Environmental influence on transmitter detection probability in biotelemetry: developing a general model of acoustic transmission

Authors


Correspondence author. E-mail: karl.gjelland@nina.no

Summary

  1. Environmental factors, such as wind, may have a strong influence on the detection probability and detection rate of acoustic telemetry tags. The effect of environmental factors may obscure biological effects and distort the interpretation of acoustic telemetry data.
  2. This study was undertaken with fish internally tagged with acoustic transmitters containing depth sensors and monitored by an array of automatic receivers. The influence of environmental factors on the hourly detection rate was evaluated using environmental data from a nearby climate station. The signal detection probability was modelled within the framework of general theory of sound propagation in water.
  3. Wind was found to have the strongest influence on the detection rate. Transmitter depth range and rain also contributed significantly to the variation in detection rate.
  4. By modelling the attenuation coefficient as a function of wind speed, we show that the probability of detecting a free-swimming acoustically tagged animal can be successfully modelled using general sound propagation theory.
  5. The approach of modelling detection probability as a function of the attenuation coefficient offers a wide applicability, as it implies a direct link between detection probability and physical characteristics of the water at the study site. Correcting for varying detection probability is in many cases extremely important to do, since rhythms in biological/behavioural factors are often confounded with environmental variables that influence detection probability (e.g. sea breeze, tide).

Introduction

The use of biotelemetry has expanded rapidly during recent years, partly due to technological advances in tagging and telemetry equipment (Heupel, Semmens & Hobday 2006). There has also been an increased academic acceptance and recognition of the typically individual-based data that are collected using telemetry and the questions that might be answered using this method (Cooke et al. 2004). Hence, the number of researchers using telemetry methods is rapidly growing. Although our imagination may put limitations on the great potentials offered by telemetry, another important challenge is the analysis of telemetry data (Heupel, Semmens & Hobday 2006).

In underwater acoustic telemetry, individual animals are tagged with acoustic transmitters and their location as a function of time is monitored using acoustic receivers placed within the water column. Receivers are either towed through the system (e.g. boat mounted) or deployed in a fixed array (e.g. attached to buoys anchored to the sea bottom) (see Heupel, Semmens & Hobday 2006). Detections are often treated as presence/absence data, that is, the animal is assumed to be within a certain detection range of a receiver during times of detection and outside the detection range when no transmissions are received. This is a simplification of reality because the probability of detection decreases as a function of range rather than being cut-off at a certain range (Heupel, Semmens & Hobday 2006; How & de Lestang 2012). Several authors have used the frequency of detections at one or several acoustic receivers as an indication of habitat use or activity in the tagged animal (Simpfendorfer, Heupel & Hueter 2002). This may well be a valid approach, but it has an underlying assumption that the rate of signal attenuation is stable over space and time. Under this assumption, patterns in the detection rate may be associated with patterns in habitat use by the tagged fish, for example movements between locations distant and closer to the receivers or between littoral and pelagic habitats.

The assumption of spatial and temporal stability in signal attenuation is however often heavily violated in shallow waters and the upper part of the water column, where the influence of changing winds and temperatures is most prominent. Spatially, attenuation is affected by bottom substrate (soft, rocky), boundaries and barriers, and attenuation is generally greater in shallow (littoral) waters than in open waters (Heupel, Semmens & Hobday 2006). Temporally, attenuation is affected by environmental noise. Payne et al. (2010) illustrated that severe misinterpretation of data could arise due to systematic variation in the probability of detection. When looking only at the detection rate, their data indicated a diurnal activity peak for the study animal, whereas when corrected for systematic variations in detection range as resolved by control tags, their data indicated a nocturnal activity peak. The reduced nocturnal probability was possibly caused by elevated nocturnal background noise. Similar potential misinterpretations could arise from other sources of systematic variation in the probability of detection, including periodic events such as the tidal cycle or land and sea breeze patterns. Rhythmic biological sound-producing activities could pose a similar problem, for example from crabs moving along the bottom or from biological activities at reefs (Payne et al. 2010). Systematic variation in detection rates may also result from behavioural characteristics of the study animal, for example the animal may be moving in and out of the littoral habitat or a refugium in a regular pattern (see Hedger et al. 2010). It is therefore valid to assume that patterns in detection rates have a biological component, but it is a great challenge to sort out the fluctuating environmental component. Identifying general relationships between environmental factors and the probability of detection would therefore be of great value for the analysis of telemetry data.

