1 ICES Journal of Marine Science, 60: doi: /s (03) A requiem for the use of 20 log 10 Length for acoustic target strength with special reference to deep-sea fishes S. McClatchie, G. J. Macaulay, and R. F. Coombs McClatchie, S., Macaulay, G. J., and Coombs, R. F A requiem for the use of 20 log 10 Length for acoustic target strength with special reference to deep-sea fishes. ICES Journal of Marine Science, 60: Although it is well known that the slopes of target strength (TS) and length relationships vary widely, it is common in fisheries acoustics to force the TS length regression through a slope of 20. Is it time to abandon this practice? The theoretical justification was that TS should be proportional to cross-sectional area, and that area should scale as the square of the linear dimension (fish length). There are now many species other than gadoids that are the subject of acoustic surveys, and many of them do not have the same morphology as the gadoid fishes. The slope of the TS length regressions deviates significantly from 20. The empirical slope should be used wherever it can be shown to be more appropriate than the 20 log 10 L model. Using the data from swimbladder models, it is shown that Macrourids, a merluccid hake and Oreosomatidae have a different relationship between swimbladder size and fish size compared with that of gadoids. It is demonstrated that the 20 log 10 L model is not appropriate for these deep-water fish and that deviations from the model arise, to a considerable degree, from variation in fish morphotypes. The TS of deep-water Macrourids, a merluccid hake and Oreosomatidae are lower than that of gadoids. This is related to the swimbladder size fish size relationship in different morphotypes, although not much evidence can be found to support the concept that swimbladder sizes are generally smaller in deep-sea fishes. Ó 2003 International Council for the Exploration of the Sea. Published by Elsevier Science Ltd. All rights reserved. Keywords: fish target strength, acoustic deepwater size morphology. Received 26 June 2002; accepted 13 October S. McClatchie, G. J. Macaulay, and R. F. Coombs: National Institute of Water and Atmospheric Research Ltd, PO Box 14901, Kilbirnie, Wellington, New Zealand. Correspondence to S. McClatchie: tel.: þ ; fax: þ ; Introduction It has become something of a paradigm to summarize the relationship between tilt-averaged, acoustic target strength, htsi, and fish length (L) by htsi ¼m log 10 L þ b, where the value of m is assumed to be 20. This equation is generally applied to TS of fish from the same species over a range of sizes that were insonified at the same frequency. A value of 20 for m is reasonable if backscattering is proportional to cross-sectional area of the main scattering structure, which in turn is directly proportional to L (acoustic cross-section, r bs, scaling proportional to L 2 ) rather than to volume (r bs scaling proportional to L 3 ), or some other proportionality. In an early review, Love (1971) combined all the available data on fish TS and obtained a regression to predict the TS of an individual fish as a function of length and wavelength. He concluded that for an individual fish, the dorsal-aspect TS increases in proportion to the square of fish length. Foote (1979) proposed area-dependent scattering ðm ¼ 20Þ to describe the htsi length relationships for caged and free-swimming clupeoids and for free-swimming gadoids. In their review, MacLennan and Simmonds (1992) stated that, in the absence of data to the contrary, the 20 log 10 L dependence of TS seemed a fair assumption and this relationship continues to be in use (Benoit-Bird and Au, 2001; Iida et al., 1998; Rose, 1998; Svellingen and Ona, 1999). When the slope of the htsi L regression is estimated from the data, m commonly has values between 18 and 30 (MacLennan and Simmonds, 1992), although Foote (1987) reported an even wider range ( ) for gadoids, clupeioids, redfish and greater silver smelt. McClatchie et al. (1996a) found m to be ranging between 11 and 25 for the TS max L regression, where TS max is the maximal TS. Since the book by MacLennan and Simmonds has been published, many new measurements of fish TS have been made, so that data are now available on the htsi length relationships for many species other than gadoids /03/040419þ10 $30.00 Ó 2003 International Council for the Exploration of the Sea. Published by Elsevier Science Ltd. All rights reserved.
