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A review of age and growth, reproductive biology, and demography of the white shark, Carcharodon carcharias Henry F. Mollet Moss Landing Marine Labs

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  • A review of age and growth, reproductive biology, and demography of the white shark, Carcharodon carchariasHenry F. MolletMoss Landing Marine Labs

  • **http://homepage.mac.com/mollet/Cc/Cc_litters.htmlTaiwan Oct 1997

    Japan Feb 1985Med Sea Summer 1934

  • **

    Update: White shark litter of 8; 50-60 cm TLTaiwan 13 October 1997 (Victor Lin p.c.)

  • **5.55 m TL Kin(-Town) white shark caught on 16 Feb 1985Uchida et al. (1987, 1996) assumed near-term embryos were aborted.192 eggcases of 3 types (66 + 20 + 101; 104, 33, and 14 g) weighing 9 kg in left uterus.Early-term more likely (Mollet et al. 2000).No blastodisc eggcases? Overlooked? How old? 66 - 192 days?

  • **Shortfin mako 3 cm TL embryos.How old?4(L) +5(R) blastodisc eggcases (3x10 cm) with 1 embryo each> 40 (3x5 cm) eggcases in each uterus with 16-20 eggs per capsule; plus empty eggcases produced before blastodisc eggcasesShell gland produces one eggcase/day (Gilmore 1993 for sandtiger)Suggested age is 40-50 days (Mollet et al. 2000)

  • **VBGF for 11 embryos and 20 free-swimmers L0 = - 0.060 m; L= 1.837 m; k = 0.977 yr-1; r2 = 0.873

    Chart1

    0-0.0597599135

    0.550.0307044673

    0.610.1168549006

    10.198897104

    1.050.2770269857

    1.10.3514311113

    1.270.4222871498

    1.30.4897642977

    1.3350.5540236833

    1.4350.6152187509

    1.440.6734956277

    1.4730.7289934728

    1.4080.7818448088

    1.4140.8321758391

    1.410.8801067487

    1.290.9257519915

    1.2190.9692205634

    1.3211.0106162626

    1.4481.0500379376

    1.3971.0875797231

    1.4731.1233312647

    1.4221.1573779334

    1.3211.1898010289

    1.2951.220677974

    1.321.2500824995

    1.461.2780848203

    1.471.3047518028

    1.221.330147125

    1.51.3543314281

    1.51.3773624617

    1.541.3992952213

    1.42018208

    1.4400729134

    1.4590152186

    1.4770542278

    1.4942330162

    1.510592605

    1.5261720589

    1.5410085801

    1.5551375967

    1.568592847

    1.5814064609

    1.5936090359

    1.6052297103

    1.6162962332

    1.6268350301

    1.6368712666

    1.6464289081

    1.6555307772

    1.6641986082

    1.672453099

    TL

    TL_VBGF

    Age (yr)

    TL (m)

    Sheet1

    HemiDateMonthTLReferenceIDMonthNorthernHemiSouthernHemiFreeSwimmersMBA1984&2004

    1217Nov8111.567.Paterson 86SH11.567

    2226Nov8211.867.Paterson 86SH11.867

    3226Nov8211.867.Paterson 86SH11.867

    4116Feb852.5710Uchida&87NH2.5710.00

    52Oct-Nov11.Bruce(92)SH11

    62Oct-Nov11.Bruce(92)SH11

    72Oct-Nov11.Bruce(92)SH11

    8212-Oct-9310.420.55Vlin_pcNH10.420.55

    91Summer19348.20.61Norman(37)NH8.20.61

    101Feb-Mar1988151Ebert_pcNH151.00

    1112Apr8616.0671.05Uchida&87NH16.0671.05

    122Jul16 199613.5161.1Cliffetal200SH13.5161.10

    132Mar 199421.51.27Stevens_pcFreeSwimmer21.51.27

    14114May9217.4521.3Uchida&96NH17.4521.30

    15125-Feb-0014.931.33514.931.335

    16122May925.71.Uchida& 96NH5.71

    17122May925.71.Uchida& 96NH5.71

    18122May925.71.Uchida& 96NH5.71

    19122May925.71.Uchida& 96NH5.71

    20122May9217.711.435Uchida& 96NH17.711.435

    21122May925.71.Uchida& 96NH5.71

    22213Nov9117.4331.44Francis 96SH17.4331.44

    23213Nov9117.433.Francis (95)SH17.433

    24122May925.71.Uchida& 96NH5.71

    25122May925.71.Uchida& 96NH5.71

    26122May925.71.Uchida& 96NH5.71

    27124Oct8122.771.473Cailliet#8FreeSwimmer22.771.473

    2813Sep7721.11.408SwiftFreeSwimmer21.11.408

    2913Oct7722.11.414SwiftFreeSwimmer22.11.414

    30127Jul7619.871.41SwiftFreeSwimmer19.871.41

    311June198118.51.29Cailliet#2FreeSwimmer18.51.29

    32117Jul8119.551.219JohnsonFreeSwimmer19.551.219

    33117Jul8119.551.321JohnsonFreeSwimmer19.551.321

    34112aug7620.391.448Sea_WorldFreeSwimmer20.391.448

    3513Jul7819.091.397Sea_WorldFreeSwimmer19.091.397

    36116Aug7820.521.473Sea_WorldFreeSwimmer20.521.473same as above?

    37125Jul8119.811.422Sea_WorldFreeSwimmer19.811.422

    3815jun8418.171.321SeigelFreeSwimmer18.171.321

    3914Jul8019.131.295JohnsonFreeSwimmer19.131.295

    40119May8417.131.32SeigelFreeSwimmer17.131.32

    412Dec198424.51.46Stevens_pcFreeSwimmer24.51.46

    42218Jan8225.581.47Bruce_pcFreeSwimmer25.581.47

    43125Aug8320.811.22C&P1985FreeSwimmer20.811.22

    4428-Nov-9917.301.5SH17.31.5

    45113-Sep-0021.471.5MBAFreeSwimmer21.471.50

    4619-Sep-8021.331.54MBAFreeSwimmer21.331.54

    HemiDateMonthTLReferenceIDMonthNorthernHemiSouthernHemiFreeSwimmersMBA

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    NorthernHemi

    SouthernHemi

    FreeSwimmers

    Month

    TL embryos or freeswimmers (m)

    Guesstimate of Gestation Period for White Shark

    VBGF

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    NorthernHemi

    SouthernHemi

    FreeSwimmers

    MBA1984&2004

    Month (6 and 18 = June 1 in NH)

    TL embryos or freeswimmers (m)

    Guesstimate of Gestation Period for White Shark

    Gompertz

    Raw data for VBGF fit to be done in Systat and Octave?

    VBGF with freeswimmersVBGF without freeswimmersVBGF without freeswimmersUsed old VBGF parameters to calculated shifted VBGFVBGF without freeswimmers

    Loo1.837297Loo2.185928N.S.!Loo2.185928Have to check using Systat once moreLoo2.185928N.S.

    Lo1.297284Lo1.297375Lo1.297375Lo-0.403771

    calcto=-1.252995767calcto=-1.2624218131

    k0.977224k0.713075k0.713075k0.713075

    4ln2/k2.83720899434ln2/k3.88821473514ln2/k3.88821473514ln2/k3.8882147351

    7ln2/k4.965115747ln2/k6.80437578647ln2/k6.80437578647ln2/k6.8043757864

    MonthAge (yr)TLAge (yr)VBGFITERATION LOSS PARAMETER VALUESAge (yr)VBGFITERATION LOSS PARAMETER VALUESAge (yr)VBGFMonthAge (yr)TLAge (yr)VBGFITERATION LOSS PARAMETER VALUES

    12.571-1.28580.000-1.50-0.5020 0.3069959D+01 0.1500D+010.1000D+010.9000D+00-1.50-0.4040 0.1071259D+01 0.1500D+010.1000D+010.1000D+010.00-0.4042.5710.21430.0000.00-0.4040 0.4758952D+00 0.1500D+010.0000D+000.1000D+01

    210.42-0.63170.550-1.45-0.3901 0.1295271D+01 0.1508D+010.1206D+010.8993D+00-1.45-0.3131 0.5304606D+00 0.1465D+010.1108D+010.9723D+000.05-0.31310.420.86830.5500.05-0.3131 0.4253137D+00 0.1603D+01-.4798D-010.1044D+01

    38.2-0.81670.610-1.40-0.2842 0.4560266D+00 0.1834D+010.1298D+010.1054D+01-1.40-0.2252 0.2574642D+00 0.1711D+010.1288D+010.1124D+010.10-0.2258.20.68330.6100.10-0.2262 0.2786008D+00 0.1719D+01-.3223D+000.1010D+01

    415-0.25001.000-1.35-0.1833 0.4251452D+00 0.1892D+010.1297D+010.8805D+00-1.35-0.1413 0.2513914D+00 0.1742D+010.1272D+010.1051D+010.15-0.141151.25001.0000.15-0.1413 0.2637131D+00 0.1875D+01-.5197D+000.8898D+00

    516.067-0.16111.050-1.30-0.0864 0.4119643D+00 0.1848D+010.1296D+010.9645D+00-1.30-0.0594 0.2476735D+00 0.1802D+010.1273D+010.9724D+000.20-0.05916.0671.33891.0500.20-0.0604 0.2466025D+00 0.1848D+01-.5191D+000.9437D+00

    613.516-0.37371.100-1.250.0055 0.4119127D+00 0.1848D+010.1297D+010.9649D+00-1.250.0195 0.2459332D+00 0.1911D+010.1284D+010.8674D+000.250.01913.5161.12631.1000.250.0195 0.2447982D+00 0.1856D+01-.4924D+000.9465D+00

    721.50.29171.270-1.200.0936 0.4118877D+00 0.1845D+010.1297D+010.9686D+00-1.200.0956 0.2437067D+00 0.1893D+010.1284D+010.8961D+000.300.09521.51.79171.2700.300.0956 0.2437970D+00 0.1875D+01-.4916D+000.9228D+00

    817.452-0.04571.300-1.150.1767 0.4118701D+00 0.1836D+010.1298D+010.9789D+00-1.150.1687 0.2418313D+00 0.1947D+010.1293D+010.8751D+000.350.16817.4521.45431.3000.350.1687 0.2423919D+00 0.1930D+01-.4731D+000.8719D+00

    914.93-0.25581.335-1.100.2558 0.4118655D+00 0.1838D+010.1297D+010.9769D+00-1.100.2398 0.2405273D+00 0.2022D+010.1295D+010.8072D+000.400.23914.931.24421.3350.400.2398 0.2404491D+00 0.2038D+01-.4269D+000.7877D+00

    1017.71-0.02421.435-1.050.3319 0.4118654D+00 0.1837D+010.1297D+010.9772D+00-1.050.3079 0.2399204D+00 0.2021D+010.1291D+010.8121D+000.450.30717.711.47581.4350.450.3079 0.2397844D+00 0.2051D+01-.4267D+000.7934D+00

    1117.433-0.04731.440-1.000.40210 0.4118654D+00 0.1837D+010.1297D+010.9772D+00-1.000.37310 0.2393492D+00 0.2069D+010.1293D+010.7770D+000.500.37317.4331.45281.4400.500.37310 0.2391730D+00 0.2081D+01-.4261D+000.7720D+00

    1222.770.39751.473Freeswimmers-0.950.47111 0.4118654D+00 0.1837D+010.1297D+010.9772D+00-0.950.43711 0.2391644D+00 0.2121D+010.1295D+010.7435D+000.550.4370.550.43611 0.2390241D+00 0.2121D+01-.4174D+000.7461D+00

    1321.10.25831.408Freeswimmers-0.900.536-0.900.49812 0.2389762D+00 0.2116D+010.1295D+010.7511D+000.600.4980.600.49812 0.2388878D+00 0.2129D+01-.4167D+000.7440D+00

    1422.10.34171.414Freeswimmers-0.850.598DEPENDENT VARIABLE IS TL-0.850.55713 0.2388371D+00 0.2165D+010.1297D+010.7239D+000.650.5570.650.55713 0.2387874D+00 0.2190D+01-.4017D+000.7099D+00

    1519.870.15581.410Freeswimmers-0.800.657-0.800.61414 0.2388102D+00 0.2185D+010.1297D+010.7140D+000.700.6140.700.61414 0.2387774D+00 0.2180D+01-.4048D+000.7165D+00

    1618.50.04171.290Freeswimmers-0.750.713MISSING DATA OR ESTIMATES REDUCED DEGREES OF FREEDOM-0.750.66915 0.2388097D+00 0.2188D+010.1297D+010.7120D+000.750.6690.750.66915 0.2387752D+00 0.2184D+01-.4042D+000.7141D+00

