Optimal planning for mitigating the impacts of roads on wildlife

Authors

  • Tal Polak,

    Corresponding author
    1. School of Biological Sciences, The University of Queensland, Brisbane, Qld, Australia
    2. ARC Centre of Excellence for Environmental Decisions, The University of Queensland, Brisbane, Qld, Australia
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  • Jonathan R. Rhodes,

    1. ARC Centre of Excellence for Environmental Decisions, The University of Queensland, Brisbane, Qld, Australia
    2. School of Geography Planning and Environmental Management, The University of Queensland, Brisbane, Qld, Australia
    3. The National Environmental Research Program (NERP) Environmental Decision hub., Brisbane, Qld, Australia
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  • Darryl Jones,

    1. Environmental Futures Centre, School of Environment, Griffith University, Brisbane, Qld, Australia
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  • Hugh P. Possingham

    1. School of Biological Sciences, The University of Queensland, Brisbane, Qld, Australia
    2. ARC Centre of Excellence for Environmental Decisions, The University of Queensland, Brisbane, Qld, Australia
    3. The National Environmental Research Program (NERP) Environmental Decision hub., Brisbane, Qld, Australia
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Summary

  1. Roads have a significant impact on wildlife world-wide. Two of the ways to mitigate the impact of roads are to improve connectivity and reduce mortality through fences and wildlife crossings. However, these are expensive actions that will have different effects in different places. Thus, deciding where and how to act in order to achieve the greatest return on investment is crucial. Currently, there are no quantitative approaches to prioritize different road mitigation options.

  2. Here, we use a decision science framework to determine the most cost-effective combination of actions to mitigate the effects of roads on wildlife under budget constraints. We illustrate our approach using a case study of a threatened koala Phascolarctos cinereus population in south-east Queensland. We applied a spatially explicit population model to explore the benefits of three kinds of mitigation actions: no action at all and fences with or without crossings, on different road segments.

  3. We explored the trade-off between expected koala population size, relative to the best outcome, and budget. There is a strong demand for mitigation as the already declining population was reduced even further when no mitigation was employed, while applying the most cost-effective combination of mitigation actions minimized that decline. Additionally, uncertainty in species attributes (speed of crossing a road and population growth rate) affected population viability but not the decision about which suite of actions (mitigation measures) to take – so our advice on the best action is robust to uncertainty even if the outcome is not. Most importantly, the trade-off curves between investment and population size are almost linear in this case study. Hence, there is no cheap solution and any reduction in the budget will result in a substantial reduction in expected population size.

  4. Synthesis and applications. This is the first time that the problem of mitigating the effects of roads on wildlife was formulated mathematically and systematically using decision science. Our approach is adaptable to a diversity of species and systems affected by road mortality allowing flexibility for a range of mitigation actions and biological outcomes. Our method will allow managers and decision-makers to increase the efficiency of mitigation actions.

Introduction

Roads are a global threat to biodiversity (Laurance & Balmford 2013). In general, roads have negative effects on species abundance by increasing mortality, reducing connectivity, reducing habitat size and quality and altering animal behaviour (Fahrig & Rytwinski 2009), all of which usually lower the viability of wildlife populations. Of these effects, direct mortality is the most significant and widespread effect of roads on wildlife (Bissonette 2002). Road mortality is relatively non-selective and can often affect healthy as well as sick or weak individuals (Bujoczek, Ciach & Yosef 2011), which means that it can affect population viability more than mortality sources that preferentially affect less-fit individuals, such as predation. Previous studies on the effects of roads on wildlife give us information on the impact of roads on populations of different species, or potential management actions that may reduce road-related mortality, but none tell us how to choose between different actions. Moreover, none had considered the conservation return on investment from these mitigation actions. Even if we know where to locate mitigation efforts and which species are more vulnerable, there is rarely enough funding to undertake every possible mitigation action.

