Introduction

Invasive species pose a significant economic and ecological threat to Canada’s forest ecosystems [1, 2]. In North America, significant funding has been allocated by federal, state and provincial agencies for large-scale control programs to prevent or mitigate these damages with mixed success [3, 4]. Controlling the spread of invasive pests can be difficult because the long-distance spread of invasive organisms is often assisted by human activities [1, 5]. For example, introduction and spread of Emerald ash borer, a harmful forest pest in the North America [6–8] has been attributed to human factors, such as vehicle transport [9] and recreational travel [10].

The growing problem of invasive species is broadly associated with human mobility, including recreational travel [1, 5, 11, 12]. Outdoor recreation is widespread in North America, and the extent of recreational activities is expected to increase [13–15]. In North America, national, provincial and state parks, national forests, and state and Crown lands are common destinations for recreational activities [16, 17]. In Canada, recreational activities, especially camper travel, often take place in forested areas and may contribute to spread of harmful invasive pests. In particular, the movement of untreated firewood by campers has been widely acknowledged as a potential introduction pathway for invasive forest pests [2, 10, 18–20]. Movement of untreated firewood has been linked to the spread of two harmful wood-boring pests, the Asian longhorned beetle (Anoplophora glabripennis Motschulsky) and the emerald ash borer (Agrilus plannipennis Fairmaire), in the United States and Canada (USaC) [21, 22].

Firewood is often moved to distant locations by campers for recreational purposes [2, 23]. For example, Haack et al. (2010) has found live bark- and wood-boring insects in 23% of the firewood pieces, surrendered at the checkpoint station at Mackinac bridge connecting Michigan’s Lower and Upper Peninsulas and an additional 41% had signs of prior borer infestation. Jacobi et al. (2011) reported the emergence of live insects from 47% of the firewood bundles purchased from various US retailers. To reduce the risk of future pest infestations, USaC have implemented various regulations on movement of untreated firewood, including bans for out-of-province movement of untreated firewood and restrictions for its transport by short distances [19, 23–25]. Also a number of public outreach campaigns have been undertaken to educate the general public about the threats associated with the movement of untreated firewood and its potential to spread harmful invasive pests. Several strategies have been developed to prevent (or minimize) the movement of firewood with recreational travel, including outreach campaigns in public media, enforcements with the inspections at check points for transported firewood, and area quarantine with the restrictions on firewood movement from/to the area of concern. In particular, public outreach campaigns have become widespread with significant funding by local, municipal, and provincial governments on measures such as advertisements along major highways and in public media and educational information in websites and printed media. The use of enforcement and quarantine options is less common but is gaining acceptance as a last resort measure and was implemented at least a few times over the past decade, to varying degrees of success [10, 18, 25].

Assessing the efficacy of the measures aimed to prevent the movement of firewood with recreational travel is a daunting task. Outreach campaigns may spread information widely but there is no guarantee that campers will pay attention and comply with the firewood restriction warnings. Many outreach activities (such as posting ads in public media or distributing flyers) are often implemented sporadically at local scales using local municipal and provincial budgets [19], which makes the assessment of their efficiency difficult. These activities may simultaneously occur in different places and times with little or no coordination, and are difficult to track in time and space.

Alternatively, the enforcement options (such as quarantine or checkpoint inspections for illegal movement of firewood) are gaining acceptance and may be perceived as more effective localized means to stop the movement of untreated firewood by campers. Nevertheless, assessing the effectiveness of enforcement actions is challenging due to a very small scale of enforcement actions (often implemented by individual states or provinces at selected locations) and lack of compliance data.

Mechanistic models of forest invasions have been studied for decades [26, 27], but explicit modelling and consideration of human factors, and the feedback between humans and the environment is relatively new. Ali et al. and Barlow et al. [18, 28] proposed two models of forest pest spread through firewood transport. The first study presented a differential equation model, and the second an agent-based model, both assuming that humans are the primary long-distance movers of forest pests. The models proposed in [18, 28] coupled infestation dynamics with the social dynamics. However both studies considered a small and idealized spatial structure: two patches in Barlow’s et al. [18] study and ten patches in Ali‘s et al. model [28]. Often, illegal movement of firewood occurs over large distances and may involve visits to multiple recreational destinations that are connected differently to one another.

