Research articlesNetwork analysis of intra- and interspecific freshwater fish interactions using year-around tracking
Abstract
A long-term, yet detailed view into the social patterns of aquatic animals has been elusive. With advances in reality mining tracking technologies, a proximity-based social network (PBSN) can capture detailed spatio-temporal underwater interactions. We collected and analysed a large dataset of 108 freshwater fish from four species, tracked every few seconds over 1 year in their natural environment. We calculated the clustering coefficient of minute-by-minute PBSNs to measure social interactions, which can happen among fish sharing resources or habitat preferences (positive/neutral interactions) or in predator and prey during foraging interactions (agonistic interactions). A statistically significant coefficient compared to an equivalent random network suggests interactions, while a significant aggregated clustering across PBSNs indicates prolonged, purposeful social behaviour. Carp (Cyprinus carpio) displayed within- and among-species interactions, especially during the day and in the winter, while tench (Tinca tinca) and catfish (Silurus glanis) were solitary. Perch (Perca fluviatilis) did not exhibit significant social behaviour (except in autumn) despite being usually described as a predator using social facilitation to increase prey intake. Our work illustrates how methods for building a PBSN can affect the network's structure and highlights challenges (e.g. missing signals, different burst frequencies) in deriving a PBSN from reality mining technologies.
1. Introduction
Most animals dwell in ecosystems populated by other mobile animals [1], hence most animals face daily challenges associated with within- or among-species interactions [2]. Social interactions among individual animals have widespread consequences across a broad range of ecological processes [3–7]. For example, they determine population development and growth [8], invasion success [9], cooperation [10], social hierarchies [11], information flow [12], resource competition [13] or predation [2]. These interactions can be positive (e.g. social facilitation, where groups of fish improve foraging outcomes), neutral (at least in the short term when resources are plentiful, e.g. associations of species in habitats preferred by both species) or agonistic (e.g. among predators and prey). Studying social interactions in aquatic animals has long been challenging as it is difficult to follow highly mobile individual fish underwater for prolonged periods of time at a precise spatial resolution.
Body size is a key trait guiding biotic interactions, especially under water [14]. Aquatic food webs are strongly size-structured, as most predator–prey interactions are driven by size-related gape-constraints and other size-structured processes [15]. Body size affects a range of physiological traits and in turn social interactions [2], social dominance [16] or competitive ability [16]. Although a long history of ecological research has studied how energy and nutrients move through aquatic food webs in response to body size variation among individuals and species [17–19], by far most available research on size-based interactions has been built on ex situ observations in laboratory settings [20] or employed a non-behavioural approach through gut content analysis [21,22], stable isotopes [23,24] or fish capture in different spatial-temporal domains [17,25–27], rather than directly observing fish behavioural decisions in the wild. Indeed, all indirect methods to infer behavioural decisions cannot quantify the frequency of important nonlethal interactions [5,28,29]. Although hydro-acoustics, video recordings or visual observation can shed light on behavioural interactions among individuals, it is challenging to keep track of individuals at sufficiently high resolution and over-extended spatial or temporal scales in freely roaming fish [30].
Two major advances have enabled the quantification of underwater interactions both within and across species (i.e. intra- and interspecifically) with an unprecedented level of detail, and we leverage both in the present study. First, reality mining and high-throughput movement ecology technologies are increasingly implemented, which consist of electronic tags attached to animals that remotely collect high-resolution data such as location or acceleration [31–33]. The specific reality mining technology employed in this study is high resolution acoustic positional telemetry, which uses a network of underwater receivers to locate the fish [32]. In short, this technology listens for an ultrasonic signal emitted by a transmitter implanted inside the fish and uses trilateration to locate the fish in the two-dimensional environment and a pressure sensor can locate the fish in the third dimension. The transmitters of modern applications are potentially able to send signals every few seconds over several years [32] and, under the condition of a high coverage of receivers in a given ecosystem, even whole-ecosystem behavioural studies can be conducted [31,33]. Second, rapid developments in network science are enabling the production of analytical tools that can make sense of the big datasets generated by reality mining studies [34,35], not only structurally, but also temporally [36–38]. Consequently, social network analysis, in particular proximity-based social networks (PBSNs), can be used to quantify behavioural interactions within and across species through large spatial and temporal scales going as far as whole-ecosystem scales [34,39].
We took advantage of high resolution acoustic positional telemetry and PBSNs to quantify the behavioural social interactions within and among four species of freshwater fish using fine-scale acoustic telemetry tracking data at a whole-ecosystem lake scale. To the best of our knowledge, our work is the first to study the social behaviour of multiple mobile aquatic species jointly at a whole-ecosystem scale. Specifically, we tracked the following species: two medium-sized species of cyprinids known to have a similar foraging niche and a benthivorous foraging mode, common carp (Cyprinus carpio), with known social tendencies [40,41] and tench (Tinca tinca), thought to be shyer and more solitary than carp [42]; one medium- and one large-bodied top predatory species, Eurasian perch (Perca fluviatilis) with known social behaviour during foraging [42], and wels catfish (Silurus glanis), a generalist predator belonging to the 20 largest freshwater fish worldwide, invasive in many areas of Europe, generally solitary, but known to sometimes form aggregations. This species choice enabled us to perform the first analysis of proximity-based social interactions relating to either foraging or predation in wild populations of freshwater fish both intra- and interspecifically with species that potentially follow size-structured predator–prey interactions.
Our more specific objectives were to examine (i) whether freshwater fish exhibit social behaviour in general, where a social tie is defined in terms of spatial distance between two fish, (ii) how social networks possibly explain predator–prey interactions and (iii) how inter- and intra-specific clustering varies diurnally and seasonally. With respect to general social interactions, we hypothesized that the non-piscivorous benthivorous carp and tench should show inter- and intra-specific social interactions to benefit from forage patch detection, shared preferred habitats and predator avoidance as group living can offer a range of benefits such as improved predator recognition and avoidance [43,44] or an improved ability to find and exploit food patches [45,46]. We also hypothesized strong intraspecific interactions from perch, as they are a known social species [47], and rare intraspecific interactions from wels catfish as they are thought to be generally solitary [48]. With respect to predator–prey interactions, we further expected no social interactions between perch and either tench or carp. Interactions between perch and the two benthivorous species, carp and tench, would likely be driven by predator–prey interactions; however, vulnerability to predation is strongly related to gape size and thus body size in fish [49], and the perch that we tracked were too small to be dangerous to the carp and tench we tagged, suggesting predator–prey interactions in our system are unlikely. By contrast, we hypothesized that the wels catfish, being a generalist predator capable of consuming fish to about 60% of its body size [50], should exhibit strong associations suggestive of predator–prey interactions with tench and perch, and weaker interactions with the larger-bodied carp that we tagged. Finally, we hypothesized that networks would vary by season in response to temperature-related changes in metabolic demand and prey availability (generally lower in cooler temperature) and be different during day and night given the visibility-induced predation risk. Catfish are known to be nocturnal [29], while perch are a daytime foragers [51]. Thus, catfish-associated networks with possibly vulnerable prey should be stronger during nighttime than during daytime.