Road attributes such as traffic intensity negatively impact population densities in many species largely via mortality (Fahrig et al. 1995; Jones 2000; Gibbs & Shriver 2002; Gunson, Chruszcz & Clevenger 2003; Summers, Cunnington & Fahrig 2011) but also by changes in behaviour (Jaeger & Fahrig 2004; Parris & Schneider 2009; Berthinussen & Altringham 2012; Northrup et al. 2012). For example, traffic noise was found to affect the frequency of communication calls in both birds and frogs which can affect their breeding success (Parris & Schneider 2009; Parris, Velik-Lord & North 2009). Roads can become dispersal barriers due to road avoidance (Shepard et al. 2008; Jackson & Fahrig 2011) or movement restriction (Pepino, Rodriguez & Magnan 2012). Even minor roads can have significant impacts on mortality rates (van Langevelde, van Dooremalen & Jaarsma 2009) and/or animal behaviour (Moreau et al. 2012). Road-related mortality affects species differentially depending on their life-history traits. For example, mammals that are large, mobile and have a low reproductive rate, highly mobile birds and amphibians with low reproductive rates and/or small body size will probably exhibit relatively high road-related mortality (Rytwinski & Fahrig 2012). Similarly, butterflies with shorter wingspan (Skórka et al. 2013) or swallows with longer wingspan (Brown & Bomberger Brown 2013) suffer from higher road mortality. For dragonflies, flight height and agility are significant determinants of road-related mortality (Soluk, Zercher & Worthington 2011).

In response to this threat, there is a growing body of literature on how to mitigate the negative impacts of roads. For example, fencing roads reduces mortality (Clevenger, Chruszcz & Gunson 2001), increases population persistence (Jaeger & Fahrig 2004) and can facilitate movement and gene flow when combined with wildlife crossings (Gunson, Chruszcz & Clevenger 2003; Roger, Laffan & Ramp 2011). Slowing traffic speed and warning signs can also mitigate the effect of roads, although the results of studies are varied, from little evidence of positive effect (Bruinderink & Hazebroek 1996; Dique et al. 2003b) to facilitation in population recovery (Jones 2000). Since road effects are a widespread ecological problem (Bissonette 2002), and the mitigation processes can often be expensive (Forman et al. 2010), there is a need to maximize the cost-effectiveness of road mitigation.

In many studies, researchers have used predictive modelling techniques to try and identify how to increase the efficiency of road mitigation. Most of these studies focused on environmental factors or road attributes that increase animal–vehicle collisions, in order to predict areas prone to high collision rates (Seiler 2004, 2005; Neumann et al. 2012) and select the best location for mitigation efforts (Malo, Suarez & Diez 2004). Other studies have focused on determining the species most vulnerable to road impacts. For example, Jaeger et al. (2005) compared population persistence depending on different road attributes and species behaviour towards roads. They found that species that avoided roads showed higher vulnerability to the negative effects of roads; further, high traffic volume has the strongest negative influence on population persistence of all road attributes examined. Langevelde & Jaarsma (2005) used traffic flow theory to calculate the probability of successfully crossing a road in a two-patch population model to estimate the impact of road mortality on population dynamics of mammals. This large volume of research on the effects of roads on wildlife has provided valuable ecological information, but in conservation, information needs to be translated into decisions and then actions.

Decision science is a rational and transparent way of determining the best action given multiple objectives. A variety of tools and approaches have been developed to allow managers and policy makers to arrive at ‘optimal’ decisions on how to apply conservation efforts within social and financial constraints (Possingham et al. 2001; Salafsky et al. 2002; Naidoo et al. 2006; McDonald-Madden, Baxter & Possingham 2008; Wilson, Carwardine & Possingham 2009; Shwiff et al. 2012).

Here, we apply decision science to the problem of mitigating the impacts of roads with the aim of finding the best solutions to this problem for a range of possible costs. We mathematically formulate the problem of prioritizing different road mitigation actions to maximize expected population size at different mitigation costs. To illustrate the approach, we solve this problem for a vulnerable koala Phascolarctos cinereus population living in habitat patches separated by roads on the Koala Coast, south-east Queensland, Australia. We delineate the trade-off between potential biodiversity benefits and economic cost by exhaustively exploring all possible combinations of three mitigation actions (fencing without wildlife passage, fencing with wildlife passage and no action) over a system of patches divided by four road segments. The flexible nature of our method allows it to be adjusted to the needs of other species in different systems, as many of the components of the formulation and the biological model can be changed to fit a new system. As such, our systematic approach can assist decision-makers world-wide to make informed decisions on where and how to invest their money, which is a crucial step in increasing the cost-effectiveness of conservation investment in mitigating the effects of roads on wildlife.