In this study we consider movement of infested firewood to multiple recreational destinations over a complex recreational travel network. We explore the efficacy of common measures aimed to stop the movement of untreated firewood by recreational travelers. To accomplish this, we propose a mechanistic differential equation model that combines human-mediated movement of forest pests through a camper travel network that includes nonlinear feedbacks from social factors, such as population response to strategies preventing the movement of untreated firewood. We identify three basic methods to stop or slow the spread of invasive pests by transport of infested firewood: public awareness campaigns, direct interception of transported firewood at checkpoints near recreational destinations, and quarantining recreational destination sites for movement of firewood. While the first option is more common, the latter has been implemented seldom over the past decade due to legal and liability constraints [24, 29–31]. We implement the options for intercepting the movement of firewood to slow the spread of invasive pests in a mechanistic metapopulation model, and use the replicator equation to represent social learning dynamics (see [18, 32–34]). We also evaluate local quarantine at recreational destinations as an alternative control method. Quarantine means closing the site to visitors for a length of time, in order to reduce the amount of transported firewood and slow spread of invasive organisms from other infested locations. Our implementation of quarantine measures follow common practices aimed to slow the spread of invasive species (such as the spread of emerald ash borer in USaC [35, 36]). We apply our mechanistic model to explore the effectiveness of these control measures to slow the spread of an idealized wood-boring invasive pest moved to a set of recreational destinations by recreational travelers transporting untreated firewood. We apply the model to a network of provincial parks and campgrounds in three provinces of central Canada—Manitoba, Ontario, and Quebec.

Materials and methods

We consider a landscape of N patches, where a patch is represented as i ∈ [1, N]. Each patch represents a recreational destination (eg. provincial parks and campgrounds) with associated neighbouring human population centres. Each patch undergoes its own internal pest and social dynamics. We describe the spread of an invasive pest with the movement of firewood through the network of N patches with a mechanistic metapopulation model based on [18] that captures the spread of an infestation between the patches. The advantage to metapopulation models in this context is suitability for capturing dynamics of a highly fragmented population spread over a broad geographic region. Using the data documenting reservations of provincial campgrounds in Ontario, Manitoba and Quebec ([37], we created a graph of camper travels which depicts a spatial travel network between origin locations (which correspond to residential addresses of camper travelers) and recreational destinations (campgrounds in provincial parks and historic sites). The camper travel network is described by a graph with coefficients P_i,j denoting the relative frequency of camper movements between origin locations j and recreational destination locations i (see more details on spatial data in section). Specifically, for a given location j, P_i,j is the fraction of trips that go from j to i each year, so we have . Consider a patch i with an enforcement intervention, such as firewood movement quarantine, or a voluntary firewood surrender checkpoint aimed to stop the flow of untreated firewood from that location. We denote C_e as the percentage of infested firewood that can be intercepted on a route between two locations i and j, 0 ≤ C_e ≤ 1. Interception at i may reduce the movement of infested firewood from a patch i to other patches j, so C_e indicates, in relative terms, the magnitude of interception efforts.

We also consider a public outreach campaign that can take place at a patch i. It is common that only a portion of campers visiting a patch i may be aware of and decide to comply with the public outreach message. We model the social awareness campaign as an increase of the net social cost of transporting firewood. We further conduct sensitivity analyses to compare the efficacy of enforcement vs. outreach measures aimed to stop the movement of firewood and reduce the rates of infestation.

