Progress 10/01/05 to 09/30/06
Outputs
OUTPUTS: ACTIVITIES PD Matlock taught a graduate course in Mathematical Biology in the Dept. of Mathematics, at Tulane U., summer (Lagniappe semester) 2006. Several course projects were based on extensions of the screwworm reaction-diffusion (RD) model. PRODUCTS REACTION DIFFUSION MODEL. Analysis of the RD model of screwworm control by the sterile insect release (SIR) method continued. The model predicts that the screwworm population will propagate as a traveling wave in an open environment. When this wave encounters a sterile barrier with a rate of sterile release exceeding a threshold value, this causes the wave to stall. At release rates beneath this threshold, fertile screwworm populations can propagate through sterile barriers. Exact and approximate analytical model solutions for sterile and fertile fly population densities, respectively, were derived. STOCHASTIC MODEL. The RD model predicts that fertile screwworm can penetrate barriers when the protected territory (which may be
continental in scale) exceeds a threshold size (a prediction similar to critical-size results of other ecological RD models). Penetration occurs by a different mechanism than travelling wave propagation, and depends on screwworm populations persisting at extremely low densities (e.g. < 10-10 per km2) through the barrier. In real barriers, stochastic fluctuations should drive such sparse populations to extinction, preventing penetration. To test this hypothesis, a stochastic simulation analogue of the RD equations was developed that models fertile and sterile population dynamics as birth and death processes, and dispersal as a random walk. This model confirms that stochastic population fluctuations drive fertile populations to extinction within barriers, preventing breaches in most cases where the RD model predicts penetration. The stochastic model predicts that barriers substantially shorter than the 300 km width of the Panamanian barrier zone can still prevent screwworm expansion.
MINIMUM SIZE-AREA MODEL. Traditionally, the sterile insect release (SIR) method has been used to control pest insects at regional scales. Small-scale applications of SIR to high-value crops with low economic thresholds, such as fruits, would be economically beneficial. An FAO/IAEA Consultant's Meeting (see SERVICES below) was convened to determine the minimum area to which SIR can be practically applied. The screwworm RD model was adapted to model farms surrounded by barriers of sterile release, and predicted that SIR can control pests at any spatial scale. Pest density decreased with barrier size, sterile release rate and pest mortality rate, but increased with size of the protected farm and pest birth rate. EVENTS PD Matlock was an invited participant at a US National Science Foundation funded conference on mathematical biology in El Salvador in July 2006 where he delivered a presentation on the screwworm RD model. SERVICES PD Matlock was invited to a joint UN FAO − IAEA
Consultants Meeting to determine the minimum area to which SIR can be practically applied. Vienna, Austria. April, 2006 (see ACTIVITIES).
PROJECT MODIFICATIONS: HURRICANE KATRINA. Research progress was disrupted in Fall 2005 and to a more limited extent in Spring 2006 due to Hurricane Katrina. CHANGE OF INSTITUTION. PD Matlock moved to a tenure-track Assistant Professor position at the College of Staten Island, City University of New York in August, 2006, which also delayed research progress. STOCHASTIC MODEL. After thorough analysis of the reaction-diffusion (RD) model, it was discovered that this model is not appropriate for estimating the length of sterile barrier zones required to stop screwworm expansion, because it predicts that fertile screwworm can penetrate the barrier when the protected territory (which may be continental in scale) is larger than a threshold size (a prediction similar to critical-size results of other ecological RD models). As explained in the OUTPUTS, PRODUCTS, STOCHASTIC MODEL section, these predictions are most probably mathematical artifacts. This necessitated development of a second,
parallel stochastic model of barrier zone length, which roughly doubled the labor involved in the modeling portion of the project research. This stochastic model has been developed and tested and appears to model the barrier zone length problem adequately. This simulation is computationally intensive, and thus has also been optimized to maximize run speed. It must be noted that although the RD model is inappropriate for investigating barrier zone length, it is still appropriate for other proposal objectives, such as: 1) predicting the proper rates of sterile fly release, 2) predicting sterile fly density and approximate fertile density, 3) predicting the proper distance between aerial dispersal flight lines, and 4) for predicting the rate of spread of screwworm outbreaks. Thus, time invested in analysis of the RD model was not wasted. Calculation of final solutions to the barrier zone length problem and the other research objectives enumerated above (see also the proposal OBJECTIVES
section) for both the RD and stochastic model awaits estimates of model parameters, which are in progress.