2. Material and methods
2.1. Fish sampling and tagging
Prior to tag implantation, we measured the wet mass and total length of each fish and only proceeded to implantation if the transmitter was less than 2% of an individual's body weight [52]. For implantation, fish were individually anaesthetized with a 9 : 1 95% EtOH : clove oil solution added to water at 1 ml l−1. All surgical tools and transmitters were sterilized with a mixture of tap-water and 7.5% povidone-iodine (PVP; Braunol; B. Braun, Kronberg, Germany) before each surgery. Transmitters were implanted into the peritoneal body cavity through a small incision made with a scalpel, following the same procedure for all fish. The incision was then closed with two to five sutures (depending on the size of the transmitter model) using PDS-II absorbable monofilament suture material and FS-1 3-0 needles (Ethicon, USA). Following surgery, fish were immediately placed in an aerated tank and, after recovery (which took up to 15 min), placed into Kleiner Döllnsee (52 59031.100 N, 13 34046.500 E)—a 25 ha (4.1 m mean depth, 7.8 m maximum depth), dimictic, weakly eutrophic natural research lake situated approximately 80 km northeast of Berlin, Germany (figure 1); this environment is detailed in [53]. The lake is unconnected to any neighbouring lakes and has been closed to the public since 1992, thus fish can be tracked without external disturbance or emigration from the system.
Figure 1. Location of the study lake (Kleiner Döllnsee) and the ecologically similar lake (Größer Vätersee).
Kleiner Döllnsee is a summer-stratified lake with an average secchi depth of 1.9 m. The lake is eutrophic with an average total phosphorus concentration of 46 mg m−3 (average of 12 monthly samples from the epilimnion). Summer stratification results in an anoxic zone, below 4 m, which disappears after autumn mixing in October. The average dissolved oxygen in the lake was 15.21 mg l−1 in the study year. The fish community consists of cyprinids (roach Rutilus rutilus, rudd Scardinius erythrophthalmus, common bream Abramis brama, white bream Blicca bjoerkna, bleak Alburnus alburnus, crucian carp Carassius carassius, tench and stocked common carp), and ruffe Gymnocephalus cernuus, Eurasian perch, northern pike Esox lucius, wels catfish, eel Anguilla anguilla and zander Sander lucioperca in small numbers. Carp, catfish, eel and a small number of zander originate from past stocking events; only catfish is now self-recruiting. The lake is surrounded by dense reed (Phragmites spp., Typha spp.) and has patches of submerged macrophytes around the shoreline. The sediments are soft.
We tracked the positions of four freshwater fish species: common carp, tench, Eurasian perch and wels catfish (figure 2a). The transmitter for common carp and wels catfish was a Lotek transmitter, model MM-M-16-50-TP weighing 21 g, measuring 16 by 85 mm, and transmitting either every 5 s (for carp) or 7.5 s (for catfish). In the case of Eurasian perch and tench, we used the model MM-M-11-28-TP weighing 6.5 g, measuring 12 by 65 mm and transmitting either every 27.5 s (for perch) or 35 s (for tench). Smaller transmitters contain smaller batteries, and therefore the transmission rate was lower for perch to enhance battery life and tracking duration. Each transmitter contained a pressure sensor and a temperature sensor, where one transmission per minute contained temperature data and the remaining transmissions contained pressure data to measure fish depth.
Figure 2. Our study system is Kleiner Döllnsee, for which the depth map (b; bottom) was provided in [53]. In this study, we are interested in the coordinates of fish over time; a snapshot of their x, y, z coordinates is provided on the top (a).
The fish used in this study were sampled from various sources. All common carp were hatchery born and lived their entire lives in earthen ponds eating both natural food and formulated pellets. Carp were sampled and released in June 2014 (n = 91) and September 2014 (n = 24). Because we stocked the lake with carp, it was the only species that had transmitters on all members in the lake. By contrast, the three other species were all wild. Perch were sampled and released in two events, first, in November 2014 (n = 31) and in second in May 2015 (n = 19), to opportunistically increase the sample size. All perch were captured by gillnets set over 30–60 min. The fish were rapidly removed by cutting out the meshes and only undamaged fish were used. Most perch were sampled from Kleiner Döllnsee, but n = 6 fish were collected from a nearby (2.3 km) ecologically similar lake, Größer Vätersee (figure 1). Tench were sampled and released between July and September 2014. Most tench (n = 22) were captured by gillnets and fyke nets in the River Oder and purchased from a commercial fisher. The remaining tench were sampled by angling from Kleiner Döllnsee (n = 5) and gillnets in Größer Vätersee (n = 9). The wels catfish were sampled and released between July and November 2014. A third of the wels catfish were sampled by angling or electrofishing from Kleiner Döllnsee (n = 6), while the remaining two-thirds were purchased from a commercial fisher who captured them from the River Oder with fyke nets (n = 12). We note that our intent in securing fish from different sources is to re-create the ecosystem normally present in Kleiner Döllnsee, as the lake normally hosts all these species [54], while also ensuring a sufficient sample size for the study. We re-introduced carp because their original stock of a few large carp was lost through senescense during previous winters as observed during a previous tagging event; no new recruitment was observed. We observed low mortality and high tag retention for tench, perch and catfish; however, carp exhibited high transmitter expulsion, thus reducing the sample size. Some carp that were recaptured were observed to have infected surgical wounds, while others retained their tags and were observed to be healthy with healed incisions. While other studies tracking carp have been successful [40,55], there are other examples of substantial transmitter expulsion from carp [56,57]. Therefore, the high degree of tag loss was not unusual.
The data collection began after all fish had been in the lake for at least two to six months (with the exception of the second perch sampling event), thus giving them time to acclimate to the environment and recover from the transmitter implantation and stocking. At this time, previous work has shown that behaviour has recalibrated to normal patterns [58,59].
