Appendix A. Table A1 shows the definitions of the VE variables along with the transformation details, Table A2 the transformation trials for the VI data, and Table A3 the variables retained by forward selection.
TABLE A1. Definitions, transformations, and skewness values of the VE variables (variables describing echo shapes).
Variable name 
Definition 
Transformation 
Skewness 

NewAlt 
The computed altitude 
Double Sqrt 
1.29 

Pmx.sE1 
Point of maximum found in the smoothed E1 
Double Sqrt 
1.24 

Pmn.s 
Point of minimum found between smoothed E1 and E2 
Sqrt 
1.26 

Pmx.sE2 
Point of maximum found in the smoothed E2 
Double Sqrt 
1.36 

Vmx.sE1 
Maximum value in the smoothed E1 
None 
0.09 

Vmn.s 
Minimum value found between smoothed E1 and E2 
Double Sqrt 
3.48 

Vmx.sE2 
Maximum value in the smoothed E2 
Double Sqrt 
4.18 

DRSx 
Time distance between rise and set area centroids of E1 
None 
0.72 

DRSy 
Intensity distance between rise and set area centroids of E1 
None 
0.14 

Area.R 
Area below the curve of E1 rise section 
Double Sqrt 
1.60 

Area.S 
Area below the curve of E1 set section 
Double Sqrt 
1.48 

Area.E2 
Area below the curve of E2 rise section 
Double Sqrt 
11.78 

Area.RE1 
Proportion between E1 rise and E1 total area 
None 
0.10 

Area.RE2 
Proportion between E1 rise and E2 rise area 
Double Sqrt 
49.80 

Time.R 
Time laps of E1 rise section 
Sqrt 
1.15 

Time.S 
Time laps of E1 set section 
Double Sqrt 
2.06 

Time.E2 
Time laps of E2 rise section 
Double Sqrt 
4.79 

Time.RE1 
Proportion between E1 rise and E1 total time laps 
Log 
0.26 

Time.RE2 
Proportion between E1 rise and E2 rise time laps 
Double Sqrt 
6.72 

Var 
E1 variance (second statistical moment) 
Double Sqrt 
2.25 

Skew 
E1 skewness (derived from third statistical moment) 
Log 
0.20 

Histo1 
1^{st} histogram class of E1 intensities, based on matrix max 
Double Sqrt 
1.60 

Histo2 
2^{nd} histogram class of E1 intensities, based on matrix max 
Double Sqrt 
1.07 

Histo3 
3^{rd} histogram class of E1 intensities, based on matrix max 
Log 
0.58 

Histo4 
4^{th} histogram class of E1 intensities, based on matrix max 
Double Sqrt 
2.28 

Histo5 
5^{th} histogram class of E1 intensities, based on matrix max 
Double Sqrt 
13.94 

Histo6 
6^{th} histogram class of E1 intensities, based on matrix max 
Double Sqrt 
32.86 

Histo7 
7^{th} histogram class of E1 intensities, based on matrix max 
Double Sqrt 
69.48 

Notes: The VE variables used in our analyses were selected out of a larger set of 66 variables in such way as to minimize collinearity among the variables. Then, out of four transformations (none, log, sqrt, and double sqrt), the transformation producing the lowest skewness values was applied to each of these variables. For all rising, setting, and complete sections found in our backscatters, the areas under the curves and the time spent were calculated. The following area and time spent proportions were also calculated: E1 rise / E1 complete and E1 rise / E2 rise. The points and values of maximum intensity found in E1 and E2, in both the original and smoothed curves, and the point and value of minimum intensity found between these maxima were also described. Finally, the statistical moments, a 7class histogram of E1 intensity values, and the distances in the x and y directions, between the centroids of the E1 rising and setting sections, were calculated.
TABLE A2. Transformation trials for the VI data table and subtables.


Second transformation 


Second transformation 

Table types 
First transformation 
None 
Arcsine 
Hellinger 
Table types 
First transformation 
None 
Arcsine 
Hellinger 
STB 
None 
2.05 
1.30 
1.05 
1–4 m 
None 
10.62 
7.70 
7.49 
Sqrt 
1.07 
0.69 
0.57 
Sqrt 
7.51 
6.06 
5.82 

Double Sqrt 
0.69 
0.44 
0.62 
Double Sqrt 
5.95 
5.51 
5.58 

Log 
1.93 
— 
— 
Log 
10.51 
— 
— 

Mod. Arcsine 
1.13 
— 
— 
Mod. Arcsine 
7.57 
— 
— 

BEST 
None 
6.04 
3.96 
3.81 
4–7 m 
None 
4.66 
3.32 
3.09 
Sqrt 
3.82 
2.75 
2.61 
Sqrt 
3.14 
2.58 
2.48 

Double Sqrt 
2.65 
2.40 
2.55 
Double Sqrt 
2.50 
2.37 
2.56 

Log 
5.96 
— 
— 
Log 
4.61 
— 
— 

Mod. Arcsine 
3.86 
— 
— 
Mod. Arcsine 
3.15 
— 
— 

ALL 
None 
13.47 
8.89 
8.52 
7–10 m 
None 
3.06 
2.32 
2.17 
Sqrt 
8.79 
6.66 
6.31 
Sqrt 
2.19 
1.87 
1.70 