The way that the environment affects attenuation is complex. Sound intensity in water generally fades with the square of the range according to geometric spreading of the sound (Medwin & Clay 1998). However, factors such as absorption and scattering also add to the fading, and these factors are strongly influenced by environmental conditions such as salinity, suspended particles and gas bubbles, temperature and macrovegetation (Medwin & Clay 1998). Salinity and temperature also influence water density, and the direction of the sound transmission will be deflected over density gradients. Finally, the receiver must be able to sort the acoustic signal from the background reverberation. The background reverberation strength is also dependent on weather and the fluid environment (Medwin & Clay 1998). Although the environmental effects on range are well known (Heupel, Semmens & Hobday 2006), field studies reporting the effects of these dependencies have largely been lacking (but see Aymes & Rives 2009; Lembo et al. 2002; Payne et al. 2010, 2011).

The objective of this study was to model the influence of the environment on the detection rate of acoustic transmitters used for fish telemetry studies. In particular, we examined the influence of wind, rain, temperature, transmitter mean depth and transmitter depth range. Having establishing the importance of wind on the detection rate, we produced a model for predicting the influence of wind on the detection probability using general acoustic theory, which may then be used to derive a priori estimates of detection probabilities. In turn, this may be used to improve the resolution of animal behaviour observed through acoustic telemetry. We investigated the following hypotheses:

  1. Wind and rain influence sound transmission in water and should be expected to negatively influence the detection rate.
  2. The vertical temperature gradients during summer stratification deflect the sound transmission path downwards, and the detection rate should therefore decrease with increasing depth for shallow-suspended receivers.
  3. Detection probability of acoustic transmitters may be described by the theory of sound propagation in water, since the signal has to be carried by sound transmission.

Materials and methods

Study area

The telemetry study was performed in Lake Skrukkebukta (surface area of 6·8 km2, geographic location 69·55 N, 30·12 E, Pasvik, Norway) in August and September 2004. Fifteen hatchery-raised brown trout (fork length 33·4 ± 1·4 cm SD) were internally tagged with acoustic transmitters containing depth sensors (V9P-6L, manufactured by Vemco Ltd, Halifax, Canada) and released as part of a yearly stocking program in the watercourse. The tags had a transmitting power of 139 dB re 1 μPa at 1 m, nominal transmitting delay of 40 s and an expected battery lifetime of 6 weeks. Signals from the 15 tagged trout were recorded on an array of 12 Vemco VR2 receivers distributed throughout the lake. The receivers were suspended 3 m below the surface by anchored buoys, with the hydrophone pointing downwards. Lead weights were attached 0·5 m beneath the lower end of the receivers to ensure that receivers remained upright during windy conditions. Minimum bottom depth at any receiver location was 6 m. The deeper areas of the lake have soft sediments and no vegetation, whereas the near-shore littoral area is more uneven and has more rocks, stones, vegetation and in some places submerged logs. More details about the receiver locations and lake bathymetry are given in the Supporting Information (including Fig. S1), and a hypsographic curve for the lake can be found in Gjelland, Bøhn & Amundsen (2007). Analyses were run on 4 weeks of data starting from 10 days after stocking, as fish behaviour appeared to have normalized within the first 10 days after they were stocked (based on subjective judgement of vertical and horizontal movements). Fish were able to migrate out of the lake, but examination of the detection pattern showed strong residency within the lake. Individuals disappearing from the study were statistically accounted for by counting the number of tagged individuals detected within the 24-h day cycle. A trout was considered resident until its last day of detection. At the end of the study, 11 of the 15 tagged trout were characterized as resident.

