Temporal clustering of prey in wildlife passages provides no evidence of a prey-trap

Wildlife passages are structures built across roads to facilitate wildlife movement and prevent wildlife collisions with vehicles. The efficacy of these structures could be reduced if they funnel prey into confined spaces at predictable locations that are exploited by predators. We tested the so-called prey-trap hypothesis using remote cameras in 17 wildlife passages in Quebec, Canada from 2012 to 2015 by measuring the temporal occurrence of nine small and medium-sized mammal taxa (< 30 kg) that we classified as predators and prey. We predicted that the occurrence of a prey-trap would be evidenced by greater frequencies and shorter latencies of sequences in which predators followed prey, relative to prey–prey sequences. Our results did not support the prey-trap hypothesis; observed prey–predator sequences showed no difference or were less frequent than expected, even when prey were unusually abundant or rare or at sites with higher proportions of predators. Prey–predator latencies were also 1.7 times longer than prey–prey sequences. These results reveal temporal clustering of prey that may dilute predation risk inside wildlife passages. We encourage continued use of wildlife passages as mitigation tools.


Study species.
We included nine taxonomic groups in this study, which we identified as species (below) or grouped in taxonomic levels that could be identified as weasels (Mustela spp. included Mustela frenata and Mustela erminea), and micromammals (shrews (Family Soricidae), mice (Family Cricetidae), moles (Family Talpidae), and voles (Family Cricetidae)). The species we classified as predators included mink, weasels, and red foxes (Vulpes vulpes). We described North American red squirrels (Tamiasciurus hudsonicus, hereafter red squirrel) as prey instead of predators because they subsist mainly on conifer seeds 33 , despite including smaller mammals and birds in their diet [33][34][35][36][37][38] . However, we conducted separate analyses that excluded red squirrels from our analyses or treated them as predators to demonstrate that these classifications did not change our conclusions about the existence of a prey-trap (Supporting Information, Tables S1 and S2). Mink are typically sit-and-wait predators whereas red foxes and weasels actively chase and hunt prey 32 . We did not observe any larger predators (e.g. wolves (Canis lupus), coyotes (Canis latrans), or Canada lynx (Lynx canadensis)) using the wildlife passages. We classified herbivores as prey and included Eastern chipmunks (Tamia striatus), marmots (Marmota monax), common muskrats (Ondatra zibethicus), snowshoe hares (Lepus americanus), and micromammals 32 . Data collection. Wildlife passages were equipped with remote cameras (Reconyx HC600 Hyperfire H.D. Covert IR, Holmen, WI, USA) to detect animals through a combination of heat and movement. We placed one camera at each entrance facing inwards at the openings of wildlife passages 29 . Following activation, five photographs were taken at up to two frames per second for each triggering event. Because snow cover and flooding caused some camera failures, we limited our observational period to times with no disturbances (June to October in all years except 2015 when the study ended in August). Although motion-activated cameras can be biased toward species that are slow-moving 39 , large 39,40 , or motile 41 , we assumed that these differences did not apply to our community of mammals.
For each series of five photos (i.e., a triggering event), we recorded location, date, temperature, time, and species. We estimated size of individuals using a reference block placed inside each wildlife passage and in the cameras' field of view to increase our ability to differentiate between individuals of the same species. We assumed temporal independence for observations of the same species that were greater than 10 min apart unless successive individuals were of the same species and size, in which case we extended this limit to 20 min (after Martinig and Bélanger-Smith 29 ). We included in our analyses only the first picture for these sequences and excluded observations of individuals we could not attribute to taxa owing to poor lighting or camera angles (2.6% of observations). This study was approved by and was carried out in accordance with relevant guidelines and regulations as set out by the Quebec Ministry of Transportation (approval number: R709.1) and Concordia University (animal care ethics protocol number: 30001331).
