Road infrastructures are an important source of biodiversity loss and are spreading across the globe (Meijer et al., 2018; Wenz et al., 2020). Besides the increase in environmental degradation and the decrease in ecological connectivity, direct removal of individuals by roadkill can be a major cause of local population decline (Fahrig and Rytwinski, 2009).Road effects on wild populations can ripple to other levels of ecological organization, affecting ecosystem functioning (van der Ree et al., 2015). To mitigate efficiently the negative impacts of roads on wildlife, sound knowledge on where deaths are concentrated is fundamental (Gunson and Teixeira, 2015 but see Teixeira et al., 2017), as well as accounting for landscape stability to ensure that proposed measures are long-term lasting (Zeller et al., 2020). Generating such high-quality information can be challenging given the usually large extent of road networks, scarce time and financial resources available for field work.

It is possible to assess roadkill patterns based on road features, landscape characteristics, and species occurrence (Patrick et al., 2012; Girardet et al., 2015; Visintin et al., 2016). Nevertheless, probably the best information to assess where roadkills concentrate along a road is still by estimating fatalities based on observation/counts of carcasses. However, fatality estimations using raw counts can be biased, as observers might not detect all available carcasses. Moreover, removal of carcass from the road by scavengers or traffic may also be an important factor affecting estimates, especially when smaller animals are the study target (Santos et al., 2011; Villegas-Patraca et al., 2012; Barrientos et al., 2018; Schwartz et al., 2018). Not properly addressing these sources of error (detection and removals) in fatality assessments might produce biased roadkill estimations. As both errors may vary in space and time, their spatiotemporal heterogeneity should also be accounted for. If such aspects are not assessed, mitigation actions may be proposed at less effective sites.

Usual approaches to estimate wildlife fatalities at man-made infrastructures, when considering the sources of error, commonly use ad-hoc formulas based on detection rates and carcass removal trials from experiments or from comparisons with an assumed perfect-detection method (e.g., surveys on foot; Simonis et al., 2018; Teixeira et al., 2013). However, there have been claims for the application of process-based approaches while accounting for imperfect detection in carcass observations (e.g., wind farms, Péron et al., 2013; roads, Guinard et al., 2012). Such process-based approaches, typically based on open population capture-recapture models, tend to represent more accurately the dynamics of carcasses entering and leaving the sampled road segment (Guinard et al., 2015; Péron, 2018).

Even when roadkill hotspots are robustly estimated, mitigation measures can result in resource wasting if populations are locally affected due to other anthropic pressures. The effectiveness of an installed mitigation structure could rapidly decline in regions where anthropogenic landscape changes are more pronounced, causing shifts in the distribution and movement patterns of a species along a road. Hence, habitat stability is an important aspect to be included in the spatial prioritization of mitigation structures, especially when planning long-term measures (Clevenger and Ford, 2010; Zeller et al., 2020).

While often neglected in road fatality assessments, amphibians are one of the most affected taxa by roadkills, representing more than 90% of the fatalities in some cases (Fahrig et al., 1995; Glista et al., 2008; Coelho et al., 2012; Silva et al., 2021). Amphibians are the most threatened vertebrate group with 41% of the species at risk of extinction (IUCN, 2021). Their life cycle, with most species presenting an aquatic larval phase, imposes to adults and juveniles challenges in arriving and leaving water bodies every reproductive season. This can increase road encounter probability by amphibians and the potential negative population-level effects, especially for anurans species with lower reproductive rates, smaller body sizes, and younger ages at sexual maturity (Rytwinski and Fahrig, 2012). Moreover, their small size results in low detection and fast removal (Teixeira et al., 2013; Pereira et al., 2018) demanding sampling on foot and with short time intervals between occasions, which would represent a challenge for the survey of extensive road networks.

Here, we develop a framework for prioritizing road segments for amphibian roadkill mitigation based on fatality estimation and landscape transition (Figure 1). Our framework is composed of the six following steps:

Pre-selection of road segments with higher potential occurrence of amphibians;

We applied this framework to define priority segments for mitigation of amphibian fatalities on two roads surrounded by a mosaic of grasslands, pastures, wetlands, rice fields, and urban areas in southernmost Brazil. In the fatality estimation step, we used dynamic N-mixture models to evaluate the influence of land use and cover on the distribution of carcasses, the impact of raining on roadkill, traffic volume and day/night time on carcass persistence. We expected that wetlands and urban areas in the surroundings of a segment would have a positive and negative influence, respectively, on the spatial distribution of carcasses; that fatality rates would be higher in rainy occasions; that at segments with higher traffic volume, carcass would persist less; and that carcass persistence would be higher at night.

