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Estimated values for VBGP resulting from bootstrapped ELEFAN GA analysis, estimated length (cm) at age (from 0 to 10) and Φ’ by sex, previous results from different geographical areas and age estimation methods (LFDA – length frequency distribution analysis; otolith)_ F – female; M – male; CS – combined sex_
| Methods | Area | Growth parameters | Mean parameter estimate | Sex | Longevity (years) |
|---|---|---|---|---|---|
| LFDA: ELEFAN-GA-Bootstrap (this study) | Eastern Atlantic | L∞(cm) | 161.2 (CS); 166.5 (M); 164.9 (F) | CS | 10 |
| k(year)−1 | 0.47 (CS); 0.31 (M); 0.33 (F) | ||||
| Φ′ | 3.97 (CS); 3.34 (M); 3.76 (F) | ||||
| tanchor(months) | 0.64 (CS); 0.62 (M); 0.71 (F) | ||||
| Sectioned Otoliths (McBride et al. 2008) | Northwest Atlantic | L∞(cm) | 170.1 (CS); 155.5 (M); 179.7 (F) | CS | 9 |
| k(year)−1 | 0.381 (CS); 0.44 (M); 0.32 (F) | ||||
| Φ′ | CS (4.04) | ||||
| t0(years) | –1.63 (CS); –1.64 (M); –1.91 (F) | ||||
| Whole Otoliths (Zischke et al. 2013) | Coral Sea off eastern Australia | L∞(cm) | 149.9 (CS); 141.7 (M); 155.4 (F) | CS | 7 |
| k(year)−1 | 1.58 (CS); 2.31 (M); 1.18 (F) | ||||
| Φ′ | CS (4.55) | ||||
| t0(years) | –0.17 (CS); 0.002 (M); –0.37 (F) | ||||
| Whole Otoliths (Hogarth 1976) | West Central Atlantic | L∞(cm) | 215.1 (CS) | CS | 4 |
| k(year)−1 | 0.152 (CS) | ||||
| Φ′ | 3.21 (CS) | ||||
| t0(years) | –3.67 (CS) | ||||
| Whole Otoliths (Kishore & Chin 2001) | West Central Atlantic | L∞(cm) | 153.97 (CS) | CS | 10 |
| k(year)−1 | 0.34 (CS) | ||||
| Φ′ | 3.76 (CS) | ||||
| t0(years) | –1.54 (CS) | ||||
| LFDA: MULTIFAN (Lee T.M. 2008) | waters off eastern Taiwan | L∞(cm) | 156.8 (CS) | CS | 9 |
| k(year)−1 | 0.245 (CS) | ||||
| Φ′ | 3.43 (CS) | ||||
| t0(years) | –1.63 (CS) |
Estimated values of fishing mortality obtained from the equation: fishing mortality rate (F), total mortality rate (Z), and natural mortality rate (M)_
| Method used to estimate M | Natural mortality | Method used to estimate Z | |||
|---|---|---|---|---|---|
| LCCC | Beverton and Holt (BH) | ||||
| M | Z | F | Z | F | |
| Gislason | 0.36 | 0.75 | 0.39 | 0.80 | 0.44 |
| ChenWatanabe | 0.67 | 0.08 | 0.13 | ||
| Brodziak_K | 0.37 | 0.38 | 0.43 | ||
| Pauly_Linf | 0.65 | 0.10 | 0.15 | ||
| Alverson_Carney | 0.33 | 0.42 | 0.47 | ||
| Then_1 | 0.64 | 0.12 | 0.17 | ||
| Then_2 | 0.44 | 0.31 | 0.36 | ||
| Hewitt Hoenig | 0.47 | 0.28 | 0.33 | ||
| Hoenig | 0.45 | 0.30 | 0.35 | ||
Wahoo fishery status in the Tropical Eastern Atlantic Ocean presented by LBB (Linf, Lc50, F/M, M/K, and B/B0 and B/BMSY and their respective 95% confidence intervals; numbers in parentheses) under different M scenarios_
| Scenarios | M/K* | Linf (CI) | M/K (CI) | F/M (CI) | Lc50 (CI) | B/BMSY (CI) | B/B0 (CI) | Stock status |
|---|---|---|---|---|---|---|---|---|
| M/K Median (Then_2) | 0.94 | 165 (164–167) | 0.89 (0.79–1.02) | 0.76 (0.48–1.1) | 115 (112–118) | 1.4 (0.38–3.1) | 0.58 (0.16–1.3) | Healthy |
| M/K Upper (Chen and Watanabe) | 1.42 | 165 (164–167) | 1.3 (1.17–1.44) | 0.4 (0.26–0.67) | 120 (116–124) | 1.9 (0.53–3.8) | 0.76 (0.21–1.6) | Healthy |
| M/K Lower (Alverson_Carney) | 0.70 | 164 (163–165) | 0.73 (0.57–0.86) | 1.48 (1–2.24) | 112 (109–115) | 1.3 (0.35–3.3) | 0.56 (0.15–1.4) | Healthy |
Von Bertalanffy growth parameter (VBGP) estimates generated by various length-frequency analysis programs for the wahoo stock sampled in the Eastern Atlantic_ Parameter estimates by different methods are presented with AIC and BIC values_ NB: ELEFAN-FI and SHEPHERD (ELEFAN and Shepherd methods in FiSAT II), ELEFAN-LFDA (ELEFAN method in LFDA v 5), ELEFAN-GA, ELEFAN-SA (TropFishR package) and ELEFAN-GA-Bootstrap, ELEFAN-SA-Bootstrap (fishboot package)_
