species modeling on 07/14/11 at UMSA, Bolivia. **Products *Video. 1 min video of pde model output and 1min video of MDiG model outpout for Mimosa pigra, and 15min video of the oral presentation at the Eighth PRYSIG meeting. *Data. Presence/absence data of Mimosa pigra and Melaleuca quinquenervia were generated by randomly sampling different sites in PR. *Databases. A database of georeferenced predicted survival probabilities for Mimosa pigra in PR. *Networks. An explicit effort has been made to meet and interact with other faculty members at the UPR in Mayaguez, personnel who use similar mathematical tools or share an interest in the applications of our research project: Drs. Castillo, Stainberg, Santana, and Rios of the Dpt. of Math. Scs.; Drs. Gutierrez and Leonardi of the Dept. of Mech. Eng.; and Dr. Kolterman of Biology. Boliviabased Dr. Morales and Hondurasbased Dr. Destephen were contacted to recruit students. We contacted Dr. Pitt, MDiG author, when in doubt about his software. *Software. A small library aimed at solving problems involving reactionconvectiondiffusion using the finite elements method was created in C++. It includes a graphic driver to make visualizations of the solutions. We also developed small routines in C++ and GRASS to automate the computation of the area infected by the species for each period and the average infected area per period when running Monte Carlo experiments. *Manuals: MDiG, R, GRASS, ArcGIS, and OpenAlea tutorials were written to help other interested researchers learn the specific software and models we used. See publications below. ***Dissemination. Presentations of the abstracts as well as one on the use of MDiG by Henriquez on 07/19/11 at UNAH, Honduras, and another on the modeling of the spread, by Barragan 07/21/11 at UMSA, Bolivia. Meetings with Drs. Castillo (Math. Sc.), and Gutierrez and Leonardi (Mech. Eng.). PARTICIPANTS: Barragan, M.J., Principal Investigator. In charge of the project at large. Robles, W., CoPI and weed science specialist. Camacho, W., Research Assistant who worked with data manipulation in ArcGIS and initiated statistical analysis in R. Auccaille, Y., Research Assistant working with secondarysource data collection, data manipulation in ArcGIS, and statistical analyses in R. Henriquez, I., Research Assistant working with data manipulation in GRASS, mathematical modeling in MDiG and with pdes, and data manipulation and visualization in OpenAlea. Almodovar, L., Research Technitian, in charge of sampling presence/absence of invasive species under study and implementing field experiments. Castillo, P., collaborating in several issues dealing with the design of the general framework needed to build a new cellular automata environment. TARGET AUDIENCES: *** At a broader level: Researchers and students in several disciplines that study the behavior of dynamic systems over space and time. Researchers and students in several life sciences disciplines with an interest in spatiotemporal behavior. Researchers and students studying the spread of invasive species as they interact with their environment. Technical staff of the Federal Government dealing with the monitoring, regulation and combating of invasive species. ***At a more local or institutional level: Faculty members, researchers and students of the Departments of Biology, Mathematical Sciences, and Mechanical Engineering of the Universty of Puerto Rico with an interest in mathematical modeling of dynamic systems over space Faculty members, researchers and students working in the fields of epidemiology, phytopathology, entomology, and weed science. Technical staff and policymaking individuals in the Government of Puerto Rico dealing with the monitoring, regulation and combat of invasive species. Students of the College of Agricultural Sciences at the University of Puerto Rico. Nonprofit organizations interested in environmental issues. Farmers with an interest in the impact of invasive species on their productive activities. PROJECT MODIFICATIONS: Leave Melaleuca quinquenervia out of the study because its presence was not important enough to give sufficient data points in order to guarantee adequate statistical analyses. Give greater emphasis to the diffusion of acquired techniques among the community of interested researchers and policy analysts. Give greater emphasis to estimating the parameters of longdistance dispersal of Mimosa pigra. Give more emphasis to developing a new library aimed at eliminating some of the limitations of MDiG. Give greater emphasis to data collection, digitalization, analysis, and modeling of spatial variables that describe plant structure.