Data analysis. Using the trophic positions (prey and predator) and independent observations (camera detections) described above, we identified pairwise sequences for all successive observations at each wildlife passage for each monitoring season wherein n observations resulted in n − 1 pairwise sequences. We attributed these sequences to one of four possible combinations: prey followed by prey (prey-prey); prey followed by predator (prey-predator); predator followed by prey (predator-prey); and predator followed by predator (predatorpredator). All analyses were done in R, version 3.6.2 42 . Data are reported as means ± one SE. www.nature.com/scientificreports/ Sequence proportions. We tested our first prediction, that the proportion of prey-predator sequences was higher than expected, by calculating the proportion of the sample comprised by prey and predators and applying the binomial distribution to generate the randomly-expected probabilities for each of the four sequences. For each wildlife passage, we recorded the number of prey (x) and predators (y), sample size (n), sequences (n − 1), and number of prey-predator sequences (k a ). Stemming from the prey-trap hypothesis that predators detect prey use of wildlife passages, we predicted that the number of prey-predator sequences would be significantly higher than the number predicted by the binomial distribution, given the proportion of prey and predators in each sampling period. We calculated the null probability (p e ) by wildlife passage for the prey-predator sequence using the equation: We calculated the expected number of prey-predator sequences (k e ) given p e using the following equation: We conducted a two-tailed binomial test using the binom.test function in the baseline 'stats' package in R, version 3.6.2 42 , to obtain the observed probability (p a ) of obtaining ≥ k a prey-predator sequences in n − 1 sequences for each wildlife passage. The binomial distribution uses the following equation for 0 < p e < 1 and p a > 0: where k a is 0, 1, 2,…, n: In addition to calculating the observed probability (p a ), the binom.test function provided the 95 percent confidence intervals (95% CIs) around p a and the p-value. A significant effect was inferred if the observed probability ± 95% CIs did not overlap with its corresponding null probability. We included all sequences without temporal censoring here for two reasons, 1) the infrequency of use by predators and prey is biologically meaningful in the context of a prey-trap, and 2) scent trails left by prey typically last between 24 h and 1 week 43,44 . We also explored the effect of temporal censoring on our results to acknowledge scent depletion (see below).
Biologically relevant metrics: restricted analyses. We tested our second prediction, that the proportion of preypredator sequences would increase under certain ecological conditions, by restricting our analyses to the associated periods or structures. First, we limited our analysis to the peak and trough of the regional population sizes for small mammals during our study, which occurred in an area that is known to exhibit population cycles 45 . Both prey and predators exhibited their highest abundances in 2012 and their lowest abundances in 2015. We conducted a second restricted analysis for the dispersal period in August, when juveniles are more prevalent for many species of small mammals 32 . Last, we analyzed a subset of wildlife passage types that experienced high predator use in a simultaneous study 29 ; those with limited visibility (openness < 0.089) and box culverts with a dry concrete ledge.
Latency between sequences. We tested our third prediction, that the latency differed among the four possible sequences (prey-prey, prey-predator, predator-prey, and predator-predator), by measuring the time between the first and second detection. Again, we classified individuals as prey or predator and ordered the observations by ascending time for each wildlife passage. We then calculated the geometric mean time between detections starting from the first observation in each June to October period. We determined the geometric mean latency for all four possible sequences of prey and predators in each wildlife passage (wildlife passage-specific latency) and then averaged across all wildlife passages for an overall latency. We used the geometric mean instead of the arithmetic mean to reduce the weight of extreme values.
We fit the latency models (all sequences or restricted to sequences ≤ 24 h of each other) using a negative binomial regression with the "glmmTMB" package, version 1.0.1 46 , because the variable's variance was larger than its mean. We included time between observations (in days for the global model and hours for the restricted model) as the response variable and sequence type, wildlife passage type, openness, year, and month as fixed effects and wildlife passage identity as a random effect. We mean-centered and standardized openness to one standard deviation 47 . We estimated pairwise comparisons using the "lsmeans" package, version 2.30-0 48 .

Results
We detected 11,278 mammals that we considered independent observations at the 17 wildlife passages between June and October of 2012 to 2015. During this time, we did not observe a single predation attempt or event on our remote cameras. We classified 88% of the detections as prey and 12% as predators. In wildlife passages, the number of prey detections ranged from 19-1521 (31-97% of detections among wildlife passages) and the number of predator detections ranged from 14 to 254 (3-69% of detections among wildlife passages; Table 1). The most prevalent taxa observed were micromammals (58%, n = 6,576), red squirrels (15%, n = 1632), marmots (11%, n = 1,215), weasels (9%, n = 960), and mink (4%, n = 409). The remaining four taxa encompassed 4% of observations (snowshoe hares: n = 217, Eastern chipmunks: n = 141, common muskrats: n = 111, and red foxes: n = 17). www.nature.com/scientificreports/ As expected from the greater proportion of prey in our observations, prey-prey sequences were observed most often overall and in 16 of the 17 wildlife passages (Fig. S1). However, there was considerable variation in the proportion of sequence types among wildlife passages and predator-predator sequences exhibited their highest percentages (50%) in the wildlife passage in which predators were more abundant than prey (Table 1; Fig. 1; Fig. S1). Prey-prey sequences ranged from 13 to 95% among wildlife passages (Table 1; Fig. S1).