The transmitter signal code consisted of an acoustic pulse train initiated by a sync signal and completed by a fixed number of pulses with a varying interval (making up the code). The receiver signal detection performance was evaluated using the code detection efficiency Ce, calculated from the receiver log reports as the number of detected complete codes divided by the number of detected syncs (Simpfendorfer et al. 2008). We also used a design test study in another lake in the area to verify the often quoted, but seldom reported, detection dependency on the depth at the transmitter location. These results are presented in the Supporting Information (Fig. S2).

Effect of environmental variables on detection rates

Environmental variables tested for potentially influencing the detection rate were water temperature (hourly linear interpolations of temperatures logged at 3-m depth every third hour), wind speed (hourly average), and rain (cumulative precipitation within an hour). The epilimnetic temperature decreased from 17°C in the beginning of the study period to 11°C at the end of the study period, whereas the depth range of the thermocline shifted from 10–15 m in the start to 18–21 m in the end of the study period. Hourly averaged wind speed and rainfall were obtained from Bioforsk Svanhovd Research Station, located 10 km from the study lake. Other explanatory variables included in the statistical test were transmitter hourly mean depth, hourly transmitter depth range (difference between deepest and shallowest transmitter for the hour) and number of resident transmitters. We defined the detection rate as the number of detected transmissions per hour and the specific detection rate as the detection rate divided by the number of resident transmitters. The relationship between the hourly integrated detection rate and environmental variables was tested in a linear model, using the square-root transformed-specific detection rate as the response variable. The full statistical model tested on 672 h of data was: (Specific detection rate)0·5 ~ a + b1*Wind + b2*Rain + b3*Water temperature + b4*mean(Depth of transmitter) + b5* (Depth range of transmitter). As the first step, the model was specified as a linear model (multiple regression) solved by ordinary least square (OLS) with R function lm(stats). Model residuals were highly autocorrelated. Therefore, the model was analysed using generalized least squares (GLS) with R function gls(nlme), accounting for nonindependence of observations in time by including an autoregressive (AR) model in the correlation structure (see Zuur et al. 2009). The cyclic shape of the autocorrelation in linear model residuals violated the AR1 (first order AR) assumption of an exponential decrease in autocorrelation. GLS-modelling was therefore iterated with increasing AR-order and the final model choice based on residual inspection, AIC and model comparison by anova (model 1, model 2). One hour lacked detections. For this hour, mean transmitter depth and transmitter depth range were interpolated between the preceding and subsequent hours in order to allow for comparisons between models. Likewise, for 2 h that had only one detection each, transmitter depth range was interpolated between the preceding and subsequent hours. All variables were centred and scaled by z-transformation (subtracting the mean and dividing by standard deviation) prior to modelling, in order evaluate the effect size by the model coefficients (Schielzeth 2010).

To aid interpretation of the effect of wind on detection rates, two echograms were made with a 70-kHz echosounder, one during calm conditions, the other during windy conditions. The echograms were recorded by a stationary Simrad EY500 echosounder (Simrad AS, Horten, Norway) equipped with a transducer (circular 11° nominal beam width) mounted at 15-m depth and beaming towards the surface. The cross-section of the acoustic beam was approximately 6·6 m2 at the surface and 2·9 m2 at 5-m depth.

A general acoustic attenuation model for detection probability

A substantial proportion of the transmissions was recorded at two or more receivers. For these multiple recordings, the detection range between the transmitting fish tag and each individual receiver detecting the signal was approximated as the distance between the mean position inline image of the receivers detecting the signal and the position (Xri,Yri) of each recording receiver. This was based on the assumption that a likely location of a transmitter whose signal was detected by several receivers and was in the middle of the receivers (cf. Hedger et al. 2008). The largest of the calculated detection ranges for each transmission was considered as a minimum estimate of the detection range for that particular transmission and termed minimum detection range Dmin (eqn 1).

display math(eqn 1)

The minimum detection ranges as defined here are likely underestimates of the true detection ranges, but allow for an exploration of the relative probability of signal detection as a function of range. This was achieved by taking the proportion of hourly transmissions N recorded at an increasing number of multiple receivers (i = 2–7) to the expected number of recorded transmissions Ne. These proportions served as an estimate of the probability of detection Pd at the associated minimum detection range Dmin(i) (eqn 2).

