Evaluation of acoustic telemetry grids for determining aquatic animal movement and survival

Acoustic telemetry studies have frequently prioritized linear configurations of hydrophone receivers, such as perpendicular from shorelines or across rivers, to detect the presence of tagged aquatic animals. This approach introduces unknown bias when receivers are stationed for convenience at geographic bottlenecks (e.g. at the mouth of an embayment or between islands) as opposed to deployments following a statistical sampling design. We evaluated two‐dimensional acoustic receiver arrays (grids: receivers spread uniformly across space) as an alternative approach to provide estimates of survival, movement and habitat use. Performance of variably spaced receiver grids (5–25 km spacing) was evaluated by simulating (1) animal tracks as correlated random walks (speed: 0.1–0.9 m/s; turning angle SD: 5–30°); (2) variable tag transmission intervals along each track (nominal delay: 15–300 s); and (3) probability of detection of each transmission based on logistic detection range curves (mid‐point: 200–1,500 m). From simulations, we quantified (i) time between successive detections on any receiver (detection time), (ii) time between successive detections on different receivers (transit time), and (iii) distance between successive detections on different receivers (transit distance). In the most restrictive detection range scenario (200 m), the 95th percentile of transit time was 3.2 days at 5 km, 5.7 days at 7 km and 15.2 days at 25 km grid spacing; for the 1,500 m detection range scenario, it was 0.1 days at 5 km, 0.5 days at 7 km and 10.8 days at 25 km. These values represented upper bounds on the expected maximum time that an animal could go undetected. Comparison of the simulations with pilot studies on three fishes (walleye Sander vitreus, common carp Cyprinus carpio and channel catfish Ictalurus punctatus) from two independent large lake ecosystems (lakes Erie and Winnipeg) revealed shorter detection and transit times than what simulations predicted. By spreading effort uniformly across space, grids can improve understanding of fish migration over the commonly employed receiver line approach, but at increased time cost for maintaining grids.