Impacts
CHANGES IN KNOWLEDGE The three models developed in the Outputs/Products Section generate quantitative, spatially-explicit, testable predictions of control by the sterile insect release (SIR) method. Heretofore, SIR has usually been applied in an ad-hoc manner, rates of sterile dosage being determined empirically. The models developed in this research provide tools that make spatially-explicit predictions about sterile release that can be used to design SIR control programs for different circumstances including eradication, containment (e.g. the screwworm barrier in Panama) and suppression (e.g. small-scale crop protection, see Outputs/Products for details). The models also identify the parameters that govern the efficacy of SIR control, which are: birth and death rate of the pest insect, maximum population density (carrying capacity) of the pest insect in the absence of control and the dispersal (diffusion) rates of fertile and sterile insects. Information on these
parameters is necessary to predict the efficacy of sterile control for any particular insect pest.
Publications
- No publications reported this period
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Progress 10/01/04 to 09/30/05
Outputs
OUTPUTS: ACTIVITIES FIELD WORK. Field experiments to measure dispersal relative to a sterile fly release lines initiated in the first year of the funding period (10/01/2004- 09/30/2005) were completed. A total of 18 replicates (10 aerial and 8 ground level releases) were conducted at 3 sites (sites 1&2: mixed forest and agricultural land; site 3: continuous forest). More replicates were conducted than originally proposed to facilitate more precise parameter estimation and better assessment of whether diffusion is an adequate model of screwworm dispersal. In aerial releases, flies were dispersed along a 10 km flight path perpendicular to a 10 km trapline (the flight path intersecting the trapline at the midpoint). Ground level releases were made at the trapline midpoint. Conduction of both ground level and aerial releases will permit measurement of horizontal drift of aerially released flies during descent to ground from release altitude. Wind data were also collected so that its
influence on screwworm dispersal could be assessed. MODELING. Work on the partial differential equation, reaction diffusion (RD) model of the screwworm barrier zone in Panama continued. A collaboration on analysis of this model between PD Matlock and John Alford (Dept. Mathematics, Tulane U.) was initiated. HURRICANE KATRINA. Research progress was disrupted in September 2005 due to PD Matlock's evacuation from New Orleans for Hurricane Katrina. PRODUCTS The completed field experiments comprise one of the largest data sets on screwworm dispersal ever collected totaling over 1.8 million released and 32,000 recaptured flies. Weather (including wind) data were also collected in these experiments. EVENTS PD Matlock was an invited participant at a US National Science Foundation funded conference on mathematical biology in El Salvador in July 2006 where he delivered a presentation on the screwworm RD model. PD Matlock made a presentation entitled "Eradication of the screwworm fly by sterile
fly release" at the Annual Meeting of the Society of Industrial and Applied Mathematics (SIAM) in July 2005. PD Matlock was an invited participant Third Research Coordination Meeting, Joint UN Food and Agriculture Organization/International Atomic Energy Agency, Division of Nuclear Techniques in Food and Agriculture, Coordinated Research Programme on: "Enabling Technologies for the Expansion of the Sterile Insect Technique for Old and New World Screwworm" 30 May-June 3, 2005, Montevideo, Uruguay.
PARTICIPANTS: John A. Alford, Department of Mathematics, Tulane University (collaborator).
TARGET AUDIENCES: The primary target audiences for this project are: 1) the scientific community, 2) the agricultural research community including USDA,ARS, 3)the USDA, APHIS, Screwworm Eradication Program and 4)THE UN Food and Agriculture Organization/International Atomic Energy Agency, Division of Nuclear Techniques in Food and Agriculture.
PROJECT MODIFICATIONS: Research progress was disrupted in September 2005 due to PD Matlock's evacuation from New Orleans for Hurricane Katrina.
Impacts
CHANGES IN KNOWLEDGE Sterile flies in the screwworm barrier zone in Panama are dispersed along flight lines 2 nautical miles (3.7 km) apart. The dispersal data from the field experiments will provide parameter estimates for the reaction diffusion model and will allow USDA, APHIS Screwworm Eradication Program in Panama to assess how well the sterile release program actually covers the territory within the barrier zone. The data suggest that sterile densities at the midpoint between release lines can be much lower than peak densities along flight lines.