2.2. Telemetry system
We collected high-resolution positional data in the wild in Kleiner Döllnsee using a whole-lake acoustic telemetry system that covered the whole lake [32], where ultrasonic signals emitted from small transmitters surgically implanted in fish are detected by a network of underwater hydrophone receivers at precise known locations. Fish positions were calculated by trilateration based on the discrepancy of the time of arrival of a transmitter signal at the receivers, which encodes information about the transmitter identification and depth based on a pressure sensor, at each hydrophone. The system we used consisted of 20 receivers (WHS 3050; 200 kHz; Lotek Wireless Inc., Newmarket, Ontario, Canada) placed within the lake based on manufacturer recommendations. In particular, the 20 receivers were positioned 2 m underwater and were distributed throughout the lake rather than arranged in a grid. A performance assessment to assess system accuracy, detection efficiency and range across seasons and habitats indicated that the accuracy of the system was on average 3.1 m, although it varied according to habitat and season as the accuracy declined in summer and in increasingly vegetated habitats (for details, see [32]). For example, in loose emerged macrophytes the accuracy is on average 10 m, while in deep open water the accuracy is on average 1.9 m. No detections can be received from the reed belt, while on average 71% of possible detections are received from deep open water.
2.3. Data pre-processing
We examined our hypotheses and questions in two stages. First, we performed an extensive pre-processing of the telemetry data, which includes handling discrepancies in the timestamps of the receivers (using temporal aggregation) and dealing with missing data due to positioning errors or a fish going near shore. We then built a PBSN and computed its clustering coefficient, which is detailed in the next subsection.
The data consist of the x, y and z time-stamped coordinates of each fish tracked. This qualifies as big data: for instance, we obtained over two million perch positions. As is common in big data studies, the data need to undergo extensive pre-processing before analysis. In our case, there were three reasons for which the position of a fish may not have been available (either entirely for x–y–z or for the depth coordinate z only) at a desired time:
| (1) | Joint use of the transmitter signal for another measurement. Once per minute, the depth value (z) was missing because it was instead used to report on the temperature. | ||||
| (2) | Burst frequency and set-up. The transmitter on the fish had different burst rates and were not synchronized. Therefore, we did not receive data for all fish at the same second (figure 3). | ||||
| (3) | Tracking issues leading to missing or erroneous coordinates. We never removed a fish from the lake, even temporarily. However, despite living in a closed environment without inflow or outflow, fish were able to go near shore into vegetation and could not be tracked in this situation. Stratification during summer can also lead to signal collisions and reduce the probability of a successful positioning event. Some fish can also lose their transmitters despite the procedure for tagging, or transmitter malfunction happens. These impact the data in different ways. For instance, malfunction usually starts with erratic signals followed by a complete stop rather than producing gaps. Additionally, some fish had a frequency burst every 5 s (carp) while others had one burst every 35 s (tench). | ||||
Figure 3. Transmitters have different burst frequencies across species, hence the measurements are not perfectly synchronized over time.
The first case was solved with imputation, which consists of replacing missing data with substituted values derived from the available data. Because the fish are mobile, it would be inadequate to replace missing data by copying their next position (next observation carried backward) or previous position (last observation carried forward). Rather, the position should be inferred based on the next and previous positions. In this case, the missing z value was taken as the average of the z value immediately before and after.
There were two ways in which the choice of a time resolution could be handled for the second case. First, we could have imputed the data for all fish at one time step where at least one other fish was emitting a signal. For instance, if one fish sends a signal at t = 583 s but other fish emitted only at t = 582 s and t = 585 s, then we could have estimated their positions at t = 583 s. Since the fish have different burst rates and initialization times, this approach would result in inferring most of the data. This is computationally expensive and, most importantly, would risk basing the analysis on data that are mostly synthetic. The second approach, which we followed here, was to explore less granular time scales. Instead of operating at every second, or for every time point where one fish was emitting, we can use a coarser scale such as every 30 s or every minute, which is still generating higher resolution than most other telemetry studies with fish.
Choosing the right temporal resolution is one of the key pre-processing steps in a network analysis such as ours [60–62]. The data scale does not only depend on the data available (as we aim for a scale leading to dense measurements) but also on the question being asked. For instance, if the question is to examine how social ties may be necessitated by food requirements, then we need to ensure that the time scale is consistent with the duration required for food consumption. A common approach is to divide the temporal evolution into meaningful time intervals [61]. An interval is ‘meaningful’ when it is not yet exceedingly coarse to the point of causing a significant change in the results. For instance, intervals on a scale of 1–30 min might yield similar results, while longer periods could possibly impart drastically different outcomes and unacceptable loss of information based on our ANOVA analysis and the speed at which the fish travel.
While our data were timestamped in seconds, there were fewer than two bursts per minute when averaged across species and seasons (table 1). This would result in too many missing values if data were aggregated to anything finer than 1-min intervals. Consequently, we considered time steps of 1, 2, 3, 4 and 5 min, which would allow us to capture foraging or predation events. The process to determine the time window proceeded in three consecutive steps. First, we performed our analysis on each of these five possible time windows. We then used an ANOVA to statistically test whether the choice affects the result to identify an appropriate time window before results start to be distorted. Finally, we applied this window by taking the average of the data points reported within the window. If no data points were reported for a certain time step, then there was a missing value (originating from case 1 or 2). This process left us with time-consistent vectors with missing values.
