Vital Rates (Life History Parameters) and Elasticities
of the Porbeagle, Lamna nasus in the western North Atlantic


Parameter Female Male References
Largest specimens
(Length and mass)
3.17 m FL,
~3.55 m TL, 230 kg;
2.62 m FL
~ 2.95 mTL;
Francis et al. (in press)
Oldest documented age 24 (validated up to age 11) 25 Natanson et al. (2002)
Size at maturity 2.10-2.30 m FL
~2.36-2.59 m TL
1.62-1.85 m FL.
~1.82-2.08 m TL
Jensen et al. (2002)
Smallest mature ~2.15 m FL ~1.65 FL; Jensen et al. (2002) Figs.2-7
Largest immature ~2.25 mFL; ~1.85 m FL; Jensen et al. (2002) Figs.2-7
Sizes at which 10, 50, and 90% are mature (c) ~2.05, 2,18, ~2.25 mFL

~1.65, 1.74, ~1.85 mFL

Jensen et al. (2002) Fig. 4
Age at maturity
13.1 yr
8.1 yr Jensen et al. 2002
Gestation time 8-9 months   Francis and Stevens 2000; Jensen et al. 2002
Reproductive cycle 1 year   Francis and Steven 2000; Jensen et al. 2002
Litter size (# of pups in litter) 4 Francis and Stevens 2000; Jenssen et al. 2002
Birth size estimate 0.58-0.67 m FL, 0.68-0.78 m TL Francis and Stevens 2000;
Smallest free-swimming 0.58-0.67 m FL, 0.68-0.78 m TL Francis et al. (in press)
First year growth ~15-25 cm FL Natanson et al. 2002
Von Bertalanffy Growth Function (VBGF)
LnVBGF.gif

FLoo = 3.098 m,
FLo = 0.936 m (unrealistically high, to = -5.90 yr),
k = 0.061 yr-1,
5ln2/k = 56.8 yr
(longevity estimate)

FLoo = 2.577 m,
FLo = 0.954 (unrealistically high, to = -5.78 yr),
k = 0.080 yr-1,
5ln2/k = 43.3 yr
(longevity estimate)

Natanson et al. 2002 (VBGF based on vertebral data, unrealistically low FLo is suggested to be due biased samples of age-0 fish)

Mass-FL relationship (a) M(kg) = 12.6 FL2.9641 (m), sexes combined;
M(kg( = 13.33 FL2.7134 (m), sexes combined

Kohler et al. 1995;
Compana et al. 1999

Elasticity estimates based on alpha = 14 yr, Assume Abar/alpha = 1.5 (thus Abar = 21 yr)

E(m) = 1/Abar = 1/21.0 =  0.0476;
E(JS)/E(m) = ER2 = alpha = 14.0, E(JS) = 0.667 
E(AS)/E(m) = ER3 = Abar - alpha = 7; E(AS) = 0.333
ER2 + ER3 = Abar;
Sum elasticities = 1 + E(n) = 1.048

Mollet 2003 (AES Manaus)
Normalized elasticities:
E(fertility = E(m)  = 4.5%;
E(juvenile survival) = E(JS) = 63.6%;
E (adult survival) = E(AS) = 31.8%

Parameter Female Male References



a) The pre-exponential constant gives the weight of a 1 m FL porbeagle because I converted the reported equation using cm for FL to meter.

Vital rates needed for demograhic analysis are age-specific mortality rate M (can be estimated from longevity), age-at-first reproduction (alpha = age-at-maturity + gestation period), longevity estimate w (can be estimated from Von Bertalanffy growth curve), and fertility m (number of female pups born per year). The following values were used by Campagna et al. (in press) in a demographics analysis (but I have suppliedthe elasticities):
A) M(pups) = 0.2 yr-1, M(juveniles) = M(adults) = 0.1 yr-1. (M = -ln(0.01)/45 = 0.1023 yr-1 is almost the same);
Alpha = 13 yr; w = 45; m ~ 3.9/2 = 1.95
Results: Lambda = 1.085, Ro = 4.87, Abar = 17.94 yr, T = 19.4 yr, mu1 = 21.2yr
Elasticity results for comparison with estimates given above: E(m) = 0.056; E(JS) = 0.725, E(JS)/E(m) = 13.0; E(AS) = 0.275, E(AS)/E(m) = 4.94 (Sum = 1.056). Normalized values: E(m) = 5.3%, E(JS) = 68.6%, E(AS) = 31.4%.
B) M(pups) = 0.2 yr-1, M(juveniles) = 0.1 yr-1; M(Adults) = 0.2 yr-1
Alpha = 13 yr ; w ~ 30; m ~ 3.9/2 = 1.95
Results: Lambda = 1.0523, Ro = 2.33, Abar = 16.31.yr (Abar is simalar to value obtained in A, thus elasticities should be similar), T = 16.6 yr, mu1 = 17.07 yr. Elasticity results for comparison with estimates given above: E(m) = 0.0613; E(JS) = 0.736, E(JS)/E(m) = 13.0; E(AS) = 0.264, E(AS)/E(m) = 5.9 (Sum = 1.061). Normalized values: E(m) = 5.28%, E(JS) = 68.6%, E(AS) = 26.1%.


Created October 2002; updated November 2002. Back to previous page
Please send comments or corrections to henry@elasmollet.org