Demographic Analysis of the Pelagic Stingray Dasyatis (Pteroplatytrygon) violacea Bonaparte, 1832)

Demographic Analysis of the Pelagic stingray Pteroplatytrygon (Dasyatis) violacea (Bonaparte, 1832)

A) Using Captive data (Mollet et al. 2002) B) Using guesstimates for field data

Age-at-first reproduction (α) 3 years ;
Longevity (ω) about 10 years ,;
Mortality, M = 0.4605 yr-1 (S = 0.6310) based on longevity of 10 years and using M = -ln(0.01)/10 ;
Llitter of 6 every year, i.e. fecundity of 6/2 =3;
Gestation period 0.167 yr (2 months)
σ/α = 1.3 (using low value of range 1.3-1.5 because species is relatively short lived), thus σ = 3.9 yr.

Age-at-first reproduction ( α) 5 years ;
Longevity (ω) about 15 years,;
Mortality, M = 0.3070 yr-1 (S = 0.7356) based on longevity of 15 years and using M = -ln(0.01)15;
Litter of 6 every year, i.e. fecundity of 6/2 =3;
Gestation period 0.167 yr (2 months)
σ/α = 1.3 (using low value of range 1.3-1.5 because species is relatively short lived), thus σ = 6.5 yr.

Elasticities from α = 3 yr, σ = 3.9 yr, and GP = 0.167 yr
E(fertility) = E(m) = E1 = 1/σ = 0.256;
E(juvenile survival) = E(JS) = E2 =(α - GP) E1 = 0.727 (ratio ER2 = alpha - GP = 2.83);
E(adult survival) = E(AS) = E3 = 1 - E2 = 0.273 (ratio ER3 = σ - α + GP = 1.07);
(E1 + E2 + E3 = 1.256);

Normalized elasticities: E1 = 20.4%, E2 = 57.8%, E3 = 21.8%

Elasticities from α = 5 yr, σ = 6.5 yr, and GP = 0.167 yr
E(fertility) = E(m) = E1 = 1/σ = 0.154;
E(juvenile survival) = E(JS) = E2 =(α - GP) E1 = 0.744 (ratio ER2 = alpha - GP = 2.83);
E(adult survival) = E(AS) = E3 = 1 - E2 = 0.256 (ratio ER3 = σ - α + GP = 1.07);
(E1 + E2 + E3 = 1.154);

Normalized elasticities: E1 = 13.3%, E2 = 64.4%, E3 = 22.2%

Solution using life history table or 10x10 Leslie matrix (Mollet and Cailliet 2002):
Lambda = 1.1739, growth rate of stable population (r = ln (λ) = 0.1604 yr^-1); Net reproductvie rate Ro = 1.9901,
Generation "times": σ = 4.11 yr (an age), T = ln(Ro)/r = 4.29 yr, μ₁ = 4.50 yr (an age) (σ/α = 1.37);
Elasticities E1 = 0.2436, E2 = 0.4871, E3 = 0.5129;
Normalized elasticites E1 = 19.6%, E2 = 39.2%, E3 = 41.2%.
At first sight the normalized elasticitied don't seem to agree well with the prediected ones given above. However, Mollet and Cailliet (2002) used the pelagic stingray example, with few age classes, as a demonstration example suitable for longer-lived sharks with a gestation period or 1 yr. Had we used a gestation period of 0.167 yr (2 months) instead of 1 year, then the normalized elasticities would have been E1 = 19.6%, E2 = 55.5%, E3 = 24.9% in good agreement with the left hand set above and clearly showing that E2 > E3 even for a species with low age-at-first reproduction.

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

Please send comments or corrections to mollet@pacbell.net

Demographic Analysis of the Pelagic stingray Pteroplatytrygon (Dasyatis) violacea (Bonaparte, 1832)
A) Using Captive data (Mollet et al. 2002)	B) Using guesstimates for field data
Age-at-first reproduction (α) 3 years ; Longevity (ω) about 10 years ,; Mortality, M = 0.4605 yr-1 (S = 0.6310) based on longevity of 10 years and using M = -ln(0.01)/10 ; Llitter of 6 every year, i.e. fecundity of 6/2 =3; Gestation period 0.167 yr (2 months) σ/α = 1.3 (using low value of range 1.3-1.5 because species is relatively short lived), thus σ = 3.9 yr.	Age-at-first reproduction ( α) 5 years ; Longevity (ω) about 15 years,; Mortality, M = 0.3070 yr-1 (S = 0.7356) based on longevity of 15 years and using M = -ln(0.01)15; Litter of 6 every year, i.e. fecundity of 6/2 =3; Gestation period 0.167 yr (2 months) σ/α = 1.3 (using low value of range 1.3-1.5 because species is relatively short lived), thus σ = 6.5 yr.
Elasticities from α = 3 yr, σ = 3.9 yr, and GP = 0.167 yr E(fertility) = E(m) = E1 = 1/σ = 0.256; E(juvenile survival) = E(JS) = E2 =(α - GP) E1 = 0.727 (ratio ER2 = alpha - GP = 2.83); E(adult survival) = E(AS) = E3 = 1 - E2 = 0.273 (ratio ER3 = σ - α + GP = 1.07); (E1 + E2 + E3 = 1.256); Normalized elasticities: E1 = 20.4%, E2 = 57.8%, E3 = 21.8%	Elasticities from α = 5 yr, σ = 6.5 yr, and GP = 0.167 yr E(fertility) = E(m) = E1 = 1/σ = 0.154; E(juvenile survival) = E(JS) = E2 =(α - GP) E1 = 0.744 (ratio ER2 = alpha - GP = 2.83); E(adult survival) = E(AS) = E3 = 1 - E2 = 0.256 (ratio ER3 = σ - α + GP = 1.07); (E1 + E2 + E3 = 1.154); Normalized elasticities: E1 = 13.3%, E2 = 64.4%, E3 = 22.2%
Solution using life history table or 10x10 Leslie matrix (Mollet and Cailliet 2002): Lambda = 1.1739, growth rate of stable population (r = ln (λ) = 0.1604 yr^-1); Net reproductvie rate Ro = 1.9901, Generation "times": σ = 4.11 yr (an age), T = ln(Ro)/r = 4.29 yr, μ₁ = 4.50 yr (an age) (σ/α = 1.37); Elasticities E1 = 0.2436, E2 = 0.4871, E3 = 0.5129; Normalized elasticites E1 = 19.6%, E2 = 39.2%, E3 = 41.2%. At first sight the normalized elasticitied don't seem to agree well with the prediected ones given above. However, Mollet and Cailliet (2002) used the pelagic stingray example, with few age classes, as a demonstration example suitable for longer-lived sharks with a gestation period or 1 yr. Had we used a gestation period of 0.167 yr (2 months) instead of 1 year, then the normalized elasticities would have been E1 = 19.6%, E2 = 55.5%, E3 = 24.9% in good agreement with the left hand set above and clearly showing that E2 > E3 even for a species with low age-at-first reproduction.

Demographic Analysis of the Pelagic stingray Pteroplatytrygon (Dasyatis) violacea (Bonaparte, 1832)