| INTRODUC TI ON
Acoustic telemetry has gained widespread popularity as a tool to understand migration, habitat use and survival of aquatic animals (Cooke et al., 2013;Hussey et al., 2015). Acoustic telemetry functions similar to radiotelemetry in terrestrial environments (White & Garrott, 2012); an animal-borne transmitter emits an acoustic signal detected by a receiver, which in this case is an underwater microphone, or hydrophone (hereafter, receiver). The signal can be continuous or intermittent, and it can be coded to identify individuals and transmit information from sensors in the tag (e.g. temperature).
At the most basic level, acoustic telemetry provides a chronology of observations from active or passive monitoring of specified areas with receivers. Compared with marking large numbers of animals in hopes that a small fraction are observed at a later time, usually, only once (Pollock, 1991), acoustic telemetry provides abundant information about individuals without the need to recapture the animal (Heupel, Semmens, & Hobday 2006). Furthermore, fates of individuals with acoustic transmitters can be known with greater temporal and spatial resolution, dramatically reducing tagged sample size requirements and increasing the diversity of inferences on animal movements than possible with conventional tagging. Just how much novel information can be obtained in an acoustic telemetry study pivots on the spatial arrangement of receivers, which are commonly moored at fixed locations to passively monitor tagged individuals.
In ecological field studies, the researcher has no control over the movement and habitat use of aquatic animals bearing acoustic tags; therefore, how to spatially distribute receiver sampling effort is a fundamental question for acoustic telemetry studies. Most acoustic telemetry studies have aimed to determine broad-scale migration across a landscape of aquatic habitats, using a one-dimensional arrangement of receivers (i.e. receiver "lines" or "gates") to detect passage of individuals through a river or along a coastline (Jackson, 2011;Welch, Boehlert, & Ward, 2002). Few studies have used two-dimensional grid deployments, where receivers are spread systematically through the environment to infer animal movements throughout a region (Hedger et al., 2008;Simpfendorfer, Heupel, & Hueter, 2002). Less frequently, movement has been determined through triangulation of a signal on multiple receivers, but such studies have been limited to small areas because of the need for overlapping detection ranges Dance & Rooker, 2015;Meckley, Holbrook, Wagner, & Binder, 2014;Romine et al., 2014). Strategic placement of receivers in bottleneck areas (e.g. narrow sections of a continental shelf, river channels or island passes) has been rationalized as a trade-off between a limited number of receivers and the need to time movements past landmarks (e.g. Wingate, Secor, & Kraus, 2011). Success of this approach is evidenced by an exponential growth of peer-reviewed literature in recent decades (Hussey et al., 2015), but the arrangement of receivers in many studies often is as much a matter of convenience as it is a demarcation of relevant zoogeographical areas. The receiverline strategy emphasizes redundancy with overlapping detection radii to ensure that every occurrence of a tagged animal is recorded on multiple receivers (Kessel et al., 2014), and in specific cases, this design is duplicated to evaluate the directionality of movement across an imaginary boundary (e.g. Hayden et al., 2014). Thus, concentration of receivers into bottleneck areas markedly reduces the area effectively sampled, and substantially increases duplicate detections of transmitters on multiple receivers. Subjective selection of receiver locations based upon luck of geography also imposes unquantified biases on the spatial interpretation of telemetry data while leaving vast sections of the ecosystem unmonitored. Moreover, some aquatic ecosystems may not have obvious bottlenecks through which animals must travel to migrate between habitats.
Like any sampling tool, the number, timing of deployment and locations of telemetry receivers define the sampling design. Use of receivers only at strategic locations (e.g. lines) represents a distribution of sampling effort that is neither random nor uniform. Such narrowly focused receiver arrangements may represent the most effective designs for addressing a specific set of questions, but may preclude inferences about animal movement and habitat use beyond parochial information needs. If movement routes are known, then arrangement of receivers (i.e. lines) along those routes will provide efficient and unprecedented detail of the movement history of tagged animals, but initially, knowledge of an animal's migration is often characterized by little more than anecdotes between mark-recapture end points. When prior knowledge regarding movement is limited, how should receivers be distributed? We know from our own experiences and through conversations with colleagues that a common solution is to recast the research question to fit the bottleneck-receiverarrangement strategy. Alternatively, some telemetry researchers have employed grids (two-dimensional receiver arrays) with nonoverlapping detection radii to gain broader spatial coverage and elucidate heterogeneous use of habitats across an aquatic landscape . Although such an approach risks large lake ecosystems (lakes Erie and Winnipeg) revealed shorter detection and transit times than what simulations predicted. 4. By spreading effort uniformly across space, grids can improve understanding of fish migration over the commonly employed receiver line approach, but at increased time cost for maintaining grids.

K E Y W O R D S
acoustic telemetry, fish movement, habitat use and survival, simulation monitoring unused habitats, importantly it provides the capability to distinguish non-use of a habitat from absence of data. Much attention has been paid to the performance of one-dimensional receiver lines (Steckenreuter et al., 2017), but rigorous evaluation of grids as a method for discerning details of acoustically tagged animal movements has been lacking. The two approaches achieve the same goal of defining when animals move between habitats; however, the grid design generates additional spatial information on the behaviour of the animal after it enters an adjacent habitat.
In terms of statistical analysis of telemetry data, systematic sampling represented by a grid is more defensible than the subjective monitoring of convenient landmarks (Krebs, 1989;Legendre et al., 2002). A stratified random sampling approach to arrange receivers may provide additional quantitative advantages, but we are not aware of any acoustic telemetry studies that have proposed this. In practice, evenly spaced sampling of a continuous environment has both statistical rigour (Stevens, 1997) and flexibility to support iterative modification through feedback from inferences on movement via adaptive sampling (Stein & Ettema, 2003;Thompson & Seber, 1996). Given the potential advantages of improved statistical inferences, and additional movement information, the one-dimensional receiver line approach surprisingly remains the favoured design over a grid or random sampling design. Two likely explanations are that: (1) field experiments to test performance of acoustic telemetry grids at realistic spatial scales could be prohibitively costly (but see, , and (2) proposing a grid design without some proof-of-concept evidence risks fatal criticism from research sponsors.
In response, we simulated tagged animal movements in a realistic virtual arena populated with a variably spaced receiver grid. We asked basic, universally applicable, questions about the capabilities of a receiver grid: how frequently is an animal within the grid detected, and if it left one receiver, how much time would pass, and how far would it travel before we would expect to detect it on a different receiver? Answers to these questions are critical for understanding study design resolution for determining when an animal dies or leaves the ecosystem and whether it occurred in a particular habitat. Scenarios in our simulation represented a fully crossed view of biological characteristics of a correlated random walk (speed and turn angle) and physical characteristics of equipment (tag transmission delay interval) and environment (grid spacing and detection range). Researchers will note that many telemetry studies have been resource limited in terms of numbers of receivers and time to deploy and maintain receiver stations, and consequently, effective grid designs with limited resources appear impractical. As the questions for the grid simulation had no analogs for receiver lines (i.e. once the animal leaves the line, there is nothing to quantify), we compared the time cost to tend grids vs. lines with a thought experiment. In developing the grid simulation, we created useful tools in the opensource programming language, r (version 3.3.3, (C) 2017 The r Foundation for Statistical Computing), and these are freely available to be adapted for specific acoustic telemetry studies in any aquatic environment that can be represented in two-dimensions . Finally, we presented pilot field studies using three fish species that demonstrated the applicability and limitations of the simulation results.