Material and methods

Study area

The Koala Coast is a 375-km2 area located 20 km south-east of Brisbane, Australia (Fig. 1). The area is a mosaic of urban, industrial, agricultural and natural habitats, fragmented by a complicated web of roads (Dique et al. 2003a). The Koala Coast contains the largest natural koala population living in an urbanized landscape adjacent to a capital city and is consequently of significant economic and cultural value (Dique et al. 2003b). The Department of Environment and Resource Management (Department of Environment & Resource Management 2012) estimated a decline in population size of 68% between the years 1996 and 2010 in the Koala Coast koala population. Additionally, they found little evidence that the population decline was due to habitat loss. Road mortality is recognized as one of the major causes of mortality in this koala population (Dique et al. 2003b; Rhodes et al. 2011) with an average of nearly 300 deaths a year (Dique et al. 2003b) in south-east Queensland. About half of the deaths of dispersing individuals are due to vehicle collisions (Dique et al. 2003a) with risk of collision increasing with both traffic volume and speed (Dique et al. 2003b). Additionally, roads were found to be a key barrier to genetic flow in the south-east Queensland koala population (Dudaniec et al. 2013). Over recent years, there has been a reduction in the number of koala–vehicle collisions, but this is probably because the population is in decline (Department of Environment & Resource Management 2012).

Figure 1.

Study area – the Koala Coast in south-east Queensland, Australia. Hatched area represents the study site within the Koala Coast.

Road mitigation problem formulation

We created a female-only population model of four populations separated by roads (for details, see Table 1, Fig. 2). For simplicity, we assumed that this is a closed system where movement can only occur among these four populations, and each year individuals have the opportunity to disperse. While decision theory can support more complex model formulations, we chose to create a relatively simple population model to serve as a tractable example, as our intent in this study was to explore decision theory application to the problem of road mitigation. We identified three alternative actions for road mitigation: (1) ‘Do nothing’ – animals are free to cross the road and may be hit by a vehicle; (2) ‘Fence only’ – the entire length of the road is fenced so that there is no road mortality at all, but connectivity is eliminated, and (3) ‘Fence and Wildlife crossing’ – the entire length of the road is fenced with a wildlife crossing in the middle, allowing safe passage to the other side to animals that find the crossing. In order to find the optimal solution, we explored the consequences of all mitigation combinations (34 = 81, each of the four road segments dividing the four populations can have one of three possible actions as mentioned above) on the mean population size with each combination run for 100 years (with 1000 simulation repeats).

Table 1. Models' input variables – Top half of the table contains attributes of the four Koala populations – patch size (ha), koala density (koala ha−1) and initial population size (overall and females only). Bottom half describes road characteristics – length (m), traffic density (vehicle h−1) and the probability for a koala to safely transverse the road at three possible koala velocities (5000–15 000 m h−1) for the four roads separating the four koala populations
 Patch size (ha)Koala density (koala ha−1)Initial pop sizeInitial females
Pop 1275·650·1514221
Pop 2580·820·0875125
Pop 3251·930·050136
Pop 4278·040·1444020
Overall1386·450·114572
 Road length (m)Traffic density (vehicle h−1)aProbability of safely traversing the road Between
5000 (m h−1)10 000 (m h−1)15 000 (m h−1)
  1. a

    The probability of safely traversing the road was calculated using Ps = e−γ∆T (Langevelde & Jaarsma 2005) for each of the 3 koala velocities. All roads had 2 lanes.

  2. b

    An estimate of traffic density.

Road 11940·91440·8740·9350·956Pop 1–3
Road 21833·03110·7480·8650·908Pop 1–2
Road 31953·22250·8110·9000·969Pop 3–4
Road 41924·5100b0·9110·9540·969Pop 2–4
Figure 2.

Study site within the Koala Coast. Checkered line is the population boundary for the four population incorporated into our analysis. The boundaries between the patches are the roads. The numbers represent the female koala population size.

Our objective is to maximize the expected number of animals across all the patches of habitat separated by roads at the end of the management period, which can be written as:

display math(eqn 1)

where math formula is the average size of population i at the terminal time T, B is our budget, s is a set of all the road segments that separate the different patches, xs is a control variable (xs = 1 if we have a fence at road segment s, 0 otherwise), and ys is a second control variable (ys = 1 if we have a wildlife crossing at road segment s, 0 otherwise), so ys, xs∈ {0, 1}. However, in our actions, there cannot be a wildlife crossing without a fence and so ys ∈ {0, xs}, which means that (when xs = 0 then ys = 0). The parameter fs is the cost of the fence along road segment s and ds is the cost of the wildlife crossing on road segment s.

