Table 11. The first- and second-best ratios retrieved from the LDA ratio extractor of either head or body characters (see Table 1) alone or combined, used for pair-wise comparisons of all contemporary specimens from the four whitefish species of Lake Brienz. For some species comparisons only a subset of characters could be used (a-l); the respective characters that were excluded are listed at the end of the table. Only external characters were used for the LDA comparisons, since internal characters (gill raker and gill arch length) cannot be measured on live specimens, and are thus not informative to assign specimens to species in the field. Due to large size differences between the species the LDA ratios were calculated with three different datasets; once each with individuals larger or smaller than 163.5mm standard length and once with the full size ranges of all species. For the multi-species comparisons, only the comparisons that yielded distinguishing ratios are shown. δ is a measure of how good shape discriminates in comparison to size (i.e., the smaller the less allometry). Ratios marked with an asterisk * have very little (for the pairwise species comparisons not more than one specimen of one species overlaps with that of the other species) or no overlap and were thus eligible for use in the species key and the diagnoses.
Characters Species comparison Size range Best ratios Range species 1 Range species 2 Standard distance δ (Shape vs. size)
(a) PelvS, PecF1, DFAd, DFAe, DFPe, TL, SL, EH, SD, SW, INW, IOW (b) PelvFS, PelvFB, PecFB, DFPe, TL, EH, ED, SD, IOW (c) PelvFB, PelvFS, PelvF, PecF1, DFB, DFAe, DFPe, AFB, AFAe, AdFB, CF, PAdC, PreP, PreA, SL, TL, BD, PostD, DHL, ED, EH, ES, PostO, HD, MW, SN, SD, SW, IOW, INW (d) PecFB, PelvFB, PelvF, PelvFS, PecF1, DFAe, DFPe, AFAe, AdFB, PreP, CF, TL, PostD (e) ED, EH, HD, SD, SW, INW (f) PelvFB, PelvFS, PelvF, PecFB, DFAe, DFAd, DFPe, CF, PreP, SL, TL, ED, EH, MW, SD, SW, IOW, INW, ES (g) PelvFS, PecF1, PecFB, DFAd, DFPe, SL, TL, ED, EH, INW, CF (h) PelvS, PecF1, DFAd, DFAe, DFPe, TL, SL, EH, SD, SW, INW, IOW (i) PelvFS (j) PelvFB, PelvFS, PelvF, PecF1,DFAe, DFPe, AFB, AFAe,CF, SL, TL, BD, ED, EH, ES, PostO, HD, MW, SN, SD, SW, IOW, INW (k) PelvFS, PecF1, CF, SL, TL (l) PelvS, TL, INW
head + body C. albellus vs. C. alpinus (a) <163.5mm 1: PreA/LJ * 6.33-7.44 9.24-9.97 27.13 0.04
2: AFAe/M 1.65-2.25 2.58-2.63 25.94 0.04
body C. albellus vs. C. alpinus <163.5mm 1: PecF2/DFAd * 0.81-1.06 0.78-0.8 9.97 0.14
2: DHL/PreD 0.34-0.42 0.32-0.34 9.4 0.15
head C. albellus vs. C. alpinus <163.5mm 1: HD/LJ 1.30-1.55 1.77-1.92 15.43 0.02
