Calculating kill intervals for a specific prey from GPS location cluster data of a predator

doi:10.21203/rs.3.rs-3139639/v1

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Calculating kill intervals for a specific prey from GPS location cluster data of a predator

https://doi.org/10.21203/rs.3.rs-3139639/v1

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published 09 May, 2024

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An increasing number of GPS telemetry studies have helped to gain important insights into predator-prey relationships in the last years. However, considerable time and effort have to be invested to evaluate whether GPS location clusters (GLCs) reflect predation events. To reduce field effort, predictive models are being developed to calculate predator kill intervals, but few studies have attempted to do this for one specific prey species. Between 2013 and 2018, we studied predation of 13 GPS-collared Eurasian lynx (Lynx lynx) on Alpine chamois (Rupicapra rupicapra) in the Northwestern Swiss Alps. Our objectives were to predict the total number of killed chamois, including potential kills in unchecked GLCs, and to evaluate if model predictions were accurate enough for practical use. We built a set of generalized linear models (GLM) predicting the occurrence of GLCs containing killed chamois versus GLCs containing other prey types or no prey and compared their predictive performance by means of k-fold cross-validation. We found that model performance was very similar for all candidate models, with the full model yielding the best cross-validation result (accuracy = 0.83, sensitivity = 0.43, specificity = 0.94). Female lynx killed on average one chamois every 11.9 days (10.6–13.0 days, 95% CI); male lynx killed one chamois every 7.2 days (6.7–7.6 days, 95% CI). We conclude that our modelling results were sufficient for practical application. However, this approach does not replace extensive fieldwork but depends both on fieldwork and thorough knowledge of the predator’s ecology and prey community. It may provide useful results only for binary classifications in rather simple predator-prey systems, and results cannot easily be extrapolated from one study area to another.

Studies on predator kill rates help evaluate the impact of predation on populations of prey species (e.g., Breitenmoser et al. 2010, Vucetich et al. 2011). In the last decades, technical advances in the field of GPS telemetry have substantially improved systematic quantification of predation (Blecha and Alldredge 2015). However, considerable time and effort have to be invested to ground-truth GPS location clusters in the field, i.e., to search for possible prey remains and to evaluate whether an observed cluster of GPS locations reflects a predation event. Many researchers have, therefore, developed predictive models to supplement field work and thus to reduce time and resources required to obtain reliable kill rate estimates. Predictive models have been developed, for example, for leopards (Panthera pardus) (Martins et al.2011, Pitman et al. 2012), cougars (Puma concolor) (Blecha and Alldredge 2015; Knopff et al. 2009), wolves (Canis lupus) (Webb et al.2008, Irvine et al. 2022), bobcats (Lynx rufus) (Svoboda et al.2013), and Eurasian lynx (Lynx lynx) (Krofel et al.2013). Large felids are especially well suited for predation studies using GPS telemetry because they are usually solitary and tend to return to their prey items on several days until they have completely consumed the carcass, thereby generating GPS location clusters (hereafter GLCs; Merrill et al. 2010). Model algorithms can be designed to distinguish 1) kill sites from non-kill sites and 2) kill sites of different prey types. Generally, model algorithms designed to identify kill sites are more efficient in predicting kill sites of large prey than of small prey (Elbroch et al.2018; Knopff et al.2009; Svoboda et al.2013; Webb et al.2008, Oliveira et al. in press). An important factor allowing for discrimination between kill sites and non-kill sites in predictive models is GLC duration, which is the time period from which GPS locations at a cluster are recorded (reviewed in Irvine et al. 2022). While large prey items usually result in GLCs of a longer duration (> 24h), smaller prey items are associated with shorter GLC duration and are more difficult to distinguish from GLCs caused by other types of behaviour (e.g., resting sites).

Prediction of a specific prey species from GPS location cluster data has so far rarely been attempted and typically showed low classification accuracy for less common prey species (e.g., Knopff et al. 2009). Especially in complex predator-prey systems with a large predator guild and a wide diversity of prey species, prediction of prey species for individual kill sites may in fact be impossible. However, for management and conservation purposes, kill rates might be required to be specific for a particular prey species, for example when the predation impact on one particular prey species is of special interest.