Double Sqrt 
6.50 
5.99 
6.09 
Double Sqrt 
1.74 
1.68 
1.66 

Log 
13.36 
— 
—  Log 
3.03 
— 
— 

Mod. Arcsine 
8.86 
— 
— 
Mod. Arcsine 
2.21 
— 
— 

Notes: The presented values are the means of all skewness values computed on all VI data tables after different sequences of transformations. The lowest (best) skewness value for each data subset is in bold. Illogical transformations were not calculated (—). In the first set of transformation, either no transformation (None) was applied, or the effect of high intensity outliers on the distribution was reduced through a square root (Sqrt), double square root (Double Sqrt), log (Log), or modified arsine transformation (Mod.Arcsine). This modified form used the table maximum as the denominator in the calculation of proportions, prior to computing the square root and then the arcsine, instead of the object’s maximum in the ordinary arcsine transformation (Sokal and Rohlf 1995). With this modification, all these transformations conserved both the strength and shape information found in backscatters. In a second step, on all the newly transformed tables, we performed either no transformation (None), an ordinary arcsine transformation (Arcsine: arcsin(y/y_{max})^{0.5}), Sokal and Rohlf 1995), or a Hellinger transformation (Hellinger: Legendre and Gallagher 2001). The last two removed the overall intensity of the signal and preserved only the shape information of the sonar returns. STB, BEST, 1–4 m, 4–7 m, and 7–10 m are subtables of ALL, which refers to the complete data set. The STB subtable contained only the echoes acquired while the visibility was optimal and the remotely operated vehicle was in a stable position, hovering at low altitude over the selected habitat. The BEST subtable contained only the best transect for each habitat type. The 1–4 m, 4–7 m, and 7–10 m subtables contained echoes acquired at different altitude ranges, respectively 1 to 4, 4 to 7, and 7 to 10 m.
TABLE A3. Variables retained by forward selection, making the FWD variable sets.
Method 
Table type 
Selected variables 

VI 
STB 
Int4650, Int2630, Int8185, Int4145, Int7175, Int15, Int1115, Int3135 

BEST 
Int6165, Int3135, Int9195, Int2125 

ALL 
Int5155, Int7175, Int2630, Int4145, Int1115 

1–4 m 
Int5560, Int4145, Int7175, Int2630, Int1115 

4–7 m 
Int5155, Int2630, Int171175, Int610, Int101105 

7–10 m 
Int181185, Int3135, Int5660, Int1115, Int96100, Int186190, Int206210 

VE 
STB 
Skew, Vmn.s, NewAlt, Histo1, Pmn.s, Time.R, Time.RE1, Histo4, Time.S, DRSx 

BEST 
DRSx, Vmx.sE1, Vmx.sE2, NewAlt, Var 

ALL 
Skew, Vmn.s, Pmx.sE1, NewAlt, Vmx.sE2, DRSx 

1–4 m 
DRSx, Vmn.s, Pmx.sE1, Vmx.sE2, Skew, NewAlt, Histo1 

4–7 m 
Skew, Histo1, Vmx.sE2, Time.RE1, Pmx.sE2, DRSx, Pmn.s 

7–10 m 
Histo1, Skew, DRSx, Vmx.sE1, Time.RE1, Time.R, Time.S 

VT 
STB 
Int4650, Int2630, Vmn.s, Int7175, NewAlt, Skew, Int15, Int4145, Int8185, DRSx, Int1620, Pmn.s 

BEST 
DRSx, Int3135, Vmx.sE2, Vmx.sE1, NewAlt, Int9195 

ALL 
Int5155, Vmn.s, DRSx, Vmx.sE1, Int7175, Int4145, Pmx.sE1, Histo2 

1–4 m 
Int5660, Vmn.s, Skew, Int4145, Int2125, Vmx.sE2, Int7175, Pmx.sE1 

4–7 m 
Skew, Int610, DRSx, Int2630, Int171175, NewAlt, Int106110, Int5155, Int2125, Vmx.sE2, Vmn.s 

7–10 m 
Int181185, Skew, DRSx, Int3135, Int7175, Vmx.sE1, Time.R, Int291295, Time.RE1 

Notes: The STB, BEST, 1–4, 4–7, and 7–10 subtables are described in the notes of Table A2. Based on their appearance frequencies, the VE variables “DRSx”, “Histo1”, “Skew”, “time.RE1”, “Vmn.s”, “Vmx.sE1”, “Vmx.sE2”, “Newalt” were selected to be included in the SEL variable set. For the VI set, the distribution of the variables selected by forward selection showed that 20% of the variables were describing the rise area of the first echo, and 60% for the set area. Consequently, based on these ratios and on the variable appearance frequencies, “Int1115”, “Int2125”, “Int3135”, “Int4650”, “Int5660”, “Int7175”, “Int9195”, and “Int181185” were also selected to be part of set SEL.
LITERATURE CITED
Legendre, P., and E. D. Gallagher. 2001. Ecologically meaningful transformations for ordination of species data. Oecologia 129:271–280.
Sokal, R. R., and F. J. Rohlf. 1995. Biometry – The principles and practice of statistics in biological research. Third edition. W. H. Freeman, New York, New York, USA.