2: IOW/UJW 0.89-1.30 1.20-1.26 14.14 0.02
head + body C. albellus vs. C. fatioi <163.5mm 1: PecF2/PreA * 0.22-0.28 0.2-0.22 5.78 0.16
2: DHL/PreP 0.31-0.38 0.30-0.32 4.49 0.2
body C. albellus vs. C. fatioi <163.5mm 1: PecF2/PreA * 0.22-0.28 0.2-0.22 6.76 0.17
2: DHL/TL 0.13-0.18 0.13-0.14 5.7 0.19
head C. albellus vs. C. fatioi <163.5mm 1: UJ/ES * 6.81-12.42 4.51-6.15 8.63 0.12
2: EH/HL * 0.27-0.31 0.23-0.27 7.3 0.14
head + body C. albellus vs. C. brienzii (b) <163.5mm 1: PreD/LJ * 3.99-4.68 5.05-5.57 47.9 0.01
2: M/ES * 5.35-9.76 3.31-4.37 47.63 0.01
body C. albellus vs. C. brienzii <163.5mm 1: PecF2/PreD * 0.36-0.45 0.29-0.32 15.95 0.06
2: DHL/TL 0.13-0.18 0.13-0.14 9.91 0.05
head C. albellus vs. C. brienzii <163.5mm 1: LJ/ES * 9.62-17.28 6.01-6.49 12.51 0.05
2: HL/UJ 2.87-3.5 3.19-3.6 8.87 0.04
Characters Species comparison Size range Best ratios Range species 1 Range species 2 Standard distance δ (Shape vs. size)
head + body C. alpinus vs. C. fatioi (b) >163.5mm 1: AFAe/UJ * 1.96-2.5 1.66-1.96 26.08 0.04
2: CL/PreA 0.14-0.18 0.17-0.21 26.46 0.04
body C. alpinus vs. C. fatioi >163.5mm 1: AFae/TL 0.1-0.11 0.09-0.1 13.41 0.11
2: CL/PreA 0.14-0.18 0.17-0.21 13.41 0.11
head C. alpinus vs. C. fatioi >163.5mm 1: HL/UJ * 3.55-3.93 3.13-3.55 11.51 0.07
2: LJW/UJW 0.33-0.44 0.38-0.55 11.02 0.07
head + body C. alpinus vs. C. brienzii (c) >163.5mm 1: CD/SW * 2.25-2.64 1.82-2.04 34.25 0.02
2: LJW/UJW * 0.33-0.44 0.45-0.55 33.91 0.02
body C. alpinus vs. C. brienzii (d) >163.5mm 1: DFAe/PAdC * 1.11-1.32 0.96-1.16 18.53 0.07
2: CD/AFB 0.61-0.68 0.52-0.62 18.31 0.07
head C. alpinus vs. C. brienzii (e) >163.5mm 1: LJW/UJW * 0.33-0.44 0.45-0.55 7.44 0.08
2: PostO/UJ 1.8-2.12 1.57-1.86 6.78 0.08
Characters Species comparison Size range Best ratios Range species 1 Range species 2 Standard distance δ (Shape vs. size)
head + body C. fatioi vs. C. brienzii (f) >163.5mm 1: CL/PAdC 0.71-0.86 0.66-0.76 7.46 0.08
2: BD/LJ 2.44-3.05 2.31-2.82 7.36 0.08
body C. fatioi vs. C. brienzii >163.5mm 1: CL/PAdC 0.71-0.86 0.66-0.76 6.04 0.1
2: CF/BD 0.87-1.13 0.93-1.12 5.92 0.1
head C. fatioi vs. C. brienzii >163.5mm 1: ED/M 1.03-1.19 1.04-1.57 3.58 0.18
2: HW/UJW 1.89-2.23 1.88-2.33 3.38 0.19
Characters Species comparison Size range Best ratios Range species 1 Range species 2 Standard distance δ (Shape vs. size)
head + body C. alpinus vs. other 3 species <163.5mm 1: DFAd/LJ * 2.57-2.58 1.6-2.1 23.47 0.03
2: AdFB/PAdC 0.26-0.28 0.21-0.42 22.66 0.03
head + body C. albellus vs. other 3 species <163.5mm 1: PostD/EH * 5.47-6.93 7.5-8.9 48.36 0.02
2: UJW/ES 4.88-9.3 3.41-5.31 48.13 0.02
head + body C. alpinus vs. C. fatioi + C. brienzii (g) >163.5mm 1: DFAe/UJ * 3.28-4.1 2.58-3.19 24.71 0.05