We found amphibian carcasses in 49 of the 50 sampled segments in at least one of the six occasions. Maximum count per visit in these segments varied from one to 127 carcasses detected by the two pairs of observers, while the mean count for all segments was 12 carcasses. Hylidae and Leptodactylidae families represented 75% of carcasses identified, whereas Dendropsophus spp. and Leptodactylus luctator, Leptodactylus gracilis, and Pseudis minuta were the most recorded species (Supplementary material 2).

The estimated average roadkill rate at the 50 segments during the 3 days was 136 (95%CrI = 130–142) amphibian fatalities per km per day. Mean roadkill rate for the 100 m segments ranged from 1.3 (95%CrI = 0.4–3.2) to 52.7 (95%CrI = 48.4–57.6) fatalities/day (Figure 2). We found a positive relationship of the initial carcass abundance with wetlands coverage (Figure 3A) and a negative relationship with urban areas coverage (Figure 3B). The number of entrant carcasses per interval was positively influenced by the wetland coverage and was twice higher when rain occurred (Figure 3C). Carcass persistence was higher during the night and very low for segments with high traffic volume (Figure 3D). The probability of each pair of observers to detect an amphibian carcass was 0.69 (95%CrI = 0.66–0.72; Table 1).

Landscape transition rate varied from 0 to 98% of conversion. The median of the estimated fatality rate was 9.99 individuals per day and the median of the landscape transition rate was 5% in a 10-year interval. Ten segments were prioritized to receive the mitigation actions with these thresholds for fatality estimates and landscape stability, meaning a 5-fold reduction of segment numbers (Figure 4).

Although amphibians are often a major group affected by roadkill (Fahrig et al., 1995; Glista et al., 2008; Coelho et al., 2012), planning efficient mitigation actions for this group imposes challenges given the usual difficulty to survey their carcasses. In order to obtain reliable estimates of amphibian roadkill rates and propose enduring mitigation measures, we present a prioritization framework based on a pre-selection of segments to be surveyed, an explicit modeling of fatalities with imperfect detection, and an evaluation of landscape stability. With this approach, we were able to identify 10 high-priority 100 m-segments to receive mitigation measures, i.e., 1 km in a context of about 100 km of road.

By choosing segments more likely to concentrate amphibian roadkills, we have reduced to 5% the length of road to be sampled. The usual small size of amphibians makes them hard to detect from traditional carcass survey methods (i.e., by car). By searching amphibian carcasses on foot, we obtained a carcass detection probability of ~70% by each pair of observers, which we considered quite good for this group. Moreover, the spatiotemporally replicated design proposed here requires carrying out counts in multiple visits at the segments, making more difficult to cover a large road extent. Therefore, given the logistic constraints to survey amphibian carcasses on foot at extensive roads, pre-selecting segments based on habitat features is a way to make sampling more feasible. Importantly, the pre-selection criteria must be chosen according to the habitat associations of each target group.

Spatiotemporally replicated counts of carcasses can be a cost-effective method to robustly estimate roadkill patterns. Fitting these counts with dynamic N-mixture models enables to explicitly derive roadkill rates for known time intervals (time between visits), while formally accommodating the potential sources of error (and their heterogeneity) in the same modelling structure. Previous studies have also used carcass counts or occurrences split into segments to model spatial variation on roadkills and identify hotspots based on a Poisson distribution (e.g., Santos et al., 2017; Lin et al., 2019). However, such approaches fail in accounting for imperfect detection (and even less the possibility of modeling the heterogeneity in persistence and detection) and do not provide reliable explicit rates of roadkills. Our directly derived roadkill rates also have the advantage of being comparable among studies, species or regions. Sources of errors (persistence and detection) in roadkill assessments are commonly addressed using trial experiments in which a known number of carcasses is disposed on the road (Barrientos et al., 2018; Gonçalves et al., 2018). However, there might be spatial and temporal variations in persistence and detection that are unfeasible to capture and represent with experiments. For example, as we found here, carcass persistence presented considerable variations according to the traffic volume at the segment and the period of the day. Not accounting in trial experiments for such heterogeneities may produce biased estimation of roadkill patterns. Some studies have made attempts to use hierarchical models in the context of roadkill data to identify priority segments while accounting for imperfect detection (e.g., Santos et al., 2018; Hallisey et al., 2022). Nevertheless, the approach adopted in these studies uses detection/non-detection data and makes inferences on “carcass occupancy” for a wide-time window, and not roadkill numbers.

Revealing effects of spatial and/or temporal covariates in the roadkill rates can be useful, for example, to predict fatalities hotspots in roads planned to be constructed or to plan carcass surveys in moments that patterns would be more highlighted in data. As expected, we found here that wetland coverage (high-quality habitat for most amphibian species in the studied region) in the road surroundings influenced the mean number of amphibians roadkilled. Segments with 90% of wetland coverage can present on average 47% more fatalities than segments with 10%. Such identified relationships could be applied to predict segments with potential higher roadkill rates in other roads with similar landscape characteristics. Moreover, the presence of rain during the interval between sampling visits resulted in about twice higher amphibian fatalities than intervals without rain. When planning carcass surveys, this kind of temporal variation should be taken into account to prioritize periods that might maximize the detection of spatial patterns in roadkill rates.