| Background
Our interest in developing a simulation was inspired by current research in Lake Erie on the migration of walleye Sander vitreus, in which a double receiver-line was initially used with overlapping detection ranges and took advantage of geographic bottlenecks between islands that naturally partitioned spawning areas from seasonal feeding habitats (Raby et al., 2018). Securing funding for that study was in part conditioned on a convincing rationale for our ability to successfully time passage of fish around the islands. Later, in the study, opportunistic deployment of receivers to the east of the islands hinted at much more interesting and complex patterns of migration. Furthermore, most of our data from receiver lines were redundant, with detection of single coded transmissions on two to five receivers. We surmised that a different arrangement of receivers could both continue to provide timing information of fish movement past the islands and additional information on time spent in various spatial management units. Simply put, we had enough receivers (n = 72) to redistribute into a 15-km grid across the central basin of the lake, but we had scant information on whether this change would still achieve our objective of timing fish passage around the islands and reduce redundancy in our data. Thus, we evaluated this question through a simulation.

| Simulations
To accomplish our simulation, we generated: (1) virtual paths as correlated random walks within a shoreline boundary represented by Lake Erie (the arena was approximately 388 km long with an area of 25,700 km 2 ); (2) tag transmissions along each track; and (3) detection of each transmission based on logistic detection range curves and tag-receiver distances for each virtual receiver grid. No single virtual track was intended to represent any actual tagged fish, because movement characteristics (i.e. random walk parameters) of walleye in the wild were unknown. Rather, we evaluated a range of characteristics to encompass typical movements of a wide range of aquatic animal species. Each movement path, tag transmission and detection scenario were evaluated on one of 26 receiver grids. Within each grid, receiver spacing was uniform, and across grids spacing ranged from 5 km (n = 1,028 receivers) to 25 km (n = 39 receivers), in 1 km increments ( Figure 1). Here, we measured spacing in the x and y directions, as opposed to the diagonal distance between receivers (which would simply be a constant 41.4% greater distance).
Virtual paths were generated by calculating points every 100 m along an azimuth drawn from a zero-mean normal distribution of turn angles. If the path crossed the shoreline boundary, the step was repeated until the path remained in the virtual lake. The starting location was randomly assigned to one of two locations where actual tagged walleye had been released in Lake Erie: Toussaint Reef in the western basin or Van Buren Bay in the eastern basin ( Figure 1). The standard deviation (SD) of turn angles was fixed within each track but varied among tracks. We simulated six turn angle schemes, which ranged from SD 5 to 30° in 5° increments ( Figure 1). A timestamp was assigned to each point based upon four swimming speeds, which ranged from 0.1 to 0.9 m/s in 0.2 m/s increments. Furthermore, we simulated three path durations: 30, 90 and 150 days.
For each path, a series of transmission timestamps was generated, and then the coordinates of each transmission were assigned using linear interpolation. We simulated four transmission delay schemes (nominal delays: 15, 30, 120 and 300 s) spanning the range of intervals commonly used in acoustic telemetry field studies (e.g. VEMCO PPM coding). Each interval between transmissions (Δt) was drawn from a uniform distribution, such that Δt ~uniform (0.5·d + b, 1.5·d + b) where d (nominal delay) was the average time between the end of one coded burst (signal) and the start of the next coded burst, and b represented the duration of each coded burst. Similar to field studies, b was fixed at 5.0 s for all transmission delay schemes.
Detection range was modelled as a nonlinear decay function typical of what has been observed in previous studies Huveneers et al., 2016). Stochastic detection (or nondetection) of each transmission based on a Bernoulli distribution with probability, p, determined by a logistic curve: where D was the distance between each tag and receiver at time of transmission, β 1 determined the steepness of the curve and β 2 was the mid-point of the curve (i.e. where p = .5). We simulated detections for three range curves (i.e. detection radii), representing poor (β 1 = 0.006; β 2 = 200 m), average (β 1 = 0.0025; β 2 = 800 m) and good (β 1 = 0.015; β 2 = 1,500 m) environmental conditions. These curves were based upon detection range data from VEMCO transmitters (model V16-6H, Amirix Systems Inc., Bedford, Nova Scotia) in lakes Erie, Huron  and Winnipeg.
Three paths were simulated for each combination of variables (21 grids × 6 turn angles × 5 swimming speeds × 4 transmission delay schemes × 3 detection radii × 3 path durations) for a total of 68,040 paths, with up to 224,474 detections per path and a total of c. 299 million detection events. Equivalently, note that for each turn angle, a single arbitrarily long path could have been used for the same purpose (applying various grid, radius, speed and transmission delay characteristics), but this approach can become memory resource limited on a typical desktop workstation. Consequently, replicate paths (n = 3) and path durations (which had no discernable effects on the characteristics of the movement metrics) were pooled. Thus, sample sizes of detection events were unbalanced for analysis, varying between 20 and c. 1.1 million among all 7,560 scenarios (mean detections per scenario = 39,488).