| species | season | daily bursts | daily bursts across seasons | daily distance swam (m) | depth (m) | total length (mm) |
|---|---|---|---|---|---|---|
| carp | winter | 5813 ± 573 | 3020 | 6879 ± 2308 | 5.07 ± 1.09 | 540 ± 81 |
| spring | 1026 ± 369 | 920 ± 1087 | 1.68 ± 0.81 | 534 ± 74 | ||
| summer | 2003 ± 794 | 2059 ± 1665 | 2.04 ± 1.18 | 537 ± 75 | ||
| autumn | 3244 ± 993 | 3309 ± 2265 | 2.16 ± 1.15 | 531 ± 72 | ||
| catfish | winter | 4649 ± 1733 | 3365 | 2164 ± 1363 | 7.42 ± 1.01 | 1233 ± 258 |
| spring | 2017 ± 1110 | 3299 ± 2351 | 1.31 ± 0.57 | 1212 ± 267 | ||
| summer | 1808 ± 287 | 2012 ± 2192 | 1.84 ± 1.04 | 1212 ± 567 | ||
| autumn | 4989 ± 430 | 3275 ± 2089 | 3.44 ± 1.73 | 1233 ± 258 | ||
| perch | winter | 1750 ± 368 | 1260 | 2578 ± 1189 | 3.98 ± 1.13 | 374 ± 20 |
| spring | 470 ± 80 | 1027 ± 1238 | 1.77 ± 0.98 | 370 ± 17 | ||
| summer | 1035 ± 287 | 4633 ± 2766 | 2.40 ± 1.99 | 345 ± 23 | ||
| autumn | 1790 ± 430 | 5191 ± 2190 | 3.02 ± 1.21 | 372 ± 21 | ||
| tench | winter | 1424 ± 335 | 733 | 2656 ± 1376 | 4.83 ± 0.69 | 459 ± 35 |
| spring | 353 ± 54 | 552 ± 625 | 1.52 ± 0.84 | 467 ± 28 | ||
| summer | 494 ± 98 | 1052 ± 1052 | 2.60 ± 1.55 | 470 ± 32 | ||
| autumn | 667 ± 299 | 1082 ± 1190 | 5.09 ± 2.79 | 469 ± 37 |
The third case required a mixture of multiple imputation and filtering. As it is impossible to accurately re-create the missing trajectory of a fish over long time periods, we removed fish from the data when they were missing for over 4 days (e.g. fish death, hiding in vegetation). When a fish was missing for a shorter period, we imputed the missing data by (i) creating a vector from the last known position to the next one and (ii) assigned a position along this vector based on time. In other words, we assume that fish moved at a constant speed in between their two known locations. For example, consider a fish that was seen at coordinates (2,2,2) and, two bursts later, at (5,5,5). The first missing burst would be assigned to (3,3,3) and the next missing burst to (4,4,4). Similarly, a fish moving from (1,3,1) to (3,1,1) with one missing position in-between would be assigned to (2,2,1). As the behaviour and movements of the fish differ across seasons, the percentage of the raw data (i.e. before using a coarser scale of 1 min) that was missing also differs across seasons (table 2).
| carp |
catfish |
perch |
tench |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| N0 | N | (%) | N | N | (%) | N0 | N | (%) | N0 | N | (%) | |
| winter | 36 | 34 | 94 | 17 | 17 | 100 | 31 | 31 | 100 | 27 | 23 | 85 |
| spring | 34 | 29 | 85 | 18 | 18 | 100 | 30 | 20 | 67 | 26 | 22 | 85 |
| summer | 28 | 28 | 100 | 22 | 22 | 100 | 37 | 35 | 95 | 21 | 19 | 90 |
| autumn | 24 | 24 | 100 | 17 | 17 | 100 | 35 | 35 | 100 | 15 | 13 | 87 |
As highlighted in §1, seasonal differences (e.g. summer versus winter) can impact animal behaviour. Behaviour is also driven by the time of day, due to the different in diurnal and nocturnal patterns. We thus categorized observations with respect to seasons and daily cycles. Specifically, our data are divided into four periods to allow for the analysis of four seasons. One ‘period’ falls into each of the seasons as follows: winter (January 01 2015 to January 31 2015), spring (12 April 2015 to 4 May 2015), summer (10 July 2015 to 30 July 2015) and autumn (16 September 2015 to 12 October 2015). A period here is not a regular calendar month but the number of consecutive days within the season for which the data in such a condition that the least amount of fish had to be discarded and the least amount of data points imputed. We used the exact sunrise and sunset times for each day in the dataset to split the data into diurnal/nocturnal cycles. The kernel densities for each species and each season are shown in figure 4. As emphasized in §1, some of the differences in behaviours across seasons are due to temperature-related changes (figure 5) in metabolic demand and prey availability.
Figure 4. Location of each species (in terms of kernel density) across seasons. White areas of the lake have infrequent detections and fall outside the 95% kernel density area. Figure 5. Water temperature across months.
2.4. Construction of proximity-based social networks
Our goal was to assess whether there are social interactions among fish, and how these vary across time (e.g. seasons, diurnal and nocturnal). We were thus interested in the construction of a temporal network, also known as a ‘time-varying network’, in which social ties (i.e. edges) exist only at certain points in time [63]. The type of networks we created fall under the category of PBSNs [64–66]. In a PBSN, an association or a tie between two individuals exists if they are at most within a distance R at a given point in time. There is no universal distance within which fish of any species would be deemed to be ‘in contact’. Rather, the distance to define a tie in previous social network analyses of fish was chosen to be a function of the fish body size (figure 6). In our case, their total lengths were as follows (mean ± s.d.): 121 ± 28 cm for catfish, 53 ± 7 cm for carp, 37 ± 2 cm for perch and 45 ± 4 cm for tench. Since previous works used 2–4 body lengths for R [67], we considered both values in our analysis. That is, for a given time in the data (i.e. a ‘snapshot’), we constructed two social networks: one for the conservative value R = 2.1 m, and one for R = 4.2 m. When building a social network for a given value of R, we created a social tie if two fish were found within a cube of size R (i.e. a Manhattan distance of less or equal to R; see equation in box 1).
Figure 6. Illustration of the notion of distance as a function of fish body size.
Box 1. Process to create a social network given a distance R and the fish present at a timestep.
| E ← Ø (Create an empty set of social ties) |
| V ← Ø (Create an empty set of fish) |
| For each fish i: (For each pair of fish) For each distinct fish j: |
| (If the Manhattan distance between two fish is <R) |
| (Add a social tie between these fish to the network) |
| (Add both fish to the set of fish in the network) G ← (V, E) |
A network can be constructed in two ways. One is to add every fish (i.e. node) encountered as well as their social ties (i.e. edges). This can result in many disconnected fish that do not interact with others at a given time step or for narrow values of R. As will be discussed in the analysis, such isolated fish are ignored by the standard formula to compute the clustering, thus it is unnecessary to account for them in the network. Consequently, we used the second approach: we only add a fish if it is connected to another one (i.e. the network is constructed only based on the social ties). In other words, when two fish are interacting, then the edge as well as the corresponding two nodes are added. Our process is summarized through the pseudocode in box 1. Note that the network is undirected as we can only tell that there is an interaction between two fish, rather than some unidirectional communication from one fish toward another.
2.5. Analysis
As differentiated in [68], there are two types of parameters that can be studied in time-varying graphs: temporal and atemporal parameters. Temporal parameters cannot simply be aggregated over time. For example, consider the network centrality or ‘importance’ of each fish. Because this is a ranking, it cannot just be aggregated by taking the average across snapshots. Temporal parameters are thus computed across all snapshots at once, for instance by using an algorithm specifically designed for dynamic centrality. By contrast, atemporal parameters are defined on static networks and their evolution over time can be observed by measuring them over the sequence of snapshots.