    1719.550.12921.219Freeswimmers-0.700.767-0.700.72216 0.2388095D+00 0.2186D+010.1297D+010.7130D+000.800.7220.800.72216 0.2387752D+00 0.2185D+01-.4038D+000.7134D+00

    1819.550.12921.321Freeswimmers-0.650.818SOURCE SUM-OF-SQUARES DF MEAN-SQUARE-0.650.77317 0.2388095D+00 0.2186D+010.1297D+010.7131D+000.850.7730.850.77317 0.2387752D+00 0.2186D+01-.4038D+000.7133D+00

    1920.390.19921.448Freeswimmers-0.600.867-0.600.8230.900.8230.900.82318 0.2387752D+00 0.2186D+01-.4038D+000.7133D+00

    2019.090.09081.397Freeswimmers-0.550.913REGRESSION 51.885063 3 17.295021-0.550.871DEPENDENT VARIABLE IS TL0.950.8710.950.871

    2120.520.21001.473Freeswimmers-0.500.957RESIDUAL 0.411865 28 0.014709-0.500.9171.000.9171.000.917DEPENDENT VARIABLE IS TL

    2219.810.15081.422Freeswimmers-0.450.999-0.450.961SOURCE SUM-OF-SQUARES DF MEAN-SQUARE1.050.9611.050.961

    2318.170.01421.321Freeswimmers-0.401.039TOTAL 52.296933 31-0.401.0041.101.0041.101.004SOURCE SUM-OF-SQUARES DF MEAN-SQUARE

    2419.130.09421.295Freeswimmers-0.351.077CORRECTED 3.255059 30-0.351.045REGRESSION 12.966238 3 4.3220791.151.0451.151.045

    2517.13-0.07251.320Freeswimmers-0.301.113-0.301.085RESIDUAL 0.238809 8 0.0298511.201.0851.201.085REGRESSION 12.966274 3 4.322091

    2624.50.54171.460Freeswimmers-0.251.148RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.992124-0.251.1241.251.1241.251.124RESIDUAL 0.238775 8 0.029847

    2725.580.63171.470Freeswimmers-0.201.181CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.873469-0.201.161TOTAL 13.205050 111.301.1611.301.161

    2820.810.23421.220Freeswimmers-0.151.212-0.151.197CORRECTED 2.024314 101.351.1971.351.197TOTAL 13.205050 11

    2917.3-0.05831.500Freeswimmers-0.101.242-0.101.2321.401.2321.401.232CORRECTED 2.024314 10

    3021.470.28891.500Freeswimmers-0.051.270PARAMETER ESTIMATE A.S.E. LOWER UPPER-0.051.265RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.9819151.451.2651.451.265

    3121.330.27781.540Freeswimmers0.001.297LOO 1.837297 0.197139 1.433476 2.2411180.001.297CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.8820291.501.2971.501.297RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.981918

    0.051.323LO 1.297284 0.023883 1.248362 1.3462070.051.3281.551.3281.551.328CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.882046

    0.101.348K 0.977224 0.234982 0.495886 1.4585620.101.3591.601.3591.601.358

    0.151.3710.151.388PARAMETER ESTIMATE A.S.E. LOWER UPPER1.651.3881.651.387

    0.201.3930.201.415LOO 2.185928 0.976994 -0.067024 4.4388801.701.4151.701.415PARAMETER ESTIMATE A.S.E. LOWER UPPER

    0.251.414ASYMPTOTIC CORRELATION MATRIX OF PARAMETERS0.251.442LO 1.297375 0.068165 1.140185 1.4545641.751.4421.751.442LOO 2.185631 0.975943 -0.064896 4.436159

    0.301.4350.301.469K 0.713075 0.513095 -0.470125 1.8962741.801.4691.801.468LO -0.403771 0.287318 -1.066328 0.258787

    0.351.454LOO LO K0.351.4941.851.4941.851.494K 0.713279 0.512814 -0.469273 1.895830

    0.401.4720.401.5181.901.5181.901.518

    0.451.489LOO 1.0000000.451.541ASYMPTOTIC CORRELATION MATRIX OF PARAMETERS1.951.5411.951.541

    0.501.506LO -0.255139 1.0000000.501.5642.001.5642.001.564ASYMPTOTIC CORRELATION MATRIX OF PARAMETERS

    0.551.522K -0.971124 0.392408 1.0000000.551.586LOO LO K2.051.5862.051.586

    0.601.5370.601.6072.101.6072.101.607LOO LO K

    0.651.5510.651.627LOO 1.0000002.151.6272.151.627

    0.701.5650.701.647LO 0.460802 1.0000002.201.6472.201.646LOO 1.000000

    0.751.5780.751.665K -0.986338 -0.339184 1.0000002.251.6652.251.665LO 0.650928 1.000000

    0.801.5900.801.6842.301.6842.301.684K -0.986316 -0.750630 1.000000

    0.851.6020.851.7012.351.7012.351.701

    0.901.6130.901.7182.401.7182.401.718

    0.951.6240.951.7352.451.7352.451.735

    1.001.6341.001.7502.501.7502.501.750

    2.551.766

    2.601.780

    2.651.795

    2.701.808

    2.751.821

    2.801.834

    2.851.847

    2.901.858

    2.951.870

    3.001.881

    VBGF

    MonthAge (yr)TLAge (yr)TL_VBGF

    12.5710.00.00-0.060

    210.420.65410.5500.050.031

    38.20.46910.6100.10.117

    4151.03581.0000.150.199

    516.0671.12471.0500.20.277

    613.5160.91211.1000.250.351

    721.51.57741.2700.30.422

    817.4521.24011.3000.350.490

    914.931.02991.3350.40.554

    1017.711.26161.4350.450.615

    1117.4331.23851.4400.50.673

    1222.771.68331.4730.550.729

    1321.11.54411.4080.60.782

    1422.11.62741.4140.650.832

    1519.871.44161.4100.70.880

    1618.51.32741.2900.750.926

    1719.551.41491.2190.80.969

    1819.551.41491.3210.851.011

    1920.391.48491.4480.91.050

    2019.091.37661.3970.951.088

    2120.521.49581.47311.123

    2219.811.43661.4221.051.157

    2318.171.29991.3211.11.190

    2419.131.37991.2951.151.221

    2517.131.21331.3201.21.250

    2624.51.82741.4601.251.278

    2725.581.91741.4701.31.305

    2820.811.51991.2201.351.330

    2917.31.22741.5001.41.354

    3021.471.57461.5001.451.377

    3121.331.56351.5401.51.399

    1.551.420

    1.61.440

    1.651.459

    1.71.477

    1.751.494

    1.81.511

    1.851.526

    1.91.541

    1.951.555

    21.569

    2.051.581

    2.11.594

    2.151.605

    2.21.616

    2.251.627

    2.31.637

    2.351.646

    2.41.656

    2.451.664

    2.51.672

    Gompertz

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    VBGF

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    VBGF

    TL

    0

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    TL

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    VBGF

    TL

    Cannot get different colors?

    TL

    TL_VBGF

    Age (yr)

    TL (m)

    TL_VBGF

    0000.0273854155

    000.550.0450431843

    000.610.0696520477

    0010.102037185

    001.050.1425657393

    001.10.1910975456

    001.270.2470091123

    001.30.3092760435

    001.3350.3765908308

    001.4350.4474921172

    001.440.520485881

    001.4730.5941457114

    001.4080.6671861322

    001.4140.7385084068

    001.410.8072218946

    001.290.8726459184

    001.2190.9342976261

    001.3210.9918709517

    001.4481.0452109361

    001.3971.0942866433

    001.4731.1391649338

    001.4221.1799865079

    001.3211.2169449766

    001.2951.2502692344

    001.321.2802090877

    001.461.3070238883

    001.471.3309738233

    001.221.3523134661

    001.51.3712872001

    001.51.3881261515

    001.541.4030463115

    01.4162475718

    01.4279134445

    01.4382112806

    01.4472928373

    01.4552950776

    01.4623411138

    01.4685412266

    01.47399391

    01.4787869077

    01.4829982149

    01.4866970298

    01.4899446452

    01.4927952744

    01.4952968097

    01.4974915137

    01.4994166464

    01.5011050306

    01.5025855599

    01.503883653

    01.5050216599

    TL

    TL_VBGF

    TL

    TL_Gompertz

    Age (yr)

    TL (m)

    Loo1.837297Lo1.324425Loo=1.5130831691

    Lo1.297284G0.133171t_inflexion=-0.7612144046

    k0.977224k2.648559

    t to reach 95% Loo=1.813OKt to reach 95% Loo=0.360OK

    4ln2/k2.837OFF4ln2/k1.047OFF

    5ln2/k

    VBGF RepeatGompertzAge (yr)L_VBGFL_Gompertz

    -1.50-0.50160.0013-27.30%0.08%

    ITERATION LOSS PARAMETER VALUESITERATION LOSS PARAMETER VALUES-1.45-0.39010.0031-21.23%0.20%

    0 0.2909906D+01 0.2000D+010.1000D+010.5000D+000 0.2610452D+01 0.1000D+010.1000D+010.1000D+01-1.40-0.28380.0066-15.45%0.44%

    1 0.1089232D+01 0.2016D+010.1322D+010.5299D+001 0.2059129D+01 0.1337D+010.9910D+000.9840D+00-1.35-0.18270.0130-9.94%0.86%

    2 0.5306960D+00 0.2136D+010.1344D+010.7390D+002 0.1426437D+01 0.1390D+010.8107D+000.8204D+00-1.30-0.08640.0235-4.70%1.55%

    3 0.4228646D+00 0.2024D+010.1289D+010.8103D+003 0.6394888D+00 0.1277D+010.6383D+000.9760D+00-1.250.00540.03930.29%2.60%

    4 0.4211642D+00 0.1936D+010.1287D+010.8413D+004 0.5437493D+00 0.1269D+010.4086D+000.1171D+01-1.200.09270.06195.05%4.09%

    5 0.4168476D+00 0.1955D+010.1291D+010.8453D+005 0.5235287D+00 0.1269D+010.4506D+000.1205D+01-1.150.17590.09209.58%6.08%

    6 0.4133764D+00 0.1904D+010.1296D+010.9093D+006 0.4570713D+00 0.1279D+010.3155D+000.1486D+01-1.100.25510.130213.89%8.60%

    7 0.4122685D+00 0.1842D+010.1298D+010.9670D+007 0.4350041D+00 0.1292D+010.2322D+000.1718D+01-1.050.33060.176517.99%11.66%

    8 0.4119590D+00 0.1853D+010.1297D+010.9586D+008 0.3912269D+00 0.1303D+010.2376D+000.1872D+01-1.000.40240.230421.90%15.23%

    9 0.4118745D+00 0.1836D+010.1297D+010.9778D+009 0.3680502D+00 0.1315D+010.1783D+000.2176D+01-0.950.47090.291025.63%19.23%

    10 0.4118657D+00 0.1838D+010.1297D+010.9766D+0010 0.3575822D+00 0.1323D+010.1271D+000.2616D+01-0.900.53600.357029.17%23.59%

    11 0.4118654D+00 0.1837D+010.1297D+010.9772D+0011 0.3544765D+00 0.1321D+010.1384D+000.2607D+01-0.850.59810.427032.55%28.22%

    12 0.4118654D+00 0.1837D+010.1297D+010.9772D+0012 0.3542143D+00 0.1324D+010.1356D+000.2624D+01-0.800.65720.499635.77%33.02%

    13 0.4118654D+00 0.1837D+010.1297D+010.9772D+0013 0.3541890D+00 0.1324D+010.1339D+000.2640D+01-0.750.71350.573238.83%37.88%

    14 0.3541856D+00 0.1324D+010.1332D+000.2648D+01-0.700.76700.646541.75%42.73%

    DEPENDENT VARIABLE IS TL15 0.3541854D+00 0.1324D+010.1332D+000.2649D+01-0.650.81810.718444.53%47.48%

    16 0.3541854D+00 0.1324D+010.1332D+000.2649D+01-0.600.86670.787947.17%52.08%

    SOURCE SUM-OF-SQUARES DF MEAN-SQUARE-0.550.91300.854449.69%56.47%

    DEPENDENT VARIABLE IS TL-0.500.95700.917152.09%60.61%

    REGRESSION 51.885065 3 17.295022-0.450.99900.975954.37%64.50%

    RESIDUAL 0.411865 28 0.014709SOURCE SUM-OF-SQUARES DF MEAN-SQUARE-0.401.03901.030456.55%68.10%

    -0.351.07711.080758.62%71.43%

    TOTAL 52.296933 31REGRESSION 51.942758 3 17.314253-0.301.11331.126860.60%74.47%

    CORRECTED 3.255059 30RESIDUAL 0.354185 28 0.012649-0.251.14781.168862.47%77.24%

    -0.201.18071.206864.26%79.76%

    RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.992124TOTAL 52.296933 31-0.151.21201.241165.97%82.03%

    CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.873469CORRECTED 3.255059 30-0.101.24181.272067.59%84.07%

    -0.051.27021.299769.14%85.90%

    RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.9932270.001.29731.324470.61%87.53%

    PARAMETER ESTIMATE A.S.E. LOWER UPPERCORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.8911890.051.32301.346572.01%88.99%

    LOO 1.837297 0.197139 1.433476 2.2411170.101.34761.366173.34%90.29%

    LO 1.297284 0.023883 1.248362 1.3462070.151.37091.383574.62%91.44%

    K 0.977224 0.234982 0.495886 1.458562PARAMETER ESTIMATE A.S.E. LOWER UPPER0.201.39321.399075.83%92.46%

    LO 1.324425 0.024032 1.275198 1.3736530.251.41431.412676.98%93.36%

    G 0.133171 0.052059 0.026533 0.2398080.301.43451.424778.08%94.16%

    ASYMPTOTIC CORRELATION MATRIX OF PARAMETERSK 2.648559 0.529647 1.563625 3.7334920.351.45371.435479.12%94.87%

    0.401.47201.444880.12%95.49%

    LOO LO K0.451.48941.453181.07%96.04%

    ASYMPTOTIC CORRELATION MATRIX OF PARAMETERS0.501.50601.460481.97%96.52%

    LOO 1.0000000.551.52181.466982.83%96.94%

    LO -0.255139 1.000000LO G K0.601.53691.472583.65%97.32%

    K -0.971124 0.392408 1.0000000.651.55121.477584.43%97.65%

    LO 1.0000000.701.56481.481985.17%97.94%

    G -0.504873 1.0000000.751.57781.485785.88%98.19%

    K 0.498843 -0.936806 1.0000000.801.59021.489186.55%98.41%

    0.851.60201.492087.19%98.61%

    0.901.61321.494687.80%98.78%

    0.951.62391.496988.38%98.93%

    1.001.63411.498988.94%99.06%

    1.051.64381.500689.47%99.18%

    1.101.65301.502289.97%99.28%

    1.151.66181.503590.45%99.37%

    1.201.67011.504790.90%99.45%

    1.251.67811.505791.34%99.52%

    1.301.68571.506791.75%99.58%

    1.351.69291.507592.14%99.63%

    Lo1.3244251.401.69981.508192.52%99.67%

    G0.1331711.451.70641.508892.87%99.71%

    k2.6485591.501.71261.509393.21%99.75%

    1.551.71861.509893.54%99.78%

    1.601.72421.510293.85%99.81%

    1.651.72961.510594.14%99.83%

    1.701.73481.510994.42%99.85%

    Gompertz1.751.73961.511194.68%99.87%

    MonthAge (yr)TLAge (yr)TL_Gompertz1.801.74431.511494.94%99.89%

    12.5710.00.00.000.02738541551.851.74871.511695.18%99.90%

    210.420.65410.5500.050.04504318431.901.75301.511895.41%99.91%

    38.20.46910.6100.100.06965204771.951.75701.511995.63%99.92%

    4151.03581.0000.150.1020371852.001.76081.512195.84%99.93%

    516.0671.12471.0500.200.14256573932.051.76451.512296.04%99.94%

    613.5160.91211.1000.250.19109754562.101.76791.512396.22%99.95%

    721.51.57741.2700.300.24700911232.151.77121.512496.40%99.96%

    817.4521.24011.3000.350.30927604352.201.77441.512596.58%99.96%

    914.931.02991.3350.400.37659083082.251.77741.512696.74%99.97%

    1017.711.26161.4350.450.44749211722.301.78021.512696.89%99.97%

    1117.4331.23851.4400.500.5204858812.351.78301.512797.04%99.97%

    1222.771.68331.4730.550.59414571142.401.78561.512797.18%99.98%

    1321.11.54411.4080.600.66718613222.451.78801.512897.32%99.98%

    1422.11.62741.4140.650.73850840682.501.79041.512897.45%99.98%

    1519.871.44161.4100.700.8072218946

    1618.51.32741.2900.750.8726459184

    1719.551.41491.2190.800.9342976261

    1819.551.41491.3210.850.9918709517

    1920.391.48491.4480.901.0452109361

    2019.091.37661.3970.951.0942866433

    2120.521.49581.4731.001.1391649338

    2219.811.43661.4221.051.1799865079

    2318.171.29991.3211.101.2169449766

    2419.131.37991.2951.151.2502692344

    2517.131.21331.3201.201.2802090877

    2624.51.82741.4601.251.3070238883

    2725.581.91741.4701.301.3309738233

    2820.811.51991.2201.351.3523134661

    2917.31.22741.5001.401.3712872001

    3021.471.57461.5001.451.3881261515

    3121.331.56351.5401.501.4030463115

    1.551.4162475718

    1.601.4279134445

    1.651.4382112806

    1.701.4472928373

    1.751.4552950776

    1.801.4623411138

    1.851.4685412266

    1.901.47399391

    1.951.4787869077

    2.001.4829982149

    2.051.4866970298

    2.101.4899446452

    2.151.4927952744

    2.201.4952968097

    2.251.4974915137

    2.301.4994166464

    2.351.5011050306

    2.401.5025855599

    2.451.503883653

    2.501.5050216599

    2.551.5060192228

    2.601.5068935973

    2.651.5076599368

    2.701.5083315444

    2.751.5089200956

    2.801.5094358352

    2.851.5098877504

    2.901.5102837239

    2.951.5106306686

    3.001.5109346459

    3.051.5112009699

    3.101.5114342993

    3.151.5116387175

    3.201.5118178036

    3.251.5119746944

    3.301.5121121387

    3.351.5122325456

    3.401.5123380258

    3.451.512430429

    3.501.5125113756

    3.551.5125822857

    3.601.5126444032

    3.651.5126988182

    3.701.5127464855

    3.751.5127882416

    3.801.5128248195

    3.851.5128568612

    3.901.5128849293

    3.951.5129095163

    4.001.5129310541

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    L_VBGF

    L_Gompertz

    000

    000.55

    000.61

    001

    001.05

    001.1

    001.27

    001.3

    001.335

    001.435

    001.44

    001.473

    001.408

    001.414

    001.41

    001.29

    001.219

    001.321

    001.448

    001.397

    001.473

    001.422

    001.321

    001.295

    001.32

    001.46

    001.47

    001.22

    001.5

    001.5

    001.54

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    L_VBGF

    L_Gompertz

    TL

    TL

    TL_Gompertz

    Age (yr)

    TL (m)

    TL_Gompertz

  • **Gompertz for 11 embryos and 20 free-swimmers L0 = 0.027 m; L= 1.513 m; k = 2.649 yr-1; r2 = 0.891

    Chart4

    00.0273854155

    0.550.0450431843

    0.610.0696520477

    10.102037185

    1.050.1425657393

    1.10.1910975456

    1.270.2470091123

    1.30.3092760435

    1.3350.3765908308

    1.4350.4474921172

    1.440.520485881

    1.4730.5941457114

    1.4080.6671861322

    1.4140.7385084068

    1.410.8072218946

    1.290.8726459184

    1.2190.9342976261

    1.3210.9918709517

    1.4481.0452109361

    1.3971.0942866433

    1.4731.1391649338

    1.4221.1799865079

    1.3211.2169449766

    1.2951.2502692344

    1.321.2802090877

    1.461.3070238883

    1.471.3309738233

    1.221.3523134661

    1.51.3712872001

    1.51.3881261515

    1.541.4030463115

    1.4162475718

    1.4279134445

    1.4382112806

    1.4472928373

    1.4552950776

    1.4623411138

    1.4685412266

    1.47399391

    1.4787869077

    1.4829982149

    1.4866970298

    1.4899446452

    1.4927952744

    1.4952968097

    1.4974915137

    1.4994166464

    1.5011050306

    1.5025855599

    1.503883653

    1.5050216599

    TL

    TL_Gompertz

    Age (yr)

    TL (m)

    Sheet1

    HemiDateMonthTLReferenceIDMonthNorthernHemiSouthernHemiFreeSwimmersMBA1984&2004

    1217Nov8111.567.Paterson 86SH11.567

    2226Nov8211.867.Paterson 86SH11.867

    3226Nov8211.867.Paterson 86SH11.867

    4116Feb852.5710Uchida&87NH2.5710.00

    52Oct-Nov11.Bruce(92)SH11

    62Oct-Nov11.Bruce(92)SH11

    72Oct-Nov11.Bruce(92)SH11

    8212-Oct-9310.420.55Vlin_pcNH10.420.55

    91Summer19348.20.61Norman(37)NH8.20.61

    101Feb-Mar1988151Ebert_pcNH151.00

    1112Apr8616.0671.05Uchida&87NH16.0671.05

    122Jul16 199613.5161.1Cliffetal200SH13.5161.10

    132Mar 199421.51.27Stevens_pcFreeSwimmer21.51.27

    14114May9217.4521.3Uchida&96NH17.4521.30

    15125-Feb-0014.931.33514.931.335

    16122May925.71.Uchida& 96NH5.71

    17122May925.71.Uchida& 96NH5.71

    18122May925.71.Uchida& 96NH5.71

    19122May925.71.Uchida& 96NH5.71

    20122May9217.711.435Uchida& 96NH17.711.435

    21122May925.71.Uchida& 96NH5.71

    22213Nov9117.4331.44Francis 96SH17.4331.44

    23213Nov9117.433.Francis (95)SH17.433

    24122May925.71.Uchida& 96NH5.71

    25122May925.71.Uchida& 96NH5.71

    26122May925.71.Uchida& 96NH5.71

    27124Oct8122.771.473Cailliet#8FreeSwimmer22.771.473

    2813Sep7721.11.408SwiftFreeSwimmer21.11.408

    2913Oct7722.11.414SwiftFreeSwimmer22.11.414

    30127Jul7619.871.41SwiftFreeSwimmer19.871.41

    311June198118.51.29Cailliet#2FreeSwimmer18.51.29

    32117Jul8119.551.219JohnsonFreeSwimmer19.551.219

    33117Jul8119.551.321JohnsonFreeSwimmer19.551.321

    34112aug7620.391.448Sea_WorldFreeSwimmer20.391.448

    3513Jul7819.091.397Sea_WorldFreeSwimmer19.091.397

    36116Aug7820.521.473Sea_WorldFreeSwimmer20.521.473same as above?

    37125Jul8119.811.422Sea_WorldFreeSwimmer19.811.422

    3815jun8418.171.321SeigelFreeSwimmer18.171.321

    3914Jul8019.131.295JohnsonFreeSwimmer19.131.295

    40119May8417.131.32SeigelFreeSwimmer17.131.32

    412Dec198424.51.46Stevens_pcFreeSwimmer24.51.46

    42218Jan8225.581.47Bruce_pcFreeSwimmer25.581.47

    43125Aug8320.811.22C&P1985FreeSwimmer20.811.22

    4428-Nov-9917.301.5SH17.31.5

    45113-Sep-0021.471.5MBAFreeSwimmer21.471.50

    4619-Sep-8021.331.54MBAFreeSwimmer21.331.54

    HemiDateMonthTLReferenceIDMonthNorthernHemiSouthernHemiFreeSwimmersMBA

    Sheet1

    000

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    NorthernHemi

    SouthernHemi

    FreeSwimmers

    Month

    TL embryos or freeswimmers (m)

    Guesstimate of Gestation Period for White Shark

    VBGF

    0000

    0000

    0000

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    NorthernHemi

    SouthernHemi

    FreeSwimmers

    MBA1984&2004

    Month (6 and 18 = June 1 in NH)

    TL embryos or freeswimmers (m)

    Guesstimate of Gestation Period for White Shark

    Gompertz

    Raw data for VBGF fit to be done in Systat and Octave?

    VBGF with freeswimmersVBGF without freeswimmersVBGF without freeswimmersUsed old VBGF parameters to calculated shifted VBGFVBGF without freeswimmers

    Loo1.837297Loo2.185928N.S.!Loo2.185928Have to check using Systat once moreLoo2.185928N.S.