| Simulation analyses
Three primary metrics were calculated to characterize each simulation: (1) detection time: elapsed time between successive detections; (2) transit time: elapsed time between successive detections on different receivers; and (3) transit distance: distance between successive detections on different receivers. The mean values of these metrics were less important to us than understanding the

| Pilot studies
Simulations of animal movement may provide a powerful tool for selecting an appropriate field sampling design (Turchin, 1998), but they are no substitute for empirical validation. We were fortunate to have pilot data from three fish species with contrasting life histories for comparison with our simulation results: a pelagic freshwater piscivore, walleye in Lake Erie; a benthic freshwater piscivore, channel catfish Ictalurus punctatus in Lake Winnipeg; and a benthic freshwater omnivore, common carp Cyprinus carpio in Lake Winnipeg.
The study on walleye was initiated to understand survival and behaviour of fish captured, tagged and released from the summer recreational fishery in Lake Erie. Adult walleye were surgically implanted with model V13-1H tags (VEMCO) with a nominal transmission delay of 180 s, following protocols described in Hayden et al. (2014). During July to August 2015, walleye were released into a grid of 25 receivers with an average spacing of 7 km ( Figure 2). The Lake Erie grid was deployed for 122 days to focus on near-term survival and behaviour. Although receivers deployed elsewhere in the lake also detected walleye, we limited our analysis to detections on the grid of 25 receivers. We also limited our analysis to fish that were known to be alive (n = 18 out of 30 total tagged individuals) for the duration of the pilot study.
The study on channel catfish and common carp was initiated to understand population connectivity and habitat use among riverine, lacustrine and marsh habitats in Lake Winnipeg. These species Only when fish entered the grid during the study period were they included for comparison.
For all species in the pilot studies, we calculated detection and transit time for graphical comparison with simulations, matching 7-km grid predictions for the 200, 800 and 1,500 m detection range scenarios.

| Time cost comparison
Financial costs of fieldwork can vary idiosyncratically given available tools, institutional facilities and ecosystem characteristics; therefore, we estimated time required to tend grids vs. comparable scenarios with receiver lines in a rectangular arena representing an estuary, coastal embayment or small lake with an area of 2,500 km 2 .
The long-side dimension of the rectangle was four times the short side (25 km). To calculate time, we assumed 12 knot average transit speed between stations and 0.5 hr to retrieve and re-deploy each receiver. We varied grid spacing from 7 to 16 km to match a relevant range of simulation scenarios, and used a fixed 1-km spacing in receiver lines-similar to other studies (e.g. Hayden et al., 2016;Knip, Heupel, & Simpfendorfer, 2012a;Raby et al., 2018;Steckenreuter et al., 2017). The time cost for receiver lines was fixed as the sum of the time to travel between sites and the time required to tend each receiver once. The total travel and tending time varied with grid scenario, and we assumed an orthogonal path weaving to and fro along the long axis. The calculations did not include time to travel between a port and the first station.

