Data pre-processing

The original NRRS data are held by USDA Animal and Plant Health Inspection Service, Plant Protection and Quarantine Division, Fort Collins, CO. The available data spanned the period January 2004–September 2009 and documented approximately 7.2 million visitor reservations, including reservations from Canada, at federally operated campgrounds and recreational facilities throughout the continental US. The format and content of the NRRS data records, each of which included geographic information for a visitor origin location and a destination campground, are described in more detail in Koch et al. [16].

Before implementing these data in the network model, we pre-processed them in two key ways. Firstly, we filtered the reservation records according to a period of peak emergence for bark- and wood-boring insects (i.e., insects most likely to be transported in firewood). As with other categories of insects, the establishment success of any borer species is contingent on its developmental stage at the time of its introduction [31], [40]. Borers typically require 1–3 years to complete a single generation, with the actual length of time depending on the individual species and the nutritional quality of its host tissue [22], [41]. Regardless, we presume that the risk of successful borer invasion is greatest during the time of year when adult insects typically emerge from their current host (a piece of firewood in this case) and begin searching for new hosts [40]. For most borers, adult emergence usually occurs during late spring and early summer [42]–[44].

When implementing the model, we only retained those NRRS reservation records where both the visitor origin location and destination campground location were in the late spring-early summer period when the visit occurred. We intended for the model to be generic for all borer species rather than any one particular species, so we defined this period using a broad (10-week) time window. However, the calendar dates corresponding to the beginning and end of this climatic season vary geographically throughout the US and Canada in relation to factors such as latitude and elevation. Our procedures for accounting for this variation, as well as some of our related assumptions, are outlined in Appendix S1 in the Supporting Information.

Our second pre-processing step related to our ability to parse the selected NRRS data into a set of unique pathway segments. Each reservation record in the NRRS data represented a single “trip” between a pair of origin and destination locations. The full data set included more than 50 000 visitor origin locations (i.e., postal codes) and more than 2 500 destination campgrounds, yielding more than 973 000 pairwise origin-destination combinations with at least one trip between them. Fundamentally, the network model was formulated as a first-order transition matrix [45] that operates on every pairwise combination of origin and destination locations (i.e., nodes) in the network. It was computationally impractical to build a transition matrix model involving this many combinations, so – in contrast with previous applications of this modeling framework [37], [39] to smaller initial data sets – we aggregated the NRRS data at a moderately coarse spatial resolution. We divided our area of interest (the contiguous US and southern Canada) into a continuous grid of 15×15 km map cells, and then assigned all of the origin and destination locations documented in the NRRS data to the map cell in which they fell. For each cell, we calculated the total number of trips associated with the origin locations it contained, and separately did the same for its destination locations. Additionally, we dropped any pairwise combination that was associated with three or fewer trips during our study period (January 2004–September 2009). This was necessary for the aggregation process to conform to our available computational resources. Although omitting these pairwise combinations limited our ability to model certain low-frequency events (e.g., campers traveling from small communities to infrequently visited campgrounds), it only had a minor effect on the aggregated map cell values and did not change the primary patterns of camper travel behavior. The aggregation process yielded a set of ≈15 000 unique map cells representing network nodes.

Model development

Briefly, we used the model to perform repeated simulations of camper movement (and thus potential firewood transport) from each location to other locations via the pathways comprising the network. We then compiled these simulation results to estimate the relative risk, φ_ij, of a forest pest being spread by campers from a given location (i.e., map cell), i, to another location (cell) of interest, j. In turn, the φ_ij output values provided a foundation for further pathways-related analyses.

In this networked set, any two cells i and j were connected by a unique pathway segment, ij. Each ij had a value, m_ij, which represented the total number of trips from i to j over the study period, as well as a value, m_ji, representing the number of return trips from j back to i over this period. Recall that we have assumed that a constant proportion of all camper travel (i.e., irrespective of direction) involves the movement of infested firewood, and that firewood is the dispersal vector of interest. To structure the model so that it depicted all relevant trips, including relevant return trips from campgrounds, we had to address the possibility that campers might not use all of their firewood upon reaching their destinations. Quantitative data about firewood transport and usage are scarce, especially with respect to wood left unburned after camping trips. We approximated m_ji based on a Wisconsin study [46], which reported that 15% of firewood-carrying campers bring unused firewood home with them. In terms of the network model, this meant adding a complementary return segment, ji, for each pathway segment ij, with an associated number of trips, m_ji = 0.15m_ij.

