Demographic Analysis of the Shortfin mako Isurus oxyrinchus Rafinesque, 1809

Demographic Analysis of the Shortfin Mako Isurus oxyrinchus Rafinesque, 1809

A) Using Cailliet et al. (1983) assumption of 1 band-pair/year B) Using Pratt and Casey (1983) assumption of 2 band-pairs/year

Age-at-maturity 13.5 years ;
Age-at-first-reproduction (α) 15.0 years ;
Longevity (ω) about 21years ,;
Mortality, M = 0.1645 yr-1 (S = 84.8%) based on longevity of 21 years and using M = -ln(0.01)/21 ;
Llitter of 12.5 every third year, i.e. fecundity of 12.5/6 =2.083
Gestation period 1.5 yr
σ/α = 1.3 (using low value of range 1.3-1.5 because species is relatively short lived), thus σ = 18.2 yr.
Age-at-maturity 6.5 years ;
Age-at-first-reproduction (α) 8.0 years ;
Longevity (ω) about 28 years,;
Mortality, M = 0.2193 yr-1 (S = 80.3%) based on longevity of 15 years and using M = -ln(0.01)/28;
Llitter of 12.5 every third year, i.e. fecundity of 12.5/6 =2.083
Gestation period 1.5 yr
σ/α = 1.3 (using low value of range 1.3-1.5 because species is relatively short lived), thus σ = 9.1 yr.

Elasticities from α = 15.0 yr, σ = 18.2 yr, and GP = 0.1.5 yr
E(fertility) = E(m) = E1 = 1/σ = 0.0513;
E(juvenile survival) = E(JS) = E2 =(α - GP) E1 = 0.689 (ratio ER2 = alpha - GP = 12.5);
E(adult survival) = E(AS) = E3 = 1 - E2 = 0.313 (ratio ER3 = σ - α + GP = 5.7);
(E1 + E2 + E3 = 1.0513);

Normalized elasticities: E1 = 4.9%, E2 = 65.9%, E3 = 29.3%

Elasticities from α = 8yr, σ = 10.4yr, and GP = 1.5 yr
E(fertility) = E(m) = E1 = 1/σ = 0.0962;
E(juvenile survival) = E(JS) = E2 =(α - GP) E1 = 0.625 (ratio ER2 = alpha - GP = 6.5);
E(adult survival) = E(AS) = E3 = 1 - E2 = 0.375 (ratio ER3 = σ - α + GP = 3.9);
(E1 + E2 + E3 = 1.0962);

Normalized elasticities: E1 = 8.8%, E2 = 57.0%, E3 = 34.2%

Solution using life history table or 21x21 Leslie matrix (Mollet and Cailliet 2002, unpublished manuscript based on (α) = 7 yr):
Lambda = 1.0810, growth rate of stable population (r = ln (λ) = 0.0779 yr^-1); Net reproductive rate Ro = 2.1944,
Generation "times": Abar = 9.71 yr (an age), T = ln(Ro)/r = 10.1 yr, μ₁ = 10.5 yr (an age) (Abar/α = 1.387);
Elasticities E1 = 0.1029, E2 = 0.7203, E3 = 0.2797; sum is 1.1029
Normalized elasticites E1 = 9.3%, E2 = 65.4%, E3 = 25.3%.
Recent aging work by others had indicated that age-at-first reproduction was more likely to be around 15 years than the 7 years we used in this withdrawn manusript. However, these calculations based on incorrect vital parameters i.e. α off by about a factor of 2, indicate that the elasticity pattern is still roughly correct with E2 by far the largest term.

Created December 2002, revised December 2002. Back to home page.

Please send comments or corrections to henry@elasmollet.org

Demographic Analysis of the Shortfin Mako Isurus oxyrinchus Rafinesque, 1809

A) Using Cailliet et al. (1983) assumption of 1 band-pair/year	B) Using Pratt and Casey (1983) assumption of 2 band-pairs/year
Age-at-maturity 13.5 years ; Age-at-first-reproduction (α) 15.0 years ; Longevity (ω) about 21years ,; Mortality, M = 0.1645 yr-1 (S = 84.8%) based on longevity of 21 years and using M = -ln(0.01)/21 ; Llitter of 12.5 every third year, i.e. fecundity of 12.5/6 =2.083 Gestation period 1.5 yr σ/α = 1.3 (using low value of range 1.3-1.5 because species is relatively short lived), thus σ = 18.2 yr.	Age-at-maturity 6.5 years ; Age-at-first-reproduction (α) 8.0 years ; Longevity (ω) about 28 years,; Mortality, M = 0.2193 yr-1 (S = 80.3%) based on longevity of 15 years and using M = -ln(0.01)/28; Llitter of 12.5 every third year, i.e. fecundity of 12.5/6 =2.083 Gestation period 1.5 yr σ/α = 1.3 (using low value of range 1.3-1.5 because species is relatively short lived), thus σ = 9.1 yr.
Elasticities from α = 15.0 yr, σ = 18.2 yr, and GP = 0.1.5 yr E(fertility) = E(m) = E1 = 1/σ = 0.0513; E(juvenile survival) = E(JS) = E2 =(α - GP) E1 = 0.689 (ratio ER2 = alpha - GP = 12.5); E(adult survival) = E(AS) = E3 = 1 - E2 = 0.313 (ratio ER3 = σ - α + GP = 5.7); (E1 + E2 + E3 = 1.0513); Normalized elasticities: E1 = 4.9%, E2 = 65.9%, E3 = 29.3%	Elasticities from α = 8yr, σ = 10.4yr, and GP = 1.5 yr E(fertility) = E(m) = E1 = 1/σ = 0.0962; E(juvenile survival) = E(JS) = E2 =(α - GP) E1 = 0.625 (ratio ER2 = alpha - GP = 6.5); E(adult survival) = E(AS) = E3 = 1 - E2 = 0.375 (ratio ER3 = σ - α + GP = 3.9); (E1 + E2 + E3 = 1.0962); Normalized elasticities: E1 = 8.8%, E2 = 57.0%, E3 = 34.2%
Solution using life history table or 21x21 Leslie matrix (Mollet and Cailliet 2002, unpublished manuscript based on (α) = 7 yr): Lambda = 1.0810, growth rate of stable population (r = ln (λ) = 0.0779 yr^-1); Net reproductive rate Ro = 2.1944, Generation "times": Abar = 9.71 yr (an age), T = ln(Ro)/r = 10.1 yr, μ₁ = 10.5 yr (an age) (Abar/α = 1.387); Elasticities E1 = 0.1029, E2 = 0.7203, E3 = 0.2797; sum is 1.1029 Normalized elasticites E1 = 9.3%, E2 = 65.4%, E3 = 25.3%. Recent aging work by others had indicated that age-at-first reproduction was more likely to be around 15 years than the 7 years we used in this withdrawn manusript. However, these calculations based on incorrect vital parameters i.e. α off by about a factor of 2, indicate that the elasticity pattern is still roughly correct with E2 by far the largest term.

Demographic Analysis of the Shortfin Mako Isurus oxyrinchus Rafinesque, 1809