Modeling Spread in Ohio
Most of the data collected in the preceding sections was a prerequisite for efforts to model the spread of the EAB. We have worked some years on a SHIFT model, designed to estimate the potential migration of trees under the northward climatic pressure (Iverson and others 1999, 2004a, 2004b; Schwartz and others 2001). This model was adapted to work for the spread of EAB. The fundamental basis of this model is a spread model that is driven by existing local density of infestations, ash BA, and the distance of habitat patches to known and modeled infestations. This basic model required modification based on the idea that EAB spread is facilitated through human activities (insect-ride model).
The formula SHIFT uses to calculate the probability of an unoccupied cell becoming colonized during each generation is:
Pcolonization, i = HQi ( Σ HQj x Fj x (C/Di,jX))
where Pcolonization, i is the probability of unoccupied cell i being colonized by at least one individual and surviving into reproductive status; HQi and HQj are habitat quality scalars for unoccupied cell i and occupied cell j, respectively, that are based on the basal area of ash in each 270- m cell; Fj, an abundance scalar (0-1), is related to the current estimated abundance of EAB in the occupied cell j; and Di,j is the distance between unoccupied cell i and an occupied cell j.
The colonization probability for each unoccupied cell, a value between 0 and 1, is summed across all occupied cells at each generation. Thus, an unoccupied cell very close to numerous occupied cells may end up with a colonization probability greater than 1.0. These cells are modeled as colonized. For cells with summed colonization probabilities less than one, a random number less than 1.0 is chosen, and all cells with a probability of colonization that exceeds the random number are colonized in that model step. Those “newly colonized” cells then contribute to the colonization probability of unoccupied cells in the next model time step. The value of C, a rate constant, is derived independently through trial runs to achieve a migration rate of approximately 20 km per year under high ash BA and moderate EAB abundance. The value of X, or dispersal exponent, determines the rate at which dispersal declines with distance. Being in the denominator, this decreases colonization with distance as an inverse power function. Further discussion on the dispersal function can be found in Schwartz and others (2001).
Insect-Flight Model
With the insect-flight model, we use the modified SHIFT model to advance the front based on the current front location, the abundance of EAB behind the front, and the quantity of ash ahead of the front. The model runs at a 270-m cell size, and based on the known progression of EAB densities and ash mortality in outlier zones, we assume an 11-year cycle for EAB initial infestation to death of all ash trees in the cell. EAB abundance in the cell was assumed to form a modified bell-shaped curve, with maximum abundance (multiplier = 1) in years 6, 7, and 8; a 0.6 multiplier in years 5 and 9; a 0.14 multiplier in year 4; a 0.011 multiplier in year 3; a 0.0003 multiplier in years 2 and 10; and a 0.0001 multiplier in years 1 and 11. The assumptions for this curve include a slow EAB population increase for the first few years after colonization, followed by peak infestation for 3 years starting with year 6, followed by a rapid decline as all the ash trees in the cell die off in years 9-11. The fine-scale ash BA for Ohio was normalized to 0-100 and also used as a multiplier. The 11-year cycle may be a liberal assumption on how fast the EAB infestations can grow, as there is some evidence that it may take as long as 10 years for populations to peak (rather than the 6 we assumed). For each cell, the program calculates the probability of new colonization, based on a small probability that the insect will fly from an occupied cell to an unoccupied cell, for all surrounding cells within a specified search window (40 km in this case). Once selected for colonization, the cell starts the 11-year cycle of EAB increasing and then decreasing as ash dies out.
Insect-Ride Model
To develop the insect-ride model, we used GIS data to weight factors related to potential human-assisted movements of EAB-infested ash wood or just hitchhiking insects: roads, urban areas, various wood products industries, population density, and campgrounds. Each of these five factors was converted into weighting layers that became multipliers for the ash BA component of the insect-ride model. That is, the increase in probability of EAB infestation by the insect-ride factors is made manifest by increasing the amount of ash available in those cells. Thus, if no ash exists in the cell, it matters not whether there is an escaped EAB from one of the human-assisted vectors, but if there is a large ash component, an escaped EAB could quickly find a place to colonize.
To register the increased probability of insects riding on windshields, radiators, or otherwise attached to vehicles moving down the road, we assigned weights to two widths of major road corridors. We used the U.S. Geological Survey major roads data and created buffers of 1 and 2 km, with a scoring of 10 for 0-1 km- and 5 for 1-2 km- distance from the roads.
For urban areas, where there is much more vehicular density and opportunity for EAB transport, we assigned values of 7 if the urban center size was less than the median size and 10 if greater than the median. We therefore assume larger cities will have greater chance of EAB infestation via human movement. Data were acquired for the State of Ohio urban centers from the Department of Transportation Office of Technical Services (Ohio Department of Transportation 2006).
Related to the urban areas, weighting is the population density scoring by zip code. This factor creates a wall-to-wall scoring and distinguishes rural from more urbanized areas. Data were acquired from the U.S. Census Bureau, which included population estimates for 2001 by zip code area. Population densities were divided into six classes with scoring as follows: 1=1-100 people/km2; 2=101-200; 4=201-800; 6=801-2000; 8=2001-4000; 10=4001-16,582.