Pest spread model

We begin with defining the equation for a population of susceptible host trees that may be attacked by an invasive pest. The pest can be introduced though untreated infested firewood. Variables, their interpretations, and corresponding baseline ranges are shown in Table 1. We assume that a tree population that is susceptible to pest attack undergoes logistic growth in the absence of infestation to a carrying capacity K. The population of susceptible trees, S_i(t), at a patch i is being infested from firewood arriving with campers at i at a rate A: (1) where θ_k(I_i) is a sigmoid function such as (2) Terms S_i and I_i are the number of susceptible and infected trees, respectively, at patch i. B_i is the quantity of infested firewood in patch i, which we assume has the same probability of pest transmission within patch as infested trees. We choose the carrying capacity K to be the same in each patch for simplicity. The term AS_iI_iθ_k(I_i − I_a) represents intra-patch infestation with a density dependent population, parameterized by k and I_a, where I_a determines population of infested trees at which transmission is halved, and k is is a constant which affects the sharpness of the transition of θ_k(x) at I_a. We assume that there is an influx of pest organisms entering a patch i with firewood which defines the propagule pressure at i. Infested trees at i are assumed to die at a constant rate γ, giving the following equation for the infested tree population of a patch. (3) The patches are spatially coupled through the transport of firewood by recreational travelers. The infestation rate at i depends on the number of visitors transporting infested firewood to i, which is also a function of the social dynamics at i, such as the enforcement, or public outreach measures described by a utility function, presented in [33], and applied to forest modelling in [18, 38]. Let L_i be the proportion of visitors to patch i who do not transport firewood and buy it locally, and d rate of exportation of infested logs. The rate of infested wood coming into patch i can be estimated as: The dynamics of L_i (the number of local transporters in patch i), is modelled by a replicator dynamics model that is suitable for describing systems where social learning occurs [33, 34], and is described in the section below.

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Table 1. Parameters and default values.

https://doi.org/10.1371/journal.pone.0238979.t001

Parameterization

We used data from [10] and [37], to quantify the risk of firewood transport to recreational destinations in Central Canada. The data documented the movements of campers to provincial campgrounds in Ontario, Quebec and Manitoba. Such data are maintained by provincial ministries of natural resources (MNRs). The dataset included a large number of potential origin sites (i.e., approximately 9000 locations). To reduce the computational burden, we reduced the size of the camper travel network by including all recreational destination locations but considering only the origin locations in the Canadian provinces of Ontario, Manitoba, and Quebec. We further reduced the size of the network by selecting most travelled routes. We selected the largest subgraph with a minimum degree of 10 (the 10-core of the graph) which considered only the most connected nodes, with largest impact on pest transmission. We implemented the procedure using the NetworkX library [42]. The final camper travel network included 2250 sites (Fig 1).

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Fig 1. Camper travel network in Ontario, Quebec and Manitoba.

Darker (more orange) lines represent more trips.

https://doi.org/10.1371/journal.pone.0238979.g001

Because the model uses a large camper travel network it has a very large parameter space, and many of the parameters, especially those in Eq 8, are difficult to estimate directly from data. In this study we are exploring the region of parameter space that most closely approximates the dynamics in real infestations, such as the typical size and duration of the recent emerald ash borer outbreak in eastern Canada. To select the most relevant range of the social influence parameters, σ, s, f, which are difficult to estimate from the literature, we did sensitivity analyses over a wide range of these parameters, and identified the parameter space where these parameters had the largest effect on the model dynamics, and where the course of the invasion was realistic. The inter-patch and intra-patch infection rate parameters, d, A, were selected to infest and eventually kill at least 95% of the tree population within 10 to 15 years.

We integrated Eqs (5)–(8) using code written in the Julia language, using the JuliaDiffEq library [43]. The integration was run on the Compute Canada clusters. Our primary focus was to explore the relative impacts of firewood enforcement versus public outreach and their abilities to reduce pest infestation rates across the camper travel network. We consider a hypothetical scenario where a harmful invasive pest is introduced in the largest urban center in eastern Canada with foreign imports (Greater Toronto Area, GTA) and assume that the bulk host tree population in the GTA is infested. This scenario is based on a history of past entries of invasive wood-boring pests to the GTA with foreign imports (such as introduction of Asian longhorned beetle in Toronto and Mississauga [44]).

Results

In our baseline scenario (Fig 2, parameters as in Table 1), the model shows a typical pest outbreak originating in the GTA infesting all campgrounds in Ontario, Manitoba and Quebec over 10-20 years. This agrees with the observed timescale of the recent infestation of emerald ash borer (EAB) which entered Ontario in 2002 and now has infested most major populated places in the province [45].