    Lo1.297284Lo1.297375Lo1.297375Lo-0.403771

    calcto=-1.252995767calcto=-1.2624218131

    k0.977224k0.713075k0.713075k0.713075

    4ln2/k2.83720899434ln2/k3.88821473514ln2/k3.88821473514ln2/k3.8882147351

    7ln2/k4.965115747ln2/k6.80437578647ln2/k6.80437578647ln2/k6.8043757864

    MonthAge (yr)TLAge (yr)VBGFITERATION LOSS PARAMETER VALUESAge (yr)VBGFITERATION LOSS PARAMETER VALUESAge (yr)VBGFMonthAge (yr)TLAge (yr)VBGFITERATION LOSS PARAMETER VALUES

    12.571-1.28580.000-1.50-0.5020 0.3069959D+01 0.1500D+010.1000D+010.9000D+00-1.50-0.4040 0.1071259D+01 0.1500D+010.1000D+010.1000D+010.00-0.4042.5710.21430.0000.00-0.4040 0.4758952D+00 0.1500D+010.0000D+000.1000D+01

    210.42-0.63170.550-1.45-0.3901 0.1295271D+01 0.1508D+010.1206D+010.8993D+00-1.45-0.3131 0.5304606D+00 0.1465D+010.1108D+010.9723D+000.05-0.31310.420.86830.5500.05-0.3131 0.4253137D+00 0.1603D+01-.4798D-010.1044D+01

    38.2-0.81670.610-1.40-0.2842 0.4560266D+00 0.1834D+010.1298D+010.1054D+01-1.40-0.2252 0.2574642D+00 0.1711D+010.1288D+010.1124D+010.10-0.2258.20.68330.6100.10-0.2262 0.2786008D+00 0.1719D+01-.3223D+000.1010D+01

    415-0.25001.000-1.35-0.1833 0.4251452D+00 0.1892D+010.1297D+010.8805D+00-1.35-0.1413 0.2513914D+00 0.1742D+010.1272D+010.1051D+010.15-0.141151.25001.0000.15-0.1413 0.2637131D+00 0.1875D+01-.5197D+000.8898D+00

    516.067-0.16111.050-1.30-0.0864 0.4119643D+00 0.1848D+010.1296D+010.9645D+00-1.30-0.0594 0.2476735D+00 0.1802D+010.1273D+010.9724D+000.20-0.05916.0671.33891.0500.20-0.0604 0.2466025D+00 0.1848D+01-.5191D+000.9437D+00

    613.516-0.37371.100-1.250.0055 0.4119127D+00 0.1848D+010.1297D+010.9649D+00-1.250.0195 0.2459332D+00 0.1911D+010.1284D+010.8674D+000.250.01913.5161.12631.1000.250.0195 0.2447982D+00 0.1856D+01-.4924D+000.9465D+00

    721.50.29171.270-1.200.0936 0.4118877D+00 0.1845D+010.1297D+010.9686D+00-1.200.0956 0.2437067D+00 0.1893D+010.1284D+010.8961D+000.300.09521.51.79171.2700.300.0956 0.2437970D+00 0.1875D+01-.4916D+000.9228D+00

    817.452-0.04571.300-1.150.1767 0.4118701D+00 0.1836D+010.1298D+010.9789D+00-1.150.1687 0.2418313D+00 0.1947D+010.1293D+010.8751D+000.350.16817.4521.45431.3000.350.1687 0.2423919D+00 0.1930D+01-.4731D+000.8719D+00

    914.93-0.25581.335-1.100.2558 0.4118655D+00 0.1838D+010.1297D+010.9769D+00-1.100.2398 0.2405273D+00 0.2022D+010.1295D+010.8072D+000.400.23914.931.24421.3350.400.2398 0.2404491D+00 0.2038D+01-.4269D+000.7877D+00

    1017.71-0.02421.435-1.050.3319 0.4118654D+00 0.1837D+010.1297D+010.9772D+00-1.050.3079 0.2399204D+00 0.2021D+010.1291D+010.8121D+000.450.30717.711.47581.4350.450.3079 0.2397844D+00 0.2051D+01-.4267D+000.7934D+00

    1117.433-0.04731.440-1.000.40210 0.4118654D+00 0.1837D+010.1297D+010.9772D+00-1.000.37310 0.2393492D+00 0.2069D+010.1293D+010.7770D+000.500.37317.4331.45281.4400.500.37310 0.2391730D+00 0.2081D+01-.4261D+000.7720D+00

    1222.770.39751.473Freeswimmers-0.950.47111 0.4118654D+00 0.1837D+010.1297D+010.9772D+00-0.950.43711 0.2391644D+00 0.2121D+010.1295D+010.7435D+000.550.4370.550.43611 0.2390241D+00 0.2121D+01-.4174D+000.7461D+00

    1321.10.25831.408Freeswimmers-0.900.536-0.900.49812 0.2389762D+00 0.2116D+010.1295D+010.7511D+000.600.4980.600.49812 0.2388878D+00 0.2129D+01-.4167D+000.7440D+00

    1422.10.34171.414Freeswimmers-0.850.598DEPENDENT VARIABLE IS TL-0.850.55713 0.2388371D+00 0.2165D+010.1297D+010.7239D+000.650.5570.650.55713 0.2387874D+00 0.2190D+01-.4017D+000.7099D+00

    1519.870.15581.410Freeswimmers-0.800.657-0.800.61414 0.2388102D+00 0.2185D+010.1297D+010.7140D+000.700.6140.700.61414 0.2387774D+00 0.2180D+01-.4048D+000.7165D+00

    1618.50.04171.290Freeswimmers-0.750.713MISSING DATA OR ESTIMATES REDUCED DEGREES OF FREEDOM-0.750.66915 0.2388097D+00 0.2188D+010.1297D+010.7120D+000.750.6690.750.66915 0.2387752D+00 0.2184D+01-.4042D+000.7141D+00

    1719.550.12921.219Freeswimmers-0.700.767-0.700.72216 0.2388095D+00 0.2186D+010.1297D+010.7130D+000.800.7220.800.72216 0.2387752D+00 0.2185D+01-.4038D+000.7134D+00

    1819.550.12921.321Freeswimmers-0.650.818SOURCE SUM-OF-SQUARES DF MEAN-SQUARE-0.650.77317 0.2388095D+00 0.2186D+010.1297D+010.7131D+000.850.7730.850.77317 0.2387752D+00 0.2186D+01-.4038D+000.7133D+00

    1920.390.19921.448Freeswimmers-0.600.867-0.600.8230.900.8230.900.82318 0.2387752D+00 0.2186D+01-.4038D+000.7133D+00

    2019.090.09081.397Freeswimmers-0.550.913REGRESSION 51.885063 3 17.295021-0.550.871DEPENDENT VARIABLE IS TL0.950.8710.950.871

    2120.520.21001.473Freeswimmers-0.500.957RESIDUAL 0.411865 28 0.014709-0.500.9171.000.9171.000.917DEPENDENT VARIABLE IS TL

    2219.810.15081.422Freeswimmers-0.450.999-0.450.961SOURCE SUM-OF-SQUARES DF MEAN-SQUARE1.050.9611.050.961

    2318.170.01421.321Freeswimmers-0.401.039TOTAL 52.296933 31-0.401.0041.101.0041.101.004SOURCE SUM-OF-SQUARES DF MEAN-SQUARE

    2419.130.09421.295Freeswimmers-0.351.077CORRECTED 3.255059 30-0.351.045REGRESSION 12.966238 3 4.3220791.151.0451.151.045

    2517.13-0.07251.320Freeswimmers-0.301.113-0.301.085RESIDUAL 0.238809 8 0.0298511.201.0851.201.085REGRESSION 12.966274 3 4.322091

    2624.50.54171.460Freeswimmers-0.251.148RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.992124-0.251.1241.251.1241.251.124RESIDUAL 0.238775 8 0.029847

    2725.580.63171.470Freeswimmers-0.201.181CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.873469-0.201.161TOTAL 13.205050 111.301.1611.301.161

    2820.810.23421.220Freeswimmers-0.151.212-0.151.197CORRECTED 2.024314 101.351.1971.351.197TOTAL 13.205050 11

    2917.3-0.05831.500Freeswimmers-0.101.242-0.101.2321.401.2321.401.232CORRECTED 2.024314 10

    3021.470.28891.500Freeswimmers-0.051.270PARAMETER ESTIMATE A.S.E. LOWER UPPER-0.051.265RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.9819151.451.2651.451.265

    3121.330.27781.540Freeswimmers0.001.297LOO 1.837297 0.197139 1.433476 2.2411180.001.297CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.8820291.501.2971.501.297RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.981918

    0.051.323LO 1.297284 0.023883 1.248362 1.3462070.051.3281.551.3281.551.328CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.882046

    0.101.348K 0.977224 0.234982 0.495886 1.4585620.101.3591.601.3591.601.358

    0.151.3710.151.388PARAMETER ESTIMATE A.S.E. LOWER UPPER1.651.3881.651.387

    0.201.3930.201.415LOO 2.185928 0.976994 -0.067024 4.4388801.701.4151.701.415PARAMETER ESTIMATE A.S.E. LOWER UPPER

    0.251.414ASYMPTOTIC CORRELATION MATRIX OF PARAMETERS0.251.442LO 1.297375 0.068165 1.140185 1.4545641.751.4421.751.442LOO 2.185631 0.975943 -0.064896 4.436159

    0.301.4350.301.469K 0.713075 0.513095 -0.470125 1.8962741.801.4691.801.468LO -0.403771 0.287318 -1.066328 0.258787

    0.351.454LOO LO K0.351.4941.851.4941.851.494K 0.713279 0.512814 -0.469273 1.895830

    0.401.4720.401.5181.901.5181.901.518

    0.451.489LOO 1.0000000.451.541ASYMPTOTIC CORRELATION MATRIX OF PARAMETERS1.951.5411.951.541

    0.501.506LO -0.255139 1.0000000.501.5642.001.5642.001.564ASYMPTOTIC CORRELATION MATRIX OF PARAMETERS

    0.551.522K -0.971124 0.392408 1.0000000.551.586LOO LO K2.051.5862.051.586

    0.601.5370.601.6072.101.6072.101.607LOO LO K

    0.651.5510.651.627LOO 1.0000002.151.6272.151.627

    0.701.5650.701.647LO 0.460802 1.0000002.201.6472.201.646LOO 1.000000

    0.751.5780.751.665K -0.986338 -0.339184 1.0000002.251.6652.251.665LO 0.650928 1.000000

    0.801.5900.801.6842.301.6842.301.684K -0.986316 -0.750630 1.000000

    0.851.6020.851.7012.351.7012.351.701

    0.901.6130.901.7182.401.7182.401.718

    0.951.6240.951.7352.451.7352.451.735

    1.001.6341.001.7502.501.7502.501.750

    2.551.766

    2.601.780

    2.651.795

    2.701.808

    2.751.821

    2.801.834

    2.851.847

    2.901.858

    2.951.870

    3.001.881

    VBGF

    MonthAge (yr)TLAge (yr)TL_VBGF

    12.5710.00.00-0.060

    210.420.65410.5500.050.031

    38.20.46910.6100.10.117

    4151.03581.0000.150.199

    516.0671.12471.0500.20.277

    613.5160.91211.1000.250.351

    721.51.57741.2700.30.422

    817.4521.24011.3000.350.490

    914.931.02991.3350.40.554

    1017.711.26161.4350.450.615

    1117.4331.23851.4400.50.673

    1222.771.68331.4730.550.729

    1321.11.54411.4080.60.782

    1422.11.62741.4140.650.832

    1519.871.44161.4100.70.880

    1618.51.32741.2900.750.926

    1719.551.41491.2190.80.969

    1819.551.41491.3210.851.011

    1920.391.48491.4480.91.050

    2019.091.37661.3970.951.088

    2120.521.49581.47311.123

    2219.811.43661.4221.051.157

    2318.171.29991.3211.11.190

    2419.131.37991.2951.151.221

    2517.131.21331.3201.21.250

    2624.51.82741.4601.251.278

    2725.581.91741.4701.31.305

    2820.811.51991.2201.351.330

    2917.31.22741.5001.41.354

    3021.471.57461.5001.451.377

    3121.331.56351.5401.51.399

    1.551.420

    1.61.440

    1.651.459

    1.71.477

    1.751.494

    1.81.511

    1.851.526

    1.91.541

    1.951.555

    21.569

    2.051.581

    2.11.594

    2.151.605

    2.21.616

    2.251.627

    2.31.637

    2.351.646

    2.41.656

    2.451.664

    2.51.672

    Gompertz

    VBGF

    TL

    Age (year)

    TL

    TL

    Embryonic growth of white shark

    VBGF

    TL

    TL

    VBGF

    TL

    TL

    VBGF

    TL

    Cannot get different colors?

