Supplemental Material
The population spread simulation is done in an iterative process described below. Each numbered step is elaborated on in separate paragraphs following the list below.
1) Initial source point in Houston Texas
2) Dispersal from initial source point with resistant kernel analysis.
3) Selection of areas of establishment.
4) Long distance dispersal through interstate highway network.
5) Source points for the next simulation time-step are produced by taking the new long distance colonization sites from 4) and adding them to the occupied cells predicted in 3).
6) This five step process iterates for 30 time-steps, corresponding to 30 years since initial colonization.
Initial source point in Houston Texas
Medley et al. (2014) suggest that the initial colonization event of the Asian tiger mosquito in North America was in Houston Texas in approximately 1985. Accordingly, we start the simulation with a single occupied cell in the resistance map at the geographical center of the Houston metropolitan area. We recognize that additional colonization events directly from Asia may have occurred in the subsequent decades of expansion. However, where and when these additional colonization events may have occurred is unknown. As noted in the text of the paper, it is not my intention in the simulation to recreate the actual pattern of colonization and range expansion that the Asian tiger mosquito invasion followed. Rather, my purpose is to provide a visual illustration of the major characteristics that such an

invasion would have had, including initial colonization at one or a few locations, contagious spread from those locations as functions of local landscape resistance, and long distance dispersal and establishment of new sites through stochastic dispersal through the interstate highway grid.
Dispersal from Initial Source Point Across Resistance Map
The resistance map used in the analysis was based on the 2001 NLCD landcover dataset,
2011 edition (Jin et al. 2014) with an extent of 1,245 km east to west and 887 km north to south, centered over eastern Texas and the lower Mississippi Valley (Figure s1). The resistance values were parameterized following Medley et al. (2014) such that urban areas had the lowest resistance (set to 1), and open water, forest and agricultural lands had higher resistance with values reflecting relative resistance suggested by Medley et al.
(2014; Table s1).
Resistant Kernel Analysis Across of Contagious Range Expansion
Pixel-level resistance to movement does not provide sufficient information in itself predict rate and pattern of population expansion from sites of initial colonization. Cushman et al.
(2009) argued that while resistance maps are point specific, connectivity is route specific.
The resistance model is the foundation for connectivity analyses, but it is explicit consideration of connectivity across the resistance surface that provides the key information for conservation and management. Specifically, functional landscape connectivity is a product of multiple factors acting simultaneously, including the dispersal ability of the species, its response to landscape conditions (the resistance map), and its distribution and density in the landscape. I utilized resistant kernel connectivity modeling

(Compton et al. 2007) to simulate the rate and pattern of contagious spread of Asian tiger mosquito population from the site of initial colonization in Houston Texas.
Resistant kernel connectivity modeling has a number of advantages as a robust approach to assessing functional landscape connectivity for multiple wildlife species. First, unlike most corridor prediction approaches, it is spatially synoptic and provides prediction and mapping of expected migration rates for every pixel in the study area extent rather than only for a few selected “linkage zones” (Compton et al. 2007). Second, scale dependency of dispersal ability can be directly included to assess how species of different vagilities will be affected by landscape change and fragmentation under a range of scenarios (e.g., Cushman et al. 2010a). Third, it is computationally efficient, enabling simulation and mapping across the entire vast geographical extents for a large combination of species (e.g., Cushman et al.
2010b, 2012).
The resistant kernel approach to connectivity modeling is based on least-cost dispersal from a defined set of sources cumulatively across a resistant landscape. The initial source in this case is Houston Texas. The resistance surface is in the form of the cost of crossing each pixel. These costs are used as weights in the dispersal function such that the expected density in a pixel is down-weighted by the cumulative cost from the source, following the least-cost route (Compton et al. 2007).
The resistant kernel analysis was conducted using UNICOR (Landguth et al. 2011). The model calculates the expected relative density of Asian tiger mosquito in each pixel around the source given the dispersal ability of the species, the nature of the dispersal function, and the resistance of the landscape (Compton et al. 2007; Cushman et al. 2010a). I chose a

dispersal ability of 50,000 cost units for the resistant kernel modeling, which indicates that over a single time step (intended to represent a single calendar year) Asian tiger mosquito would have the potential to spread contagiously up to 50km through continuously ideal habitat (e.g. urban areas with resistance 1) and up to 2.5 km through the most resistant land cover features (e.g. open water with resistance 20; Figure S2a).
Selection of Areas of Establishment
The resistant kernel dispersal model describe immediately above predicts spread from currently occupied sites. However, not all of the locations that are within the spread kernel would be suitable for establishment of a population. For example, the kernel may predict spread to occupy areas the landscape, such as open ocean, which have zero fitness value for this species. To address this I transformed the cumulative resistant kernel prediction of density of dispersers with a raster layer of site-specific fitness values for establishment once dispersers reach the spot. In the absence of further information on the effects of different landscape features on fitness and establishment of Asian tiger mosquito, I assumed that suitability for establishment would be an inverse function of the resistance layer, such that fitness for establishment would be zero in open water, one in urban and developed areas, with values in between proportional to the inverse of the resistance layer.
This essentially assumes that the same factors that govern population spread also govern population establishment.
Establishment was modeled by multiplying the resulting cumulative resistant kernel map with a selection surface. The product of the cumulative kernel and selection surfaces was then multiplied by a raster of random numbers between 0 and 1. Establishment locations

