Source: UNIVERSITY OF PUERTO RICO AT MAYAGUEZ submitted to
MODELING AND CONTROLLING THE SPREAD OF INVASIVE SPECIES OVER HETEROGENEOUS LANDSCAPES: MELALEUCA QUINQUENERVIA AND MIMOSA PELLITA IN PUERTO RICO.
Sponsoring Institution
National Institute of Food and Agriculture
Project Status
TERMINATED
Funding Source
Reporting Frequency
Annual
Accession No.
0222253
Grant No.
2010-34135-21021
Project No.
PR00TSTAR-132
Proposal No.
2010-03011
Multistate No.
(N/A)
Program Code
AH
Project Start Date
Sep 1, 2010
Project End Date
Aug 31, 2013
Grant Year
2014
Project Director
Barragan, M. J.
Recipient Organization
UNIVERSITY OF PUERTO RICO AT MAYAGUEZ
P. O. BOX 9000
MAYAGUEZ,PR 00681
Performing Department
Agri Economics & Rural Sociol
Non Technical Summary
The problem: Why did Melaleuca quinquenervia thrive in Florida wetlands and not in those of Puerto Rico or the Bahamas Could it be that limited wetland connectivity in small islands had something to do with it And if so, why did Mimosa pellita thrive in Puerto Rico's wetlands Could this be due to Mimosa pellita's more aggressive long distance dispersal mechanisms These questions point to potential interactions between the dispersal mechanisms available to an invasive species and its environmental setting in determining the ultimate rate of spread observed. The present research project attempts to throw some light onto these issues by adopting a modeling framework that takes explicit account of landscape heterogeneity as well as of the dispersal mechanisms. This same approach will be used to evaluate the cost-effectiveness of alternative policies aimed at controlling the spread of an invading species. Objectives: The general objective of the present proposal is to explain-- and help decide on the best way to control-- the rate of spread of two weeds that are invading Puerto Rico's wetlands (Mimosa pellita and Melaleuca quinquenervia). Our specific objectives are to: 1. Construct suitability maps identifying the places with conditions under which invasive species are most likely to thrive. 2. Model invasive species spread over time under alternative scenarios, among which are a set of alternative chemical control programs. 3. Improve public awareness. Methods: In order to capture the texture and heterogeneity of landscape, a Geographical Information Systems (GIS) framework is adopted. Temperature, precipitation and other variables that determine the survival of invading species are translated into suitability maps. These maps are supplemented by a series of programs aimed at capturing the alternative dispersal mechanisms available to an invading species. For instance, contiguous spread behavior is captured with rules that establish whether a particular place will be invaded or not depending on whether there exists an invasive species in its immediate neighborhood. On the other hand, long distance dispersal is captured through a sequence of draws from chance mechanisms that determine the occurrence of a long distance dispersal event, its direction, and its distance. Once an invasive species exists in a given place, the probability of surviving into the following period is determined by using the suitability maps mentioned above. The model built has to be calibrated to capture the actual spread observed in Puerto Rico. The model is then used to simulate a control and several alternative policy scenarios. A cost is assigned to each policy scenario allowing models to be compared on a cost-effectiveness basis. The results of the research will be communicated to policy officials in Puerto Rico through seminars, to the academic community through workshops and peer-reviewed publications, and to a wider public audience through the use of videos and printable material, all made available through an interactive website.
Animal Health Component
95%
Research Effort Categories
Basic
5%
Applied
95%
Developmental
(N/A)
Classification

Knowledge Area (KA)Subject of Investigation (SOI)Field of Science (FOS)Percent
1360790107020%
1360790208030%
1360790301010%
1360790303030%
1360790311010%
Goals / Objectives
The general objective of the present proposal is to explain-- and help decide on the best way to control- the rate of spread of two weeds that are invading Puerto Rico's wetlands (Mimosa pellita and Melaleuca quinquenervia). Our specific objectives are to: 1. Construct suitability maps for each of the selected invasive species. 2. Model invasive species spread over time under alternative scenarios, among which are a set of alternative chemical control programs. 3. Improve public awareness. Primary and secondary data collection as well as MDIG installation and setup will be done during the first three quarters of the first year. Construction of suitability and survival maps as well as estimation of spread parameters will be done during the second half of the first year. Model calibration and simulations and sensibility analysis will be made during the first half of the second year. Visual representation of results, measures to increase public awareness, and activities to share modeling skills will be made throughout the second year. The following will be among the deliverables of the project: a computer model for the dispersion of two invasive plant species calibrated to Puerto Rico's reality; journal articles summarizing the results of the research as well as modeling approaches and methodologies; model simulations of alternative policy scenarios presented in alternative communication formats (videos, power point presentations, booklets); seminars with government officials presenting results; workshops with other researchers and students to share modeling techniques; a curriculum and a syllabus for a graduate course on the modeling of invasive species; and presentations at several professional meetings.