    TL

    TL_VBGF

    Age (yr)

    TL (m)

    TL_VBGF

    Loo1.837297Lo1.324425Loo=1.5130831691

    Lo1.297284G0.133171t_inflexion=-0.7612144046

    k0.977224k2.648559

    t to reach 95% Loo=1.813OKt to reach 95% Loo=0.360OK

    4ln2/k2.837OFF4ln2/k1.047OFF

    5ln2/k

    VBGF RepeatGompertzAge (yr)L_VBGFL_Gompertz

    -1.50-0.50160.0013-27.30%0.08%

    ITERATION LOSS PARAMETER VALUESITERATION LOSS PARAMETER VALUES-1.45-0.39010.0031-21.23%0.20%

    0 0.2909906D+01 0.2000D+010.1000D+010.5000D+000 0.2610452D+01 0.1000D+010.1000D+010.1000D+01-1.40-0.28380.0066-15.45%0.44%

    1 0.1089232D+01 0.2016D+010.1322D+010.5299D+001 0.2059129D+01 0.1337D+010.9910D+000.9840D+00-1.35-0.18270.0130-9.94%0.86%

    2 0.5306960D+00 0.2136D+010.1344D+010.7390D+002 0.1426437D+01 0.1390D+010.8107D+000.8204D+00-1.30-0.08640.0235-4.70%1.55%

    3 0.4228646D+00 0.2024D+010.1289D+010.8103D+003 0.6394888D+00 0.1277D+010.6383D+000.9760D+00-1.250.00540.03930.29%2.60%

    4 0.4211642D+00 0.1936D+010.1287D+010.8413D+004 0.5437493D+00 0.1269D+010.4086D+000.1171D+01-1.200.09270.06195.05%4.09%

    5 0.4168476D+00 0.1955D+010.1291D+010.8453D+005 0.5235287D+00 0.1269D+010.4506D+000.1205D+01-1.150.17590.09209.58%6.08%

    6 0.4133764D+00 0.1904D+010.1296D+010.9093D+006 0.4570713D+00 0.1279D+010.3155D+000.1486D+01-1.100.25510.130213.89%8.60%

    7 0.4122685D+00 0.1842D+010.1298D+010.9670D+007 0.4350041D+00 0.1292D+010.2322D+000.1718D+01-1.050.33060.176517.99%11.66%

    8 0.4119590D+00 0.1853D+010.1297D+010.9586D+008 0.3912269D+00 0.1303D+010.2376D+000.1872D+01-1.000.40240.230421.90%15.23%

    9 0.4118745D+00 0.1836D+010.1297D+010.9778D+009 0.3680502D+00 0.1315D+010.1783D+000.2176D+01-0.950.47090.291025.63%19.23%

    10 0.4118657D+00 0.1838D+010.1297D+010.9766D+0010 0.3575822D+00 0.1323D+010.1271D+000.2616D+01-0.900.53600.357029.17%23.59%

    11 0.4118654D+00 0.1837D+010.1297D+010.9772D+0011 0.3544765D+00 0.1321D+010.1384D+000.2607D+01-0.850.59810.427032.55%28.22%

    12 0.4118654D+00 0.1837D+010.1297D+010.9772D+0012 0.3542143D+00 0.1324D+010.1356D+000.2624D+01-0.800.65720.499635.77%33.02%

    13 0.4118654D+00 0.1837D+010.1297D+010.9772D+0013 0.3541890D+00 0.1324D+010.1339D+000.2640D+01-0.750.71350.573238.83%37.88%

    14 0.3541856D+00 0.1324D+010.1332D+000.2648D+01-0.700.76700.646541.75%42.73%

    DEPENDENT VARIABLE IS TL15 0.3541854D+00 0.1324D+010.1332D+000.2649D+01-0.650.81810.718444.53%47.48%

    16 0.3541854D+00 0.1324D+010.1332D+000.2649D+01-0.600.86670.787947.17%52.08%

    SOURCE SUM-OF-SQUARES DF MEAN-SQUARE-0.550.91300.854449.69%56.47%

    DEPENDENT VARIABLE IS TL-0.500.95700.917152.09%60.61%

    REGRESSION 51.885065 3 17.295022-0.450.99900.975954.37%64.50%

    RESIDUAL 0.411865 28 0.014709SOURCE SUM-OF-SQUARES DF MEAN-SQUARE-0.401.03901.030456.55%68.10%

    -0.351.07711.080758.62%71.43%

    TOTAL 52.296933 31REGRESSION 51.942758 3 17.314253-0.301.11331.126860.60%74.47%

    CORRECTED 3.255059 30RESIDUAL 0.354185 28 0.012649-0.251.14781.168862.47%77.24%

    -0.201.18071.206864.26%79.76%

    RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.992124TOTAL 52.296933 31-0.151.21201.241165.97%82.03%

    CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.873469CORRECTED 3.255059 30-0.101.24181.272067.59%84.07%

    -0.051.27021.299769.14%85.90%

    RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.9932270.001.29731.324470.61%87.53%

    PARAMETER ESTIMATE A.S.E. LOWER UPPERCORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.8911890.051.32301.346572.01%88.99%

    LOO 1.837297 0.197139 1.433476 2.2411170.101.34761.366173.34%90.29%

    LO 1.297284 0.023883 1.248362 1.3462070.151.37091.383574.62%91.44%

    K 0.977224 0.234982 0.495886 1.458562PARAMETER ESTIMATE A.S.E. LOWER UPPER0.201.39321.399075.83%92.46%

    LO 1.324425 0.024032 1.275198 1.3736530.251.41431.412676.98%93.36%

    G 0.133171 0.052059 0.026533 0.2398080.301.43451.424778.08%94.16%

    ASYMPTOTIC CORRELATION MATRIX OF PARAMETERSK 2.648559 0.529647 1.563625 3.7334920.351.45371.435479.12%94.87%

    0.401.47201.444880.12%95.49%

    LOO LO K0.451.48941.453181.07%96.04%

    ASYMPTOTIC CORRELATION MATRIX OF PARAMETERS0.501.50601.460481.97%96.52%

    LOO 1.0000000.551.52181.466982.83%96.94%

    LO -0.255139 1.000000LO G K0.601.53691.472583.65%97.32%

    K -0.971124 0.392408 1.0000000.651.55121.477584.43%97.65%

    LO 1.0000000.701.56481.481985.17%97.94%

    G -0.504873 1.0000000.751.57781.485785.88%98.19%

    K 0.498843 -0.936806 1.0000000.801.59021.489186.55%98.41%

    0.851.60201.492087.19%98.61%

    0.901.61321.494687.80%98.78%

    0.951.62391.496988.38%98.93%

    1.001.63411.498988.94%99.06%

    1.051.64381.500689.47%99.18%

    1.101.65301.502289.97%99.28%

    1.151.66181.503590.45%99.37%

    1.201.67011.504790.90%99.45%

    1.251.67811.505791.34%99.52%

    1.301.68571.506791.75%99.58%

    1.351.69291.507592.14%99.63%

    Lo1.3244251.401.69981.508192.52%99.67%

    G0.1331711.451.70641.508892.87%99.71%

    k2.6485591.501.71261.509393.21%99.75%

    1.551.71861.509893.54%99.78%

    1.601.72421.510293.85%99.81%

    1.651.72961.510594.14%99.83%

    1.701.73481.510994.42%99.85%

    Gompertz1.751.73961.511194.68%99.87%

    MonthAge (yr)TLAge (yr)TL_Gompertz1.801.74431.511494.94%99.89%

    12.5710.00.00.000.02738541551.851.74871.511695.18%99.90%

    210.420.65410.5500.050.04504318431.901.75301.511895.41%99.91%

    38.20.46910.6100.100.06965204771.951.75701.511995.63%99.92%

    4151.03581.0000.150.1020371852.001.76081.512195.84%99.93%

    516.0671.12471.0500.200.14256573932.051.76451.512296.04%99.94%

    613.5160.91211.1000.250.19109754562.101.76791.512396.22%99.95%

    721.51.57741.2700.300.24700911232.151.77121.512496.40%99.96%

    817.4521.24011.3000.350.30927604352.201.77441.512596.58%99.96%

    914.931.02991.3350.400.37659083082.251.77741.512696.74%99.97%

    1017.711.26161.4350.450.44749211722.301.78021.512696.89%99.97%

    1117.4331.23851.4400.500.5204858812.351.78301.512797.04%99.97%

    1222.771.68331.4730.550.59414571142.401.78561.512797.18%99.98%

    1321.11.54411.4080.600.66718613222.451.78801.512897.32%99.98%

    1422.11.62741.4140.650.73850840682.501.79041.512897.45%99.98%

    1519.871.44161.4100.700.8072218946

    1618.51.32741.2900.750.8726459184

    1719.551.41491.2190.800.9342976261

    1819.551.41491.3210.850.9918709517

    1920.391.48491.4480.901.0452109361

    2019.091.37661.3970.951.0942866433

    2120.521.49581.4731.001.1391649338

    2219.811.43661.4221.051.1799865079

    2318.171.29991.3211.101.2169449766

    2419.131.37991.2951.151.2502692344

    2517.131.21331.3201.201.2802090877

    2624.51.82741.4601.251.3070238883

    2725.581.91741.4701.301.3309738233

    2820.811.51991.2201.351.3523134661

    2917.31.22741.5001.401.3712872001

    3021.471.57461.5001.451.3881261515

    3121.331.56351.5401.501.4030463115

    1.551.4162475718

    1.601.4279134445

    1.651.4382112806

    1.701.4472928373

    1.751.4552950776

    1.801.4623411138

    1.851.4685412266

    1.901.47399391

    1.951.4787869077

    2.001.4829982149

    2.051.4866970298

    2.101.4899446452

    2.151.4927952744

    2.201.4952968097

    2.251.4974915137

    2.301.4994166464

    2.351.5011050306

    2.401.5025855599

    2.451.503883653

    2.501.5050216599

    2.551.5060192228

    2.601.5068935973

    2.651.5076599368

    2.701.5083315444

    2.751.5089200956

    2.801.5094358352

    2.851.5098877504

    2.901.5102837239

    2.951.5106306686

    3.001.5109346459

    3.051.5112009699

    3.101.5114342993

    3.151.5116387175

    3.201.5118178036

    3.251.5119746944

    3.301.5121121387

    3.351.5122325456

    3.401.5123380258

    3.451.512430429

    3.501.5125113756

    3.551.5125822857

    3.601.5126444032

    3.651.5126988182

    3.701.5127464855

    3.751.5127882416

    3.801.5128248195

    3.851.5128568612

    3.901.5128849293

    3.951.5129095163

    4.001.5129310541

    L_VBGF

    L_Gompertz

    0

    0.55

    0.61

    1

    1.05

    1.1

    1.27

    1.3

    1.335

    1.435

    1.44

    1.473

    1.408

    1.414

    1.41

    1.29

    1.219

    1.321

    1.448

    1.397

    1.473

    1.422

    1.321

    1.295

    1.32

    1.46

    1.47

    1.22

    1.5

    1.5

    1.54

    L_VBGF

    L_Gompertz

    TL

    TL

    TL_Gompertz

    Age (yr)

    TL (m)

    TL_Gompertz

  • **Comparison of VBGF and Gompertz for 11 embryos and 20 free-swimmers

    Chart2

    00.0273854155-0.0597599135

    0.550.04504318430.0307044673

    0.610.06965204770.1168549006

    10.1020371850.198897104

    1.050.14256573930.2770269857

    1.10.19109754560.3514311113

    1.270.24700911230.4222871498

    1.30.30927604350.4897642977

    1.3350.37659083080.5540236833

    1.4350.44749211720.6152187509

    1.440.5204858810.6734956277

    1.4730.59414571140.7289934728

    1.4080.66718613220.7818448088

    1.4140.73850840680.8321758391

    1.410.80722189460.8801067487

    1.290.87264591840.9257519915

    1.2190.93429762610.9692205634

    1.3210.99187095171.0106162626

    1.4481.04521093611.0500379376

    1.3971.09428664331.0875797231

    1.4731.13916493381.1233312647

    1.4221.17998650791.1573779334

    1.3211.21694497661.1898010289

    1.2951.25026923441.220677974

    1.321.28020908771.2500824995

    1.461.30702388831.2780848203

    1.471.33097382331.3047518028

    1.221.35231346611.330147125

    1.51.37128720011.3543314281

    1.51.38812615151.3773624617

    1.541.40304631151.3992952213

    1.41624757181.42018208

    1.42791344451.4400729134

    1.43821128061.4590152186

    1.44729283731.4770542278

    1.45529507761.4942330162

    1.46234111381.510592605

    1.46854122661.5261720589

    1.473993911.5410085801

    1.47878690771.5551375967

    1.48299821491.568592847

    1.48669702981.5814064609

    1.48994464521.5936090359

    1.49279527441.6052297103

    1.49529680971.6162962332

    1.49749151371.6268350301

    1.49941664641.6368712666

    1.50110503061.6464289081

    1.50258555991.6555307772

    1.5038836531.6641986082

    1.50502165991.672453099

    TL

    TL_Gompertz

    TL_VBGF

    Age (yr)

    TL (m)