were chosen as those that have a value greater than 1 in the product of the random number grid * selection surface * cumulative resistant kernel surface, and resampled such that points were located every 10km within areas meeting the establishment threshold (Figure
S2b).
Long Distance Dispersal through the Interstate Highway Network
Simulation of long distance dispersal through the interstate highway network was done in four steps. First an interstate highway resistance layer was created with value 1 along the interstate highway network and a value of 1000 elsewhere (Figure S3). Second, a cost distance matrix is calculated between all cells in the landscape that are in urban areas across this interstate highway resistance layer. This produces a matrix of costs of moving through the interstate highway network between all urban cells (suitable locations for long distance colonization via transport of tires and other vessels carrying larvae; Figure S3).
Third, the urban cells that are occupied in by established local populations of Asian tiger mosquito, as predicted above using the combination of resistant kernel and establishment prediction, are selected as columns from this cost distance matrix. This produces the locations that are occupied in urban areas that could be sources for long distance dispersal via the interstate highway network, and the associated cost distances from those locations to all other urban cells in the landscape through the cost distance network. Fourth, these cost distance vectors are multiplied by vectors of the square of uniform random numbers between 0 and 1 given that probability of dispersal in a two dimensional surface decreases with the square of the distance (e.g. Landguth and Cushman 2010). All values in the

product between the cost distance vectors and the squared uniform random number vectors that are less than 1000 were selected as new colonization sites.
Defining Source Points for the Subsequent Time Step
Source points for the next simulation time-step are produced by taking the new long distance colonization sites as identified above and adding them to the occupied cells predicted by the resistant kernel and site establishment steps. This combined set of source points is then used as input for the resistant kernel modeling in the subsequent time step.
This five step process iterated for 25 time-steps, corresponding to 25 years since initial colonization. Using this iterative simulation I modeled a plausible pattern of population expansion across a 25 year period. I provide a video file showing this spread to help visualize the combination of contagious spread and long-distance dispersal establishing new population centers along the interstate highway network (Video S1).

References
Compton B, McGarigal K, Cushman SA, Gamble L (2007) A resistant kernel model of connectivity for vernal pool breeding amphibians. Conservation Biology, 21, 788-799.
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368-376.
Cushman SA, Chase MJ, Griffin C (2010a) Mapping landscape resistance to identify corridors and barriers for elephant movement in southern Africa. Pages 349-368 In:
Cushman, S.A. and F. Huettman (eds). Spatial Complexity, Informatics and Wildlife
Conservation, Springer, Tokyo.
Cushman SA, Compton BW, McGarigal K (2010b) Habitat fragmentation effects depend on complex interactions between population size and dispersal ability: modeling influences of roads, agriculture and residential development across a range of life-history characteristics. Pages 369-387 In: Cushman, S.A. and F. Huettman (eds). Spatial
Complexity, Informatics and Wildlife Conservation, Springer, Tokyo.
Cushman SA, Landguth EL, Flather CH (2012) Evaluating the sufficiency of protected lands for maintaining wildlife population connectivity in the U.S. northern Rocky Mountains.
Diversity and Distributions. doi: 10.1111/j.1472-4642.2012.00895.x
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Landguth EL, Hand BK, Glassy J, Cushman SA (2012b) UNICOR: a species connectivity and corridor network simulator. Ecography, 35, 9-14.
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Table S1. Resistance values assigned to NLCD cover types for resistant kernel dispersal modeling
NLCD Class
Open Water
Developed Open Space
Developed Low Intensity
Developed Medium Intensity
Developed High Intensity
Barren Land
Deciduous Forest
Evergreen Forest
Mixed Forest
Pasture/Hay
Cultivated Crops
Woody Wetlands
Emergent Herbaceous Wetlands
2
2
3
7
7
7
1
3
7
Assigned Resistance
1
1
20
1

Figure s1. Resistance map showing areas of low resistance in dark (resistance 1 in full black) and areas of high resistance in white (resistance 20 in full white). The site of initial colonization is Houston Texas, shown within the black circle on the map.

Figure S2. Illustration of first time step of contagious spread from a single location at the center of Houston Texas (a), plus the transformation through multiplying by the selection surface and resampling to produce a set of source points for the subsequent time step distributed at 10km spacing within the occupied zone (b).

Figure s3. Resistance map overlain with the least cost path density network among all major urban areas as function of resistance where resistance along the interstate highway network is 1 and elsewhere resistance is 100. This is done to calculate a matrix of cost distances among all potential urban long-distance colonization sites as function of cost through the interstate highway network from areas occupied by the population. Red pixels indicate locations where many least cost paths among potential urban colonization sites pass, and the density of least cost paths decreases to 1 in the darkest blue color pixels.