proportion of prey-predator sequences. If predators track prey in wildlife passages, we predicted that prey-predator sequences would occur more often than expected from the proportion of prey and predators. Our results did not support this prediction, instead exhibiting a significant departure in the other direction. When all 17 wildlife passages were combined, the observed proportion of a prey-predator sequence was lower than expected (Table 1; p a = 0.07, 95% CI (0.06, 0.07), p e = 0.11, p < 0.001). Among the 17 wildlife passages we monitored, ten (59%) exhibited significantly lower proportions of prey-predator sequences than expected, while the other seven (41%) showed no difference between observed and expected proportions of prey-predator sequences (Table 1; Fig. 1a). We present only the frequencies for prey-predator sequences in the main results because the frequencies of predator-prey sequences are ± 1 value of the prey-predator sequences within each wildlife passage by year (Table S3; Fig. S3).
proportion of prey-prey sequences. In contrast to the lack of support for a prey-trap hypothesis, we found evidence in seven (41%) of the wildlife passages that prey were more likely to follow prey than would be expected by their numerical frequency alone (Table 1; Fig. 1b). When all 17 wildlife passages were combined, the observed proportion of a prey-prey sequence was higher than expected (Table 1; p a = 0.81, 95% CI (0.80, 0.82), p e = 0.77, p < 0.001). The remaining 10 wildlife passages (59%) showed no difference between observed and expected proportions of prey-prey sequences (Table 1).
Biologically relevant metrics: restricted analyses. Similar to our analysis with the combined dataset, our second test was unsupportive of the prey-trap hypothesis when analyses were restricted to ecological conditions that might be expected to increase the benefits of a prey-trap to predators. When observations were restricted to 2012, when prey abundance was highest, or to 2015, the year with the lowest prey abundance, all wildlife passages showed either no difference or had lower observed proportions of prey-predator sequences than expected (Tables S4 and S5; Fig. S2). Results from observations limited to August were similar (Table S6; Fig. S2). Restricting the analyses to the kinds of wildlife passages with limited visibility or concrete ledges that are favoured by predators also failed to support the prey-trap hypothesis (Fig. S3). In all cases, observed proportions of prey-predator sequences did not differ from expected or were lower than expected (Table 1; Fig. S3). Table 1. Information on passage type and mammal sequence data for 17 wildlife passages located along Highway 175 in the Laurentian Wildlife Reserve, Quebec, Canada from 2012 to 2015. Number of detections on remote cameras are provided for prey, predators, and pairwise sequences of successive detections. The number of prey-predators and prey-prey sequences (k) are tallied for observed sequences (k a ) and expected sequences (k e ) based on the binomial distribution of observed (p a ) and expected (p e ) proportions, with corresponding p-values and 95% confidence intervals (CI) from a two-tailed binomial test. Asterisk denotes significance at α = 0.05.

Number of sequences Prey Predators
Prey-predators sequences (k a (k e )) Proportions (p a (p e )) P (95% CI) Prey-prey sequences (k a (k e )) Proportions (p a (p e )) P (95% CI)  Fig. 2), with prey-prey sequences having the shortest latency and predator-prey sequences having the longest (Fig. 2). Latencies in August were shorter than in all other months and latencies increased with year ( Table 2). There was no effect of openness on latency ( Table 2). Results were consistent when considering only sequences ≤ 24 h apart ( Table 2). Observed proportion (p a ) of (a) prey-predator and (b) prey-prey sequences with 95% confidence intervals obtained from binomial tests compared to corresponding expected (null) proportions (p e ) of (a) prey-predator and (b) prey-prey sequences for 17 wildlife passages from 2012 to 2015. Wildlife passages where predator-predator sequences were most common in white. Line with slope = 1 plotted. Table 2. Sources of variation in latency for all sequences (days, n = 11,278) and only sequences ≤ 24 h apart (hours, n = 9,650) for predator and prey occurrences in 17 wildlife passages from 2012 to 2015. We provide point estimates from univariate generalized linear mixed effects models for fixed effects (β) with 95% confidence intervals (CI) and the random effect (σ 2 ; variance) ± one standard deviation (SD). Asterisk denotes significance at α = 0.05. a Reference categories for fixed effects were set to 'prey-prey' (sequence), 'concrete ledge' (wildlife passage type), '0' (i.e., 2012 for year) and ' August' (month). Openness was mean centered and standardized to one standard deviation. b Obtained from pairwise comparisons. Interpret as effect of the first variable relative to second.