display math(eqn 2)

The probabilities of detection Pd were calculated for detection data grouped by wind speeds W in 0·5-m·s−1 bins ranging from 0 to 5·5 m·s−1. In order to avoid depth dependency of the detection probability, this analysis was confined to transmissions in the 0–6-m depth interval. The expected number of recorded transmissions was calculated as the number of expected transmissions per hour (Nt) adjusted for the mean code detection efficiency Ce and the proportion Sz of the total recorded transmissions transmitted within the depth interval z (eqn 3).

display math(eqn 3)

To calculate Sz for any given hour, the number of depth recordings within each one metre interval was divided by the number of depth recordings integrated over all depths for that hour. The sound pressure I (μPa) at distance D can be modelled according to (eqn 4), where I0 is the transmitter power in dB (re 1 μPa at 1 m) and αe is the sound attenuation coefficient in Nepers m−1 (Medwin & Clay 1998).

display math(eqn 4)

The first part (the power function) of (eqn 4) accounts for losses due to spherical spreading, and the latter part (the exponential function) for the attenuation losses (primarily absorption and scattering). Wind mixing of air bubbles into the water should theoretically increase the attenuation by increasing both absorption and scattering. It was therefore assumed that the probability of detection was a constant P0 (P0 = 1) until a sound pressure threshold It at range D0 (see also Melnychuk & Walters 2010), beyond which the probability of detection could be described by a scaled sound profile. In the present study, we chose to use P0 = 1. Multiple recordings associated with distance Dmin and probability of detection Pd (see (eqn 2)) were used as data input to the model. An estimator of the probability of detection inline image was then obtained by scaling the sound profile by a sound pressure threshold parameter It (eqn 5).

display math(eqn 5)

The attenuation coefficient α [dB m−1] relates to αe [Nepers m−1] by a factor, such that α = αe∙8·686 (Medwin & Clay 1998). As it is the more common representation, the attenuation coefficient was chosen to be presented in dB m−1 in this paper. The dependence of α on wind was modelled by a power function (eqn 6), where W denotes mean wind speed (m s−1) for the data interval, α0 denotes the attenuation coefficient under no wind influence and β the power dependence of α on wind speed.

display math(eqn 6)

An acoustic transmission model that can be used as an estimator of the probability of detection as a function of range and wind can be created by combining (eqn 5) with (eqn 6) as follows (eqn 7):

display math(eqn 7)

In this sound transmission model, the parameters It, α0 and β were estimated by nonlinear least squares regression on the Pd (Dmin,W) obtained from (eqn 2). After the parameter fitting, the estimated It was used with (eqn 5) to estimate attenuation coefficients for each wind interval. The wind speed interval 0–0·5 m s−1 was considered to have a positively biased attenuation coefficient since the wind speed interval in the preceding hour could only be equal or higher. For all other wind speed intervals, the wind speed during the preceding hour could be either lower, equal or higher, and these intervals were thus considered unbiased. The 0–0·5-m s−1 wind speed interval was therefore excluded from the nonlinear regression parameter estimation.

A similar procedure as for the wind dependence was used to model the depth dependence. The detection data were divided into 1-m-depth intervals, and Pd (Dmin,z) was calculated for each depth interval and Dmin combination using eqns 2 and 3. Only one wind speed interval was used [0–1 m s−1]. Within each depth interval, the attenuation coefficient was then estimated by nonlinear regression with (eqn 5) and detection probability modelled for 0–1500 m range.

Results

Effect of environmental variables on detection rates

A total of 119 514 recorded transmissions from the 4-week study period were used for the analyses. The mean time difference between detections was 49 s (first quartile = 26 s, third quartile = 103 s). Although the total number of detections varied between the receivers, there was a common pattern in the relative distribution of detections with the hour of the day (Fig. 1). An average of 4·17% of the detections should have been observed within each hour of the day, if the detections had been randomly distributed throughout the day. Generally, the hourly percentage of detections was much higher than 4·17% during night-time and much lower during daytime, especially in the afternoon (Fig. 1).

Figure 1.

