Preliminary Demography of the Whale Shark Rhincodon typus Smith, 1828
In progress, evaluation of age-at-maturity (18),
first year suvival rate of P1 = 10% & subsequent survival of P = 93.2%; and litter size (300)

ELALMO-L Posting 5 April 2001: The whale shark reproductive strategy shows enormous growth potential. Now all we have to do is to figure out which parameter(s) might be "off". Then the whale shark can be "managed" for a come back. I see somebody with a big bucket of krill in the Indo-Pacific Ocean and only one person will qualify to carry it!

Pauly (2001) suggested k (VBGF)=0.031 yr-1 and a longevity of > 100 years which he considered to be rather high. The corresponding first year growth would be 0.39 m. The observed growth rate in captivity at the National Museum fo Marine Biology-Aquarium, Taiwan ROC was 0.81 cm in 120 days (Fang et al. 1996, AES New Orleans Abstract). The corresponding annual growth would be over 2m which I consider to be to high for growth in the wild. I guesstimated that first year growth of a a whale shark in the wild is 0.80 m, This would be about twice as high as what the Pauly (2001) VBGF suggests and roughly about 1/3 of what growth in captivity might have been in one year with feeding to satiation with a good soup of krill. This yields k (VBGF) = 0.0637 yr-1, in combination with TLo = 0.58 m (Joung et al. 1996) and TLoo = 13.7 m (Compagno, 1984). I further assume that maturity is reached at 70% of TLoo, which would be 9.6 m with corresponding age-at-maturtiy of about 18 years. Age at maturity 18 years. Longevity about 55 years (5ln2/k)) Mortality, a) assume that first year survival is 10% only and b) subsequent survival is 93.2% (from M = 0.0704 yr-1 based on longevity of 55 years and using Hoenig (1983) for cetaceans; The litter size was 300 in a 10 m TL, 16000 kg female (Joung et al. 1996, AES meeting New Orleans abstract). I assumed that the reproductive cycle is 2 years which gives an effective annual female fecundity of 300/2x2) = 75. We know little about gestation period and the reproductive cycle, so that's what I asssumed for a start. I doubt that this is going to be a critical assumption, because the elasticity of the fertility matrix element is expected to be low. The total litter mass was estimated to be 300 kg, which is a mere 2% of the reported mass of 16000 kg of the mother. A litter every year is a good possibility and the population growth rate would be even higher.

Solution using life history table or 55x55 Leslie matrix: Lambda = 1.1482, growth rate of stable population (r = ln (lambda) = 0.1382 yr-1); Net reproductvie rate Ro = 31.04!, Generation "times": Abar = 22.30 yr (an age), T = ln(Ro)/r = 24.86 yr, mu1 = 28.9 yr (an age) (Abar/alpha = 1.24; T/alpha = 1.38)

Elasticities from life history table or 55x55 Leslie matrix (assuming gestation period (GP) of 1.0 yr) E(fertility) = E(m) = E1 = 1/Abar = 0.0448; E(juvenile survival) = E(JS) = E2 =( alpha - GP) E1 = 0.7624 (ratio ER2 = alpha - GP = 17.0); E(adult survival) = E(AS) = E3 = 1 - E2 = 0.2376 (ratio ER3 = Abar - alpha + GP = 5.3); (E1 + E2 + E3 = 1.0448; could normalize to 1.0 if needed; ER2 + ER3 = Abar = 22.30)

Estimated elasticities from age-at-first reproduction alone! (Abar was assumed to be same a T and T was approximated as 1.3 alpha = 23.4 yr (versus "correct" Abar = 22.30). (Gestation time was assumed to be 1.0.) E(fertility) = E(m) = E1 = 1/Abar = 0.0427; E(juvenile survival) = E(JS) = E2 = 0.73 (ratio ER2 = 17.0); E(adult survival) = E(AS) = E3 = 0.27 (ratio ER3 = 6.4); (E1 + E2 + E3 = 1.0427; could normalize to 1.0 if needed; ER2 + ER3 = Abar = 23.4)