2 420 S. McClatchie et al. The objective of this article was to use some of these data, derived from swimbladder modelling of the TS of deep-water fishes ( m), to test whether the 20 log 10 L relationship is valid for these species, and to test whether the TS length relationships of deep-water fish with air-filled swimbladders are different from more shallow-living species. In the process of determining as to why this might be so, the generalization that deep-water fish have smaller swimbladders is examined critically. The question, whether reframing the TS length relationship in terms that account for a greater extent of the diversity of fish morphology and provide a clearer summary of the size dependence of TS, is discussed. Many studies addressing the relationship between fish size and TS begin from a physics or engineering perspective, i.e. assume a model fish of x, y, z dimensions. This study takes a more biological approach, combining experimental measurements with empirical model results in a meta-analysis to test the validity of a statistical relationship. As pointed out by a reviewer, the 20 log 10 L relationship is no better or worse than another, but if another relationship can be shown to be more appropriate, then the best one should be used. One of our points is simply that the 20 log 10 L relationship should not be used without first determining whether it is the most suitable one. Methods Dataset The data used in this article were from swimbladder modelling and from a dataset of published experimental measurements of TS, where the TS of individual fish could be matched to their sizes (McClatchie et al., 1996a) (Table 1). The published data included fish that were either alive, stunned or killed. There were no species in this dataset in which TS was measured on both live and dead fish. In this analysis, we include both live and dead fish, but not the fish that had been frozen. It is now known that when fish have been frozen, the TS of dead and live fish can differ owing to air inclusions (McClatchie et al., 1999) and the differences in the tissue characteristics after death (Gytre, 1987), though these are less important for swimbladder fish as 95% of the backscattering comes from the swimbladder (Foote, 1980). To minimize these biases, we excluded nonswimbladder fish from the analyses. Swimbladder modelling Swimbladder-model data were produced using methods detailed in Macaulay et al. (2002). The methods for estimating TS were the same as in McClatchie et al. (1996b), except that a resin was used to produce better swimbladder casts, the volume of the cast was adjusted to that required for neutral buoyancy and the shape was estimated using a hand-held laser scanner rather than by crosssectioning, digitization and triangulation (Macaulay et al., 2002). Analyses All the statistical analyses were performed using the R programming language and environment (Ihaka and Gentlemen, 1996). All the regressions in this article were orthogonal least-squares rather than geometric regressions, despite the x, y, data being bivariate and assumed normal. Table 1. Species plotted in Figure 1, including those used for swimbladder modelling, listed with their species codes. Common name Species Species code Morpho-type Black oreo Allocyttus niger BOE Oreo Smooth oreo Pseudocyttus maculatus SSO Oreo Lookdown dory Cyttus traversi LDO Oreo Javelinfish Lepidorhynchus denticulatus JAV Whiptail Hoki Macruronus novaezelandiae HOK Whiptail Ridge scaled rattail Macrorurus carinatus MCA Whiptail Bollon s rattail Caelorinchus bollonsi CBO Whiptail Serrulate rattail Corypaenoides serrulatus CSE Whiptail White rattail Trachyrinchus aphyodes WHX Whiptail Notable rattail Caelorinchus innotabilis CIN Whiptail Four-rayed rattail Coryphaenoides subserrulatus CSU Whiptail Black javelinfish Mesobius antipodum BJA Whiptail Red cod Pseudophycis bachus RCO Other Ling Genypterus blacodes LIN Other Barracouta Thyrsites atun BAR Other Frostfish Lepidopus caudatus FRO Other Hake Merluccius australis HAK Gadoid Southern blue whiting Micromesistius australis SBW Gadoid Atlantic cod Gadus morhua Gadoid Pollack Pollachius pollachius Gadoid Saithe Pollachius virens Gadoid Silverside Menidia menidia Gadoid
3 A requiem for the use of 20 log 10 Length 421 Table 2. The linear regression equations and measures of goodness-of-fit for the htsi L (units, db, cm) relationship at 38 khz for each of species for which we have sufficient data points ðn [ 30Þ. s.e., standard error. The t-value here is for a test that the slope is 20. Significance indicates a difference from the slope value of 20 (two-tailed test); ***significance level of p \ 0:001; *p \ 0:05; NS indicates p [ 0:05. The overall regressions are significant at p \ 0:001. Species Intercept (s.e.) Slope (s.e.) t-value Adj r 2 DF Black oreo ÿ68.4 (2.7) 21.5 (1.8) 0.9 NS , 98 Ribaldo ÿ63.4 (1.8) 19.8 (1.1) ÿ0.2 NS , 30 Bollon s rattail ÿ76.2 (6.9) 26.4 (4.2) 1.5 NS , 83 Ling ÿ64.6 (2.2) 18.5 (1.2) ÿ1.3 NS , 45 Hake ÿ67.4 (3.6) 20.6 (2.0) 0.3 NS , 28 Hoki ÿ75.4 (2.2) 22.5 (1.2) 2.1* , 263 Smooth oreo ÿ104.7 (3.6) 41.6 (2.4) 9.2*** , 42 Ridge scaled rattail ÿ81.4 (1.8) 28.2 (1.1) 7.8*** , 51 Frostfish ÿ91.1 (1.9) 29.6 (0.9) 10.4*** , 85 Lookdown dory ÿ75.9 (2.0) 29.1 (1.4) 6.5*** , 28 Figure 1. Morphotypes (oreo, whiptail and cod morphs) illustrated by fishes from the New Zealand fauna. Species representing each morphotype are given in Table 1. Fish sizes are not to scale.