Wind rose plots of the relative distribution of detections with the hour of the day. The area of the sectors is proportional to the relative number of detections. The receiver number is indicated by R and the hour of day is indicated by the numbers at the outer circle (midnight at top, morning at right-hand side, midday at bottom and afternoon at the left-hand side of the polar plots). The radial dotted circle at 4·17% is the expected value if the detections were evenly distributed by the hour of day.

Accordingly, the total number of detected transmissions increased during evening hours, reached a maximum in the first few hours after midnight and decreased thereafter to the minimum in the afternoon (Figs 1, 2a). The opposite pattern was seen in the hourly averaged wind speeds, which were highest during daytime and lowest during night-time (Fig. 2a). Tag depth was closer to the surface during daytime than during night-time, and the depth range was largest during daytime (Fig. 2b).

Figure 2.

(a) The mean hourly specific detection rate (grey triangles connected by solid line, right y-axis) compared to the mean hourly wind speed (black circles connected by solid line, left y-axis), with dotted lines indicating 95% confidence intervals. (b) Box plot of hourly averages of individual mean transmitter depth within the different hours of the day.

The detection rate was strongly dependent on wind speed (Fig. 3a). The average number of receivers detecting the transmission also decreased with increasing wind speed, further indicating a reduction in detection range with increasing wind speed (Fig. 3b). All of the variables tested, except water temperature, had a statistically significant influence at the 0·05 level on the specific detection rate as determined by the OLS and GLS model selection procedure. However, there was a negative correlation between transmitter mean depth and range of depth (r = −0·38) indicating confounding between these variables, and inclusion of mean transmitter depth contributed relatively marginally with an AIC-reduction of 3·1. We therefore chose to drop mean depth from the model (inclusion of transmitter depth range gave substantially lower AIC than inclusion of transmitter mean depth). Wind was by far the most important predictor (b1 = −0·294), followed by the depth range of transmitters (b5 = 0·131) and rain (b2 = −0·067) (see Table S1 in Supporting Information for a full overview of model parameter estimates and confidence intervals). The strong autocorrelation was accounted for by including a 7-order AR-model, supported by a significantly negative partial autocorrelation at lag 7, an AIC-reduction of 32 points as compared to the AR1-model and a significantly better performance of the 7-order model as compared to lower-ordered AR models (anova, P < 0·001).

Figure 3.

(a) The number of detections per hour (detection rate) against wind speed. (b) The average number of receivers detecting a transmission against wind speed.

Comparisons of recordings from the up-looking, bottom-mounted echosounder during one hour of no wind and one hour with a mean wind speed of 3·8 m s−1 illustrated wind-induced change in acoustic conditions in the upper metres of the water column (Fig. 4). During the hour with wind, sound reflections from entrained ‘bubble clouds’ could be seen reaching as deep as 4–5 m beneath the surface.

Figure 4.

Echograms from a bottom-fixed 70-kHz echosounder beaming from 15-m depth towards the surface. Colour intensity (grayscale) indicates backscattering strength, from low (white) to high (black). During an hour of no wind, there was little scattering in the water column (a), whereas during an hour with mean wind speed of 3·8 m s−1, there was considerable backscattering from the upper three metres of the water column (b).

General acoustic theory model

The probability of detection dropped rapidly with range, but the rate of decrease was much lower at long ranges, and there were still a few signals detected at a range of 1500 m at low wind speeds (Fig 5a). Fitted by the acoustic transmission model (eqn 7), minimum detection range and wind speed explained 99·38% of the total variance in the probability of detection (Fig. 5a, 28 d.f.). The sound pressure threshold was estimated to be 92·6 dB re 1 μPa at 1 m (91·0 and 94·0 dB lower and upper 95% confidence intervals, respectively). The acoustic attenuation coefficient at zero wind speed (α0) (0–6-m depths combined) was estimated to be 7·05 × 10−3 dB m−1 (5·61 × 10−3 and 8·81 × 10−3 dB m−1 lower and upper 95% confidence limits, respectively). The attenuation coefficient increased with wind by a power of 1·78 (1·63 and 1·93 for the lower and upper confidence interval, respectively). Attenuation coefficients estimated separately for each wind interval were well fitted by the power function (eqns 6, 7, Fig. 5b).