The predator-prey system of the Eurasian lynx, the roe deer (Capreolus capreolus), and the Alpine chamois (Rupicapra rupicapra) is suitable for studying the feasibility of prey species prediction from GLC data because the two prey species in this system differ in their habitat selection (Morellet et al. 2011, Nesti et al. 2010). Lynx return to their prey repeatedly, and GPS location clusters can be used to find kill sites (even of smaller prey such as neonate ungulates), as has been shown in several previous studies (Krofel et al. 2013, Vogt et al. 2018). Moreover, predation impact of lynx on ungulate species is often of strong interest for wildlife managers and conservationists. In Switzerland, the Alpine chamois currently receives special attention, since both population sizes and hunting bags have been declining in several areas during the last decades (Breitenmoser et al. 2016). Regulation of the Eurasian lynx is a possible management measure that could be legally applied by responsible state agencies to increase chamois numbers (BAFU 2016).

Here, we studied predation of GPS-collared lynx on Alpine chamois in the Northwestern Swiss Alps. The objectives of our study were 1) to predict the total number of killed chamois, including potential kills in GLCs that could not be ground-truthed due to extreme steepness or risk of avalanches, and 2) to evaluate if our model predictions were accurate enough for practical use.

Study area

The study area was mainly situated in the Northwestern Swiss Alps of the Canton of Bern and comprised the main ridges and valleys from the Stockhorn to the Niesen mountain chains. It also included parts of the Central Swiss Alps (Augstmatthorn mountain chain) and covered approximately 1,300 km² (Fig. 1). The landscape is composed of a mixture of forests, grazed pastures, and rocky grounds, interspersed with human settlements. The area is intensively used for tourism year-round. Elevations range from 600 m a.s.l. up to 3,050 m a.s.l. at the highest peak.

Study species

The Eurasian lynx is the only widespread large carnivore species in the study area, with an estimated density of 3.16 (2.54–3.78, 95% compatibility interval; Amrhein and Greenland 2022) independent lynx (i.e., subadults and adults) per 100 km² of suitable habitat (suitable habitat covers 95% of total study area; Zimmermann et al. 2018). The main prey of the lynx in the area are roe deer and Alpine chamois; alternative prey species include red fox (Vulpes vulpes), badger (Meles meles), European brown hare (Lepus europaeus), mountain hare (Lepus timidus), Alpine marmot (Marmota marmota), black grouse (Tetrao tetrix), and hazel grouse (Tetrastes bonasia) (Molinari-Jobin et al. 2002, Vogt et al. 2018). Red deer (Cervus elaphus) have started to recolonise the area in the 1970s and still occur in low densities in most parts of the study area. Alpine ibex (Capra ibex) occur only locally. The area is sporadically visited by wild boar (Sus scrofa) and solitary wolves (Canis lupus), but no resident populations of these species have established yet. The vertebrate species most commonly observed scavenging at lynx kills are red foxes, corvids (Common raven Corvus corax, Carrion crow Corvus corone) and several raptor species (e.g., Common buzzard Buteo buteo, Golden eagle Aquila chrysaetos).

Link Fig. 1

Between 2013 and 2018, we captured and radio-collared 13 Eurasian lynx (6 males, 7 females) and recaptured 2 of them, following established standard protocols (described in Ryser-Degiorgis et al. 2002; Ryser et al. 2005; Vogt et al. 2016) and with all animal experimentation permits required according to Swiss legislation. We used 2 trapping techniques: unbaited double-door box traps made from solid wood (5 captures) and foot snares made from 3 mm wire cables (10 captures). Box traps and foot snares were equipped with an alarm system allowing for constant monitoring. Any non-target species were directly released from the traps. Lynx were immobilized with medetomidine hydrochloride (Domitor®, Orion Corporation, Espoo, Finland) and ketamine hydrochloride (Ketasol®, Graeub, Switzerland). Atipamezole hydrochloride (Antisedan®, Orion Corporation, Espoo, Finland) was used as an antagonist for medetomidine (Ryser-Degiorgis et al. 2002). Each individual was equipped with a GPS/GSM tracking unit (Wild Cell SL/SD GPS-GSM collars, LoTek wireless, Ontario, Canada) weighing 250–300 g. Collars contained a break-off device (a seam stitched with 1.2–1.5 mm corrodible annealed wire), allowing the unit to drop off after 1–4 years. All lynx caught were examined by a veterinarian and intensively monitored after release until we could confirm that they were hunting successfully.