Although the principal reason for including these m_ji values was to depict potential forest pest transport in unburned firewood brought back to campers’ homes, aspects of our network model implementation afforded them a somewhat broader role. Because the underlying NRRS data were aggregated at the level of 15 km cells (i.e., each cell incorporated multiple origin and destination points from the initial data set), and because each cell served as both a potential origin and destination location in the model, the m_ji values can be seen as generally enhancing the possibility of secondary transmission of forest pests between map cells. Conceptually, secondary transmission may not just involve the movement of infested firewood from a campground to a camper’s home, but also from one campground to another, or even between communities. Hence, the m_ji values, as implemented in this case, may provide the model with a certain degree of realism. At the same time, the limited evidence for our fundamental assumption (i.e., m_ji = 0.15m_ij) emphasizes that the model output values should be interpreted cautiously.

We incorporated the m_ij and m_ji values into an n×n matrix of travel frequencies, M, where n represents the total number (≈15 000) of unique map elements (15 km×15 km map cells) in the aggregated NRRS data. The non-diagonal elements of M were the m_ij and m_ji values for the pathway segments connecting each pair of map cells:(1)All diagonal elements of M (i.e., elements where i = j) were set to 0. Overall, M was a sparse matrix with a large proportion of the non-diagonal elements also set to 0; even after the NRRS data aggregation process, many map cell pairs had no recorded travel between them during the study period, so the number of non-zero m_ij (and m_ji) values was far below the theoretical maximum (≈15 000*≈15 000).

From M, we developed another matrix, P_t, which depicted, in relative terms, the risk of forest pest (i.e., wood-and bark-boring insect) dispersal via camper travel along the pathway segments during the study period t. In estimating the elements of P_t, we assumed that p_ij, the risk of dispersal along a given segment ij, was linearly related to the frequency of camper travel, i.e., the number of trips from i to j during t:(2)where λ_t is a scaling parameter. Preferably, this parameter would allow us to calculate the total likelihood (i.e., over the study period t) of camper transport of infested firewood from i to j in the matrix. Indeed, knowing the precise value of λ_t would be critical if one wanted to estimate an exact probability of a specific pest being moved from a given i to a given j. However, we did not need absolute estimates of p_ij to achieve our goal of ranking map locations using the model output values as a relative risk measure. In this case, the only requirement for λ_t was that it was sufficiently small to guarantee that the sum of the values in each row of P_t was below 1.

Each row of P_t included an additional variable, p_{i term}, which represented the chance that no camper travel (i.e., to any j) would proceed from i:(3)As this equation suggests, if p_{i term} was equal to 1 for any row, then the map cell i associated with that row did not function as a point of origin in the pathway model. However, this did not preclude the location from functioning as a potential destination j.

The matrix, P_t, of the relative risk of dispersal by campers traveling along each pathway segment was thus specified as follows:(4)We used P_t as the basis for stochastic pathway simulations of camper travel (and the corresponding dispersal risk) from a particular map cell i to other map cells in the study area. Setting i as the origin location, the model extracted the vector of values associated with i (i.e., the values in row i) and used them to simulate camper travel from i through the network to other map cells. In short, for each i, the model used the associated vector of values to select the next map cell. The simulation of an individual trip’s path proceeded until reaching a final destination (i.e., a map cell with no outgoing travel), or instead, when a terminal, no-travel state was selected based on the p_{i term} value. The summary risk, φ_ij, of camper-facilitated forest pest dispersal from a given cell i to a cell j of interest was then estimated as follows:(5)where M_ij is the number of times pathway travel from i to j was simulated to occur, and M is the total number of simulations (M = 4×10⁶ in this study). As a proportional measure, φ_ij is bounded between 0 and 1, and is perhaps most easily interpreted as an ordinal score indicating the level of dispersal risk from i to j.

The large number of repeated model simulations allowed us to represent multi-destination itineraries (i.e., campers traveling to multiple campgrounds before returning home), despite certain data limitations. Multi-destination recreational travel is common in the US and Canada; it may be motivated by such considerations as cost-efficiency or the wider array of recreational opportunities that are available when incorporating several destinations into a single trip [47], [48]. Unfortunately, due to privacy concerns, all personally identifiable information was deleted from the original NRRS reservation records, so we had no documentation of instances where a camper made reservations at multiple campgrounds on consecutive or near-consecutive dates. However, through repeated model simulations, we constructed a comprehensive set of travel paths originating from each map cell. Many of these paths included one or more intermediate destination cells in addition to the final destination map cell. These multi-destination paths were incorporated in the φ_ij values, which summarized all travel paths involving cells i and j, whether or not the paths actually ended at j.