4 422 S. McClatchie et al. It should be noted that the slopes obtained can be quite different from those produced by geometric regressions (Saenger, 1989). The first step was to test the hypothesis that the slopes of the htsi L regression of each deep-water species was different from a value of 20. The analysis was limited to species for which there were sufficient data (see degrees of freedom in Table 2). A linear regression was fitted relating htsi to log 10 L for each species in turn and a t-value was calculated as (fitted slope-20)/standard error of fitted slope. Significance was estimated from the t-distribution for the two-tailed case, and deviation of the slope from a value of 20 was considered true if the p-value for t was significant. Next, we examined whether the TS of deep-water fish might be lower than shallow-living species because of their smaller swimbladders. It has been suggested that deepwater fish using low-density oils, watery tissues and reduced ossification to maintain buoyancy would need smaller swimbladders (Marshall, 1979). Following this idea, we investigated as to how the concentration of oil in whole fish (Vlieg, 1988) varies with their weighted-mean depth of occurrence (X z ) and with their swimbladder surface area (A sb ). For these analyses, we used swimbladder-modelling data for the New Zealand species on which there were published data for oil content. X z was obtained from Anderson et al. (1998). To compensate for differences in fish sizes, swimbladder surface areas were normalized to fish length ða sb =L 2 Þ: Fish length was measured as fork length, for species with forked tails, or total length in the cases of whiptails and oreos. We plotted A sb =L 2 as a function of X z and fitted a LOWESS smooth to the data to detect any trend towards smaller swimbladder size with increasing depth. Results Which fish deviate from the 20 log 10 Length relationship? Of the species for which we have sufficiently large datasets to fit htsi L regressions, five out of 10 had slopes that were significantly different from a value of 20 (Table 2). Slope values varied between 18.5 and 41.6, with the highest slope estimated for smooth oreo. The species that deviated Figure 2. Maximal acoustic cross-section r max in relationship to fish length L expressed in wavelength-normalized form ðr max =k 2 and L=k) for species grouped into three morphological types (gadoids, oreos and whiptails). The species representing each morphotype are given in Table 1. r max is the maximal acoustic cross-section (m), where TS max ¼ 10 log 10 ðr max Þ, L is fish length (m), and k is the acoustic wavelength (m). The whiptails and oreo-like fishes were from deep-water.
5 A requiem for the use of 20 log 10 Length 423 strongly from the 20 log 10 L relationship (i.e. p \ 0:001) included smooth oreo, lookdown dory, ridge-scaled rattail and frostfish (Table 2; species in Table 1). Black oreo did not deviate from the 20 log 10 L relationship. This is odd because black oreo are almost identical in shape to smooth oreo. The slope for hoki was only marginally significantly different from 20. The slopes for Bollon s rattail, ribaldo, ling and hake did not deviate significantly from a value of 20 at p \ 0:05 level. The unusually high slope obtained for smooth oreo appears to arise from the differences in the shape of swimbladders in small and large fish that warrant further investigation. Do deep-water fish have lower TS? The wavelength-normalized universal graph (Love, 1971) provides a convenient way of comparing the TS of deepwater fish with those of more shallow-living gadoids. Normalizing by k shows length-dependent scattering at a single frequency (Love, 1971). Twelve species of fish with Figure 3. The relationship between swimbladder length and fish length for species from several families (Gadidae, Gempylidae, Macrouridae, Merluccidae, Oreosomatidae). Species and morphotypes are listed in Table 1. Deep-water fish are denoted by open symbols to differentiate them from shallower-living species, marked by filled symbols.