As in other studies on wild felids (i.e. Blecha and Alldredge 2015; Krofel et al. 2013), GPS collars were programmed to record 7 GPS fixes per day with one location taken at noon and the others between 18:00 and 06:00 CET, with hourly intervals around dusk – the time when lynx are most likely to feed on their kills (Krofel et al. 2013, Krofel et al. 2019, Mattisson et al. 2011). GPS location clusters (GLCs) were generated in R (version 4.0.2, R Development Core Team 2020) using the cluster algorithm developed by Svoboda et al. (2013). We defined a GLC as a set of at least 2 GPS fixes obtained within 72 h and within a maximum distance of 100 m.

Kill sites were identified by ground-truthing GLCs in the field as described in Vogt et al. (2018). The coordinates of kill sites were logged with a handheld GPS, and prey species and the distance to the nearest GPS location within the GLC were noted for each kill. Scavenging occurs rarely in Eurasian lynx (von Arx et al. 2017). We classified animal remains as kills if they matched the following criteria: found within 150 m of the GLC centroid, state of decay corresponds to date of GLC initiation, typical characteristics of lynx feeding activities (e.g., throat bite, kill covered with plant material, stomach and intestine not eaten, skin around legs turned inside out), no sign of other trauma. Prey remains were, on average, found 8 m (± 10 m SD) from the nearest GPS location within a GLC. If kills were completely consumed, prey species could usually still be identified from skulls, horns and antlers, legs and hooves as well as by comparison against hair reference samples.

All GPS collared lynx were resident adults (≥ 2 years). 6 out of the 7 females had young. The mean observation duration was 12 months on average (ranging from 7.5 to 21 months). For one male lynx, we had only 6 months of data before his collar failed. He was, however, the direct successor of another GPS collared male lynx whose home range he had taken over. In this case, we combined data from both males to cover a full year. The 13 GPS-collared lynx provided a total of 3,144 GLCs, of which 1,457 could be ground-truthed in the field (46%). We attempted to reduce bias towards larger prey and more accessible areas as much as possible (as explained in Vogt et al. 2018), with the help of experienced field researchers checking GLCs in steep terrain whenever snow conditions permitted access. However, 14% of formed GLCs could not be checked because access was too dangerous due to extreme steepness or high risk of avalanches. If time constraints did not allow us to check all newly formed GLCs, we gave priority to those GLCs with a duration of at least 6 h and containing at least one night location (between 18:00 and 06:00 CET). In this way, we reduced the likelihood of checking GLCs containing only daybeds while reducing the chance of systematically missing small prey items (e.g., neonate ungulates) as much as possible (Krofel et al. 2013, Vogt et al. 2018).

Selection of predictors for chamois occurrence

We built a set of generalized linear models (GLM) predicting the occurrence of GLCs containing killed chamois (1) versus GLCs containing other prey types or no prey (0). In order to find predictors for the presence of killed chamois within a given GLC, we selected a set of variables from the literature that were found to be associated either with the prediction of kill sites from GPS location data (Krofel et al. 2013, Svoboda et al. 2013) or with different habitat selection of the 2 most common prey species, chamois and roe deer (Baumann & Struch 2000, Fankhauser & Enggist 2004, Darmon et al. 2012, Gehr et al. 2017, Morellet et al. 2011, Nesti et al. 2010). These factors comprised GLC characteristics (GLC duration, proportion of night locations in the GLC) as well as habitat variables calculated for GLC centroids (elevation, slope, aspect, distance to rocks, and forest (yes, no)). GLC duration was calculated as the time spent within a given GLC (Vogt et al. 2018). Elevation, slope and aspect were calculated from a digital elevation model (DEM) for Switzerland with a grid cell size of 25 m (BFS GEOSTAT, http://www.geostat.admin.ch). Rocky areas and forest were extracted as vector data from the SwissTLM3D geodatabase of the Swiss Federal Office of Topography (ESRI File Geodatabase 10.1, http://www.swisstopo.admin.ch). We further included lynx sex in all our models, since male lynx kill chamois more frequently than do females (Molinari et al. 2002).