Figure 5.

(a) The observed probability of detection (Pd) for the wind speed intervals as indicated with the symbols in the figure key, with the corresponding lines indicating the detection probabilities predicted from the fitted acoustic transmission model estimator (inline image) (see Methods for estimation details). In order to avoid too many different symbols and lines, only a subset of datapoints are plotted, but the overall model fit was very good (99·4% explained variance). (b) The estimated attenuation coefficient (circles) for the wind speed intervals, and fitted by a power function (solid line). The x on the lower end of the y-axis marks the theoretical absorption coefficient for pure freshwater, which is 1·29 dB km−1 at 69-kHz sound frequency and temperature 13·7 °C.

Detection probability predictions from (eqn 7) demonstrated that the change in minimum detection range with increasing wind was much higher for a low detection probability than for a high detection probability (Fig. 6a,b). By increasing wind speed from 0 to 6 m s−1, the threshold range (the range of maximum detection probability) decreased by a factor of 3·4 from 181 to 54 m, whereas the range of 50% detection probability decreased by a factor of 4·6 from 322 to 70 m.

Figure 6.

(a) Model predictions for wind speeds 0, 1, 2 and 5 m s−1, with 95% confidence intervals indicated by grey shading and delineated by dotted lines. (b) Contour lines showing the 1, 0·5, 0·25, 0·1, 0·05 and 0·01 isoclines of detection probabilities as a function of wind speed and range.

The mean depth of the fish when transmissions were detected was 4·3 m (±1·1 m SD). The range of hourly individual mean depths was 12·1 m, minimum and maximum observed individual depths 0 and 18·4 m, respectively. The probability of detection at long range was highest for signals transmitted at 4–5 m depth, lower close to the surface and lowest at depths below 8 m (Fig. 7). The largest observed minimum detection range was 1·98 km, from a fish tag transmitting at 4·2-m depth.

Figure 7.

Colour plot of depth-specific detection probabilities. The solid, dashed and dashed-dotted lines represents estimated ranges with probability of detection as indicated by the figure key.

Discussion

Highlight of the study–modelling detection probability and answer to the hypotheses

The present study demonstrated that the probability of detecting signal transmissions from acoustic tags could be successfully modelled using general laws for sound transmission in water. The probability of detection as a function of minimum detection range was well described by a scaled sound intensity profile. The attenuation coefficient increased systematically with increasing wind and was fitted well by a power function. The estimated attenuation coefficient with no wind influence was 7·0 dB km−1 [confidence interval (5·4, 8·7)]. This is somewhat higher than the theoretical absorption coefficient for pure freshwater, which is 1·29 dB km−1 at sound frequency 69 kHz, for a temperature of 13·7°C at 3-m depth (according to eqn A2·1 in Simmonds & MacLennan 2005, p. 67). However, the presence of acoustic scatterers such as suspended particles, plankton and fish will all contribute to increased attenuation. An attenuation coefficient higher than the theoretical minimum (which is the absorption coefficient without scattering and absorption influence from suspended particles and organisms) should therefore be expected (Voegeli & Pincock 1996; Medwin & Clay 1998; Simmonds & MacLennan 2005).

Effect of environmental variables on detection rates

The consistency in the diel pattern of detections across all receivers suggests that there were some strong common drivers in this periodicity, potentially both environmental and biological. Wind and rain are known to mix air bubbles into the upper water column, which attenuate sound by absorption and scattering, strongly degrading the sound propagation and signal range (see Medwin & Clay 1998). Entrained air in water also produces sound, but this effect is relatively small at 69 kHz at moderate wind speeds, so it is unlikely that this had a large effect on our results (Medwin & Clay 1998; Simmonds & MacLennan 2005). Wind can mix the air far deeper into the water than can rain, and accordingly, theoretical expectations of a strong negative effect of wind and a less strong negative effect of rain were confirmed. The echosounder recordings made at a similar frequency as the frequency of the acoustic transmitters visualized the wind effect.