6 424 S. McClatchie et al. oreo-like or whiptail morphologies (Figure 1), occurring in deep-water off New Zealand, had significantly lower r max =k 2 (and hence TS max ) than that of gadoids of the same length at the same frequency (Figure 2). Why do these deep-water fish have lower TS? Relatively smaller swimbladder size is an important factor explaining as to why the TS max of the deep-water species, we examined, was lower than that of gadoids. For fish longer than 30 cm, swimbladder length is shorter in hoki, macrourids and oreos compared with that in gadoids and barracouta (Figure 3). Macrourids and merluccid hake (hoki) with swimbladders that are relatively short compared with that of their long whiptailed bodies, group together with the oreos (Oreosomatidae) that are short-bodied with egg-shaped swimbladders. The trend for whiptails and oreos differs from that for gadoids (pollack, cod and southern blue whiting) and barracouta. Among the species examined, whiptails and oreos are common morphotypes in deep-water. Despite differences in swimbladder morphology, the data show a consistent relationship between swimbladder length and htsi (Figure 4). However, it is the surface area of the swimbladder, which has a rather complicated relationship with fish shape, rather than its length that determines the backscattering from it. The Figure 4. The tilt-averaged TS in relationship to swimbladder length for species from several families. Species and morphotypes are listed in Table 1.
7 A requiem for the use of 20 log 10 Length 425 relationship between swimbladder area and htsi was more variable than the relationship between swimbladder length and htsi, suggesting that it would be incorrect to say that deep-water fish have a lower htsi because their swimbladders are smaller. In fact, as is discussed subsequently, there is no strong evidence that deep-water fish in general have smaller swimbladders. Also, the observed differences in relative swimbladder size do not segregate cleanly into deep- and shallow-living species, because some species like hoki (Macruronus novaezelandiae) span depths from 50 to 1250 m, although their preferred depth is 650 m (Table 3). The allometric slopes relating the log of swimbladder cross-section to the log of fish length are steeper for hoki, smooth oreo, frostfish and white rattail than for the isometric case (Figure 5). In contrast, pollack and hake did not deviate from the isometric case, i.e. the 20 log 10 L relationship holds. This indicates that the swimbladder cross-section grows more rapidly, in relation to fish size, in these deep-water fish than in pollack and hake, and suggests a reason as to why deep-water fish do not follow the 20 log 10 L relationship. Are swimbladders smaller with depth? The relationship between swimbladder size and depth was investigated and the rationale as to why swimbladders might be smaller at depth was looked into. No relationship was found between the %oil content of the whole fish and their weighted-mean depth of occurrence, X z (Table 3). Also, no relationship was found between the %oil content of the whole fish and the mean surface area of the swimbladder corrected for fish length ða sb =L 2 Þ, although a negative correlation was expected based on the buoyancy considerations. Although a relationship was found between A sb =L 2 and X z (Table 3), it was weak and thus should not be over-interpreted. The variability in A sb =L 2 was also considerable owing to the differences in swimbladder sizes between the individuals of approximately the same length. The depth ranges over which individual species are found is also wide (Table 3). Does a shape correction help? The TS data are now available for marine organisms with a wide variety of shapes. Among fish, the diversity of forms is very wide. Length measurements are dependent upon shape as, for example, in the length of the body and tail. This introduces a problem when comparing the length dependence of TS for organisms of different shapes. One way to adjust for different shapes is to calculate a shape coefficient, r M, as a volumetric length, defined as Volume 1=3 Length ÿ1. Length is multiplied by r M to compensate for the shape (Kooijman, 2000). Where the volume is unknown, the shape coefficient may be estimated from the wet weight, W w, and the density, q, such that r M ¼ðW w =qþ 1=3 L ÿ1 : Comparing the length dependence of frequency-independent echo amplitudes using r bs =k 2 versus L=k for fishes of different shapes without correcting r M, introduces a shape-related error of unknown magnitude. The same problem would arise if length-normalized TS ¼ TS=L were calculated for fish of different shapes. To test whether shape correction merges the distinct regressions for different morphotypes, the lengths of pollack, oreos and hoki were corrected using shape coefficients calculated with respect to fish length and the data were plotted on a modified universal graph (r bs =k 2 versus L=k). Weights were obtained from length weight regressions, and densities were assumed to be close to seawater. It was found that the shape coefficient as calculated in this study did not provide sufficient correction to narrow the gap in the htsi L relationship between gadoid and deep-water whiptails and oreos. Shape correction appears to be a more complicated matter than was presumed. Table 3. A comparison of the swimbladder surface area and the whole-fish oil content (Vlieg, 1988) for fish species inhabiting different depth ranges off New Zealand. X z is the weighted-mean depth of occurrence for adults and the depth ranges are the approximate 5% quartiles of the depth distributions for adult fish (Anderson et al., 1998). A sb =L 2 is the swimbladder surface area normalized to the square of fish length. The species were listed only if oil-content data were available and so were a subset of species used in swimbladder modelling (Table 1). NA indicates data not available. Common name Species X z (range) m A sb /L 2 X Oil (range) % Orange roughy Hoplostethus atlanticus 1112 ( þ) NA 17.6 ( ) Black oreo Allocyttus niger 924 ( ) ( ) Smooth oreo Pseudocyttus maculates 1101 ( þ) ( ) Javelinfish Lepidorhynchus denticulatus 629 ( ) ( ) Frostfish Lepidopus caudatus 237 (50 550) ( ) Lookdown dory Cyttus traversi 511 ( ) ( ) Barracouta Thyrsites atun 182 (0 450) ( ) Hake Merluccius australis 665 ( ) ( ) Southern blue Whiting Micromesistius australis 503 ( ) ( ) Hoki Macruronus novaezelandiae 651 ( ) ( ) Ridge-scaled rattail Macrourus carinatus 1164 ( þ) ( ) Red cod Pseudophyycis bachus 250 (50 500) ( ) Ling Genypterus blacodes 481 (50 850) ( )
8 426 S. McClatchie et al. Figure 5. The allometric relationship between a measure of swimbladder cross-section and fish size (total fish length for hoki and smooth oreos, or fork length for hake, Merluccius australis, and pollack, Pollachius pollachius). The heavy solid line in the lower panel is the isometric relationship (y ¼ aw b, where b ¼ 1). Curves are plotted in the lower panel only for species with slopes significantly different from b ¼ 1 ðp \ 0:05Þ. Species codes in the legend are given in Table 1.