Model selection and cross-validation

The full model contained all predictors and those interactions that were considered biologically meaningful. We compared the performance of the full model to 6 simpler candidate GLMs built from combinations of the selected predictors (Table 1) and compared their performance by means of 10-fold cross-validation with 3 repeats using the function train() of the R package caret (Kuhn 2019). The GLMs were fitted to the data from 1,457 checked GLCs, assuming a binomial error distribution. The response variable was occurrence of killed chamois (1 = GLC contains a killed chamois, 0 = GLC contains other prey species or no kill). GLC duration and lynx sex were included in all candidate models. Some models contained GLC duration as quadratic term to allow for very long-lasting clusters (e.g., den sites of female lynx) to be classified as non-kills. Numeric variables were transformed as follows: elevation = (elevation-1,000)/100; slope = (slope-30)/10; aspect = aspect/10; GLC duration = log(GLC duration); distance to rocks = log(distance to rocks + 1). Factors (forest, sex) were transformed into dummy variables for analysis. We used the function confusionMatrix() of the package caret to calculate confusion matrices and several metrics for measuring model performance (accuracy, sensitivity, specificity).

Table 1

Prediction of kill intervals for chamois

We fitted the best model to the data of all checked GLCs and then made predictions for unchecked GLCs. We simulated fitted values (5,000 simulations) and Bayesian compatibility intervals (Amrhein and Greenland 2022; “credible intervals”) for the unchecked GLCs using the function sim() of the package arm (Gelman et al. 2021). In order to estimate the total number of chamois killed by each lynx individual, we added the number of verified chamois from the dataset of the checked GLCs to the number of predicted chamois from the dataset of the unchecked GLCs (mean of the 5,000 simulations). We then calculated kill intervals as the mean number of days between 2 killed chamois and reported these means together with the Bayesian compatibility intervals.

Accuracy of kill-interval predictions

In order to evaluate whether our calculated kill intervals for chamois were realistic and of practical use, we present metrics of model performance (accuracy, sensitivity, specificity) and discuss the width of the Bayesian compatibility intervals for kill rate predictions. Accuracy is defined as the number of correct predictions divided by the total number of predictions. Sensitivity is the true positive rate, i.e., the number of GLCs correctly classified as chamois divided by the true number of GLCs containing chamois (true positives + false negatives). Conversely, specificity is the true negative rate, i.e., the number of GLCs correctly classified as non-chamois divided by the true number of GLCs not containing chamois (true negatives + false positives). We also compared predicted kill intervals (days between consecutively killed chamois), with kill intervals calculated from field data (kill series). A kill series consisted of at least 2 consecutive kills from the same lynx individual that were found by ground-truthing of GLCs in the field, under the condition that all GLCs with a duration of ≥ 6 h formed in between the GLCs containing these 2 kills had been checked as well. GLCs with a duration of < 6 h only have a low probability of containing a kill (< 10%, Vogt et al. 2018) and were not considered. We then calculated the kill intervals for chamois from the number of kills found per year (extrapolated from kill-series data) and the proportion of chamois in the prey spectrum for male and female lynx separately.

Regional extrapolation

To test how well model predictions could be extrapolated to other areas, we split our dataset into 3 regions (Fig. 1). The 3 regions differed topographically (Fig. 1) and also concerning chamois density (LANAT 2018, Vogt et al. 2019). 5 lynx (452 GLCs) were tracked in the Stockhorn region, 6 (762 GLCs) in the Niesen region and 2 (243 GLCs) in the Augstmatthorn region. We used data from 2 regions to train the model and then used the data from the third region as test dataset to make new predictions. For this analysis, we only used the model yielding the best overall performance for the whole dataset. In order to evaluate how well one region could be predicted with data from the other two, we compared model performance and deviance between predicted and ground-truthed number of chamois between the 3 regions.