    Sheet1

    HemiDateMonthTLReferenceIDMonthNorthernHemiSouthernHemiFreeSwimmersMBA1984&2004

    1217Nov8111.567.Paterson 86SH11.567

    2226Nov8211.867.Paterson 86SH11.867

    3226Nov8211.867.Paterson 86SH11.867

    4116Feb852.5710Uchida&87NH2.5710.00

    52Oct-Nov11.Bruce(92)SH11

    62Oct-Nov11.Bruce(92)SH11

    72Oct-Nov11.Bruce(92)SH11

    8212-Oct-9310.420.55Vlin_pcNH10.420.55

    91Summer19348.20.61Norman(37)NH8.20.61

    101Feb-Mar1988151Ebert_pcNH151.00

    1112Apr8616.0671.05Uchida&87NH16.0671.05

    122Jul16 199613.5161.1Cliffetal200SH13.5161.10

    132Mar 199421.51.27Stevens_pcFreeSwimmer21.51.27

    14114May9217.4521.3Uchida&96NH17.4521.30

    15125-Feb-0014.931.33514.931.335

    16122May925.71.Uchida& 96NH5.71

    17122May925.71.Uchida& 96NH5.71

    18122May925.71.Uchida& 96NH5.71

    19122May925.71.Uchida& 96NH5.71

    20122May9217.711.435Uchida& 96NH17.711.435

    21122May925.71.Uchida& 96NH5.71

    22213Nov9117.4331.44Francis 96SH17.4331.44

    23213Nov9117.433.Francis (95)SH17.433

    24122May925.71.Uchida& 96NH5.71

    25122May925.71.Uchida& 96NH5.71

    26122May925.71.Uchida& 96NH5.71

    27124Oct8122.771.473Cailliet#8FreeSwimmer22.771.473

    2813Sep7721.11.408SwiftFreeSwimmer21.11.408

    2913Oct7722.11.414SwiftFreeSwimmer22.11.414

    30127Jul7619.871.41SwiftFreeSwimmer19.871.41

    311June198118.51.29Cailliet#2FreeSwimmer18.51.29

    32117Jul8119.551.219JohnsonFreeSwimmer19.551.219

    33117Jul8119.551.321JohnsonFreeSwimmer19.551.321

    34112aug7620.391.448Sea_WorldFreeSwimmer20.391.448

    3513Jul7819.091.397Sea_WorldFreeSwimmer19.091.397

    36116Aug7820.521.473Sea_WorldFreeSwimmer20.521.473same as above?

    37125Jul8119.811.422Sea_WorldFreeSwimmer19.811.422

    3815jun8418.171.321SeigelFreeSwimmer18.171.321

    3914Jul8019.131.295JohnsonFreeSwimmer19.131.295

    40119May8417.131.32SeigelFreeSwimmer17.131.32

    412Dec198424.51.46Stevens_pcFreeSwimmer24.51.46

    42218Jan8225.581.47Bruce_pcFreeSwimmer25.581.47

    43125Aug8320.811.22C&P1985FreeSwimmer20.811.22

    4428-Nov-9917.301.5SH17.31.5

    45113-Sep-0021.471.5MBAFreeSwimmer21.471.50

    4619-Sep-8021.331.54MBAFreeSwimmer21.331.54

    HemiDateMonthTLReferenceIDMonthNorthernHemiSouthernHemiFreeSwimmersMBA

    Sheet1

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    NorthernHemi

    SouthernHemi

    FreeSwimmers

    Month

    TL embryos or freeswimmers (m)

    Guesstimate of Gestation Period for White Shark

    VBGF

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    NorthernHemi

    SouthernHemi

    FreeSwimmers

    MBA1984&2004

    Month (6 and 18 = June 1 in NH)

    TL embryos or freeswimmers (m)

    Guesstimate of Gestation Period for White Shark

    Gompertz

    Raw data for VBGF fit to be done in Systat and Octave?

    VBGF with freeswimmersVBGF without freeswimmersVBGF without freeswimmersUsed old VBGF parameters to calculated shifted VBGFVBGF without freeswimmers

    Loo1.837297Loo2.185928N.S.!Loo2.185928Have to check using Systat once moreLoo2.185928N.S.

    Lo1.297284Lo1.297375Lo1.297375Lo-0.403771

    calcto=-1.252995767calcto=-1.2624218131

    k0.977224k0.713075k0.713075k0.713075

    4ln2/k2.83720899434ln2/k3.88821473514ln2/k3.88821473514ln2/k3.8882147351

    7ln2/k4.965115747ln2/k6.80437578647ln2/k6.80437578647ln2/k6.8043757864

    MonthAge (yr)TLAge (yr)VBGFITERATION LOSS PARAMETER VALUESAge (yr)VBGFITERATION LOSS PARAMETER VALUESAge (yr)VBGFMonthAge (yr)TLAge (yr)VBGFITERATION LOSS PARAMETER VALUES

    12.571-1.28580.000-1.50-0.5020 0.3069959D+01 0.1500D+010.1000D+010.9000D+00-1.50-0.4040 0.1071259D+01 0.1500D+010.1000D+010.1000D+010.00-0.4042.5710.21430.0000.00-0.4040 0.4758952D+00 0.1500D+010.0000D+000.1000D+01

    210.42-0.63170.550-1.45-0.3901 0.1295271D+01 0.1508D+010.1206D+010.8993D+00-1.45-0.3131 0.5304606D+00 0.1465D+010.1108D+010.9723D+000.05-0.31310.420.86830.5500.05-0.3131 0.4253137D+00 0.1603D+01-.4798D-010.1044D+01

    38.2-0.81670.610-1.40-0.2842 0.4560266D+00 0.1834D+010.1298D+010.1054D+01-1.40-0.2252 0.2574642D+00 0.1711D+010.1288D+010.1124D+010.10-0.2258.20.68330.6100.10-0.2262 0.2786008D+00 0.1719D+01-.3223D+000.1010D+01

    415-0.25001.000-1.35-0.1833 0.4251452D+00 0.1892D+010.1297D+010.8805D+00-1.35-0.1413 0.2513914D+00 0.1742D+010.1272D+010.1051D+010.15-0.141151.25001.0000.15-0.1413 0.2637131D+00 0.1875D+01-.5197D+000.8898D+00

    516.067-0.16111.050-1.30-0.0864 0.4119643D+00 0.1848D+010.1296D+010.9645D+00-1.30-0.0594 0.2476735D+00 0.1802D+010.1273D+010.9724D+000.20-0.05916.0671.33891.0500.20-0.0604 0.2466025D+00 0.1848D+01-.5191D+000.9437D+00

    613.516-0.37371.100-1.250.0055 0.4119127D+00 0.1848D+010.1297D+010.9649D+00-1.250.0195 0.2459332D+00 0.1911D+010.1284D+010.8674D+000.250.01913.5161.12631.1000.250.0195 0.2447982D+00 0.1856D+01-.4924D+000.9465D+00

    721.50.29171.270-1.200.0936 0.4118877D+00 0.1845D+010.1297D+010.9686D+00-1.200.0956 0.2437067D+00 0.1893D+010.1284D+010.8961D+000.300.09521.51.79171.2700.300.0956 0.2437970D+00 0.1875D+01-.4916D+000.9228D+00

    817.452-0.04571.300-1.150.1767 0.4118701D+00 0.1836D+010.1298D+010.9789D+00-1.150.1687 0.2418313D+00 0.1947D+010.1293D+010.8751D+000.350.16817.4521.45431.3000.350.1687 0.2423919D+00 0.1930D+01-.4731D+000.8719D+00

    914.93-0.25581.335-1.100.2558 0.4118655D+00 0.1838D+010.1297D+010.9769D+00-1.100.2398 0.2405273D+00 0.2022D+010.1295D+010.8072D+000.400.23914.931.24421.3350.400.2398 0.2404491D+00 0.2038D+01-.4269D+000.7877D+00

    1017.71-0.02421.435-1.050.3319 0.4118654D+00 0.1837D+010.1297D+010.9772D+00-1.050.3079 0.2399204D+00 0.2021D+010.1291D+010.8121D+000.450.30717.711.47581.4350.450.3079 0.2397844D+00 0.2051D+01-.4267D+000.7934D+00

    1117.433-0.04731.440-1.000.40210 0.4118654D+00 0.1837D+010.1297D+010.9772D+00-1.000.37310 0.2393492D+00 0.2069D+010.1293D+010.7770D+000.500.37317.4331.45281.4400.500.37310 0.2391730D+00 0.2081D+01-.4261D+000.7720D+00

    1222.770.39751.473Freeswimmers-0.950.47111 0.4118654D+00 0.1837D+010.1297D+010.9772D+00-0.950.43711 0.2391644D+00 0.2121D+010.1295D+010.7435D+000.550.4370.550.43611 0.2390241D+00 0.2121D+01-.4174D+000.7461D+00

    1321.10.25831.408Freeswimmers-0.900.536-0.900.49812 0.2389762D+00 0.2116D+010.1295D+010.7511D+000.600.4980.600.49812 0.2388878D+00 0.2129D+01-.4167D+000.7440D+00

    1422.10.34171.414Freeswimmers-0.850.598DEPENDENT VARIABLE IS TL-0.850.55713 0.2388371D+00 0.2165D+010.1297D+010.7239D+000.650.5570.650.55713 0.2387874D+00 0.2190D+01-.4017D+000.7099D+00

    1519.870.15581.410Freeswimmers-0.800.657-0.800.61414 0.2388102D+00 0.2185D+010.1297D+010.7140D+000.700.6140.700.61414 0.2387774D+00 0.2180D+01-.4048D+000.7165D+00

    1618.50.04171.290Freeswimmers-0.750.713MISSING DATA OR ESTIMATES REDUCED DEGREES OF FREEDOM-0.750.66915 0.2388097D+00 0.2188D+010.1297D+010.7120D+000.750.6690.750.66915 0.2387752D+00 0.2184D+01-.4042D+000.7141D+00

    1719.550.12921.219Freeswimmers-0.700.767-0.700.72216 0.2388095D+00 0.2186D+010.1297D+010.7130D+000.800.7220.800.72216 0.2387752D+00 0.2185D+01-.4038D+000.7134D+00

    1819.550.12921.321Freeswimmers-0.650.818SOURCE SUM-OF-SQUARES DF MEAN-SQUARE-0.650.77317 0.2388095D+00 0.2186D+010.1297D+010.7131D+000.850.7730.850.77317 0.2387752D+00 0.2186D+01-.4038D+000.7133D+00

    1920.390.19921.448Freeswimmers-0.600.867-0.600.8230.900.8230.900.82318 0.2387752D+00 0.2186D+01-.4038D+000.7133D+00

    2019.090.09081.397Freeswimmers-0.550.913REGRESSION 51.885063 3 17.295021-0.550.871DEPENDENT VARIABLE IS TL0.950.8710.950.871

    2120.520.21001.473Freeswimmers-0.500.957RESIDUAL 0.411865 28 0.014709-0.500.9171.000.9171.000.917DEPENDENT VARIABLE IS TL

    2219.810.15081.422Freeswimmers-0.450.999-0.450.961SOURCE SUM-OF-SQUARES DF MEAN-SQUARE1.050.9611.050.961

    2318.170.01421.321Freeswimmers-0.401.039TOTAL 52.296933 31-0.401.0041.101.0041.101.004SOURCE SUM-OF-SQUARES DF MEAN-SQUARE

    2419.130.09421.295Freeswimmers-0.351.077CORRECTED 3.255059 30-0.351.045REGRESSION 12.966238 3 4.3220791.151.0451.151.045

    2517.13-0.07251.320Freeswimmers-0.301.113-0.301.085RESIDUAL 0.238809 8 0.0298511.201.0851.201.085REGRESSION 12.966274 3 4.322091

    2624.50.54171.460Freeswimmers-0.251.148RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.992124-0.251.1241.251.1241.251.124RESIDUAL 0.238775 8 0.029847

    2725.580.63171.470Freeswimmers-0.201.181CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.873469-0.201.161TOTAL 13.205050 111.301.1611.301.161

    2820.810.23421.220Freeswimmers-0.151.212-0.151.197CORRECTED 2.024314 101.351.1971.351.197TOTAL 13.205050 11

    2917.3-0.05831.500Freeswimmers-0.101.242-0.101.2321.401.2321.401.232CORRECTED 2.024314 10

    3021.470.28891.500Freeswimmers-0.051.270PARAMETER ESTIMATE A.S.E. LOWER UPPER-0.051.265RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.9819151.451.2651.451.265

    3121.330.27781.540Freeswimmers0.001.297LOO 1.837297 0.197139 1.433476 2.2411180.001.297CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.8820291.501.2971.501.297RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.981918

    0.051.323LO 1.297284 0.023883 1.248362 1.3462070.051.3281.551.3281.551.328CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.882046