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Fig 2. Time series of model variables as a function of interventions, direct (raising C_e, panels a—d) and through social pressure (raising U, panels e—h).

The former intervention, panels a-d, means an increase of social pressure on people who choose to transport firewood (i.e. increasing the U value), and the latter refers to direct interception of firewood (i.e. increasing the C_e value). Terms , , , are the averages of the state variables over all patches. S(t) has been omitted for brevity.

https://doi.org/10.1371/journal.pone.0238979.g002

First we discuss the timeseries plot of the baseline parameters (Table 1), where the model variables are averaged over all of the patches for easier visualization (Fig 2). Accordingly, we define , , , to be the average infested tree population at t, the average quantity of infested logs at t, and the average fraction of local strategists at t, respectively. In Fig 2, we find that increasing U (the social cost to transport firewood) increases the number of local strategists L(t) (Fig 2h)—people who choose not to transport firewood between patches— and also reduces the size of the invasion, (Fig 2f) and the average number of infested logs, B(t) (Fig 2g). Although the reduction in B(t) is significant (as shown by the large differences in light red and dark red time series in Fig 2g), the flattening of the curve for infested trees (Fig 2f) is comparatively less significant. We can compare this with the result of increasing the fraction of infested logs intercepted between patches, C_e (2a,b,c,d). Increasing C_e decreases the number of infested trees, the delays the peak of the outbreak (Fig 2b and 2c). The delay in the peak of the outbreak also appears to cause the lag in L(t) (Fig 2d). Social incentives appear to be very effective at reducing B(t) while being less effective at reducing I(t). This indicates that a shift from transport strategists to local strategists primarily occurs in areas that have already been infested. This effect does not occur with direct interception of infested firewood. Notably, direct interception is difficult to implement effectively, as even after intercepting high proportions of the infested wood transport, the corresponding decrease in I(t) remains low (Fig 2b).

In Fig 3 we show the total number of infested trees at time t, T(t), with respect to combinations of U, the social cost to transport firewood, and the fraction of infested firewood intercepted, C_e. If the fraction of intercepted infested firewood, C_e, is greater than 80%, we see a sharp reduction in the total infestation, T, even after 20 years (Fig 3c), but lower interception rates have little effect unless the social cost to transport U is above the threshold seen in panel c) (Fig 3). Over a shorter time scale, increasing C_e appears to be effective at all interception rates.

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Fig 3. Total infestation per node over 5, 10 and 20 years.

Neither increasing U nor C_e are effective at long time scales.

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The parameter f controls how the proportion of strategists in a given patch i (L_i(t)) responds to the population of infested trees (I_i) in that patch (Eq 8). Since social incentives (such as an intervention to human-mediated pest transport) tend to be less effective because they prevent firewood transport mostly in the areas that have already been colonized by pests (as suggested in Fig 2), we consider how the parameter f affects the marginal returns on U over time (Fig 4). The shade of the blue region in Fig 4 represents the degree to which increasing U is beneficial, corresponding to a negative slope in the linear approximation of the change in T with respect to U (Fig 4 inset). Similarly, a red cell indicates non-negative slope and therefore a neutral or detrimental marginal effect. We begin to see the benefit of increasing U after about 10 years, shown by the transition from lighter blue to dark blue as we move from the bottom of the image to the top (Fig 4. This relationship is only affected slightly by altering the impact of local infestation on local strategy, f, where we begin to see slightly detrimental marginal returns after 10 years if f < 0.04.

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Fig 4. Efficacy of social incentives on infestation after time T.

Inset graph shows an example of cross-section along the line f = 0.11 The influence of infestation on transport strategy, f, can hinder the intervention by public outreach, in the long-term (after approximately 20 years). The inset figure illustrates how one column in the heat map, shown by the dotted line, is constructed from the slopes of linear approximations of T(t) over U ∈ [−5, 5]. The blueness of the lines going left to right is a function of their slope, corresponding to the color of the cells in the heatmap.