Model selection and cross-validation

Model performance was very similar for all candidate models, with the full model yielding the best cross-validation result (accuracy = 0.83, sensitivity = 0.43, specificity = 0.94; Table 2). The model output of the full model is presented in Table 3.

Table 2

Table 3

Prediction of kill intervals for chamois

Kill intervals for chamois inferred from the total number of chamois killed during the observation period of each lynx differed between the sexes. Female lynx killed on average one chamois every 11.9 days (10.6–13.0 days, 95% Bayesian compatibility interval) while male lynx killed one chamois every 7.2 days (6.7–7.6). This calculation included chamois of all age classes. There was regional variation, with female lynx in the Niesen region killing less chamois than in the other 2 regions (Table 4).

Table 4

Comparison with kill intervals calculated from kill series

When we extrapolated from the subsample of consecutive kills found in the field (n = 155), female lynx killed on average one prey every 3.7 days. 27.5% of all kills found from female lynx (n = 403) were chamois. This would lead to a calculation of one chamois killed every 13.4 days for females. Male lynx killed on average one prey every 4.2 days (n = 155), while 43.7% of all kills found from males (n = 320) were chamois. This would lead to a calculation of one chamois killed every 9.6 days for males.

Regional extrapolation

Predicting data from one region with the full model trained on data of the other 2 regions showed that our model could not be generalized to all regions with the same success. Accuracy was lowest for predictions for the Augstmatthorn region made from the model trained on data from the other 2 regions. Predictions for the Niesen region had the highest accuracy, but the number of chamois in the dataset was overestimated by 20% (Table 5).

Table 5

Accuracy of kill interval predictions

Classification accuracy was rather high in all compared models (83% in the best model) and was comparable to other studies using different modelling approaches for classification of kill sites (kills versus non-kills: 74–77%, Franke et al. 2006; 72%, Webb et al. 2008; 67%, Svoboda et al. 2013) or prey types based on prey size or species (88%, Webb et al. 2008; 75%, Knopff et al. 2009; 66–75%, Oliveira et al. in press). Our approach of classifying 2 categories (chamois, no chamois) provided higher accuracies than the multi-class model generated by Knopff et al. (2009) for classification of several prey species. More in-depth analyses of confusion matrices showed that our models were much more successful in correctly predicting GLCs that did not contain chamois (93–94% in all models) than in correctly predicting GLCs containing chamois (38–43% in all models, similar to Irvine et al. 2022). However, since non-chamois GLCs make up the largest part of the dataset (78%), wrongly classifying them would lead to a strong overestimation of killed chamois in the dataset. A high specificity is, therefore, essential for useable kill interval estimates (Knopff et al. 2009).

In our predator-prey system, killed chamois could potentially be confused with killed roe deer or Alpine ibex. While Alpine ibex (n = 5) made up only 0.7% of all found kills (n = 722) in our study area, killed roe deer (n = 263) were found nearly as often as chamois (n = 318). GLCs containing chamois show certain similarities to GLCS containing roe deer and the latter were contained in the non-chamois category within our model. Chamois tend to prefer steeper, rockier areas at higher elevations than roe deer, but both species can also be found in mountain forests, especially in winter when chamois migrate to lower altitudes for feeding (Lovari et al. 2006, Unterthiner et al. 2012). There is also an overlap in body weight between chamois and roe deer of different age classes, leading to overlapping handling times (Vimercati 2014). To solve this problem at least partially, we calculated the total number of killed chamois as the sum of chamois found empirically in the field (for checked GLCs) and the number of predicted chamois (for unchecked GLCs). We assumed that easily accessible GLCs in less steep and rocky areas would potentially be harder to classify correctly as either chamois or roe deer kills, but that these GLCs would also be more likely to be ground-truthed in the field.