Applying the network model for analysis

The network model can be used to create maps where any individual location in the potential area of concern can be set as the origin (for forward pathway analysis) or destination (for reverse pathway analysis) location of interest. These types of location-specific maps are useful for analyzing particular invasion scenarios, such as identifying the most likely source locations if an individual map cell was invaded by a pest of interest. For example, Appendix S2 in the Supporting Information presents both forward and reverse pathway analysis maps for the Yosemite Valley area of Yosemite National Park in California. Yet, pathway analysis maps have limited utility for establishing regional-scale management priorities, since they do not provide a comprehensive overview of the invasion risks associated with camper travel (and firewood transport). An extra analytical step is required to summarize the model results in a broader geographic context. Previous work [15], [16], [19], [23] suggests that campers often travel across state or provincial borders. Furthermore, regulatory decision making with respect to invasive species, such as the enactment of firewood restrictions to reduce pest spread, usually takes place at the state or provincial level [49]. Therefore, we developed model outputs that identified those locations outside a state or province of interest that were most strongly linked to locations inside the state or province.

For each US state and Canadian province, we constructed a map where, for each cell i outside the target state (province), we summed the model-derived risk values (i.e., the φ_ij values) for all pathways between that cell i and any destination cell j within the target state (province). Each map thus depicts the most likely external source locations if a camper-associated forest pest were to be found within the state (province) of interest. Note that for the Canadian provinces, we assume that campers returning from the US could still be transporting forest pests despite biosecurity measures that restrict cross-border movement of firewood. A primary purpose of these maps is to identify significant “bottleneck” locations where surveillance, firewood inspections, public awareness campaigns, or other response procedures may be most cost-effective in terms of protecting the state (province) of interest from camper-facilitated forest pest invasions [50].

We created origin risk maps for the 48 contiguous US states as well as seven Canadian provinces bordering the US. We omitted New Brunswick, Prince Edward Island, Newfoundland and Labrador, and the three Canadian territories because the amount of camper travel associated with each was insufficient to generate a meaningful origin risk map. As noted earlier, the φ_ij values shown in the maps should only be interpreted as a relative measure of camper-related pest dispersal risk. However, the maps share a single frame of reference because they were generated using the same underlying pathway matrix, which encompassed the entire study area.

Decision making implications of the observed risk patterns

The distinct patterns observed in the origin risk maps suggest that no single response strategy may work for all states and provinces. For example, the origin risk map for Alabama (Figure 1) suggests that most of the campers coming from outside the state originate in adjacent areas of neighboring states like Georgia and Mississippi; thus, most out-of-state camper-transported firewood is sourced locally. These campers are probably more familiar with the region’s geography and local road network than campers from farther away. So, when traveling to campgrounds in the neighboring state (i.e., Alabama), they are probably less restricted to interstate highways or other primary roads. If one were attempting to establish a surveillance or firewood inspection campaign in such a region, an area-distributed approach that targeted a variety of locations (e.g., gas stations, grocery stores, and home and garden stores, in addition to campgrounds) throughout the region might work better than exclusively targeting locations along interstate highways or other high-traffic routes. Furthermore, wide distribution of public awareness materials throughout the region might be necessary for those materials to reach their intended audience of potential campers (e.g., roadside billboards about firewood and forest pests, as well as advertisements on television, radio, and social media).

In contrast, the origin risk map for Arizona (Figure 2) suggests that an area-distributed response strategy may not be practical for that state. Compared to Alabama, much more of the firewood coming into Arizona from out-of-state probably originates a long distance away. This may reduce the effectiveness of area-based surveillance or inspection schemes designed to detect emerging pest problems at a regional scale. It may also make coordinating public awareness efforts with neighboring states less effective. Consequently, for Arizona and similar states or provinces, it might be expedient to target locations (e.g., truck stops, rest areas) near interstate highways and other major roads, since these routes could essentially represent bottlenecks in the movement of campers and firewood. Another option might be to direct efforts toward the most heavily visited campgrounds, so response actions are focused on specific destinations rather than a large and diffuse set of likely origin locations. A state or province facing such circumstances might also consider joining with other states or provinces in national-scale public awareness efforts, which may lack the immediate impact of local- or regional-level efforts but are still likely to provide some benefit.

A few broadly operating factors might help explain the observed patterns of origin risk. Within the context of our model, any factor that substantially affected the number of people traveling to (and from) particular locations likely had some influence on the observed patterns. For instance, because the network model was bi-directional (i.e., it also simulated return travel by campers), the human population of a target state or province probably influenced the φ_ij values depicted in its origin risk map, even though these values corresponded to cells outside the state or province. Indeed, we did see evidence of this: the origin risk maps of heavily populated states and provinces tended to display a greater range of φ_ij values, and higher values overall, than sparsely populated states and provinces. Another potentially influential factor was the extent of the recreational opportunities available in a target state. States containing a small number of highly popular recreational destinations, such as Arizona (Figure 2), seemed to exhibit a dispersed pattern of origin risk, while states with many but comparatively low-traffic recreational destinations, such as Alabama (Figure 1), typically exhibited a more localized pattern. Admittedly, our interpretations of the roles of these factors are conjectural. Quantitative analysis of these and other possible explanatory drivers could be a fruitful direction for future work.