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Similarly, we have compared the marginal returns on increasing U with respect to the intra-patch transmission rate A and time t (Fig 5). When A is small (A ≤ 0.0009, beneficial marginal returns on U can be observed over the whole duration of the infestation. We further explore the impact of varying the rate of transmission of infested firewood between patches, d (Fig 6). We find a roughly parabola-shaped region in the parameter plane of intra-patch and inter-patch transmission rates (A and d respectively), above which the marginal returns of increasing U are zero or possibly detrimental to the size of the total infested population after 10-20 years. Larger intra-patch transmission rates enable the pest population to establish earlier in a given patch by propagules. We see good marginal return in parameter regimes where few transport strategists (high L(t)) would reduce the reproductive ratio of the infection below 1. For instance, at the point (A, d) = (0.00126, 0.103), increasing U is able to delay and eventually prevent a second wave, which decreases the total number of infected trees significantly (S1 Fig). If the transmission rates A, d are high enough that even with no transport strategists, we get a second wave of infection, the effect of increasing U can be slightly detrimental (S2 Fig). Panel f) of the aforementioned figures plots the number of patches where I ≥ 1 over time, showing that the detrimental effect is largely due to the infection persisting longer in the network.

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Fig 5. Efficacy of social incentives on infestation after time period T with respect to A, the intra-patch infestation parameter.

This intervention becomes ineffective over time if A is sufficiently large.

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Fig 6. Efficacy of social incentives on infestation after time T intra-patch spreading rate A, affects infestation outcomes.

The social incentive to not transport firewood, U, is more effective with lower pest spread rates.

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We also explored the effectiveness of patch quarantine by replacing model Eqs (6) and (7) with Eqs (9)–(12). This replacement prevents individual patches (nodes in a set V) with the highest betweenness centrality (with respect to the weights P_ij) from interacting with their neighbours during the time of the quarantine (t ∈ [t₀, t₀ + Δt]). Imposing quarantine on these nodes is expected to have the greatest impact on pest transmission rate. If the quarantine is initiated one year after the pest is introduced into the system (that is, t₀ = 1.0) then we find a significant reduction in total infestation even if only 50 patches are quarantined (|V| = 50) assuming they are quarantined for more than a year, shown in Fig 7. However, in our model, we find that quarantines need to be longer than approximately three years, and involve more than 150 nodes to still be effective in reducing the total infested population after 20 years T(20). An interesting result in our quarantine plots is that we see a slightly larger range of effective parameter values if the quarantine begins after two years, t₀ = 2.0 (Fig 8), rather than one, t₀ = 1.0. This effect is probably due to the delay in infestation after the model is initialized, which can be seen by the local minimum in the infestation timeseries (Fig 2b and 2f).

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Fig 7. Average total infested trees (T(t)) after 5, 10 and 15 years (panels a),b), and c) respectively), assuming the quarantine begins one year after the pest is introduced.

Total infestation plotted with respect to the number of nodes quarantined (|V|) and the length of the quarantine (Δt). The quarantine is effective over 5 years with only 50 patches, provided they are closed for over a year.

https://doi.org/10.1371/journal.pone.0238979.g007

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Fig 8. Average total infested trees (T(t)) after 5, 10 and 15 years (panels a),b), and c) respectively), assuming the quarantine begins two years after the pest is introduced.

Total infestation plotted with respect to the number of nodes quarantined (|V|) and the length of the quarantine (Δt).

https://doi.org/10.1371/journal.pone.0238979.g008

Conclusion

We presented a model coupling human social behaviour regarding transport of infested firewood through recreational travel with a model of the spread of an invasive forest pest. Our main focus was to compare, in relative terms, common measures for slowing the spread of invasive species with firewood transport, such as public outreach campaigns aimed to raise awareness about the problem, and enforcement measures, including inspections at checkpoints to control the movement of firewood, and location-specific quarantine. The model is parameterized with campground reservation data for provincial parks and campgrounds in the provinces of Ontario, Manitoba and Quebec, Canada and incorporated spatial information on the topology and geographical configuration of the camper travel network.