Of course, the ability of our model to correctly predict chamois occurrence in very steep and rocky areas would depend on such GLCs being part of the training dataset, in order to avoid projections outside the data range. With the help of experienced field researchers, we went to great lengths to also include a subsample of the most “extreme” GLCs in our dataset. Nevertheless, further studies on the potential effects of biased field sampling on model classification accuracy would be very useful. The low sensitivity of our models remains somewhat unsatisfying at the level of individual GLCs, for example if one envisions an analysis of habitat parameters associated with predicted chamois kill sites. Sensitivity could potentially be further improved by restricting the dataset only to chamois of a certain age, since many model algorithms are less successful in distinguishing kill sites of small prey (such as juvenile chamois) from non-kill sites, due to short handling times resembling other behaviours such as resting (Elbroch et al.2018; Knopff et al.2009; Svoboda et al.2013; Webb et al.2008, Oliveira et al. in press). Also, the use of more advanced machine-learning methods such as multi-class random forest (Oliveira et al. in press) or the inclusion of activity inferred from accelerometer data (Blecha & Alldredge 2015, Petroelje et al. 2020) might further improve predictions not only of prey type but potentially also of prey species.

While some classification error at the level of individual GLCs could not be removed, the overall number of chamois predicted by our models matched the actual number of found chamois very closely in our training dataset. False positives and false negatives seemed to cancel each other out, similar to what was observed by Knopff et al. (2009), who used logistic regression models to distinguish kill sites of cougars from non-kills. The widths of Bayesian compatibility intervals for the number of chamois predicted by our models were reasonably narrow (Table 4). We therefore conclude that estimates of the overall number of chamois killed within our study area were accurate enough for practical use for conservation and wildlife management purposes. Moreover, spatial plots of our model predictions showed plausible patterns, and areas with high predicted probability of killed chamois overlapped well with empirical data (Fig. S1) and with our own knowledge of chamois distribution in the study area (from own observations and expert opinion of local game wardens).

Kill intervals for chamois calculated with the approach presented here (number of verified chamois from the dataset of the checked GLCs + number of predicted chamois from the dataset of the unchecked GLCs) were 1.5 to 2 days shorter than kill intervals calculated only from field data (combining information from consecutive kills found in the field and proportion of chamois in the prey spectrum). This probably reflects an underrepresentation of chamois in the total number of verified kills found in the field and highlights how the inclusion of “virtual kills” can help to reduce potential bias in field work, if the limitations of the modelling approach are critically discussed as well.

Regional extrapolation

Biologists not only seek to complement datasets and reduce field work effort by including information from GLCs that were not ground-truthed (e.g., Webb et al. 2008, Svoboda et al. 2013, Irvine et al. 2022, Oliveira et al. in press), but there is also the intention to extrapolate from well-studied individuals or areas to situations where less fieldwork was conducted. Irvine et al. (2022) suggest that predictive models are system-specific and emphasize the need for field visits to GLCs. In our study, predicting data from one region with the model trained on data from the other 2 regions showed that predictions could not be generalized to all regions with the same success. In the Niesen region, for example, female lynx killed less chamois than in the other 2 regions; and even though model accuracy was highest, predicting the Niesen region from the other 2 regions resulted in a 20% overestimation of chamois in the dataset. Regional differences can arise from differences in lynx behaviour or in environmental conditions such as prey availability or prey community structure. In the Niesen region, the prey community seems the same as in the other 2 regions, but the density of chamois compared to roe deer is lower (Vogt et al. 2019). However, ungulate census data were available only at a very coarse spatial resolution for our study area (LANAT 2018), so that we were not able to include this parameter in our models. If regional variation is unknown or cannot be accounted for, extrapolations from one study area to another can result in substantial bias and should be critically discussed.

Concluding remarks

It is possible, with some reservations, to calculate species-specific kill intervals from GPS location cluster data of solitary predators like the Eurasian lynx. The sensitivity of the models should be further improved, but the results can be sufficient for practical application. However, this approach does not replace but is dependent on extensive fieldwork and thorough knowledge of the predator’s ecology, habitat and prey community. It may provide useful results only for binary classifications in rather simple predator-prey systems, and results cannot easily be extrapolated from one study area to another. Use of more complex machine-learning approaches combining data from different study areas may help to further improve classification results in the future and expand knowledge in this field.