9 A requiem for the use of 20 log 10 Length 427 Discussion The results from the swimbladder-modelling data showed that five of the 10 species did not conform to the 20 log 10 L relationship. How general is this result? McClatchie et al. (1996a) reported the slopes and the 95% confidence intervals on the slopes of the TS max L regressions for 26 species. Of these 26 slopes, 19 had confidence intervals indicating that the slope did not fit the 20 log 10 L relationship. This suggests that many deviations from the 20 log 10 L relationship will be found as more data are collected on htsi L relationships for a wider variety of species. The idea that swimbladders of mesopelagic fish are, in general, smaller than those of more shallow-living species was advanced by Marshall (1979). He did not provide empirical data to support the claim, but relied on calculations of the volume of air in the swimbladder that would be required to provide neutral buoyancy (Harden- Jones and Marshall, 1953). Koslow et al. (1997) repeated the claim for small swimbladders when trying to explain observations of lower-than-expected TS of mesopelagic fish calculated from the regressions of Foote (1987, Table 2, pp. 983). However, the generalization that deep-water fish have smaller swimbladders, and hence smaller TS, is not well supported by the evidence presented in this study. Nevertheless, it appears to be true that the TS of some deep-water fish is smaller or, more accurately, that the TS max of deepwater fish of the same size at the same frequency is lower than that of shallow-living fish. The explanation for this phenomenon can reasonably be attributed to the peculiar morphology of the deep-water fish, mainly whiptails and oreo-type forms, which were examined. These morphotypes are among the commonest in our deep-water ( m) fish fauna. It is not claimed, however, that all the deep-water fish have lower TS. Another consequence of this un-cod-like morphology is that the scaling of the TS length regression is different and deviates from the rule of scaling by L 2.It would seem that the differences in relative swimbladder size are more clearly related to morphology than to the depth. A challenge remains to explain fully as to why the htsi of deep-water fish are lower. It has been shown that the difference is partly due to morphology. How the allometry of growth in swimbladder length, swimbladder crosssection and fish length combine to affect the TS of deepwater fish compared with other species is a subject that could be explored in the future work. The differences observed in this article show that gadoid-like htsi L relationships cannot be extrapolated to these deep-sea fish. It would seem that whenever new TS data are collected, the empirical TS length relationship should be established rather than a priori fitting the 20 log 10 L relationship to the data. Authors of htsi L regressions should also state as to what kind of regression they used, as the slopes can be quite different depending on the least-squares minimization applied. Acknowledgements Preparation of swimbladder casts was performed with impressive dedication at sea and in the laboratory by Paul Grimes and Alan Hart. We thank Brian Bull for guidance with the statistical analyses and Richard Barr for a helpful review of an early draft. We thank Lars Rudstam and Ian H. McQuinn for their constructive reviews on behalf of the journal. This work was funded in part by NZ Ministry of Fisheries project code OEO References Anderson, O., Bagley, N., Hurst, R., Francis, M., Clark, M., and McMillan, P Atlas of New Zealand fish and squid distributions from research bottom trawls. National Institute of Water and Atmospheric Research Technical Report, 42. Benoit-Bird, K., and Au, W Target strength measurements of Hawaiian mesopelagic boundary community animals. 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