| Methods | Parameter | Mean parameter estimate | AIC Score | BIC Score |
|---|---|---|---|---|
| ELEFAN-FI | L∞(cm) | 183.75 | −10602 | −10617 |
| k(year−1) | 0.69 | |||
| t0(years) | −0.518 | |||
| SHEPHERD | L∞(cm) | 175 | 987 | 965 |
| k(year−1) | 0.12 | |||
| t0(years) | −3.22 | |||
| ELEFAN-LFDA | L∞(cm) | 163.3 | −10583 | 10598 |
| k(year−1) | 0.57 | |||
| t0(years) | −0.652 | |||
| ELEFAN-G.A. | L∞(cm) | 159.94 | 805 | 790 |
| k(year−1) | 0.49 | |||
| tanchor(months) | 0.68 | |||
| ELEFAN-S.A. | L∞(cm) | 194.51 | −10309 | −10324 |
| k(year−1) | 0.08 | |||
| tanchor(months) | 0.54 | |||
| ELEFAN-SA-Bootstrap* | L∞(cm) | 201.56 | −10648 | −10663 |
| k(year−1) | 0.12 | |||
| tanchor(months) | 0.64 | |||
| ELEFAN-GA-Bootstrap* | L∞(cm) | 161.21 | −11407 | −11422 |
| k(year−1) | 0.47 | |||
| tanchor(months) | 0.64 |
Natural mortality (M) methods and equations used_ L∞, K and t0 are von Bertalanffy growth function parameters, Tmax is the maximum observed age, a and b are length–weight relationship parameters_ L50 is length at first maturation, L is the observed length, T is temperature (°C), and t is age_ In this study, the temperature was T = 18_43°C_
| Acronym | Equations | M by age | References |
|---|---|---|---|
| Gislason | ln (M )=0.55−1.61 ln (L)+1.44 ln (L)+ln (K ) | Yes | Gislason et al. 2010 |
| ChenWatanabe | Yes | Chen and Watanabe 1989 | |
| Brodziak_K | Yes | Brodziak et al. 2011 | |
| Pauly_Linf | No | Pauly, 1980 | |
| Alverson_Carney | No | Alverson and Carney, 1975 | |
| Then_1 | M = 4.899 *Tmax0.916 | No | Then et al. 2014 |
| Then_2 | M = 4.118 *K0.73*L∞−0.33 | No | Then et al. 2014 |
| Hewitt Hoenig | M = e1.44−0.98*ln (Tmax) | No | Hewitt and Hoenig 2005 |
| Hoenig | M = e1.46−0.101* ln (Tmax) | No | Hoenig 1983 |
Per-recruit results_ Current F/F0_1 and Current E references obtained for different Z and M parameters_ Stock state indication per M method; green color indicates healthy state, red indicates overfished state, and yellow indicates one of the two references indicating overfished state_
| Z-M | Current F | F0.1 | Fmax | Current F/F0.1 | Current E | Stock state indication | |
|---|---|---|---|---|---|---|---|
| LCCC-Gislason | F1 | 0.36 | 0.47 | 0.53 | 0.77 | 0.52 | Overfished in terms of E |
| LCCC-ChenWatanabe | F2 | 0.67 | 0.49 | 0.59 | 1.37 | 0.11 | Overfished in terms of F |
| LCCC-Brodziak_K | F3 | 0.37 | 0.46 | 0.53 | 0.80 | 0.51 | Overfished in terms of E |
| LCCC-Pauly_Linf | F4 | 0.65 | 0.49 | 0.59 | 1.33 | 0.14 | Overfished in terms of F |
| LCCC-Alverson_Carney | F5 | 0.33 | 0.47 | 0.53 | 0.70 | 0.56 | Overfished in terms of E |
| LCCC-Then_1 | F6 | 0.64 | 0.50 | 0.58 | 1.28 | 0.15 | Overfished in terms of F |
| LCCC-Then_2 | F7 | 0.44 | 0.46 | 0.53 | 0.96 | 0.41 | Healthy |
| LCCC-Hewitt Hoenig | F8 | 0.47 | 0.46 | 0.54 | 1.02 | 0.37 | Overfished in terms of F |
| LCCC-Hoenig | F9 | 0.45 | 0.46 | 0.54 | 0.98 | 0.39 | Healthy |
| BH-Gislason | F10 | 0.44 | 0.49 | 0.56 | 0.90 | 0.55 | Overfished in terms of E |
| BH-ChenWatanabe | F11 | 0.13 | 0.53 | 0.62 | 0.25 | 0.17 | Healthy |
| BH-Brodziak_K | F12 | 0.43 | 0.49 | 0.56 | 0.88 | 0.54 | Overfished in terms of E |
| BH-Pauly_Linf | F13 | 0.15 | 0.53 | 0.62 | 0.28 | 0.19 | Healthy |
| BH-Alverson_Carney | F14 | 0.47 | 0.49 | 0.56 | 0.96 | 0.59 | Overfished in terms of E |
| BH-Then_1 | F15 | 0.17 | 0.54 | 0.62 | 0.31 | 0.21 | Healthy |
| BH-Then_2 | F16 | 0.36 | 0.49 | 0.57 | 0.73 | 0.45 | Healthy |
| BH-Hewitt Hoenig | F17 | 0.33 | 0.49 | 0.58 | 0.67 | 0.41 | Healthy |
| BH-Hoenig | F18 | 0.35 | 0.49 | 0.58 | 0.71 | 0.43 | Healthy |
| Median-LCCC | 0.98 | 0.40 | Healthy | ||||
| Mean-LCCC | 1.02 | 0.35 | Overfished in terms of F | ||||
| Median-BH | 0.71 | 0.43 | Healthy | ||||
| Mean-BH | 0.63 | 0.39 | Healthy |