The population model

The population was simulated using a stochastic discrete-time metapopulation model where the numbers of individuals in patch i at time t + 1, Ni,t+1, are a function of birth, death, immigration and emigration

display math(eqn 2)

where Ri,t = (1−αi)Ni,t λi, represent both birth and death processes (λi is the growth rate of population i); αi is the proportion of individuals that emigrate from population i, so the number of emigrants, Ei,t, leaving population i is Ei,t = αiNi,t. The number of immigrants Ii,t coming into population i from the neighbouring patches is math formula, where n is the number of populations which are adjacent to population i (j = 1…n), m is the number of populations that population j has a common road with and ps is the probability of crossing the road between population i and population j and reaching the other side safely. The number of immigrants coming into the population i is divided by m because emigrants from each population were divided equally between the populations to which they could move. There are many different ways to model immigration and emigration, and we have used a fairly basic density-independent approach. When emigrants cannot cross to the other side of the road due to fencing, they will return to their population of origin. The return emigrants are given as math formula, where the number of emigrants leaving population (E) i was divided equally between the n neighbouring populations they can move and those that are blocked by fences (xs = 1) will return to their original population i depending on the probability ps.

ps(xs,ys) is the probability of an individual crossing a road and reaching the other side safely, which depends on the action taken for the mitigation for segment s, where xs and ys are the control variables. If we ‘Do nothing’, ps(0,0) = e−γ∆T is the probability of successfully crossing the road segment (Langevelde & Jaarsma 2005), where γ is the hourly traffic volume and math formula is the time that it takes to cross the road, W is the width of the road, l is the koala length from head to tail, and v is the velocity of movement of koalas. We assumed that lane width is 2 m and the width of the road (W) is the number of lanes times the width of the lane. We estimated the length (l) of a female koala to be 0·66 m, and its velocity (v) is 5000–15 000 m h−1 (Rhodes et al. in press). Because of the uncertainty in the koalas' velocity, we performed a sensitivity analysis so that the probability of crossing the road depends on three different koala velocities: 5000, 10 000 and 15 000 m h−1 (low, medium and high). If we exclude access to the road with a fence ‘Fence only’, the probability of an individual reaching the other side is zero, ps(1,0) = 0 because we assumed a perfect fence. In this case, the dispersing individuals return to the original population. If we add a wildlife crossing to the fence ‘Fence and Wildlife crossing’, then we assume that ps(1,1) = 0·5; we assumed that a koala reaching the fenced road will turn either left or right (50% chance for each direction), so it has a 50% chance of finding the crossing. If the koala turns in the direction of the wildlife crossing, we assume that it will find and cross to the other side safely; if it turns away from the wildlife crossing, it will remain in the original population.

For simplicity, we allowed only one road crossing movement for dispersing individuals each year. Our decision to allow movement away from the population before letting the population grow is because we assume that only adult koalas move and reproduction occurs after dispersal.

Case study specifics

We used the female-only growth rate (λ) from the age-structured model in Rhodes et al. (2011), but removed the vehicle mortality rates from the analysis as vehicle mortality is explicitly incorporated in our model through failed dispersal. Using the model described by Rhodes et al. (2011), we had 9900 combinations of plausible values of λ, representing birth and death rates of the koala population residing in the Koala Coast area, with an average value of λ = 0·977 ± 0·014 (mean ± SD). At every run of the model, four values of λ were selected randomly from the pool of 9900 λ values and were assigned as that run's growth rates for each of the four populations. As the average growth rate extrapolated from Rhodes et al. (2011) was lower than 1·0 (see above), the populations declined in all model runs. Hence, we performed an additional set of runs where we added 0·05 to λ to achieve a positive population growth, our high growth rate scenario. This was done to test if our results will change should additional actions, to increase population growth rate, are employed. Using information on koala densities (Department of Environment & Resource Management 2009), we generated initial population sizes for the four patches for the study site (Fig. 2, Table 1). We assumed a dispersal probability of 14% for female koalas based on Preece (2007).

Applying cost

Each of the 81 mitigation combinations was given a cost depending on the actions in that combination. Actions were taken at the beginning of each run and were assumed to be constant throughout the runtime of 100 years, where improvements in technology are assumed to balance discount rates. A fence was costed at $120 m−1, and as fences need to be replaced on average every 20 years (Caneris & Jones 2009), the cost of the fence was multiplied by five to account for the 100-year model run. We assumed there is only one kind of wildlife crossing, and it costs $200 000 (Veage & Jones 2007). We also added a maintenance cost of 2·5% year−1 for any infrastructure over the 100 years (Clapperton 2001). If we do nothing along a road segment, it is assumed to cost nothing.