The atemporal parameter of interest in this study is the clustering coefficient. This is one of the most common measures in social networks generally [69], and in studies of fish networks particularly [67,70,71]. The clustering coefficient of a network is measured as the average clustering coefficient of its nodes. That is, given the graph Gspecies,time,R built for a specific set of species at a given time and defined based on interactions within a distance R, the clustering of the network is the average clustering of its nodes V:
In a random network, the clustering coefficient tends toward zero as the number of entities (i.e. fish in our context) increases. The reason is that, as there are more fish, the probability that they form dense groups is lower [69]. By contrast, a large clustering coefficient sustained over time would indicate a prolonged and purposeful social behaviour.
To ensure that an observed clustering is statistically significant, it is necessary to compare it with a randomized version of the network. This ensures that the clustering is specifically produced by the interaction of individual fish [72], rather than merely a function of the space [64] or an artefact found in random movements. Consequently, we generated several random networks that had the same distribution of degrees (i.e. matching histograms for the number of social ties), computed the mean clustering across these randomized networks and compared it with the clustering in our real network. These randomized networks were generated by providing the expected degree sequence, using the NetworkX library in Python 3.
We used an ANOVA to identify whether the impact of a time window between successive fish positions would distort the clustering coefficient. To provide a robust analysis, we computed the mean clustering coefficient across values of R at 1, 2, 3, 4 and 5 min.
To provide full transparency into our methods, we note that our code can be freely downloaded from a third-party repository, as detailed in Data accessibility. The code is provided as a set of Jupyter Notebooks (which use Python 3) and R scripts (for the analysis of day/night differences).
3. Results
3.1. Characteristics of the sample after pre-processing
The pre-processing resulted in discarding some fish as they were missing from the dataset for too long to use imputation techniques. The number of fish retained across species and seasons is summarized in table 2. In the worst case (spring), we used 89 out of the 108 fish tracked in that season (82.4%).
Mean clustering increased with large time windows (table 3), which is expected because aggregating social ties over longer time periods leads to more ties and hence a higher likelihood of clustering. Nonetheless, the increase in clustering was small as the ANOVA did not find a statistically significant difference between the time windows. Thus, we used the most conservative window of 1 min, which resulted in the data imputation summarized by table 4.
| species | mean clustering for a given time window of t minutes |
ANOVA |
|||||
|---|---|---|---|---|---|---|---|
| t = 1 | t = 2 | t = 3 | t = 4 | t = 5 | F | p | |
| carp | 0.1660 | 0.1710 | 0.1760 | 0.1790 | 0.1830 | 0.076 | 0.989 |
| catfish | 0.0740 | 0.0746 | 0.0749 | 0.0754 | 0.0761 | 0.003 | 0.999 |
| perch | 0.0271 | 0.0273 | 0.0276 | 0.0276 | 0.0278 | 0.002 | 0.999 |
| tench | 0.0190 | 0.0191 | 0.0191 | 0.0191 | 0.0194 | 0.001 | 0.999 |
| carp |
catfish |
perch |
tench |
|||||
|---|---|---|---|---|---|---|---|---|
| avg per minute | points interpolated (%) | avg per minute | points interpolated (%) | avg per minute | points interpolated (%) | avg per minute | points interpolated (%) | |
| winter | 0.33 | 11.95 | 0.36 | 31.78 | 0.72 | 38.58 | 0.80 | 43.50 |
| spring | 3.04 | 29.50 | 2.23 | 56.30 | 0.21 | 60.45 | 0.10 | 86.02 |
| summer | 1.21 | 65.77 | 2.42 | 74.46 | 0.20 | 65.81 | 0.57 | 89.35 |
| autumn | 0.34 | 46.82 | 0.20 | 32.85 | 0.33 | 38.67 | 0.71 | 80.10 |
3.2. Clustering
For each of our four species, we computed the distribution of clustering within each of the four seasons and for each of the two distances R = 2.1 m and R = 4.2 m. This led to a total of 4 × 4 × 3 = 54 distributions of clustering. Distributions for R = 2.1 and R = 4.2 are presented in figure 7 through compact box plots for intra-species interactions. Similarly, we computed and visualized the distributions of clustering for interactions among species (figure 8). The analysis was repeated for day and night, leading to an additional set of 2 × (32 + 48) = 160 distributions (table 5). To conveniently contrast results across species, seasons, and time of days, we summarized them in figure 9. For ease of interpretation, we offer qualitative categorizations to indicate when the clustering was low or high. Comparing the clustering coefficients to a statistical null model revealed that the clustering we found was statistically significant across all species to various extents (table 6).
Figure 7. Clustering for each species across four seasons, with both values of the distance threshold R (2.1 m and 4.2 m) for social ties. Clustering is minimal at 0 (i.e. no clustering) and maximal at 1 (i.e. complete clustering). Figure 8. Clustering for multiple species across four seasons, with both values of the distance threshold R (2.1 m and 4.2 m) for social ties. Figure 9. Clustering within (diagonal) and across species (rows) for all four seasons and parts of day. Qualitative categories are only indicative.