| Transit time
Transit time increased more rapidly with grid spacing for the 1,500 m detection radius than for the 200 m detection radius; the 800 m

| Transit distance
As the spatial complement to time, the pattern for transit distance was essentially the same as transit time, except that minimum values were constrained by grid spacing (Figure 3, lower). Transit distance was lowest and increased most rapidly with grid spacing for the longest detection radius (1,500 m; Figure 3, lower). Transit distance for the 1,500 m detection radius ranged from 6.9 to 57.4 km, which, respectively, corresponded to 1.3 to 2.3 times the grid spacing value

| Generalized linear models
Linear models of transit time emphasized that variation due to detection radius was greater than either biological variables (swimming Although not presented here, similar plots were inspected for other grid spacing scenarios: for the 5-km grid, the pattern was similar but shifted to lower transit times, and for the 25-km grid, the detection radius scenarios were broadly overlapping with less evident trends in the other variables. In each of the models (one for each detection radius), residuals were approximately normally distributed with some evidence of minor heteroscedasticity (increasing variance at higher transition times), this contributed to the lack of pattern at the largest grid spacing.

| Empirical examples
In the pilot studies, 95th percentiles of detection and transit time were typically shorter than simulated values, ranging from 28 to 56 min and from 37 min to 1.2 days respectively ( Figure 5). One exception was common carp, which had slightly higher detection and transit times than the 1,500 m detection radius scenario. The  axis is plotted on a log-scale simulated scenarios with 7 km spacing predicted ranges of 0.8 hr to 1.9 days and 12 hr to 5.7 days, respectively, for detection and transit time ( Figure 5). Mean detection and transit times for walleye were nearly identical, reflecting a tendency for successive detections to occur on different receivers. Channel catfish and common carp showed a tendency for successive detections to occur on the same receiver as evidenced by mean transit times that were approximately 5-24 hr higher than detection time for these species ( Figure 5).

| Grid-line time cost comparison
Given 25

| D ISCUSS I ON
The simulation approach for evaluating two-dimensional acoustic telemetry grids represents a useful tool for researchers wishing to determine the fates of aquatic animals. Surprisingly, even under the least favourable conditions (200 m detection radius with a sparse 25-km receiver grid), the time step at which individual fates could be inferred (<10 days) represents far greater resolution than existing stock assessment methods (yearly). Intuitively, grids provide coarser resolution for timing fish passage at specific locations (e.g. around islands) than the bottleneck-receiver-arrangement used in Lake Erie (Raby et al., 2018), but more importantly, simulation results can be used to optimize resource allocation (study design) when high-resolution timing is not required. Better grid performance observed in the pilot field studies (i.e. shorter time undetected) reinforced our results ( Figure 5). This result provides a basis both for study design and the analysis and interpretation of acoustic telemetry data, which is critical for classifying telemetry data to understand animal movements and survival, but the overall pattern from the simulations was entirely expected. If an animal goes undetected for longer than predicted, the researcher may infer emigration from the receiver grid or mortality (excepting tag expulsion or tag failure events). The grid design for receivers is fundamentally different from other approaches in which the researcher can determine only whether an animal occurred in the vicinity of the receiver line or gate. On either side of this narrow strip, an animal may show unobservable complex behaviour or survive to leave the system permanently (the latter would be indistinguishable from mortality). Obviously, failing to observe an animal across a broad area is only important with respect to study objectives. We simply caution that the design of a receiver network follow from specific questions about animal movement rather than the other way around. The design of a network is a challenging task primarily because the deployment and mainte- SD of turn angle) of simulated movement paths, which we selected to represent a range of possible species, were important but small relative to the effects of grid spacing and detection range ( Figure 4). Thus, a researcher with knowledge of detection range but little or no knowledge of the movement characteristics of the study animal would be able to develop a receiver grid design using the simulations we presented.