    0.101.348K 0.977224 0.234982 0.495886 1.4585620.101.3591.601.3591.601.358

    0.151.3710.151.388PARAMETER ESTIMATE A.S.E. LOWER UPPER1.651.3881.651.387

    0.201.3930.201.415LOO 2.185928 0.976994 -0.067024 4.4388801.701.4151.701.415PARAMETER ESTIMATE A.S.E. LOWER UPPER

    0.251.414ASYMPTOTIC CORRELATION MATRIX OF PARAMETERS0.251.442LO 1.297375 0.068165 1.140185 1.4545641.751.4421.751.442LOO 2.185631 0.975943 -0.064896 4.436159

    0.301.4350.301.469K 0.713075 0.513095 -0.470125 1.8962741.801.4691.801.468LO -0.403771 0.287318 -1.066328 0.258787

    0.351.454LOO LO K0.351.4941.851.4941.851.494K 0.713279 0.512814 -0.469273 1.895830

    0.401.4720.401.5181.901.5181.901.518

    0.451.489LOO 1.0000000.451.541ASYMPTOTIC CORRELATION MATRIX OF PARAMETERS1.951.5411.951.541

    0.501.506LO -0.255139 1.0000000.501.5642.001.5642.001.564ASYMPTOTIC CORRELATION MATRIX OF PARAMETERS

    0.551.522K -0.971124 0.392408 1.0000000.551.586LOO LO K2.051.5862.051.586

    0.601.5370.601.6072.101.6072.101.607LOO LO K

    0.651.5510.651.627LOO 1.0000002.151.6272.151.627

    0.701.5650.701.647LO 0.460802 1.0000002.201.6472.201.646LOO 1.000000

    0.751.5780.751.665K -0.986338 -0.339184 1.0000002.251.6652.251.665LO 0.650928 1.000000

    0.801.5900.801.6842.301.6842.301.684K -0.986316 -0.750630 1.000000

    0.851.6020.851.7012.351.7012.351.701

    0.901.6130.901.7182.401.7182.401.718

    0.951.6240.951.7352.451.7352.451.735

    1.001.6341.001.7502.501.7502.501.750

    2.551.766

    2.601.780

    2.651.795

    2.701.808

    2.751.821

    2.801.834

    2.851.847

    2.901.858

    2.951.870

    3.001.881

    VBGF

    MonthAge (yr)TLAge (yr)TL_VBGF

    12.5710.00.00-0.060

    210.420.65410.5500.050.031

    38.20.46910.6100.10.117

    4151.03581.0000.150.199

    516.0671.12471.0500.20.277

    613.5160.91211.1000.250.351

    721.51.57741.2700.30.422

    817.4521.24011.3000.350.490

    914.931.02991.3350.40.554

    1017.711.26161.4350.450.615

    1117.4331.23851.4400.50.673

    1222.771.68331.4730.550.729

    1321.11.54411.4080.60.782

    1422.11.62741.4140.650.832

    1519.871.44161.4100.70.880

    1618.51.32741.2900.750.926

    1719.551.41491.2190.80.969

    1819.551.41491.3210.851.011

    1920.391.48491.4480.91.050

    2019.091.37661.3970.951.088

    2120.521.49581.47311.123

    2219.811.43661.4221.051.157

    2318.171.29991.3211.11.190

    2419.131.37991.2951.151.221

    2517.131.21331.3201.21.250

    2624.51.82741.4601.251.278

    2725.581.91741.4701.31.305

    2820.811.51991.2201.351.330

    2917.31.22741.5001.41.354

    3021.471.57461.5001.451.377

    3121.331.56351.5401.51.399

    1.551.420

    1.61.440

    1.651.459

    1.71.477

    1.751.494

    1.81.511

    1.851.526

    1.91.541

    1.951.555

    21.569

    2.051.581

    2.11.594

    2.151.605

    2.21.616

    2.251.627

    2.31.637

    2.351.646

    2.41.656

    2.451.664

    2.51.672

    Gompertz

    VBGF

    TL

    Age (year)

    TL

    TL

    Embryonic growth of white shark

    VBGF

    TL

    TL

    VBGF

    TL

    TL

    VBGF

    TL

    Cannot get different colors?

    TL

    TL_VBGF

    Age (yr)

    TL (m)

    TL_VBGF

    00.0273854155

    0.550.0450431843

    0.610.0696520477

    10.102037185

    1.050.1425657393

    1.10.1910975456

    1.270.2470091123

    1.30.3092760435

    1.3350.3765908308

    1.4350.4474921172

    1.440.520485881

    1.4730.5941457114

    1.4080.6671861322

    1.4140.7385084068

    1.410.8072218946

    1.290.8726459184

    1.2190.9342976261

    1.3210.9918709517

    1.4481.0452109361

    1.3971.0942866433

    1.4731.1391649338

    1.4221.1799865079

    1.3211.2169449766

    1.2951.2502692344

    1.321.2802090877

    1.461.3070238883

    1.471.3309738233

    1.221.3523134661

    1.51.3712872001

    1.51.3881261515

    1.541.4030463115

    1.4162475718

    1.4279134445

    1.4382112806

    1.4472928373

    1.4552950776

    1.4623411138

    1.4685412266

    1.47399391

    1.4787869077

    1.4829982149

    1.4866970298

    1.4899446452

    1.4927952744

    1.4952968097

    1.4974915137

    1.4994166464

    1.5011050306

    1.5025855599

    1.503883653

    1.5050216599

    TL

    TL_VBGF

    TL

    TL_Gompertz

    Age (yr)

    TL (m)

    TL

    00.0273854155

    0.550.0450431843

    0.610.0696520477

    10.102037185

    1.050.1425657393

    1.10.1910975456

    1.270.2470091123

    1.30.3092760435

    1.3350.3765908308

    1.4350.4474921172

    1.440.520485881

    1.4730.5941457114

    1.4080.6671861322

    1.4140.7385084068

    1.410.8072218946

    1.290.8726459184

    1.2190.9342976261

    1.3210.9918709517

    1.4481.0452109361

    1.3971.0942866433

    1.4731.1391649338

    1.4221.1799865079

    1.3211.2169449766

    1.2951.2502692344

    1.321.2802090877

    1.461.3070238883

    1.471.3309738233

    1.221.3523134661

    1.51.3712872001

    1.51.3881261515

    1.541.4030463115

    1.4162475718

    1.4279134445

    1.4382112806

    1.4472928373

    1.4552950776

    1.4623411138

    1.4685412266

    1.47399391

    1.4787869077

    1.4829982149

    1.4866970298

    1.4899446452

    1.4927952744

    1.4952968097

    1.4974915137

    1.4994166464

    1.5011050306

    1.5025855599

    1.503883653

    1.5050216599

    TL

    TL_Gompertz

    TL_VBGF

    Age (yr)

    TL (m)

    Loo1.837297Lo1.324425Loo=1.5130831691

    Lo1.297284G0.133171t_inflexion=-0.7612144046

    k0.977224k2.648559

    t to reach 95% Loo=1.813OKt to reach 95% Loo=0.360OK

    4ln2/k2.837OFF4ln2/k1.047OFF

    5ln2/k

    VBGF RepeatGompertzAge (yr)L_VBGFL_Gompertz

    -1.50-0.50160.0013-27.30%0.08%

    ITERATION LOSS PARAMETER VALUESITERATION LOSS PARAMETER VALUES-1.45-0.39010.0031-21.23%0.20%

    0 0.2909906D+01 0.2000D+010.1000D+010.5000D+000 0.2610452D+01 0.1000D+010.1000D+010.1000D+01-1.40-0.28380.0066-15.45%0.44%

    1 0.1089232D+01 0.2016D+010.1322D+010.5299D+001 0.2059129D+01 0.1337D+010.9910D+000.9840D+00-1.35-0.18270.0130-9.94%0.86%

    2 0.5306960D+00 0.2136D+010.1344D+010.7390D+002 0.1426437D+01 0.1390D+010.8107D+000.8204D+00-1.30-0.08640.0235-4.70%1.55%

    3 0.4228646D+00 0.2024D+010.1289D+010.8103D+003 0.6394888D+00 0.1277D+010.6383D+000.9760D+00-1.250.00540.03930.29%2.60%

    4 0.4211642D+00 0.1936D+010.1287D+010.8413D+004 0.5437493D+00 0.1269D+010.4086D+000.1171D+01-1.200.09270.06195.05%4.09%

    5 0.4168476D+00 0.1955D+010.1291D+010.8453D+005 0.5235287D+00 0.1269D+010.4506D+000.1205D+01-1.150.17590.09209.58%6.08%

    6 0.4133764D+00 0.1904D+010.1296D+010.9093D+006 0.4570713D+00 0.1279D+010.3155D+000.1486D+01-1.100.25510.130213.89%8.60%

    7 0.4122685D+00 0.1842D+010.1298D+010.9670D+007 0.4350041D+00 0.1292D+010.2322D+000.1718D+01-1.050.33060.176517.99%11.66%

    8 0.4119590D+00 0.1853D+010.1297D+010.9586D+008 0.3912269D+00 0.1303D+010.2376D+000.1872D+01-1.000.40240.230421.90%15.23%

    9 0.4118745D+00 0.1836D+010.1297D+010.9778D+009 0.3680502D+00 0.1315D+010.1783D+000.2176D+01-0.950.47090.291025.63%19.23%

    10 0.4118657D+00 0.1838D+010.1297D+010.9766D+0010 0.3575822D+00 0.1323D+010.1271D+000.2616D+01-0.900.53600.357029.17%23.59%

    11 0.4118654D+00 0.1837D+010.1297D+010.9772D+0011 0.3544765D+00 0.1321D+010.1384D+000.2607D+01-0.850.59810.427032.55%28.22%

    12 0.4118654D+00 0.1837D+010.1297D+010.9772D+0012 0.3542143D+00 0.1324D+010.1356D+000.2624D+01-0.800.65720.499635.77%33.02%

    13 0.4118654D+00 0.1837D+010.1297D+010.9772D+0013 0.3541890D+00 0.1324D+010.1339D+000.2640D+01-0.750.71350.573238.83%37.88%

    14 0.3541856D+00 0.1324D+010.1332D+000.2648D+01-0.700.76700.646541.75%42.73%

    DEPENDENT VARIABLE IS TL15 0.3541854D+00 0.1324D+010.1332D+000.2649D+01-0.650.81810.718444.53%47.48%

    16 0.3541854D+00 0.1324D+010.1332D+000.2649D+01-0.600.86670.787947.17%52.08%

    SOURCE SUM-OF-SQUARES DF MEAN-SQUARE-0.550.91300.854449.69%56.47%

    DEPENDENT VARIABLE IS TL-0.500.95700.917152.09%60.61%

    REGRESSION 51.885065 3 17.295022-0.450.99900.975954.37%64.50%

    RESIDUAL 0.411865 28 0.014709SOURCE SUM-OF-SQUARES DF MEAN-SQUARE-0.401.03901.030456.55%68.10%

    -0.351.07711.080758.62%71.43%

    TOTAL 52.296933 31REGRESSION 51.942758 3 17.314253-0.301.11331.126860.60%74.47%

    CORRECTED 3.255059 30RESIDUAL 0.354185 28 0.012649-0.251.14781.168862.47%77.24%

    -0.201.18071.206864.26%79.76%

    RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.992124TOTAL 52.296933 31-0.151.21201.241165.97%82.03%

    CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.873469CORRECTED 3.255059 30-0.101.24181.272067.59%84.07%

    -0.051.27021.299769.14%85.90%

    RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.9932270.001.29731.324470.61%87.53%

    PARAMETER ESTIMATE A.S.E. LOWER UPPERCORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.8911890.051.32301.346572.01%88.99%