| day only |
night only |
overall |
|||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| R = 2.1 m |
R = 4.2 m |
R = 2.1 m |
R = 4.2 m |
R = 2.1 m |
R = 4.2 m |
||||||||
| mean | s.d. | mean | s.d. | mean | s.d. | mean | s.d. | mean | s.d. | mean | s.d. | ||
| carp and catfish | Jan | 0.26 | 0.21 | 0.47 | 0.16 | 0.08 | 0.19 | 0.18 | 0.22 | 0.14 | 0.21 | 0.28 | 0.27 |
| Apr | 0.04 | 0.16 | 0.12 | 0.23 | 0.02 | 0.13 | 0.08 | 0.18 | 0.03 | 0.15 | 0.11 | 0.26 | |
| July | 0.04 | 0.15 | 0.12 | 0.22 | 0.05 | 0.17 | 0.12 | 0.23 | 0.04 | 0.16 | 0.12 | 0.27 | |
| Oct | 0.11 | 0.23 | 0.27 | 0.26 | 0.04 | 0.15 | 0.10 | 0.23 | 0.07 | 0.20 | 0.18 | 0.29 | |
| carp and tench | Jan | 0.26 | 0.21 | 0.46 | 0.17 | 0.07 | 0.18 | 0.16 | 0.22 | 0.13 | 0.21 | 0.27 | 0.28 |
| Apr | 0.04 | 0.17 | 0.12 | 0.24 | 0.02 | 0.13 | 0.08 | 0.17 | 0.03 | 0.15 | 0.11 | 0.26 | |
| July | 0.05 | 0.18 | 0.14 | 0.25 | 0.05 | 0.19 | 0.14 | 0.25 | 0.05 | 0.19 | 0.14 | 0.29 | |
| Oct | 0.09 | 0.22 | 0.27 | 0.28 | 0.03 | 0.13 | 0.09 | 0.22 | 0.06 | 0.18 | 0.18 | 0.3 | |
| carp and perch | Jan | 0.26 | 0.21 | 0.46 | 0.17 | 0.06 | 0.18 | 0.16 | 0.22 | 0.13 | 0.21 | 0.26 | 0.28 |
| Apr | 0.04 | 0.17 | 0.11 | 0.24 | 0.02 | 0.13 | 0.07 | 0.18 | 0.03 | 0.15 | 0.09 | 0.26 | |
| July | 0.04 | 0.16 | 0.13 | 0.22 | 0.04 | 0.17 | 0.11 | 0.21 | 0.04 | 0.17 | 0.13 | 0.27 | |
| Oct | 0.09 | 0.20 | 0.24 | 0.21 | 0.03 | 0.12 | 0.09 | 0.19 | 0.06 | 0.17 | 0.16 | 0.25 | |
| catfish and tench | Jan | 0.02 | 0.12 | 0.11 | 0.20 | 0.04 | 0.16 | 0.10 | 0.21 | 0.03 | 0.15 | 0.11 | 0.24 |
| Apr | 0.00 | 0.06 | 0.04 | 0.17 | 0.00 | 0.02 | 0.02 | 0.13 | 0.00 | 0.05 | 0.04 | 0.21 | |
| July | 0.02 | 0.12 | 0.06 | 0.19 | 0.02 | 0.14 | 0.09 | 0.24 | 0.02 | 0.13 | 0.07 | 0.26 | |
| Oct | 0.06 | 0.22 | 0.14 | 0.30 | 0.02 | 0.14 | 0.04 | 0.17 | 0.04 | 0.19 | 0.09 | 0.28 | |
| catfish and perch | Jan | 0.02 | 0.12 | 0.10 | 0.19 | 0.04 | 0.17 | 0.10 | 0.21 | 0.04 | 0.16 | 0.10 | 0.24 |
| Apr | 0.00 | 0.06 | 0.02 | 0.12 | 0.00 | 0.03 | 0.01 | 0.09 | 0.00 | 0.05 | 0.02 | 0.18 | |
| July | 0.02 | 0.11 | 0.10 | 0.20 | 0.01 | 0.10 | 0.05 | 0.15 | 0.02 | 0.11 | 0.08 | 0.24 | |
| Oct | 0.07 | 0.20 | 0.18 | 0.24 | 0.02 | 0.13 | 0.05 | 0.17 | 0.04 | 0.17 | 0.12 | 0.26 | |
| tench and perch | Jan | 0.02 | 0.11 | 0.10 | 0.17 | 0.01 | 0.08 | 0.05 | 0.15 | 0.01 | 0.09 | 0.07 | 0.20 |
| Apr | 0.00 | 0.01 | 0.04 | 0.18 | 0.00 | 0.00 | 0.02 | 0.12 | 0.00 | 0.03 | 0.03 | 0.22 | |
| July | 0.03 | 0.15 | 0.10 | 0.23 | 0.01 | 0.10 | 0.07 | 0.21 | 0.02 | 0.14 | 0.09 | 0.27 | |
| Oct | 0.03 | 0.14 | 0.14 | 0.23 | 0.01 | 0.06 | 0.05 | 0.16 | 0.02 | 0.11 | 0.09 | 0.25 | |
| R = 2.1 m |
R = 4.2 m |
R = 6 m |
|||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| our data |
random net |
our data |
random net |
our data |
random net |
||||||||
| mean | s.d. | mean | s.d. | mean | s.d. | mean | s.d. | mean | s.d. | mean | s.d. | ||
| carp | Jan | 0.123 | 0.227 | 0.021 | 0.110 | 0.294 | 0.316 | 0.078 | 0.188 | 0.389 | 0.359 | 0.106 | 0.251 |
| Apr | 0.026 | 0.158 | 0.011 | 0.117 | 0.098 | 0.289 | 0.029 | 0.209 | 0.172 | 0.354 | 0.039 | 0.269 | |
| July | 0.033 | 0.178 | 0.014 | 0.134 | 0.123 | 0.318 | 0.034 | 0.228 | 0.213 | 0.385 | 0.047 | 0.291 | |
| Oct | 0.044 | 0.174 | 0.012 | 0.111 | 0.172 | 0.308 | 0.042 | 0.197 | 0.244 | 0.369 | 0.063 | 0.261 | |
| catfish | Jan | 0.029 | 0.165 | 0.010 | 0.113 | 0.108 | 0.277 | 0.022 | 0.179 | 0.189 | 0.346 | 0.038 | 0.242 |
| Apr | 0.001 | 0.076 | 0.001 | 0.074 | 0.011 | 0.181 | 0.005 | 0.168 | 0.029 | 0.274 | 0.012 | 0.250 | |
| July | 0.008 | 0.108 | 0.004 | 0.090 | 0.044 | 0.247 | 0.018 | 0.205 | 0.134 | 0.385 | 0.042 | 0.304 | |
| Oct | 0.034 | 0.182 | 0.015 | 0.131 | 0.099 | 0.315 | 0.042 | 0.236 | 0.130 | 0.374 | 0.047 | 0.287 | |
| tench | Jan | 0.003 | 0.080 | 0.002 | 0.071 | 0.039 | 0.215 | 0.014 | 0.174 | 0.104 | 0.304 | 0.024 | 0.237 |
| Apr | 0.001 | 0.074 | 0.001 | 0.074 | 0.019 | 0.200 | 0.006 | 0.178 | 0.045 | 0.291 | 0.017 | 0.255 | |
| July | 0.013 | 0.135 | 0.007 | 0.111 | 0.046 | 0.260 | 0.020 | 0.213 | 0.100 | 0.370 | 0.042 | 0.308 | |
| Oct | 0.001 | 0.068 | 0.001 | 0.068 | 0.002 | 0.148 | 0.002 | 0.148 | 0.003 | 0.216 | 0.003 | 0.216 | |
| perch | Jan | 0.004 | 0.085 | 0.002 | 0.076 | 0.035 | 0.204 | 0.011 | 0.166 | 0.084 | 0.283 | 0.015 | 0.222 |
| Apr. | 0.001 | 0.074 | 0.001 | 0.074 | 0.003 | 0.162 | 0.002 | 0.161 | 0.007 | 0.242 | 0.005 | 0.239 | |
| July | 0.008 | 0.112 | 0.004 | 0.096 | 0.054 | 0.245 | 0.016 | 0.195 | 0.115 | 0.340 | 0.025 | 0.273 | |
| Oct | 0.013 | 0.116 | 0.004 | 0.088 | 0.089 | 0.258 | 0.019 | 0.179 | 0.151 | 0.325 | 0.028 | 0.239 | |
In terms of key results, the clustering coefficient revealed that common carp was the most social species of all, showing strong intraspecific clustering coefficients, particularly in winter when pooling the entire day. The pattern of high social interactions among carp during winter was also found when looking at day and night separately, but effects were reduced in the pooled analysis. During winter, carp were also strongly associated with all other three species, (i.e. tench, perch and catfish), where the association with tench during daytime was particularly strong.