Limitations of the analysis

In implementing the network model, we adopted two simplifying assumptions that merit further discussion. Firstly, we assumed that all visitors to campgrounds, regardless of where they originated, were equally likely to be transporting infested firewood. This may seem like a questionable assumption, since one might expect that visitors traveling to campgrounds in adjacent states are more likely to be transporting firewood than campers who travel across several states to reach their destinations. Indeed, some longer-distance campground visits could involve air travel, which would almost certainly prevent a visitor from bringing firewood from home. Nonetheless, because of the relative remoteness of the campgrounds from urban (or rural) settlements, we can confidently infer that virtually all visitors documented in the NRRS data – even those who may have flown part of the way – arrived at their destination campgrounds via car or some other passenger vehicle, and thus had some opportunity to bring firewood with them. Certainly, any camper bringing firewood into a campground could have procured the wood locally rather than transporting it from home or another distant location, thereby greatly reducing the chance of introducing a truly alien forest pest. Unfortunately, the NRRS data do not provide information about firewood transport and usage, so we cannot quantify the likelihood of local firewood acquisition for any class of camper. Given our data restrictions, it seemed appropriate to assign all visitors an equal likelihood of transporting infested firewood.

Secondly, in making the assumption of equal probability of carrying firewood, we also implicitly assumed that all campers who transported firewood carried roughly the same quantity of wood, and that a constant proportion of this wood was infested. Both assumptions are debatable. For instance, campers traveling to higher-elevation destinations might be expected to bring more firewood than the average camper because they are likely to encounter colder weather. With respect to the infested firewood proportion, it may be worth noting that wood infestation rates can vary substantially between different insect species. For example, Haack et al. [57] estimated that a single infested log of moderate size (≈1 m in length and ≈10 cm in diameter) could contain 100–250 individual bark beetles, but only 20–30 buprestids (e.g., Agrilus species) or 5–10 cerambycids (e.g., Anoplophora species). This has important implications for successful establishment; a given bundle of infested firewood is far more likely to support a sufficient population of bark beetles than of large borers.

Ultimately, we adopted the aforementioned assumptions because we felt they allowed us to provide meaningful information about camper-related dispersal risk for decision makers, even if that information was only in relative, generalized terms. Of course, our study falls short of being a true probabilistic assessment of the risk of pest dispersal in camper-transported firewood. As illustrated by Haack et al. [57], this risk is at least partially species-dependent. A rigorous probabilistic assessment would therefore require that we focus on one actual species of interest, rather than an unspecified number of hypothetical pests from the broad category of wood- and bark-boring insects. Focusing on one species would permit us to incorporate certain factors into our modeling efforts: the species’ current geographic distribution, including whether campers are traveling to or from an already infested region, as well as the impacts of the current regulatory climate for the species. The geographic distribution of potential hosts would also be relevant. Nevertheless, the data requirements for such an analysis would be substantial. In particular, we would need more specific data on both campers (e.g., the true, distance-dependent proportion of campers that bring wood with them) and firewood (e.g., the real infestation rate of the species of interest) than is available from existing studies [15], [20], [23].

Beyond these assumptions, we should also note that the NRRS data underlying our network model only included visits to federal recreational facilities. We have assumed these data are a reasonable sample of all camper travel, and indeed, we believe these data provide a realistic depiction of the long-distance movements of campers. Nevertheless, our output origin risk maps could change were we to include data from state, provincial, or private campgrounds. In particular, such data might increase the proportion of local, short-distance trips to lesser-known campgrounds in the model. In future work, we will evaluate how camper travel patterns differ when the network model includes state- and provincial-level reservation data in addition to the NRRS data.

Finally, there were computational limitations imposed by the network modeling approach. The aggregation of the NRRS data at the level of 15×15 km cells allowed us to execute a sufficiently large number of pathway simulations within a reasonable amount of computing time. However, through further optimization of the network model and parallelization of the simulations, it would be possible to increase the size of the transmission matrix and run the model at a finer spatial resolution more comparable to the actual resolution of the NRRS data. Note that improving the spatial resolution would not substantially alter the general patterns of camper travel behavior that we described here.