Acknowledgements

We thank the game wardens of the Canton of Bern for their essential help with capturing and monitoring of lynx and for monitoring of prey species in our study area. We also thank the game wardens of the Cantons of Luzern, Obwalden, Fribourg and Vaud for their help with monitoring transboundary lynx. We further thank the following wildlife veterinarians of the Institute for Fish and Wildlife Health (FIWI), Bern for their participation in lynx captures: Marie-Pierre Ryser-Degiorgis, Mirjam Pewsner, Roman Meier, Iris Marti, and Simone Pisano. We also thank all involved KORA personnel, interns, civil servants, and students for their help with field work.

Funding

This study could be realized thanks to a grant from a charity foundation from Liechtenstein and financial support from the hunting inspectorate of the canton of Bern as well as from the following foundations: Stotzer-Kästli Stiftung, Zigerli-Hegi Stiftung, MAVA foundation and Fondation de bienfaisance Jeanne Lovioz.

Ethics Approval

Lynx were captured with all permits required according to Swiss legislation for capturing, immobilizing, and radio tagging lynx (capture permits from the Federal Office for the Environment: Bewilligung_KORA_Luchsfang_Kompartimente I, III und IV_2011-2015, Bewilligung_KORA_Luchsfang_Schweiz_2017-2020/Q342-1667; animal experimentation permit from the Animal Welfare Commission of the Office for Agriculture and Nature of the Canton of Bern: 111/13 and BE3/17+).

Authors' contributions

KV designed the study, conducted field work, performed data analyses, and wrote the draft of the manuscript. TR helped with developing the modelling approach and with data analysis. SS collected field data and performed analyses of kill intervals. CW helped with study design and project planning. VA provided general support and helped revising the manuscript. All authors reviewed the manuscript.

Competing interests

The authors declare no competing interests.

Availability of data and materials

Data can be obtained from the authors upon reasonable request.

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Table 1. Structure of the 7 candidate GLMs to predict the probability of a GLC containing a killed chamois. GLC duration and lynx sex were included in all models. * denote interaction terms
Model	Fixed factors
Full model	duration + (duration)²+ proportion of night locations + slopeelevation + distance to rockselevation + distance to rocksforest + slopeforest + aspect + sex
model1	duration + proportion of night locations + slope + elevation + distance to rocks + forest + aspect + sex
model2	duration + proportion of night locations + slope + distance to rocks + elevation*forest + aspect + sex
model3	duration + proportion of night locations + slope + elevation + distance to rocks*forest + aspect + sex
model4	duration + proportion of night locations + slope + elevation + distance to rocks + sex
model5	duration + (duration)²+ slope + elevation + distance to rocks + sex
model6	duration + (duration)²+ slope + distance to rocks*forest + sex

Table 2. Cross-validation performance of the 7 candidate models (GLMs, Tab. 1) to predict the probability of a GLC containing a killed chamois. Performance metrics were calculated using the function confusionMatrix() of the R package caret. Models were fitted to data of 1,457 ground-truthed GLCs using repeated k-fold cross-validation with 10 folds and 3 repeats. The true number of chamois in the training dataset was 318. CI = 95% (Bayesian) compatibility intervals (Amrhein and Greenland 2022).
Candidate model	Accuracy (CI)	Sensitivity	Specificity	chamois predicted (CI)
model0 (full model)	0.83 (0.81–0.84)	0.43	0.94	320 (295–348)
model1	0.82 (0.80–0.83)	0.38	0.94	320 (294–347)
model2	0.82 (0.81–0.83)	0.40	0.94	320 (294–346)
model3	0.82 (0.81–0.83)	0.40	0.94	320 (295–345)
model4	0.82 (0.80–0.83)	0.39	0.93	319 (293–346)
model5	0.82 (0.81–0.83)	0.41	0.94	319 (293–346)
model6	0.82 (0.81–0.83)	0.42	0.93	319 (293–346)