Sensitivity analysis

We performed six runs of the model using three koala velocity values (low, medium and high) and two koala population growth rates (low and high). The outputs of each run were the average population size at the end of the 100 years (for 1000 repeats). In order to standardize our results, we divided the result of each of the 81 possibilities by the highest population average to achieve a conservation benefit between one and zero. We plotted the standardized results against the cost of the mitigation efforts for each one of the six runs. From these plots, we extracted an efficiency frontier (Polasky et al. 2005, 2008) of the non-dominated solutions (Moffett, Dyer & Sarkar 2006). Non-dominated solutions are those that cannot be beaten on both cost and conservation benefit by another solution.

Results

In all of the model runs, the ‘Do Nothing’ approach of no mitigation on any road segment was the worst for population abundance. Surprisingly, full mitigation (Fence + Wildlife crossing) on all road segments did not maximize mean population abundance – in addition to it being the most costly solution (Table 2). When looking only at the non-dominated solutions along the efficiency frontier for each of the two growth rates separately, we found that there are common non-dominated solutions between the different velocities and the two growth rates (Table 2). For example, when the budget is large, the non-dominated solution is to fence all road segments and add a wildlife crossing to cross at least one of the road segments. However, when the budget dropped below $4 000 000, the non-dominated solution becomes to fence road segments one and two (Table 2). Below that amount, we needed to spend over $1 600 000 and employ only one mitigation action – fence road number two. At this point, conservation benefit has dropped (7% and 48% for low and high growth rates, respectively) from the outcome with a budget of ~$4 000 000. A budget of less than $1·6 million was not sufficient to achieve a significant conservation benefit given the scenarios considered (Table 2). Furthermore, the common non-dominated solutions (for costs of between $0 and ~$5 100 00) between the two growth rates (Table 2), indicating that the efficiency frontier is relatively independent of demographic uncertainty. This means that the actions are less sensitive to parameter uncertainty than the outcome (McCarthy, Andelman & Possingham 2003).

Table 2. Efficiency frontier solutions common between the three koala velocities (5000–15 000 m h−1) – the right side of the table presents the non-dominated solutions for the low population growth rate and the left side presents the solutions for the high growth rate. Each solution provides female population size, the cost of the solution (that specific combination of mitigation actions) and the specific action taken at each road (NM, No Mitigation; F, Fence only; F + P, Fence + Passage). Shaded areas are solutions common between both growth rates. All solutions were non-dominated for all of koala road crossing velocities
Average growth rate: R = 0·977Average growth rate: R = 0.977+0.05
Population sizeaCost ($)Road 1Road 2Road 3Road 4Population sizeaCost ($)Road 1Road 2Road 3Road 4
  1. a

    Population size is the average female population size between the three velocities for each growth rate.

41·837 086 386FFF + PF690·787 286 386FF + PF + PF
36·615 128 524FFNMF687·157 086 386FF + PFF
29·513 396 483FFNMNM564·975 128 524FFNMF
27·381 649 709NMFNMNM472·903 396 483FFNMNM
15·860NMNMNMNM245·901 649 709NMFNMNM
      194·510NMNMNMNM

Using the non-dominated solutions that were shared between scenarios, we created trade-off curves containing these solutions only (Fig. 3a,b). The shape of the plots was barely affected by changes in population growth rate or koala crossing speeds. On the other hand, the koala's crossing speed was positively correlated with mean population size.

Figure 3.

Trade-off curves of non-dominated solutions. X-axis is the cost of the mitigation possibilities and y-axis is the conservation benefit represented as the proximity to the maximum population size (1 is the highest proximity) the population achieved under a given scenario. ‘a’ and ‘b’ are the different growth rates (r = 0·977 and r = 0·977 + 0·05, respectively). Curves (dashed lines) represent the three koala' velocities tested, and symbols represent the solutions along the curves, low (filled circles), medium (blank circles) and high (filled triangles). The mitigation actions that are needed to be taken at each solution brake are stated on the figure. Scattered dots (filled circle) in graph ‘a’ is an example of all the different mitigation variations tested in the low velocity at that growth rate.

Discussion

The impact of roads on wildlife is a world-wide problem which will increase with human population growth and increasing vehicles per capita (Laurance & Balmford 2013), therefore requiring mitigation to reduce its effects (Forman et al. 2010). These mitigation efforts are costly, but up until now this problem has not been tackled using decision science. In this paper, we formulated and solved a road mitigation problem and tested it using a decision science approach. We illustrated our approach using information about a koala population in south-east Queensland and found the non-dominated solutions for that system over a range of costs.