Wood products industries also have been responsible for some EAB movement, so a scheme was developed to weight buffers around individual businesses dealing in wood products. We performed an analysis of potential industries carrying wood products, based on the listing of SIC codes from Dunn and Bradstreet. We scored each industry for likelihood of EAB getting to the site and emerging based on our estimate of the amount and status of ash used in the industry: 0=none; 2=small likelihood; 4=somewhat likely; 6=higher likelihood. For example, forest nurseries and wood pallet industries scored a 6, whereas manufacturers of decorative woodwork or wooden desks scored a 4 (mostly used kiln-dried wood), and manufacturers of pressed logs of sawdust or woodchips scored a 2. Movement of material from nurseries historically has been a source for several infestations, which are not accounted for in this model. Presumably, this source has been slowed recently via quarantine regulation. Next, buffer distances around the businesses were created based on the number of employees (surrogate for size or volume of wood) working at the facility. For 1-10 employees, the buffer of 0-1 km scored 8, and the 1-2 km buffer scored 3; for 11-50 employees, the buffer of 0-1.5 km scored 9, and the 1.5-3 km buffer scored 4; and if the facility had more than 50 employees, the 0-2 km buffer scored 10, and the 2-4 km buffer scored 5. Because facilities could be within each other’s buffer space, scores were added, and the maximum score over the study area was 22.
Finally, campgrounds were considered likely destinations of human-assisted EAB transport, primarily through the (mostly illegal) movement of firewood. The general public is the primary vector, so it is much more difficult (relative to industry vectors) to achieve education, regulation, and enforcement goals related to stopping EAB spread. Campgrounds were treated in two ways: through the weighting scheme described here and the gravity model described in the next section. Campground locations were acquired from Dunn & Bradstreet (unpublished data purchased by Iverson) and the AAA Travel and Insurance Company (unpublished data provided to Bossenbroek). Similar to that described for wood products industries, we base the weighting on both distance (from the camp headquarters) and number of campsites. For campgrounds with less than 50 campsites, the buffer of 0-0.5 km scored 10, and the buffer of 0.5-1 km scored 5; for 51-200 campsites, the equivalent buffers were 0-1 (10 points) and 1-2 km (5 points); for 201-400 campsites, buffers were 0-1.5 and 1.5-3 km; for 401-600 campsites, buffers were 0-2 km and 2-4 km; and for more than 600 campsites, buffers were 0-2.5 km and 2.5-5 km.
Gravity Model Scenarios
In the second approach used with campgrounds, we are developing a gravity model (Bossenbroek and others 2001) that considers traffic volumes and routes between EAB source areas and various distances to campgrounds (Muirhead and others 2006). Muirhead and others (2006) presented an initial model predicting human-mediated dispersal of the EAB through the movement of campfire wood. Given the rapid spread of the EAB and a need for a quick response, simple models based on simple assumptions, such as developed by Muirhead and others (2006), are an essential step. One of the goals of this project is to incorporate more detail into the models of long-distance dispersal of the EAB. Empirical data on the use of campgrounds, i.e., reservation data, is only available for public campgrounds; thus to incorporate private campgrounds, a modeling framework is necessary. Here we develop a gravity model for Ohio to predict the relative number of campers traveling from EAB infested areas to the campgrounds of Ohio.
Gravity models calculate the number of individuals, (e.g., campers) who travel from location i to destination j, (e.g., a campground), Tij, as estimated as
where, Ai is a scalar for location i (see below), Oi is the number of people at location i, Wj is the attractiveness of location j, cij is the distance from location i to location j, and α is a distance coefficient, or distance-decay parameter, which defines how much of a deterrent distance is to interaction. Ai is estimated via
where N represents the total number of destinations, and j represents each destination in the study region. A production-constrained gravity model of the movement of firewood thus requires information on the number of campers, the residency of the campers, the location of potential destinations, (i.e., campgrounds), the attractiveness of those destinations, and the distribution of the emerald ash borer, (i.e., source locations). The spatial resolution of our gravity model is based on zip code regions for the residency of campers and the point locations of campgrounds.
Based on data from Dunn & Bradstreet and the AAA Travel and Insurance Company, we identified the location of 241 public and private campgrounds in Ohio. For a measure of attractiveness for each campground (W), we initially are using the number of camp sites at each location. Other factors, such as proximity to boating, fishing, and hiking, are likely to influence the attractiveness of individual campgrounds, but these data are unavailable on a regional and consistent basis. The distance between a zip code and a campground (c) was calculated as the road network distance between these locations. For simplification, the road network is based on all roads with either a State or Federal designation and excludes local roads. The point of origin for each zip code was determined as the road location nearest the centroid of the zip code region. Likewise, for each campground, the point location was determined as the point on the nearest road to the campground. The result of the gravity model is a prediction of the number of campers that travel from an area of EAB infestation to each particular campground.
To estimate the distance coefficient (α), we compared our gravity model with reservation data obtained from the Ohio Division of Parks and Recreation for 58 state parks. These records contained the number of reservations for each campground summed by zip code of the camper’s residence. We used sum of squares to measure goodness-of-fit between model predictions and the observed data. To identify the best-fit model, the value of α was systematically assessed over a range from 0.1 to 10. By fitting the model to the reservation data for Ohio state parks, we assume that campers using private and public campgrounds behave in the same manner, i.e., distance and attraction affect their travel decisions in the same manner.
Once the gravity model was parameterized, we used the estimated distance coefficient value to determine the expected number of campers that would travel to all 241 campgrounds within Ohio. We reported the percentage of campers coming from EAB-infested zip codes (as of 2003) traveling to each campground in Ohio to give a relative estimate of risk.
Encyclopedia ID: p3379