Discussion
Researchers have speculated that wildlife passages directing animals into a confined structure could result in predators using these structures to facilitate prey capture 12,17,39 . We tested this hypothesis using the temporal sequences of animals detected by remote cameras in 17 wildlife passages over a four-year period. If predators used wildlife passages as prey-traps, we predicted that prey detections would be followed by predator detections more often than expected given the frequency of prey and predators. We predicted this tendency would be even greater at the times and locations where ecological circumstances might increase the opportunity for a prey-trap to occur, such as when prey were especially abundant or rare, while naïve animals were dispersing, and in the kinds of crossing structures favoured by predators. We also expected that prey-predator sequences would exhibit shorter internals. None of these predictions were supported by our analyses, lending no support to this form of the prey-trap hypothesis. Instead, the proportion of sequences in which predators followed prey were either equal to or less than expected. Moreover, the proportion of sequences in which prey followed prey was higher than expected, while the latency between these detections was the lowest, together suggesting that temporal clustering by prey, whether incidental or intentional, might dilute their predation risk in wildlife structures. The patterns we observed in this system appear to be driven by prey, which presumably used the wildlife passages in greater frequencies than predators because of their greater abundance in the surrounding landscape. Along with prey occurring at the highest frequency, prey-prey sequences showed the lowest latency periods, indicating closer proximity in time, and space, of prey to other prey. Although the species we studied do not travel in groups, this spatiotemporal grouping may have resulted from pulses of resource availability or foraging activity, which could produce temporal clusters of prey incidentally (e.g., in red squirrels; Boutin et al. 49 )). However, temporal clustering by prey could also occur if prey responded to cues from other prey 50,51 and exhibited greater gregariousness to dilute their risk of predation [52][53][54] . Such a mechanism would equate to the behavioural expectations of a selfish herd, as described by Hamilton 53 . This might also explain the greater latency of prey-predator sequences in our data. Our interpretation of such dilution is speculative, but consistent with other studies that found aversion to predators by prey 50,[55][56][57] .
An alternative to our conclusion that prey avoid a prey-trap (whether or not it was through temporal clustering by prey) is that predators track prey, but we failed to detect those efforts. A recent study inferred spatiotemporal avoidance from a significantly smaller sample size than seen here, while still not documenting interspecific interactions in the wildlife passages 23 . While we cannot rule out the possibility that the use of the wildlife passages here was still too infrequent for scent trails to be readily used in this study system this possibility is unlikely, especially given this earlier study. Although scent trails left by prey typically last 24 h 43 , even week-old scent trails can attract predators 44 . When we tested for an effect of scent age by restricting our analysis to sequences that occurred within one day, maximizing conditions for prey detection by predators, the observed frequencies of prey-predator sequences were no higher than for the whole sample. Similarly, there was no evidence of a prey-trap in the types of wildlife passages used most by predators, wildlife passages where they would have had more opportunity to detect scent trails from prey. Thus, diminished scent cues are an unlikely explanation for why we did not find support for the prey-trap hypothesis.
Our conclusions were similarly unchanged by restricting our analyses to ecological conditions that might be expected to increase the likelihood of a prey-trap. There were no differences in our results as a function of high (2012) or low (2015) prey abundance, the season (August) of high prey dispersal, or in the subset of wildlife www.nature.com/scientificreports/ passages (i.e., limited visibility or concrete ledges) that we know are favoured by predators on this landscape 29 . Each of these circumstances could have increased the benefit or ease of prey tracking by predators by increasing detection rates or learning opportunities by predators [26][27][28][29] . A viable interpretation of our results is that low predator, relative to prey, abundance generally limits the likelihood of prey-traps at wildlife passages here and elsewhere 19,24 . For a prey-trap to occur, predators would have to detect (i.e., visually or olfactorily) and encounter prey inside wildlife passages with sufficient frequency to develop search images (sensu [57][58][59]. Surprisingly, there have been no documented cases of predators killing prey in wildlife passages; there has only been one documented case of an (unsuccessful) predation attempt on an arboreal marsupial 25 and the presence of a carcass near a wildlife passage 19 . Both encounter rates and capture success by predators may be too infrequent in wildlife passages for predators to learn to associate them with hunting opportunities (sensu 60, 61 ), or otherwise influence their foraging behaviour 62 , particularly if small and medium-sized predators hunt differently from larger predators. By contrast, many species may use wildlife passages to forage in habitat in highway verges or the median, and predators may traverse wildlife passages with prey that they captured outside of them 63 . conclusions In summary, we found no support for the hypothesis that wildlife passages built to mitigate the barrier effects of roads could function as prey-traps for small and medium-sized mammals 17,19 . If predators targeted prey in this way, we predicted that it would increase the interspersion of prey-predator sequences in wildlife passage use relative to the frequency predicted by prey and predator abundance alone. None of our results supported this prediction. Instead, the frequency of prey-prey sequences was higher than expected, with corresponding low latencies. We speculate that prey may dilute their predation risk through spatiotemporal clustering when using wildlife passages, either incidentally or adaptively. Our results are consistent with the few other studies that tested the prey-trap hypothesis in association with wildlife passages, suggesting such traps do not occur or are difficult to detect 19,24 . Despite our lack of support for it, we suggest that the prey-trap hypothesis merits additional study in other systems, areas, and taxa. In the meantime, we support the conclusions by others that wildlife passages are effective tools for mitigating movement across roads for diverse taxa that include assemblages of prey and predators 10,11 .