Temperature influences sound propagation in water, primarily by affecting the speed of sound (Medwin & Clay 1998). An important effect of this is that the sound propagation will be deflected when travelling through temperature gradients. Therefore, it is not the effect of a specific temperature that should be expected to affect the number of detections, and there was no significant effect of the changing epilimnetic temperatures during the present study. It is, however, highly likely that detection probability will be influenced by the thermocline. This will be discussed further below.

The transmitter depth range results from the habitat choice and movement of tagged fish and must be considered as a biological effect. Increasing depth range may be seen as an indicator of increasing pelagic use, since a large depth range is impossible when the fish is in the shallow littoral habitat. Thus, the positive effect of depth range on the number of recorded transmissions was attributed to an increased use of the pelagic habitat. This interpretation is consistent with our design test study, where we found pelagic locations to have a higher transmission range than littoral locations (Supplemental Figure S2).

The strong autocorrelation may have both environmental and biological causes. In general, temporal and spatial autocorrelation may be expected both in environmental variables as well as in the activity and habitat use of a tagged animal. The strong autocorrelation in our model underlines the importance of considering autocorrelation in acoustic telemetry data.

General acoustic theory model of detection probability

Increasing wind severely reduced the minimum detection range and detection probability, in a manner that could be successfully modelled with general theory of acoustic transmission in water. Varying weather will thus strongly amplify the probabilistic nature of signal detection; an acoustically tagged animal detected one or a few times under good conditions might be far away, whereas it might be close to the receiver without being detected when conditions are less favourable for sound transmission. The ‘detection range’ is therefore a problematic concept, as it is evidently not a constant range within which all transmissions are detected, and outside of which are not (see also Heupel, Semmens & Hobday 2006). Models of detection probability as a function of range may far better describe the true detection pattern. Other authors have recommended different models of detection probability than the model used by us: Melnychuck & Walters (2010) identified a logistic shaped detection probability model as being optimal, whereas How & de Lestang (2012) identified sigmoidal and exponential detection probability models as being optimal. Like our model, their models had nonlinear relationships between detection probability and range, but theirs most often approached a position of maximum detection probability asymptotically. Theoretically, detection probability should decline proportionally to the decline in sound pressure, which has a combination of geometric and exponential decline. But the change from maximum detection probability to an exponential-like decline is abrupt, and it may be difficult to verify the exact shape of the detection probability curve. The strengths of the acoustic model approach presented here are at least threefold: (i) it connects the detection probability directly to the sound transmission properties of the water, as expressed by the attenuation coefficient, (ii) by knowing how the attenuation coefficient changes with the environmental condition, predictions of detection probability may be modelled as a function of fluctuations in the environment and (iii) it allows for different transmitter powers to be included in the same detection probability model. In particular, modelling environmental effects on the detection probability is crucial, and is something that has been neglected by previous researchers. Melnychuck et al. (2010) did include increased attenuation in one of their models to account for the presence of wind, but did not allow for a relationship between wind speed and attenuation. The models of Melnychuck et al. (2010) and How & de Lestang (2012) have been tested across multiple systems: in the former case, in small and large rivers and in inner coastal waters; in the latter case, in ocean reefs and deep water. Although we have still not tested our model across different systems, we propose that the generality of the model allows it to be used across a wide range of different freshwater and marine systems as well as tag and receiver manufacturers.

We modelled detection rate as constant until a certain threshold, with a maximum detection probability of 1. We lack data for short ranges, but the assumption of a high and constant detection probability at short ranges has support from other publications (How & de Lestang 2012). It may be as realistic to use a maximum probability of detection value around 0·9 (How & de Lestang 2012). This can easily be implemented in the suggested framework, by simply reducing maximum constant detection probability from 1 to for example 0·9. We did not implement this, since we lacked data at sufficiently short ranges for the constant part. The sound intensity threshold parameter will have to be identified for different types of receivers, but could also be expected to differ between internal and external tagging, as well as for large size differences between internally tagged fish. The model does not account for variation in the background noise, which may influence the threshold. However, fluctuations in the background noise may be measured and used to adjust the sound intensity threshold according to a relevant signal-to-noise ratio. Modelling the detection probability according to the laws of sound transmission in water may therefore accommodate both variation in sound attenuation and background noise caused by biotic and abiotic factors. One reason why previous authors have disfavoured the acoustic transmission model may be that they did not allow the attenuation coefficient to vary with varying environmental conditions.