Relative to carp, all three other species (tench, perch and catfish) showed no or very small intraspecific clustering; that is, they exhibited a rather individualistic behaviour. Catfish showed particularly few interactions with the other species at night, while interspecific clustering was more pronounced during daytime across the year with carp, during autumn and winter with perch and winter with tench. Catfish showed some interactions with perch and tench during the day in the wintertime, and with perch during the day in the summer and autumn.
Perch also showed very low or no intraspecific clustering, except during daytime in autumn, while interspecific clustering was more pronounced in autumn during daytime with tench, carp and catfish. By contrast, clustering with other species vanished during nighttime in perch.
Tench behaved strikingly differently from carp. By contrast to carp, tench was found to be highly individualistic with regards to conspecifics across the year. There was some intraspecific clustering with the benthivorous carp throughout the year during daytime and less pronounced across seasons during nighttime. Further, tench displayed some daytime interactions with catfish in the winter season and perch in the autumn.
4. Discussion
Social interactions are one of the essential drivers of collective behaviour [73]. PBSNs have been widely used to characterize social interactions in dynamic networks [64–66]. We applied these methods to a rare multi-species high-resolution dataset of fish locations in a natural lake. We found the presence of proximity-based social interactions varied by species, season and time of the day. We identified one species, the benthivorous common carp, to exhibit moderate to strong intraspecific clustering, but only during the cooler periods of the year. At the intraspecific level, all other investigated species showed only little intraspecific social interactions in terms of proximity. In other words, perch, tench and catfish showed rather solitary behaviour at the individual level.
The fact that carp can form strong social interactions is known for this species. Carp have been described as a social species, often foraging in smaller groups [74]. The exceedingly large clustering coefficients, particularly in winter, can be considered evidence for winter aggregations as previously described in the literature for the species [75,76]. It has also been commonly reported (but not yet fully explained) that in some lakes carp move to deeper waters and form aggregations as the water cools in later autumn and early winter, continuing this behaviour until spawning begins in May to June [76–78], though in other lake systems carp have been observed to overwinter nearer to the surface [40]. Although the level of activity reported varies from torpid and sedentary [75,79] to active [80], the degree of winter behaviour revealed by carp in our study is unparalleled with previous work in this species [55,76]. Post hoc visualizations (https://www.youtube.com/watch?v=9gdi6NLuHug) of the movement patterns revealed that the carp in our study lake showed aggregations and very active movements, particularly during daytime during winter, showing patterns of shoaling. These cohesive movements conducted as a large group explain the consistently high clustering coefficients of this species during winter in the study lake. Unlike perch, catfish and tench, the carp also showed strong interspecific clustering with all other three studied species during autumn and winter. This finding may reflect that all species share the same overwintering habitat. Catfish is a warm-water adapted fish that feeds very little during cold water [48] and tench has the same foraging guild as carp [79]. The perch we tagged were too small to pose any predation risk to the rather large-bodied carp, which is why we can exclude predator–prey interactions to explain the moderate clustering coefficients between carp and the other three species during autumn and winter.
Although tench and carp share the same foraging niche in terms of benthivory, their intra- and interspecific social interactions were substantially different. Specifically, tench did not reveal any patterns of intraspecific clustering and only exhibited moderate intraspecific clustering with carp. Previous analyses of linear movement trajectories of carp and tench in the study lake have already revealed that the two species behave differently [53]. Pond studies have also shown that tench and carp are in direct food competition, with tench often being competitively inferior to carp and suffering from productivity decline in systems where the carp are intensively stocked [79]. This high degree of food competition might explain the small interactions among the two species witnessed here. Moreover, it is possible that the smaller body size of tench rendered the denser reed belt habitat more accessible to tench relative to carp, and therefore the tench may be able to forage on small macroinvertebrates without competition from carp. Tench have been described as cryptic and sometimes quite lethargic fish [42,80], with nocturnal foraging activities peaking at dawn and dusk [81–83]. Therefore, the foraging activity of tench may not have aligned with that of carp or perch, and the habitat of tench may not have overlapped with the nocturnally foraging catfish either. An additional explanation for the low level of interaction between tench and carp might be related to the carp being domesticated, while the tench exhibited a wild behaviour. While tench have occasionally been observed to form social groups during periods of inactivity [84], our analysis indicates that this was not common in our study system. Furthermore, unlike carp, tench do not form winter aggregations and are rather thought to slow down and hibernate [42,79], which agrees with the lack of clustering for tench during wintertime.
Perch have been described in laboratory studies as being social facilitators, e.g. where hunting success is improved by social interactions [47] and who feed primarily during the day [51] as they are visual predators [85]. The perch we tagged were very large for the species and fully piscivorous. For this size group and in the wild, our work suggests limited intraspecific clustering and rather individualistic behaviour. This does not mean that social foraging is not involved, especially during daytime in autumn when there was some evidence for clustering. Rather, it is possible that the group behaviour is characterized by fission–fusion dynamics [86], such that no temporally stable individual networks are developed. Interspecifically, clustering was more pronounced during the cooler seasons and during daytime with tench, carp and catfish. The foraging niches of tench and carp differ substantially from perch [87,88] and the tench and carp were too large to be predated upon by the tagged perch. We thus exclude that the spatial clustering was related to predator–prey relationships. The spatial overlap with catfish in the cooler period may coincide with the reduced foraging intensity of the warm-water species catfish, which would make overlap with perch safe from a perch perspective. Moreover, perch tend to move to deeper open waters during the winter months [89,90], which may lead to an increase in potential interactions between perch and catfish in the pelagic area of the lake. The moderate spatial clustering of the four species during daytime in autumn suggests that all species use a similar, likely profitable or safe habitat. No clustering with other species happened during nighttime, when perch typically stop feeding and remain rather motionless on the sediments [51,90], in contrast to the often night-active carp, tench and catfish.