Impacts **Change in knowledge. *Although the definitive simulations of our models are not expected until next year, our work has allowed for significant improvement in modeling skills and has already revealed some interesting results and findings. *The greatest outcome during this first year was the honing of the team's modeling knowledge and skills. Greater knowledge of modeling using cellular automata, stochastic, partial differential equations, and spatial analysis methods was acquired. We learned the use of mathematical modeling software such as MDiG; geographical information system software, such as GRASS; statistical software such as R; and plant structure analysis software, such as OpenAlea. *A related, equally important yet unexpected, finding was the realization that these methods are in high demand in this and several other applied fields of study and that the skills needed to use these modeling techniques are either in short supply or disconnected from potential fields of application. *The field trips to sample the presence/absence of both invasive species under study showed us, with one exception, that Melaleuca quinquenervia was not actively invading the ecosystems. Not enough data points were found to make significant statistical analysis for this species. Mimosa pigra, on the other hand, was found to be aggressively invading several ecosystems. *The first regression analyses showed that maximum temperature is an important variable in determining the survival probability of Mimosa pigra. *The predicted survival probabilities for all the Island allowed us to build a suitability map giving us a clear picture of the geographic regions where Mimosa pigra is most likely to survive. *The statisticalbased suitability map predicted well the presence of Mimosa pigra. In contrast, the indexbased suitability map proved to be a poor predictor of the invasive species presence. *The sensitivity analysis with MDiG revealed that longdistance dispersal parameters are much more influential on model results than shortdistance diffusion parameters. *We identified several limitations in MDiG. *Explorations with OpenAlea software made us visualize the potential that the analysis of plant structuralfunctional models has for the modeling of spread of plants over space. ***Changes in actions. *As a result of our realization of the importance of the modeling methods and skills acquired by the team during the first year, we developed stepbystep tutorials of the software and procedures used in our research and decided that next year we will organize a series of workshops with other interested researchers and students at the UPR. *As a result of our finding that longdistance parameters have the greatest influence on simulation results, we decided to focus next year's attention on ways to better estimate these parameters experimentally. *As a result of the limitations found in MDiG, we are working on building a library of our own that has greater independence from GRASS and is more efficient. *As a result of our explorations with OpenAlea, we decided that next year we will measure, digitalize and analyze spatial parameters of the structure of Mimosa pigra.
Publications
 Working Papers: Barragan, M.J.; and Henriquez, I. 2011. A basic GRASS tutorial. Working Paper 201103. Department of Agricultural Economics and Rural Sociology, UPRRUM. Mayaguez, Puerto Rico.
 Barragan, M.J.; and Henriquez, I. 2011. Digitizing and analyzing plant structure: An OpenAlea tutorial and results of a case study with a Garcinia madruno seedling Working Paper 201107. Department of Agricultural Economics and Rural Sociology, UPRRUM. Mayaguez, Puerto Rico.
 Abstracts: Barragan, M.J.; Robles, W.; Camacho, W.; and Auccaille, Y. 2010. Modeling and controlling the spread of invasive species over heterogeneous landscapes. Proceedings of the Eighth National Meeting on Remote Sensing and Geographical Information Systems (PRYSIG), Mayaguez, Puerto Rico. (In Press). [Will be available on the internet at http://cohemis.uprm.edu/prysig/conferencias.html].
 Barragan, M.J. and Henriquez, I. 2011. Dispersal patterns of an invasive species with the use of MDiG: Exploring the sensibility of simulations to different parameter values in the case of Mimosa pigra in Puerto Rico. SIDIM XXVI Abstract Book. Humacao, Puerto Rico. (Page 16). [http://sidim.uprh.edu/sidim2011/es/Libro_SIDIM_XXVI_v4.pdf].
 Barragan, M.J., Henriquez, I. and BarraganHerbas, I. 2011. Digitizing and analyzing plant structure: An illustration with a Garcinia madruno seedling. SIDIM XXVI Abstract Book. Humacao, Puerto Rico. (Pages 1617). [http://sidim.uprh.edu/sidim2011/es/Libro_SIDIM_XXVI_v4.pdf].
 Barragan, M.J.; Robles, W.; Camacho, W.; and Auccaille, Y. 2011. A statistical suitability map for Mimosa pigra in Puerto Rico: Preliminary results based on presence/absence, temperature and precipitation data. SIDIM XXVI Abstract Book. Humacao, Puerto Rico. (Page 27). [http://sidim.uprh.edu/sidim2011/es/Libro_SIDIM_XXVI_v4.pdf].
 Barragan, M.J.; and Henriquez, I. 2011. A basic MDiG tutorial. Working Paper 201104. Department of Agricultural Economics and Rural Sociology, UPRRUM. Mayaguez, Puerto Rico. Barragan, M.J.; Camacho, W.; and Auccaille, Y. 2011. Handling and statistical analysis of geographically indexed data: A stepbystep example from Puerto Rico using ArcGIS and R. Working Paper 201105. Department of Agricultural Economics and Rural Sociology, UPRRUM. Mayaguez, Puerto Rico.
 Barragan, M.J.; and Henriquez, I. 2011. A suitability map for Mimosa pigra in Puerto Rico based on a subjective index: Results and tutorial using ArcGIS and GRASS. Working Paper 201106. Department of Agricultural Economics and Rural Sociology, UPRRUM. Mayaguez, Puerto Rico.
 Barragan, M.J.; Robles, W.; Camacho, W.; and Auccaille, Y. 2011. A logistic suitability map for Mimosa pigra in Puerto Rico: Results based on presence/absence, temperature and precipitation data. Proceedings of the Anual SOPCA Scientific Meeting. Ponce, Puerto Rico. (In Press).
 Barragan, M.J.; and Henriquez, I. 2011. Using sensibility analysis to optimize the calibration of mathematical models: An application to the study of the spread of Mimosa pigra in Puerto Rico.