Project Methods
Objective 1: In order to construct suitability maps, data from variables that are deemed important in the establishment and spread of the selected invasive species will be obtained from secondary sources. Maps will be constructed for each of the variables. ArcGIS will be used to transform and store these data as well as to create suitability maps. Objective 2: Two maps will be constructed for each species. The initial base line map, will record invasive presence for a period set some time in the past. Thepresent base line map will describe present day occurrence. The initial baseline maps will be inputted into the MDiG spread model. Spread parameters will be estimated by using historical records available at the Mayaguez MAPR Herbarium. These data will be supplemented with field visits along the potential lowland habitats of these two species. In the case of the long distance dispersal module, three distributions need to be estimated. The first is a Poisson process, which will be used to sample the number of long distance dispersal events originating in a given cell. For each long distance dispersal event, two additional distributions will be sampled. First a uniform distribution [0,2π] needs to be sampled to determine the direction of the dispersal. Then a Cauchy distribution needs to be sampled in order to determine the distance of the dispersal. In the local spread module, the faster resolution is chosen so as to match the average contiguous spread distance in a time step. A simple spread rule will be used: Each patch will be occupied in the next-time step if an immediate neighboring cell is occupied in the present period. In order to use the survival module, a probability must be assigned to each habitat suitability category built in the first objective. Each of these probabilities indicates the likelihood that invading species present in a given cell will survive to the next period. Each model will then be validated and calibrated by using a Monte Carlo approach. Alternative policy scenarios will be simulated and compared to a base or control simulation. The impact of each control program will be measured in terms of how well they control the spread of the invading population and how much they cost. A choice will be made among alternative control programs on the basis of cost effectiveness. This will be followed by sensibility analyses to see how the results vary when changed for different values of the spread and survival parameters. In order to improve public awareness, the results of the study will be shared with personnel of the Puerto Rico Department of Agriculture and of other local offices of federal agencies interested in the subject. The results will also be shared through a webpage for the project and through the attendance at important local events such as the annual professional meetings such as the Sociedad Puertorriquena de Ciencias Agricolas (SOPCA) and other general public events such as Cinco Dias con Nuestra Tierra. The research project also contemplates the creation of opportunities to share modeling techniques with other researchers and students in Puerto Rico.

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 spatio-temporal 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 policy-making 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 general-use 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 one-dimensional space, and one with a two-dimensional space. *Mentoring-2011. . Yetsabel Auccaille and Iván Henríquez, graduate students majoring in statistics and mathematics, respectively, were hired as RAs and are mentored by the project PI. *Mentoring-2012. . Yetsabel Auccaille and Iván Henríquez, graduate students majoring in statistics and mathematics, respectively, were hired as RAs and are mentored by the project PI. *Mentoring-2013. 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 peer-reviewed 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 one-on-one approach (see section on Networks). **Dissemination-2011. *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. **Dissemination-2012. * 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 2-3). Using a mathematical model of the spread of Mimosa pigra in Puerto Rico to estimate cost-effectiveness 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 2-3) 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 2-3). 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. **Dissemination-2013. * 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 PR-AEE”. 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 PR-AEE”. 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 temporal-spatial 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 multi-species 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. *Seminars-2011. 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. *Seminars-2013. 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 ]. *Exhibitions-2013.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 TSTAR-132 and McIntire Stennis-019. The exhibition was part of the Open House activities of the UPRM held on November1, 2013. *Exhibitions-2014.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 month-long 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 spatio-temporal control using a mixed-integer programming (MIP) framework. * We presented our results in several scientific forums, and on one-on-one 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 McIntire-Stennis 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 long-distance 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 grid-based 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 knowledge-2011 *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 statistical-based suitability map predicted well the presence of M pigra. In contrast, the index-based suitability map proved to be a poor predictor of the IS presence. *The sensitivity analysis with MDiG revealed that long-distance dispersal parameters are much more influential on model results than short-distance diffusion parameters. *We identified some limitations in MDiG. *Explorations with OpenAlea software made us visualize the potential that the analysis of plant structural-functional models has for the modeling of spread of plants over space. **Change in knowledge-2012 *The findings of the suitability map with a spatial logistic regression gave similar coefficients that those obtained with a non-spatial 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 water-based contamination, erosion, and the sequestration of greenhouse gases. *A major problem of the CA-based 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 knowledge-2013. * The efforts to model forest ecosystems under the auspices of project McIntire-Stennis-019 enabled us to confirm our initial belief that the dispersal module developed with our TSTAR-132 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 spatio-temporal 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 long-distance dispersal. **Changes in actions-2011. *As a result of importance of the modeling methods and skills acquired during the first year, we developed step-by-step tutorials of the software and procedures used to help us share this know-how. *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 actions-2012. *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 actions-2013. *For the spatio-temporal part of the project we chose MIP over DP. * Further grid-based modeling efforts to include processes at the landscape-level. Candidate processes include (1) plant-light-atmosphere processes, (2) plant-soil 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 high-priority 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 grid-based 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 spatio-temporal 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 grid-based spatio-temporal 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 2011-03. Department of Agricultural Economics and Rural Sociology, UPR-RUM. 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 2011-04. Department of Agricultural Economics and Rural Sociology, UPR-RUM. 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 step-by-step example from Puerto Rico using ArcGIS and R. Working Paper 2011-05. Department of Agricultural Economics and Rural Sociology, UPR-RUM. 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 2011-06. Department of Agricultural Economics and Rural Sociology, UPR-RUM. 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 2011-07. Department of Agricultural Economics and Rural Sociology, UPR-RUM. Mayag�ez, Puerto Rico.