| Developing a receiver grid to understand habitat use
Analogous to plot-based census studies of plants or animals in terrestrial environments, the key for applying our results to telemetry studies is matching the grid with the desired scale of inference. For instance, consider a researcher who wishes to understand whether an animal makes diel movements between adjacent habitats in a system where the mean detection radius is 800 m. At a grid spacing of 15 km, 95% of simulated detection time intervals were <12 hr ( Figure 3, upper); therefore, this maximum grid spacing would likely provide multiple detections within a 12-hr period to assess habitat occupancy. If the researcher also wished to understand whether movement between habitats was crepuscular (to within ±1 hr of sunrise or sunset: a 2-hr period), then the maximum spacing should be no more than 5 km (Figure 3, upper). While one could conceivably achieve useful results for a system in which the habitat area approached the grid spacing (i.e. a minimum of one receiver per habitat), we advocate a complementary spatial benchmark for transit distance.
The simulation arena (Lake Erie) was relatively large compared with the range of grid spacing values, and for spatially explicit study design, the researcher would need to evaluate the density of receiv- Particular study objectives may require alternative benchmark development, but the above scenario illustrates how our simulations can aid the design of telemetry sampling. In reality, habitats are amorphous, and selection of appropriate grid spacing will require adaptation instead of strict application of the guidelines above. Furthermore, the researcher should account for temporal and spatial variations in detection efficiency to ensure observed patterns are reflective of actual movement instead of changes in grid performance. Diel changes in detection range performance have previously been interpreted as animal movement (Payne, Gillanders, Webber, & Semmens, 2010); thus, the researcher may be able to account for spatial heterogeneity of receiver performance with habitat-specific grid spacing. A number of dynamic variables, including weather, boat traffic, density gradients across an estuary or thermocline, and noise from other organisms (reviewed by Kessel et al., 2014), can introduce uncertainty in grid performance, but we did not evaluate these in our simulations. However, more important than these dynamic variables is the placement and orientation of receivers, which can have a substantial effect on detection range and is not generalizable between systems (Huveneers et al., 2016). For spatial heterogeneity in detection range, more closely spaced receivers in one habitat may be required to equal the detection efficiency in adjacent habitats. In habitats with high bathymetric relief where detection efficiency varies substantially, adaptive receiver placement is a paramount consideration . For temporal heterogeneity, if the research question F I G U R E 6 Estimated time cost of tending various grids (spacing in km shown as text on symbols) as a function of the number of receivers in a 2,500 km 2 rectangular arena in which the long side was four times the short side. For comparison, two receiver line scenarios with 1 km spacing (dashed lines with dots showing number of receivers tended) are plotted for single and double lines of receivers spanning the short side (79 km) of the rectangle. The plotted values assume vessel speed between receivers was 12 knots and that time on station to retrieve and re-deploy a receiver was 0.5 hr requires confirmation of the presence of an animal on time-scales much longer than sporadic interference from dynamic variables, then it may not be necessary to quantify such effects. Otherwise, additional system-specific simulations with the tool developed here ) may be needed.