    LOO 1.837297 0.197139 1.433476 2.2411170.101.34761.366173.34%90.29%

    LO 1.297284 0.023883 1.248362 1.3462070.151.37091.383574.62%91.44%

    K 0.977224 0.234982 0.495886 1.458562PARAMETER ESTIMATE A.S.E. LOWER UPPER0.201.39321.399075.83%92.46%

    LO 1.324425 0.024032 1.275198 1.3736530.251.41431.412676.98%93.36%

    G 0.133171 0.052059 0.026533 0.2398080.301.43451.424778.08%94.16%

    ASYMPTOTIC CORRELATION MATRIX OF PARAMETERSK 2.648559 0.529647 1.563625 3.7334920.351.45371.435479.12%94.87%

    0.401.47201.444880.12%95.49%

    LOO LO K0.451.48941.453181.07%96.04%

    ASYMPTOTIC CORRELATION MATRIX OF PARAMETERS0.501.50601.460481.97%96.52%

    LOO 1.0000000.551.52181.466982.83%96.94%

    LO -0.255139 1.000000LO G K0.601.53691.472583.65%97.32%

    K -0.971124 0.392408 1.0000000.651.55121.477584.43%97.65%

    LO 1.0000000.701.56481.481985.17%97.94%

    G -0.504873 1.0000000.751.57781.485785.88%98.19%

    K 0.498843 -0.936806 1.0000000.801.59021.489186.55%98.41%

    0.851.60201.492087.19%98.61%

    0.901.61321.494687.80%98.78%

    0.951.62391.496988.38%98.93%

    1.001.63411.498988.94%99.06%

    1.051.64381.500689.47%99.18%

    1.101.65301.502289.97%99.28%

    1.151.66181.503590.45%99.37%

    1.201.67011.504790.90%99.45%

    1.251.67811.505791.34%99.52%

    1.301.68571.506791.75%99.58%

    1.351.69291.507592.14%99.63%

    Lo1.3244251.401.69981.508192.52%99.67%

    G0.1331711.451.70641.508892.87%99.71%

    k2.6485591.501.71261.509393.21%99.75%

    1.551.71861.509893.54%99.78%

    1.601.72421.510293.85%99.81%

    1.651.72961.510594.14%99.83%

    1.701.73481.510994.42%99.85%

    Gompertz1.751.73961.511194.68%99.87%

    MonthAge (yr)TLAge (yr)TL_Gompertz1.801.74431.511494.94%99.89%

    12.5710.00.00.000.02738541551.851.74871.511695.18%99.90%

    210.420.65410.5500.050.04504318431.901.75301.511895.41%99.91%

    38.20.46910.6100.100.06965204771.951.75701.511995.63%99.92%

    4151.03581.0000.150.1020371852.001.76081.512195.84%99.93%

    516.0671.12471.0500.200.14256573932.051.76451.512296.04%99.94%

    613.5160.91211.1000.250.19109754562.101.76791.512396.22%99.95%

    721.51.57741.2700.300.24700911232.151.77121.512496.40%99.96%

    817.4521.24011.3000.350.30927604352.201.77441.512596.58%99.96%

    914.931.02991.3350.400.37659083082.251.77741.512696.74%99.97%

    1017.711.26161.4350.450.44749211722.301.78021.512696.89%99.97%

    1117.4331.23851.4400.500.5204858812.351.78301.512797.04%99.97%

    1222.771.68331.4730.550.59414571142.401.78561.512797.18%99.98%

    1321.11.54411.4080.600.66718613222.451.78801.512897.32%99.98%

    1422.11.62741.4140.650.73850840682.501.79041.512897.45%99.98%

    1519.871.44161.4100.700.8072218946

    1618.51.32741.2900.750.8726459184

    1719.551.41491.2190.800.9342976261

    1819.551.41491.3210.850.9918709517

    1920.391.48491.4480.901.0452109361

    2019.091.37661.3970.951.0942866433

    2120.521.49581.4731.001.1391649338

    2219.811.43661.4221.051.1799865079

    2318.171.29991.3211.101.2169449766

    2419.131.37991.2951.151.2502692344

    2517.131.21331.3201.201.2802090877

    2624.51.82741.4601.251.3070238883

    2725.581.91741.4701.301.3309738233

    2820.811.51991.2201.351.3523134661

    2917.31.22741.5001.401.3712872001

    3021.471.57461.5001.451.3881261515

    3121.331.56351.5401.501.4030463115

    1.551.4162475718

    1.601.4279134445

    1.651.4382112806

    1.701.4472928373

    1.751.4552950776

    1.801.4623411138

    1.851.4685412266

    1.901.47399391

    1.951.4787869077

    2.001.4829982149

    2.051.4866970298

    2.101.4899446452

    2.151.4927952744

    2.201.4952968097

    2.251.4974915137

    2.301.4994166464

    2.351.5011050306

    2.401.5025855599

    2.451.503883653

    2.501.5050216599

    2.551.5060192228

    2.601.5068935973

    2.651.5076599368

    2.701.5083315444

    2.751.5089200956

    2.801.5094358352

    2.851.5098877504

    2.901.5102837239

    2.951.5106306686

    3.001.5109346459

    3.051.5112009699

    3.101.5114342993

    3.151.5116387175

    3.201.5118178036

    3.251.5119746944

    3.301.5121121387

    3.351.5122325456

    3.401.5123380258

    3.451.512430429

    3.501.5125113756

    3.551.5125822857

    3.601.5126444032

    3.651.5126988182

    3.701.5127464855

    3.751.5127882416

    3.801.5128248195

    3.851.5128568612

    3.901.5128849293

    3.951.5129095163

    4.001.5129310541

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    L_VBGF

    L_Gompertz

    000

    000.55

    000.61

    001

    001.05

    001.1

    001.27

    001.3

    001.335

    001.435

    001.44

    001.473

    001.408

    001.414

    001.41

    001.29

    001.219

    001.321

    001.448

    001.397

    001.473

    001.422

    001.321

    001.295

    001.32

    001.46

    001.47

    001.22

    001.5

    001.5

    001.54

    00

    00

    00

    00

    00

    00

    00

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    00

    L_VBGF

    L_Gompertz

    TL

    TL

    TL_Gompertz

    Age (yr)

    TL (m)

    TL_Gompertz

  • **von Bertalanffy (1938)dM/dt = M2/3 - M, differential equation eta and kappa are anabolic catabolic parameters but no physiological interpretation neededSubstitution method y = M1/3: dy/dt = /3 - /3y; ( = 3k will be used later)Separation of variable: dy/(/3 - /3y) = dtIntegration: -3/ ln(/3 - /3y ) = t + constant *Constant to be determined by value of y at t = 0*Final result: y = / - (/ - yo) e-(x/3) tBack-substitution: M(t) = [/ - (/ - w01/3) e-(x/3) t]3 [will become L(t) = L - (L - L0) e-k t ]

  • **L0 versus t0VBGF using L0 (von B. 1938) can be transformed mathematically to use x-axis intercept instead of y-axis intercept as 3rd parameter: L(t) = L ( e -k (t - to)); t0 = 1/k ln[(L - L0 )/ L]. The two formulations are mathematically equivalent.However, L0 has a biological meaning whereas t0 has none. Therefore, unreasonable L0 are easily detected but not unreasonable t0.

  • **1995 Edmonton in the Lions Den Slidevon Bertalanffy was at U of Alberta in Edmonton.I said it in 1995 and now Tampa 2005: von Bertalanffy (1938) did not use t-zero (not in any of his publications).t-zero was introduced by Beverton (1954) to simplify yield calculationsCame in widespread use after Beverton and Holt (1957) but it is not helpful for interpretation of VBGFs of elasmos with well defined size at birth (L0).

  • **k is a rate constant with units of reciprocal timeDifficult to deal with/understand reciprocal time.Better to interpret k in terms of half-life (ln2/k) with units of time.The time it takes to reach fraction x of L is given by tx = 1/k ln[(L - L0)/L(1- x)]. Can use x = 0.95 (Ricker 1979) and L0 = 0.2L: t0.95 = longevity = 2.77/k = 4.0 ln2/k (4 half-life). Could use x = 0.9933 and L0 = 0: t0.9933% = longevity = 5.00/k = 7.21 ln2/k (~ 7.2 half-life, Fabens 1965)x = 0.95 vs. x = 0.9933 produces large range of longevities that differ by almost a factor of 2! (7.21/4 = 1.80)

  • **L is inversely proportional to k We started with dM/dt = M2/3 - MSteady state means dM/dt = M2/3 - M = 0 after a long time when t = i.e. M () = M (L() = L )Therefore M1/3 = / (L = q (/) will become L = 3q (/k) L is inversely proportional to kThe steady state value (final mass or length) is determined by both and k, the time it takes to get there is determined by k only.

  • **Various 2-parameter VBGFs2-parameter VBGF (using size at age data) by using observed size at birth for L0. Justification: If one had age versus length data for neonates thats what the data would have to be.Fabens for tag-recapture data, also a 2-parameter VBGF (k and L). Length at tagging and recapture and time-at-large data are used.Gulland-Holt, yet another 2-parameter VBGF (k and L) which is usually used in graphical form by plotting annualized growth versus average size.

  • **Observed # of band-pairs in 3 populations. White sharks in SA appear to be younger for given TL?

    Chart1

    01.291.29

    01.3651.365

    01.4691.469

    01.51.5

    01.671.67

    11.4731.473

    11.591.59

    11.6761.676

    11.8321.832

    21.991.99

    22.0992.099

    22.2582.258

    22.342.34

    32.1342.134

    32.7752.775

    93.933.93

    134.5914.591

    134.6094.609

    145.0295.029

    145.0795.079

    154.9424.942

    1.2711.27

    1.4511.45

    1.4731.47

    1.5211.52

    1.5311.53

    1.5521.55

    1.5621.56

    1.7521.75

    1.7631.76

    1.7921.79

    1.7921.79

    1.811.8

    1.8321.83

    1.8921.89

    1.9231.92

    222

    2.0432.04

    2.0632.06

    2.1642.16

    2.232.2

    2.2952.29

    2.442.4

    2.5772.57

    2.5942.59

    2.672.6

    2.6842.68

    2.762.7

    2.7262.72

    2.7762.77

    2.7792.77

    2.7862.78

    2.9172.91

    2.9162.91

    3.0773.07

    3.1553.15

    3.3683.36

    3.593.5

    3.5383.53

    3.8103.8

    3.9573.95

    4144

    4.14114.14

    4.394.3

    4.3124.3

    4.5104.5

    4.5124.5

    4.6134.6

    4.7214.7

    4.9124.9

    5.18165.18

    5.2215.2

    5.2175.2

    1.653351.653351

    1.690881.690880

    1.828491.828491

    1.8397491.8397491

    1.866021.866021

    1.9098051.9098051

    1.941081.941081

    2.016142.016141

    2.066182.066182

    2.078692.078691

    2.153752.153751

    2.178772.178771

    2.178772.178772

    2.203792.203793

    2.2250572.2250572

    2.2300612.2300612

    2.2475752.2475753

    2.253832.253831

    2.2638382.2638382

    2.2775992.2775992

    2.2801012.2801013

    2.2826032.2826031

    2.291362.291363

    2.353912.353912

    2.416462.416462

    2.428972.428972

    2.4314722.4314723

    2.441482.441482

    2.46652.46652

    2.4727552.4727552

    2.4865162.4865163

    2.491522.491523

    2.5065322.5065322

    2.5140382.5140384

    2.529052.529053

    2.541562.541563

    2.541562.541563

    2.5465642.5465643

    2.554072.554073

    2.5815922.5815923

    2.5853452.5853454

    2.59162.59163

    2.6103652.6103653

    2.6228752.6228754

    2.629132.629134

    2.654152.654153

    2.6604052.6604052

    2.679172.679173

    2.691682.691682

    2.704192.704194

    2.704192.704194

    2.741722.741722

    2.741722.741725

    2.7504772.7504774

    2.754232.754234

    2.766742.766745

    2.7729952.7729953

    2.779252.779253

    2.779252.779254

    2.7892582.7892585

    2.7980152.7980154

    2.804272.804272

    2.804272.804274

    2.804272.804273

    2.8105252.8105253

    2.816782.816784

    2.816782.816784

    2.829292.829293

    2.854312.854314

    2.866822.866824

    2.879332.879334

    2.8855852.8855853

    2.904352.904352

    2.904352.904354

    2.9106052.9106055

    2.929372.929374

    2.9356252.9356253

    2.9606452.9606455

    2.96692.96694

    2.9894182.9894185

    2.991922.991924

    3.004433.004433

    3.029453.029456

    3.0519683.0519684

    3.0607253.0607254

    3.079493.079494

    3.129533.129535

    3.179573.179574

    3.179573.179575

    3.21713.21715

    3.2333633.2333634

    3.2483753.2483755

    3.254633.254635

    3.267143.267145

    3.3309413.3309415

    3.3359453.3359457

    3.367223.367224

    3.392243.392246

    3.429773.429776

    3.454793.454795

    3.46733.46736

    3.579893.579898

    3.617423.617427

    3.679973.679976

    3.692483.692485

    3.7187513.7187518

    3.742523.742526

    3.7487753.7487757

    3.7650383.7650386

    3.8863853.8863857

    4.017744.0177410

    4.71834.718313

    Bands CA

    Bands A

    Bands SA

    TL (m)

    Band count

    Cailliet

    Copied from Systat file Cc_Cailliet1985April 2005, check using reported VBGF

    Loo7.635591

    Lo1.418812

    k0.058302Redone in Systat April 2005 and confirming earlier values

    MyIDsexAge (y)TL (m) CalifBandsCD (mm) CalifTL (m) CalifAgeTL_VBGFITERATION LOS