  • Type: Theses/Dissertations Status: Other Year Published: 2014 Citation: Yetsabel, A. Optimal spatio-temporal control of an invasive species  A mixed-integer 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 45-46).
  • Type: Conference Papers and Presentations Status: Published Year Published: 2012 Citation: Barrag�n, M.J.; Henr�quez, I.; Alvarado, A.; Robles, W. 2012 (March 2-3). Using a mathematical model of the spread of Mimosa pigra in Puerto Rico to estimate cost-effectiveness of alternative control measures. SIDIM XXVII Abstract Book. Presentation made at the XXVII SIDIM conference held at Mayag�ez, Puerto Rico. (Pages 12-13). [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 2-3) 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 temporal-spatial 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 multi-species 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 2-3). 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., Co-PI and weed science specialist. Yetsabel, A., Research Assistant working with secondary-source 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 life-science disciplines with an interest in spatio-temporal 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 policy-making 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 long-distance dispersal of Mimosa pigra are unavailable, we decided to model instead some of the most important processes involved in long-distance dispersal. This is the case of hydrochory, or long-distance 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 non-spatial 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 water-based contamination, erosion, and the sequestration of greenhouse gases. *A major problem of the cellular automata-based 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 nitrogen-related 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 45-46).
  • *Barragan, M.J.; Henriquez, I.; Alvarado, A.; Robles, W., 2012 (March 2-3). Using a mathematical model of the spread of Mimosa pigra in Puerto Rico to estimate cost-effectiveness of alternative control measures. SIDIM XXVII Abstract Book. Presentation made at the XXVII SIDIM conference held at Mayaguez, Puerto Rico. (Pages 12-13). [http://www.sidim.pr/programa.pdf]
  • *Barragan, M.J.; Auccaille, Y.; Robles, W., 2012 (March 2-3) 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. Index-based 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 automata-based 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 1-min video of MDiG model outpout for Mimosa pigra, and 15-min 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. Bolivia-based Dr. Morales and Honduras-based 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 reaction-convection-diffusion 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., Co-PI 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 secondary-source 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 spatio-temporal 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 policy-making 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 long-distance 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 statistical-based suitability map predicted well the presence of Mimosa pigra. In contrast, the index-based suitability map proved to be a poor predictor of the invasive species presence. *The sensitivity analysis with MDiG revealed that long-distance dispersal parameters are much more influential on model results than short-distance diffusion parameters. *We identified several limitations in MDiG. *Explorations with OpenAlea software made us visualize the potential that the analysis of plant structural-functional 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 step-by-step 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 long-distance 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 2011-03. Department of Agricultural Economics and Rural Sociology, UPR-RUM. 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 2011-07. Department of Agricultural Economics and Rural Sociology, UPR-RUM. 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 Barragan-Herbas, I. 2011. Digitizing and analyzing plant structure: An illustration with a Garcinia madruno seedling. SIDIM XXVI Abstract Book. Humacao, Puerto Rico. (Pages 16-17). [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 2011-04. Department of Agricultural Economics and Rural Sociology, UPR-RUM. Mayaguez, Puerto Rico. Barragan, M.J.; Camacho, W.; and Auccaille, Y. 2011. Handling and statistical analysis of geographically indexed data: A step-by-step example from Puerto Rico using ArcGIS and R. Working Paper 2011-05. Department of Agricultural Economics and Rural Sociology, UPR-RUM. 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 2011-06. Department of Agricultural Economics and Rural Sociology, UPR-RUM. 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.