| Autonomous receiver sampling for survival
Quantitative methods for determining the mortality rates of animals have relied on gridded telemetry sampling for system-wide spatial coverage to satisfy the assumption that all marked animals have the same probability of being observed (Hightower, Jackson, & Pollock, 2001;Pollock, Jiang, & Hightower, 2004). In previous studies where sampling occurred during discrete events from a boat (i.e. active tracking) that travelled to each grid intersection to listen for tag signals for a prescribed period, inverse correlation between animal and observer movement could obscure detection. If such a phenomenon occurs, the probability of observing a dead fish (or one not moving) would be greater than the probability of observing an animal that avoids the observer (e.g. one that moves away from boat noise). This situation would violate a key assumption and be difficult to diagnose without autonomous receiver sampling. Thus, many small-scale studies combine mobile tracking with limited autonomous receiver sampling to understand whether an animal may be present in the system yet go undetected by mobile tracking (e.g. Wingate et al., 2011). Alternatively, exclusive use of autonomous receiver arrays (passive) of the kind we simulated satisfies the assumption of equal detection probability, and has provided mortality estimates for highly mobile (e.g. elasmobranchs) as well as highly resident (e.g. reef teleosts) species in a variety of semi-enclosed and open coastal marine ecosystems , 2011Knip, Heupel, & Simpfendorfer, 2012b;Topping & Szedlmayer, 2011.
One of the most difficult aspects of determining the fates of tagged animals is distinguishing mortality from non-detection, and here, our simulations also provided insight. Generally, the likelihood of mortality increases with time elapsed since the last detection. In a closed system, when this period exceeds the simulated 95th percentile of transit time (or other appropriate benchmark), and no evidence exists that the animal was removed by fishing or similar activities, our simulations support an inference of mortality or tag loss. One source of mortality that would complicate this interpretation is a predation event. As Romine et al. (2014) observed, for predators that consumed a tagged fish, ingesting the tag would appear as an unexpected change in the behaviour of the prey. Presumably, subsequent detections would be a relatively short-term change as the prey is digested and the tag is either regurgitated or excreted by the predator (Kerstetter, Polovina, & Graves, 2004;Wahlberg et al., 2014). In addition, a nontrivial 3.5% of simulated tracks represented animals that were rarely or never detected, and were removed from our analyses of transit time and distance. In nature, such cases would be indistinguishable from fish that died. Note that inclusion of these data would have lowered our 95th percentiles; therefore, censoring of these data resulted in more conservative (slightly longer) values of transit time. Although data quantifying the probability that an animal survived undetected would be difficult to obtain, we view non-detection as an important consideration for mortality estimation from acoustic telemetry data.
Observation of such events would be limited to high exploitation fisheries and situations with high numbers of tagged fish, in which tags with few or no detections were reported by the fishery.
In semi-enclosed or open systems, emigration may be confounded with mortality when an animal leaves the monitored portion of the system. Determining the fate of animals in this situation would necessarily rely on complementary information from other data sources, such as conventional tag reporting from fisheries (Pollock et al., 2004). For an embayment, estuary or other discrete zoogeographical area, a properly constructed receiver grid may provide information about timing of immigration/emigration as well as preferred habitats within the system (Heupel, Semmens, et al., 2006;Heupel, Simpfendorfer, Collins, & Tyminski, 2006;Knip et al., 2012a). As mentioned above, grid sampling designs would have several advantages over receiver lines that have been more commonly employed. To understand seasonality of habitat use for migratory fish of conservation concern, grid sampling may help maximize information gained about the animal (e.g. Papastamatiou et al., 2015). Furthermore, grid sampling provides a more rigorous foundation to evaluate the interconnectedness of receiver locations through application of network analysis (Jacoby, Brooks, Croft, & Sims, 2012). Prior to conducting work in the field, our simulation would help the researcher answer a key sampling design question: how long must an animal be present in the grid before it will be detected? Extrapolations to completely open systems may also be worthwhile, but depend importantly on characteristics and habits of the animal. For species with a high affinity for small physical features in the environment (e.g. patch reefs) that punctuate an expanse of non-preferred habitat, successful telemetry studies have been conducted in open systems by simply populating preferred habitats with autonomous receivers (Topping & Szedlmayer, 2011).