Table 3. Model parameters of the best GLM (model0, Tab. 1) predicting the probability of a GLC containing a killed chamois (1) versus no chamois (0).
Predictor	Estimate	SE	p-value
Intercept	-11.313	1.402	< 0.001
GLC duration	5.04	0.698	< 0.001
(GLC duration)2	-0.553	0.102	< 0.001
aspect	0.011	0.008	0.143
proportion of night locations in GLC	1.42	0.521	0.006
slope	0.663	0.209	0.002
elevation	0.058	0.073	0.429
forest	1.239	0.476	0.009
distance to rocks	-0.142	0.104	0.172
lynx sex	-1.101	0.158	< 0.001
distance to rocks*forest	-0.372	0.103	< 0.001
distance to rocks*elevation	0.001	0.016	0.964
forest*slope	-0.234	0.184	0.202
elevation*slope	-0.039	0.028	0.162
The model was fitted to the data of 1,457 ground-truthed GLCs by maximum likelihood. Factors were transformed to dummy variables (lynx sex: 1 = female, 0 = male; forest: 1 = forest, 0 = open area). The estimates show the effect of factor level = 1 (forest/female). Numeric factors were transformed to fit the scale of the other variables as described in the methods section. * denote interaction terms.

Table 4. Predicted kill intervals for chamois (days between consecutive kills). Total chamois = number of chamois found in checked GLCs + number of predicted chamois in unchecked GLCs (mean over 5,000 simulations). CI = 95% (Bayesian) compatibility intervals.
Lynx individual	Chamois found	Total chamois	CI	Days observed	Kill interval	CI
Stockhorn region
NEVE	32	60	55–65	510	8.5	7.8–9.3
CATO	25	47	43–51	384	8.2	7.5–8.9
EYWA	25	40	37–43	345	8.6	8.0–9.3
LUPO/MISO	28	60	56–65	365	6.1	5.6–6.5
Niesen region
GIRO	33	44	42–46	278	6.3	6.0–6.6
LARY	42	73	69–77	538	7.4	7.0–7.8
ISIS	26	40	38–44	479	12.0	10.9–12.6
WEGA	13	21	19–24	313	14.9	13.0–16.5
LYRA	14	25	22–31	398	15.9	12.8–18.1
LELA	12	21	19–23	284	13.5	12.3–14.9
Augstmatthorn region
AMOR	53	80	75–87	631	7.9	7.3–8.4
CARA	15	22	21–24	219	10.0	9.1–10.4

Table 5. Performance of models trained on data from the other 2 regions for predicting the number of chamois killed by lynx in the third region. Performance metrics were calculated using the confusionMatrix() function of the R package caret. CI = 95% (Bayesian) compatibility intervals.
Region	Accuracy (CI)	Sensitivity	Specificity	chamois predicted (CI)	true number of chamois	difference
Stockhorn	0.80 (0.76–0.83)	0.35	0.94	102 (90–115)	110	-7%
Niesen	0.86 (0.83–0.88)	0.49	0.94	168 (146–192)	140	+20%
Augstmatthorn	0.74 (0.68–0.79)	0.35	0.89	62 (55–69)	68	-9%

No competing interests reported.

FigureS1.tif
Fig. S1 Kernel densities of model predictions (blue shaded area) and overlap with GLCs containing chamois (green circles), GLCs not containing chamois (red circles) and unchecked GLCs (grey circles) in the southern part of the study area (Stockhorn and Niesen region). Kernel densities were calculated on classification probabilities with a 1-km search radius. Dark blue areas correspond to areas with the highest probability of finding killed chamois.

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Calculating kill intervals for a specific prey from GPS location cluster data of a predator

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Journal Publication

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Abstract

Figures

Introduction

Methods

Study area

Study species

Selection of predictors for chamois occurrence

Model selection and cross-validation

Prediction of kill intervals for chamois

Accuracy of kill-interval predictions

Regional extrapolation

Results

Model selection and cross-validation

Prediction of kill intervals for chamois

Comparison with kill intervals calculated from kill series

Regional extrapolation

Discussion

Accuracy of kill interval predictions

Regional extrapolation

Concluding remarks

Declarations

References

Tables

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1