Publications
- No publications reported this period
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Progress 10/01/03 to 09/30/04
Outputs
The screwworm fly, Cochliomyia hominvorax, is a livestock pest and human health hazard that was eradicated from the US, Mexico and Central America southward to the Panama Canal by the sterile insect release method. In this method, sterilized flies are liberated into the environment from aircraft. These sterile flies then mate with the native fly population, inhibiting its reproduction and causing its eradication. USDA APHIS currently maintains a 300 km wide sterile fly release barrier in eastern Panama to prevent screwworm reintroduction to Central America and the US. Within this barrier, sterile screwworms are released from aircraft along parallel flight lanes 2 miles apart. This grant supports development of a mathematical (reaction-diffusion) model of the screwworm sterile fly release barrier and field experiments to gather data for the estimation of model parameters and for validation of model predictions. These experiments are being conducted in Panama in
collaboration with Co-PI Steven Skoda, USDA ARS, Screwworm Research Unit and USDA APHIS. In these field experiments, flies are released from aircraft along a single release line, as in Eradication Program releases, and then censused in traps to 5 km either side of the release line. The purpose of these experiments is to measure how far sterile flies disperse perpendicular to these flight lanes, so that sterile fly coverage within the barrier zone can be estimated, and to estimate sterile fly mortality. These data will also be used to test model predictions of sterile fly distribution. Because screwworm abundance differs in forested and non-forested habitats, these experiments are being replicated at two sites in agricultural landscapes, comprised of patchy forest, pasture and other agricultural habitats, and at in one site in primary forest. A total of six replicates will be conducted, three of which are complete. Three remaining replicates will be completed in spring 2005. Model
parameters have been estimated for the completed replicates and for 16 other screwworm release-recapture data sets collected by other investigators (1, 10 and 5 data sets from Mexico, Costa Rica and Panama, respectively), totaling over 1,000,000 released and 50,000 recaptured flies. The model has been used to derive an algebraic expression for the spatial distribution of sterile flies within the barrier zone. Numerical solutions of the model for interacting fertile and sterile fly populations in the barrier zone have also been completed. These results suggest that the sterile release barrier could be shortened without compromising eradication zone security. An algebraic expression for the maximum distance that sterile release flight lanes can be separated while still guaranteeing screwworm extirpation has also been derived and expressed in terms of the screwworm birth, death and dispersal rates, and the rate of sterile fly release. Manuscripts describing 1) the model of interacting
fertile and sterile flies in the barrier zone and parameter estimation and 2) flight lane separation are in progress. A presentation on the model results was given by Matlock at the Ecological Society of America in August 2004.
Impacts
The annual cost of maintaining the sterile screwworm fly barrier zone in Panama (discussed in the progress report) is approximately $10M. Because of the breadth of northern South America, there are no current plans to eradicate the screwworm south of Panama. Hence, the Screwworm Eradication Program currently plans to maintain the Panamanian barrier zone permanently. Both the planned permanence of the barrier and the annual maintenance costs provide strong incentives for optimizing the sterile release program to reduce barrier maintenance costs without compromising its impermeability to fertile screwworms. The purpose of this research is to develop a mathematical model of screwworm control by sterile fly release. This model is being used to determine whether the current 300 km barrier zone width could be shortened without increasing the risk of screwworm reintroduction to eradicated territory. As requested by Dr. Harold C. Hofmann, USDA, APHIS, the model is also being
used to investigate how far apart the aircraft sterile release flight lanes can be spaced while still guaranteeing screwworm extirpation. This determines the flight time required to cover the barrier, an important component of program costs. The model will also be used to design control strategies for potential screwworm outbreaks. The primary goal of this research is to improve the efficiency and security of the screwworm control program. A broader goal is to derive general principles that will facilitate application of the sterile insect release method to the control other insect pests.
Publications
- Matlock, Jr., R. B. and P. J. Edwards. 2005. The Influence of Habitat Variables on Bird Communities in Forest Remnants in Costa Rica. Submitted to Biological Conservation. Revisions completed awaiting final acceptance.
- Matlock, Jr., R. B. 2005. The effect of prey size and vulnerability on the ability of the predatory pentatomid bug, Perillus bioculatus, to grow, survive, recruit and regulate its prey. In revision, Environmental Entomology.
- Dyer, L. A., Matlock, Jr., R. B., Chehrezad, D. and R. Omalley. 2005. Predicting caterpillar parasitism in banana plantations. Environmental Entomology. In Press.
- Stireman, J.O. III, Dyer, L.A., and R.M. Matlock. 2005. Top-down forces in managed versus unmanaged habitats. In: Barbosa, P. and I. Castellanos (eds.). Ecology of Predator-Prey Interactions. Oxford University Press. In press.
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