| Comparisons with real animals
Despite lack of a priori models of individual movement for species in the pilot studies, our generic correlated random walk simulations provided a reasonable match to the field results, and on average pilot studies performed better (i.e. lower detection and transit times) than simulations predicted. A likely explanation for the improved performance is that detection ranges in the field were often longer than simulated ranges. For example, stationary transmitters placed within a line of receivers in Lake Erie had occasional detections at distances of up to 5 km (M. Faust, unpublished data). Although the probability of detecting a transmission from 3.5 km (half of the pilot study grid spacing) was predicted to be negligible in the simulations, it was still greater than zero, and periodic quiescent field conditions may have increased detection range substantially beyond the average. Due to the need to minimize detection of a single transmission on multiple receivers (which is ideal for triangulation studies but potentially problematic for grid-based sampling designs of the type we simulated), in ecosystems where long-range detection occurrences are non-trivial, a detection radius based on a lower predicted probability of detection (e.g. p < .5) might be advantageous for planning a grid-based sampling design. This could also be accomplished by benchmarking to a longer detection range from our simulations (i.e. 1,500 m). Alternatively, developing methods for analysis of the timing of signal arrival for short intervals would aid in the assignment of an animal to the nearest receiver (Hedger et al., 2008;Simpfendorfer et al., 2015).
Field data are also subject to false detections, which occur due to signal collision from multiple tags on the same receiver. Filtering out false detections can be accomplished by removing data with long intervals between successive detections (Pincock, 2012). The selection of a filtering rule is subjective and dependent upon the number of tags expected at a single receiver and the nominal transmission delay. The process can also eliminate some authentic detections, but in total removes only a small fraction of data. We did not apply false detection filtering to the pilot study data, but we note that it would tend to reduce the quantity of long detection and transit times in these data, resulting in lower 95th percentile values for the pilot studies. Thus, further improvement in the pilot study results could be achieved through analysis of false detections. Decisions about how to account for false detections should account for habitat and species characteristics from the individual ecosystems where these studies occurred, and were beyond the scope of this study.
The comparison of three species with contrasting life histories from two large lake ecosystems reinforced the applicability of the simulations to other species. Walleye are pelagic piscivores and seasonally migratory across Lake Erie (Knight, Margraf, & Carline, 1984;Raby et al., 2018;Vandergoot & Brenden, 2014;Wang et al., 2007). In Lake Winnipeg, common carp are primarily benthic herbivores or omnivores and channel catfish are benthic predators on both invertebrates and fishes (Stewart & Watkinson, 2004 (Kessel et al., 2014). Additional analyses beyond the scope of this study would be needed to further explore these inferences. For these species, the pilot studies were executed during summer and fall non-reproductive feeding periods; therefore, we would expect different results (e.g. smaller transit times due to a reduction in path tortuosity) during reproductive periods when these species show more directed movements to and from spawning sites.

| Time cost comparison
Because so many variables are potentially involved and financial considerations vary uniquely by project, detailed evaluation of the financial practicality of grid designs relative to receiver lines would be difficult. Time is a useful surrogate here because it can be converted to financial terms based upon a researcher's specific circumstances.
Our approach to quantify the time cost of tending lines vs. grids confirmed that receiver lines can be maintained with less time-a useful quantification but nevertheless an expected outcome. Receiver lines can be less costly to maintain than grids because the receivers are

| CON CLUS IONS
A quantitative description of individual aquatic animal movements has long been an active area of research, and random walk models have frequently provided either useful descriptions or valuable null models (Gurarie et al., 2016;Turchin, 1998). Here, we demonstrated how random walks simulating aquatic animal movements in an acoustic telemetry receiver grid compared with three fish species from two different large lake systems. The results have prompted spatially extensive application of two-dimensional telemetry grid sampling in Lake Erie (http://glatos.glos.us/map) and bolster outcomes of previous smaller scale studies (Collins, Heupel, & Motta, 2007;Dance & Rooker, 2015;Heupel, Semmens, et al., 2006;Heupel, Simpfendorfer, et al., 2006;Knip et al., 2012aKnip et al., , 2012b. We are hopeful that other researchers will see utility in our simulations, and respond with a more rigorous quantitative approach to autonomous receiver sampling. Finally, although we did not explicitly consider rivers, which can usually be monitored efficiently with lines of receivers, our results would also apply to river systems large enough to deploy a two-dimensional receiver array with non-overlapping detection ranges. Secor (2015) criticized telemetry work as suffering an embarrassment of riches from descriptive studies with too much data on too few animals. While recent advances in the field are making it possible to scale up to population-level inferences (Hussey et al., 2015), what we have characterized as the bottleneck-receiverarrangement strategy (i.e. receiver lines with overlapping detection ranges concentrated in geographical areas of convenience) is more prone to an embarrassment of data redundancy. Additionally, employing a gridded receiver design combined with releasing organisms with animal-borne logging devices (e.g. thermal or depth sensors; Hussey et al., 2015) can further improve population-level inferences with acoustic telemetry studies. Thus, our simulations support a growing cadre of new telemetry studies that are being developed via experimental design. Coordinated inter-agency efforts with infrastructure for multiple projects (e.g. GLATOS, IMOS and OTN) will be essential for realizing the insights that acoustic telemetry technologies promise.

ACK N OWLED G EM ENTS
We thank Tom Binder and two anonymous reviewers for constructive comments on this manuscript. All applicable international, national and/or institutional guidelines for the care and use of animals

DATA ACCE SS I B I LIT Y
Data deposited in the Dryad Digital Repository https://doi. org/10.5061/dryad.hm60m7n .