Catfish have previously been described as a solitary predator [48,91], possibly exhibiting territoriality [29,92,93], although the species can temporarily aggregate and form large clusters [94]. While we did observe similar clustering tendencies in the study lake during a post hoc video analysis (https://www.youtube.com/watch?v=9gdi6NLuHug) in the colder phases of the year, our clustering analyses suggested rather solitary behaviour at the intraspecific level overall. The catfish was the largest predator among the four species and the individuals we tagged might have been dangerous enough to exert predation risk on all species in our sample, specifically perch and tench. Catfish is a nocturnal forager [95] and thus unsurprisingly there was limited clustering with the possible preys during night. Spatial clustering was more pronounced during daytime in autumn and winter (perch) and winter (tench)—a period when catfish largely stop foraging under temperate climates. The carp were generally too large to be predated upon by catfish, which might explain why the spatial clustering was more pronounced and likely related to similar habitat preferences as both species are warm-water adapted.
From a methodological standpoint, our work contributes to the literature on choosing the distance threshold under which two fish are considered to have an interaction. We performed the analysis using three values of this threshold (2.1, 4.2, 6), which are expressed as a function of the body size of a fish (e.g. 6 means ‘six times the body size of a fish’). Using twice the body size of a fish (i.e. R = 2.1) tends to lead to more consistent results and, as is noteworthy from tables 5 and 6, figure 9 distinguished between diurnal and nocturnal activity.
Despite leveraging advances in reality mining to build a PBSN from millions of positions at a detailed temporal and spatial scale, our study has several limitations. First, there are data gap issues (e.g. as a fish moves into the littoral zone into refuge) and the transmitters send signals at different times. This requires aggregating data and dealing with missing data. Very few fish were discarded in our analysis (table 2): we retained 100% in several species depending on the season and used at least 82.4% of the data (n = 89 out of 108 individual fish). However, a significant portion of the fish positions had to be inferred based on the previous and following positions, particularly in summer. We note that aggregating our data over a larger time window (e.g. 2 min instead of one) would lead to inferring less data (since we are more likely to find one recorded position within 2 min than one) but this would not have a statistically significant effect on our results as evidenced by the ANOVA. Furthermore, the missing data were not randomly dispersed throughout the dataset, but were caused by systematically poor detection in submerged macrophytes and reeds. Therefore, our insights into fish social interactions should be considered to represent interactions in open water, rather than in sheltered habitats. Future studies could potentially employ scattered underwater cameras, passive integrated transponder tag arrays or manual tracking via radio telemetry to better study social interactions in habitats that are less suitable for automated acoustic telemetry. Also, while we had long acclimation periods for most individuals in our studies, the impact of transmitter implantation on fish behaviour remains to be fully studied [96]. Generally, when the ratio between transmitter weight and fish body weight is low (approx. 2% or less) the effects from transmitter implantation are thought to be absent or negligible [97–99]; however, in some cases transmitter implantation has been found to adversely affect proxies of behaviour such as growth or behaviour directly [58,100]. We did not observe any anomalous behaviours to suggest the individuals in our study were not behaving naturally and the transmitter to fish body mass remained low, suggesting biases from transmitter implantation were unlikely. Finally, our analysis focused on clustering as the sole measure for social interactions. There are many other ways to assess social interactions or examine their dynamics. For instance, a same clustering coefficient may be obtained when there are consistent social groups (as measured by subgraphs) or when groups change in seemingly random patterns. Consequently, analysing the subgraphs may provide further insight into intra- and interspecific social interactions, specifically whether there are stable subgroups of individuals that use the habitats together. Given the large variety of possible subgraphs depicting combinations of interactions, such analysis and its interpretation could be the object of future studies, for example using the data made available to the community. It is also possible that the species interactions would differ if individuals of different size were used. In particular, species interactions would particularly increase if one were to tag fish of smaller body size, which is now possible with the latest generation of transmitters, but was not possible at the time when we did the experiment. Data would then only cover a few weeks. For the future, it is highly recommendable to repeat multi-species experiments and add a larger gradient of body length differences among predators and possible prey to increase the odds of seeing interspecific interactions.
To conclude, our work demonstrates that reality mining and network analysis are possible with multiple species at the scale of an entire aquatic ecosystem, complementing other recent high-resolution studies [36]. Our work underscores that there are seasonal and daytime effects on social interactions and that different species vary in their tendency to cluster with conspecifics and with other species. Our work also shows that strong social interactions among the species carp, tench, perch and catfish are rather unlikely and may be confined to selected species in specific seasons (e.g. carp in winter). Spatial aggregations during specific seasons, specifically by ecosystem engineers such as carp, may affect information flow, competition and may also leave a legacy in ecological states [101].
Ethics
The invasive animal procedures (including surgeries and recaptures) were ethically approved by the responsible State Animal Welfare and Animal Experimentation Agency (Landesamt für Umwelt, Gesundheit und Verbraucherschutz) in Brandenburg, Germany (project reference 2347-21-2014) according to the German Animal Protection Act.
Data accessibility
The raw data consisting of 3.2 Gb of positions can be arranged for transfer by contacting Robert Arlinghaus. Our analysis relies on pre-processed data, which includes aggregation over a large time window (1 min), multiple imputation for missing values, and discarding when the transmitters was missing for an entity during an extended time period. These pre-processed data are archived together with our results and scripts on a third-party repository on the Open Science Framework at https://osf.io/5hqyf/.
Authors' contributions
S.V. and D.H. wrote the scripts for data pre-processing. S.V. performed the analysis. S.V., C.T.M., P.J.G. and R.A. wrote the manuscript. P.J.G. designed the methods and supervised S.V. and D.H. C.T.M. collected the data under supervision from R.A. R.A. acquired funding and coordinated the telemetry project in Berlin. The network project was managed by P.J.G.
Competing interests
We declare we have no competing interests.
Funding
S.V., D.H. and P.J.G. used a high-performance workstation acquired through start-ups funds from the Department of Computer Science at Furman University. The NetSci presentation, which contributed to shaping this manuscript, was made possible thanks to travel support from Furman University. This work was also funded by the B-Types grant (Gottfried-Wilhelm-Leibniz-Community, grant no. SAW-2013-IGB-2) to R.A.
Acknowledgement
The authors thank Andreas Mühlbradt for coordinating the transfer of the data for analysis. We are also indebted to Alex Türck, Jan Hallermann, Daniel Hühn, Jacob Weinrautner and Jonathan Nickl for their extremely supportive assistance in the fieldwork. We also thank participants at the 2019 International School and Conference on Network Science (NetSci), who provided feedback on an oral presentation describing our work-in-progress on this project and reviewers for feedback.