2: CD/SW * 2.25-2.64 1.76-2.27 24.37 0.05
Characters Species comparison Size range Best ratios Range species 1 Range species 2 Standard distance δ (Shape vs. size)
head + body C. albellus vs. C. alpinus (h) 100-290 1: PreD/LJ * 3.99-4.68 5.6-6.81 22.86 0.13
2: DFAe/UJ * 2.14-2.79 3.25-4.1 21.65 0.14
head C. albellus vs. C. alpinus 100-290 1: HD/UJ * 1.87-2.2 2.38-2.78 14.39 0.18
2: LJ/IOW * 1.53-1.99 1.33-1.57 13.25 0.19
head + body C. albellus vs. C. fatioi 100-290 1: PreP/EH * 6.56-7.98 8.94-11.43 15.95 0.13
2: CL/UJ 1.44-2.02 1.93-2.72 15.09 0.14
head + body C. albellus vs. C. brienzii (i) 100-290 1: PreD/EH * 6.1-7.58 8.12-10.32 50.86 0.04
2: CL/LJ 0.99-1.45 1.38-1.65 50.6 0.04
head C. albellus vs. C. brienzii 100-290 1: EH/HL * 0.27-0.31 0.22-0.27 9.33 0.18
2: LJ/ES 9.62-17.28 6.08-12.43 8.57 0.22
Characters Species comparison Size range Best ratios Range species 1 Range species 2 Standard distance δ (Shape vs. size)
head + body C. alpinus vs. C. brienzii (j) 100-290 1: DFAd/LJW * 9.84-14.82 6.05-8.91 20.72 0.03
2: DHL/LJ * 1.84-2.22 1.63-1.82 20.47 0.02
body C. alpinus vs. C. brienzii (k) 100-290 1: PecF2/DFAd * 0.74-0.85 0.85-1.03 87.52 <0.01
2: CD/PostD 0.17-0.2 0.15-0.18 87.48 <0.01
head C. alpinus vs. C. brienzii 100-290 1: HD/LJW * 6.72-9.39 5.23-6.66 11.94 0.04
2: HL/LJ * 2.54-2.96 2.19-2.47 11.61 0.04
head + body C. alpinus vs. C. fatioi (h) 100-290 1: DFAe/UJ * 3.25-4.1 2.45-3.17 18.98 0.03
2: PecF2/AFAe 1.24-1.47 1.37-1.63 18.63 0.03
body C. alpinus vs. C. fatioi 100-290 1: PecF2/DFAe 0.77-0.89 0.87-1.02 9.25 0.08
2: AFAe/PostD 0.27-0.32 0.22-0.29 8.71 0.08
head C. alpinus vs. C. fatioi 100-290 1: LJW/UJW 0.33-0.47 0.37-0.55 5.62 0.08
2: HL/UJ 3.43-3.93 3.13-3.63 4.98 0.08
Characters Species comparison Size range Best ratios Range species 1 Range species 2 Standard distance δ (Shape vs. size)
head + body C. fatioi vs. C. brienzii (l) 100-290 1: AFB/BD 0.45-0.67 0.44-0.58 28.19 <0.01
2: PreD/M 8.87-14.85 9.13-11.41 28.16 <0.01
body C. fatioi vs. C. brienzii 100-290 1: AFB/BD 0.45-0.67 0.44-0.58 2.76 0.05
2: PreP/PreA 0.58-0.65 0.57-0.64 2.51 0.05
head C. fatioi vs. C. brienzii 100-290 1: ED/M 1.04-1.57 1.03-1.28 1.72 0.1
2: SN/MW 2.09-2.63 1.78-2.87 1.52 0.1
Characters Species comparison Size range Best ratios Range species 1 Range species 2 Standard distance δ (Shape vs. size)
head + body C. albellus vs. other 3 species 100-290 1: PreD/EH * 6.1-7.58 8.12-10.5 10.89 0.16
2: CL/UJ 1.44-2.02 1.85-2.72 9.79 0.17
head + body C. alpinus vs. other 3 species 100-290 1: DFAe/UJ * 3.25-4.1 2.14-3.19 9.59 0.11
2: LJW/UJW 0.33-0.47 0.34-0.55 8.98 0.12