Preliminary Demographic Analysis of the Basking Shark Cetorhinus maximus (Gunnerus, 1765)

Preliminary conclusion and perhaps as expected: Fecundity (litter size) is not the "problem". We need better mortality data and a better estimate of age-at-maturity.
Note: Population growth rate reported below is a purely analytical projections assuming that the environment is constant and that density effects are unimportant (Caswell 2001).

Age at maturity (alpha) 18 years (Pauly 1978); Longevity (w) about 40 years (Pauly 1978),; Mortality, assume M = 0.1151 yr-1 (S = 0.8913) based on longevity of 40 years and using M = -ln(0.01)/w; Fecundity, assume litter of 6 every third year, i.e. effective annual females fecundity of 6/(2x3) =1 (A litter of 6 is expected to weigh around 200 kg, which would be about 10% of the mass of the mother and falls into the expected range of 10-15%), ( A model using pregnant and resting stages in combination with actual fertility (6/2 = 3)would be better and produce a higher population growth rate)

Solution using life history table or 40x40 Leslie matrix: Lambda = 1.0030, growth rate of stable population (r = ln (lambda) = 0.003 yr-1); Net reproductvie rate Ro = 1.076, Generation "times": Abar = 24.35 yr (an age), T = ln(Ro)/r = 24.40 yr, mu1 = 24.44 yr (an age) (Abar/alpha = 1.35; T/alpha = 1.36)

Elasticities from life history table or 40x40 Leslie matrix (assuming gestation period (GP) of 1.5 yr) E(fertility) = E(m) = E1 = 1/Abar = 0.04107; E(juvenile survival) = E(JS) = E2 =( alpha - GP) E1 = 0.6777 (ratio ER2 = alpha - GP = 16.5); E(adult survival) = E(AS) = E3 = 1 - E2 = 0.3224 (ratio ER3 = Abar - alpha + GP = 7.85); (E1 + E2 + E3 = 1.04107; could normalize to 1.0 if needed; ER2 + ER3 = Abar = 24.35)

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 = 24.35). (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)