Under the assumptions of our model and a particular camper travel network configuration used in our model, checkpoints to control the movement of untreated firewood are unlikely to be effective at slowing the spread of invasive forest pests with firewood transport given typical moderate levels of funding and long delays in the response measures. We find the rate of interception to halve the total infested tree population after 5 years is about 30% (Fig 3), which is unlikely to be achieved in practice given typical limited budgets and personnel constraints in present-day firewood control programs. Given that our model uses somewhat simplified assumptions and does not account for fine-scale logistical constraints (which are inspectors may face in various spatial locations) the actual rate of interception is likely to be lower in practical conditions. While a previous study [18] that used a similar model has demonstrated that social incentives may improve outcomes in a two-patch model under equilibrium conditions, we have found that in our complex landscape network, the outcomes of infestation and invasion control measures are highly dependent on the time scale and the characteristics of the invaders, such as the inter-patch and intra-patch infestation rate. Social incentives (which aim to decrease the transport of firewood, U), are generally able to reduce the infestation rate in the short term but its effectiveness is highly dependent on the ability of the pest to spread and infest other locations (Figs 5 and 6) under the conditions we have explored. Humans in our model tend to reduce their transport of firewood between patches in already infested areas, which causes the pest to persist longer in the network (Fig 2). Our results show that there could exist a threshold in the pest transmission rate A and the proportion of the infested wood which is turned into firewood, d (Fig 6). Below this threshold, it would not be beneficial to increase social outreach (i.e., increase U). This insight could be helpful in determining the spatial allocation of firewood movement control efforts for a particular pest species. We have also found that the location-specific quarantines that aim to restrict the movement of firewood to/from a particular location, might only be effective at slowing the invasion spread if a sufficiently large number (at least 140 in our case) of highly connected locations is quarantined, and the quarantine is established at early stages of infestation (Figs 7 and 8).

Given the typical cost limitations and logistics constraints faced by today’s firewood control programs, and the assumptions made in our modeling framework, it is unlikely that local quarantine measures could significantly slow the spread of invasive pests through firewood unless drastic control and quarantine measures are undertaken. Public outreach campaigns, while helping increasing awareness of problem, cannot reliably slow the spread of pests within the parameter values tested, when the invasion spreads through a network based on camper travel data in Manitoba, Ontario and Quebec. Within our model, public outreach could be more effective for slow-spreading pests when the organism is able to kill host trees quickly but does not have significant spread capacity (that is, the inter-patch and intra-patch infestation rates are sufficiently small). Direct intervention, such as checkpoint inspections for illegally transported firewood, is also not an option, because meaningful outcomes can only be achieved if significant fractions of firewood transports can be intercepted. We find that patch quarantine is effective at slowing, or even stopping, the spread of an invasive forest pest when a large number of highly-connected patches are quarantined, for a long enough period. Our results in general terms agree with a present-day situation when numerous outreach and local quarantine measures had limited impact on illegal transport of firewood by campers and failed to slow the spread of wood-boring pests transported with untreated firewood. Our results also indicate that the enforcement campaigns aimed to intercept illegal movement of untreated firewood can only be effective if implemented at very large spatial scales in timely fashion (which, in turn, would require massive amounts of funding and personnel support).

There are some shortcomings to our model that could be addressed in future work. The interventions we study do not have spatial or time specifications for individual locations in the camper travel network. Deciding where and when, to deploy the outreach and enforcement measures in a particular location would be a major enhancement of the model. Second, our model depicted a general problem of an invasive pest spreading with untreated firewood moved by recreational travelers. To adapt the problem to a particular pest species, a more specialized spread model will be required. We simplified the model by assuming that each infested patch provides similar propagule pressure to recreational travellers leaving the infested site. This assumption was made because no data about the actual proportions of infested wood carried by recreational travellers leaving the infested sites were available. Also, our analysis did not offer much insight at the level of individual spatial locations in a camper travel network. A simpler mechanistic model that applies unique pest control decisions at individual spatial locations could potentially address that aspect. Another possible way to simplify the model would be to remove the tree growth dynamics —since it operates on a longer time scale than the infestation spread— and so an invasion model without the forest growth component could be a reasonable approximation for short-term planning horizons. This will be the focus of future efforts.

Supporting information

Acknowledgments

The authors would like to thank Dr. Hanno Seebens and an anonymous reviewer for their contributions. Their detailed and thorough suggestions have significantly improved the quality of our paper.