One advantage of the modeling approach we used is that it allows ecologists to estimate the dynamic parameters without marking individuals (Dail and Madsen, 2011; Dénes et al., 2015), as it was proposed by Péron et al. (2013). An important assumption of capture-recapture models is that marked and unmarked individuals have the same persistence and detection probabilities. By fitting carcass count data with N-mixture models, we avoided the need of marking the small amphibian carcasses, procedure that is logistically difficult and could, for example, influence later detections or affect the persistence of carcasses that were adhered to the substrate. However, because of the lack of information on individual capture histories, dynamic N-mixture models could sometimes present problems in parsing out entry and persistence processes (Kéry and Royle, 2021). Despite this issue may result in biased absolute roadkill estimation, this approach is still useful in relative terms (i.e., which sites present higher roadkill rates) to identify priority sites for mitigation. One alternative to ensure unbiased absolute roadkill estimations is to mark just a few individuals to directly inform entry and persistence processes.

Our framework recognized the priority road segments for amphibian mitigation not only identifying at which places animals tend to die more, but also including landscape conversion as a long-lasting criterion. We highlight the importance of considering the endurance of mitigation actions jointly with higher roadkill rates to ensure effective measures in long-term. Other criteria than lower landscape conversion rates could be used depending on the context of the surrounding landscape, such as where roads which are built in pristine areas (e.g., Amazonian Arc of Deforestation). Moreover, depending on the mitigation objectives, prioritization could consider other criteria, such as the number of threatened species per site, or per capita mortality, if cascading population effects are the main concern (Teixeira et al., 2017). When data on the population in the surroundings are available and when the maintenance of a population is a conservation target, this kind of information can provide important assets to use in the prioritization step. There have been cost-effective manners of obtaining population data for one or more amphibian species in the surrounding of roads, in order to integrate information in mitigation planning, such as automatic acoustic recordings (Marques et al., 2013) or citizen science programs that monitor amphibian migrations [e.g., Toads on Roads (Petrovan et al., 2020); Big Night programs (Sterrett et al., 2019)].

We proposed our sampling and analytical framework to estimate amphibian roadkill rates accounting for imperfect detection and its heterogeneity. The modeling approach can be expanded in order to accommodate other sources of variation, for example, differentiating species and including them as random effects in multi-species models (Yamaura et al., 2012; Dorazio et al., 2015). This might be particularly important when there is interest in threatened species. Also, although we have focused on amphibians, this framework could be useful to identify locals for mitigation measures for any roadkill target, especially when marking individuals is a difficult task.

Our study set out to better support mitigation prioritization decisions and such information can be used to inform where to implement road management actions. However, in terms of conservation, an imperative further step is to indicate and implement appropriate mitigation measures for road management to reduce roadkill of the target group studied here. Fencing is the most suitable spatial mitigation structure to maintain amphibians off the road and mitigate roadkills (Cunnington et al., 2014). Also, it is essential to promote safe crossings for amphibians daily movements with the implementation of wildlife passages (Woltz et al., 2008; Beebee, 2013; Jarvis et al., 2019). We highlight that the implementation of those mitigation measures is not the final step either since their effectiveness should be evaluated with robust designs aiming to collect the relevant evidence (Helldin and Petrovan, 2019; Ottburg and van der Grift Edgar, 2019; Schmidt et al., 2020).

In conclusion, our study developed a sampling and analytical framework to improve road management toward spatial prioritization of mitigation measures for amphibian roadkill. We proposed six steps to better support amphibian conservation decision making and such information can be used to inform where to implement road management actions. Our findings are also useful to plan future carcass surveys in locations and moments that patterns would be more suitable.

The original contributions presented in the study are publicly available. This data can be found here: https://figshare.com/s/0cebdfcedb591dea6fed.

All authors conceived the idea of the manuscript, designed the survey, interpreted the results, wrote sections in all drafts, contributed critically to the writing, and gave final approval for publication. IB developed the analytical approach. JB and CZ collected roadkill data. JB, CZ, and LG compiled and synthesized data. JB and IB performed data analyses. JB, CZ, and IB made figures and tables. LG and IB led the writing process, working on the final version of the manuscript. All authors contributed to the article and approved the submitted version.

Financial support was provided by Fundação Empresa Escola de Engenharia da Universidade Federal do Rio Grande do Sul for LG, IB, CZ, JB, and AK (Projects FEENG/307 and FEENG/437). LG is funded by Programa USP Sustentabilidade da Superintendência de Gestão Ambiental da Universidade de São Paulo.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.