For the koala population mitigation problem, we discovered that there is no ‘win-win’ solution. In all the model runs, the curves (Fig. 3) are close to linear, lacking the L or J shape that would have indicated good conservation benefits for low economic cost (Halpern et al. 2013). Our analysis shows that achieving very good outcomes for koalas will be expensive and reducing investment will result in a much smaller population. This kind of decrease in population size can be quite significant especially in small populations. Moreover, the population in the Koala Coast is declining, not just because of road mortality but also because of disease and dog predation (Rhodes et al. 2011). Recent work (C. Ng unpublished data) suggests that all these issues must be tackled with cost-effective investments. That said, the benefits of koalas to tourism make koala conservation a profitable investment (Hamilton, Lunney & Matthews 2000).

It is important to note that solutions along the efficiency frontier (Table 2, Fig. 3) were not affected by uncertainty in the koala's biological attributes (speed and population growth rate). This suggests that the solutions presented here are relatively insensitive to these biological uncertainties, and given a fixed budget, one can identify a robust optimal solution. In our case study, the trade-off curve between cost and conservation benefit was fairly linear, suggesting no cheap gains. Other systems, which exhibit more variability, in either population dynamics or road attributes, such as traffic intensity and the cost of mitigation actions, may generate trade-off curves where a relatively large conservation benefit could be generated at low cost.

We recognize that our population model is relatively simple. It does not incorporate age structure, density dependence or daily movements across roads. We also did not account for the effects roads have on inhibiting gene flow (Holderegger & Di Giulio 2010; Dudaniec et al. 2013), which would require a more complex genetic model. That said, the main purpose of our analysis was to show how decision science can be applied to the question of road mitigation, using the koala as a case study to demonstrate our method. For this purpose, using a relatively simple model was necessary in order to focus on the problem formulation and approach. Another caveat in our analysis is that we only considered three mitigation options for each road segment, fences and only one type of wildlife crossing. However, the problem can be adjusted to explore a diversity of crossings structures (i.e. clovers, overpass, bridges; Forman et al. 2010) accounting for their different costs and mitigation successes. Further, we assumed that there can be only one crossing per road segment per year, and we did not consider different options for where that crossing is placed. We also assumed that our fences were impermeable to animal crossing, which may not be true in many cases (Ascensao et al. 2013).

There are many possible extensions of the basic problem presented here. Our approach can be expanded to accommodate a much wider variety of mitigation options for each road segment including more populations, additional road segments and multiple possible crossing points. In addition, crossing for one species often assists the viability of others species, so we are formulating a multispecies road mitigation problem. However, because the number of mitigation options grows geometrically with the number of road segments, the exhaustive examination of a large system will be computationally intensive.

The greatest asset of our problem formulation is that it can be easily adjusted to the needs of other species. The literature is replete with recent studies of the effects of roads on wildlife that have the necessary information needed to implement this decision-making tool (Dekker & Bekker 2010; Beebee 2013; Nafus et al. 2013; Soanes et al. 2013). Parameters in the problem formulation can change according to the specific mitigation actions needed in that system; the population model can be adjusted or even replaced altogether, as long as the link to the problem formulation, via the probability of crossing the road safely (ps), is maintained. In particular, the information gathered by Beebee (2013), in a thorough review of the effects of road mortality and mitigation on amphibians, can be incorporated along with mitigation costs into our formulation. Furthermore, where a species has a monetary value to a region, our approach could be used to choose mitigation options in a classical cost–benefit analysis approach. While other mitigation prioritization work is becoming available (Ascensao et al. 2013), our work is the first that includes a well-defined mathematical problem that incorporates financial costs, which is essential for application in the real world.

Acknowledgements

We would like to thank the Department of Environment and Heritage Protection of the Queensland government for the use of their data on koala densities in the Koala Coast area. We thank Joseph Bennett, Omer Polak, Doug P. Armstrong and an anonymous reviewer for their comments which improved the manuscript and Fei Ng for her assistance with the analysis of the koala demographic parameters. We acknowledge the support of the Australian Government's National Environmental Research Program, the Australian Research Council Centre of Excellence for Environmental Decisions and the University of Queensland. Possingham was supported by an Australian Research Council Federation Fellowship.

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