The probability of detection was also dependent on the depth of the tagged fish, being highest for fish at 4 to 5-m depth. Sound speed in water increases with temperature. Acoustic waves travelling along or through a temperature gradient will decelerate on the colder side. During the summer stratification period, this mechanism will cause the acoustic signal to bend downwards (Medwin & Clay 1998). If the distance between the transmitter and receiver is large compared to the depth difference, the straight line between them will be in a low angle to the thermocline, and most of the signal will be deflected down below the thermocline. Thus, at larger distances the receiver may be in an acoustic ‘blindzone’ relative to the transmitter (Medwin & Clay 1998; Simmonds & MacLennan 2005), resulting in a lower detection probability of transmitters located deep in the water column. Thus, the thermal gradient likely reflected signals coming from below away from the receivers, which were submerged at 3-m depth and well above the thermocline. The probability of detection was also reduced for fish above 4-m depth. This is the zone where air was mixed in by wave action, and although wind and waves calm down, it will take some time before residual air bubbles have disappeared. It is also the zone of highest biological productivity, with the highest densities of phyto- and zooplankton adding to the sound attenuation.

Systematic variations and sorting of biological and environmental effects

As addressed in the Introduction, it may be valid to assume that patterns in detection rate may be related to patterns in the littoral-pelagic habitat use. The tagged fish in the present study primarily used the upper 6 m of the water column, where the influence of wind may also be expected to be strongest. The receiver deployment at 3-m depth was within the depths influenced by wind mixing, and the detection probability was therefore affected by wind even if the tagged fish were deeper. Our results may thus act to pinpoint the potentially strong effects of wind, and the relevance to other studies may vary depending on the study organisms and characteristics of the water body. The upper metres of the water column are on the other hand very important both in lakes and at sea, and bubble entrainment may extend tens of metres down in the water column during harsh weather conditions in the sea (Dalen & Løvik 1981). Deeper deployment of the receivers could reduce wind effects on receiver performance, but will also tend to reduce the likelihood of a straight transmission path from fish in the littoral zone and further reduce their detection probability. These considerations will therefore be important for most deployments of acoustic telemetry in lakes and to varying extent in sea and ocean applications. It is also clear that range testing must be performed during varying environmental conditions, and 1 day of range testing may often not be sufficient. For marine and estuarine studies, at least one full tidal cycle should be included. It is also strongly recommended to include a few stationary reference tags in the study. Doing so enables tracking of changes in detection range, which can be used during the data analyses and give much more confidence in the presented results and interpretation of the data.

In summary, the characteristics of acoustic signal detection illustrated here demand awareness of the implications for the choice of analyses and interpretation of acoustic telemetry data. Scientists strive to report the biologically relevant information from their data, and great care must be taken to avoid bias and pitfalls resulting from detection range variation over time. A strong wind pattern or tidal signal could amplify biological signals, or it could counteract and even overshadow the pattern that should be expected from a biological pattern in movement. Likewise, readers and referees of papers dealing with acoustic telemetry should be aware of these problems and how the presented results could be influenced by them. Researchers designing new telemetry studies should also bear this in mind, and determine if it is sufficient to pick up only a small proportion of the transmitted signals, or if the loss of a transmission or two means the lost possibility to detect a fast-migrating animal passing by. And last but not least; it is good practice to evaluate the functional links between detection rates and environmental variables as well as tagged animal behaviour. The linking of probability of detection with the principles of sound propagation in water offers a large potential for a wide range of acoustic telemetry applications.

Acknowledgements

We thank Professor P.A. Amundsen and K.S. Johannessen at the University of Tromsø, and Dr. Eva B. Thorstad and Finn Økland at the Norwegian Institute for Nature Research, for great help with the design and implementation of the field study. Two anonymous referees provided helpful and constructive comments and suggestions for the manuscript.

Data accessibility

The source data for these analyses can be found as Supporting Information.

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