Demography of the Sevengill shark Notorynchus cepedianus

Preliminary Demography of the Sevengill shark Notorynchus cepedianus

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). I used the following values for a preliminary demographics analysis:

A) M ~-ln(0.01)/45 = 0.1023 yr^-1 (S = 90%) for pups, juveniles, and adults (fraction of females left at age 45 yr is 1%);
Alpha ~16 yr;
w ~ 45 years;
m ~ 79/(2x2) ~ 20 . B) M (pups) = 0.69 yr^-1 (S = 50%) ,M (juveniles) = 0.2231 (S = 80%) then M ~-ln(0.01)/45 = 0.1023 yr^{-1 (S = 90%) (fraction of
females left at age 45 yr is 0.1%);}
Alpha ~16 yr (same as in A);
w ~ 45 years (same as in A);
m ~ 79/(2x2) ~ 20 (same as in A).

Solution using life history table or 45x45 Leslie matrix:
Lambda = 1.1898, (r = ln (lambda) = 0.1738 yr^-1);
Net reproductvie rate Ro = 38.13;
Generation "times": Abar = 19.14 yr (an age), T = ln(Ro)/r = 20.96 yr, mu1 = 23.82 yr (an age)
(Abar/alpha = 1.20; T/alpha = 1.31) Solution using life history table or 45x45 Leslie matrix:
Lambda = 1.0082, (r = ln (lambda) = 0.0816 yr^-1);
Net reproductvie rate Ro = 6.163;
Generation "times": Abar = 20.91 yr (an age), T = ln(Ro)/r = 23.11 yr, mu1 = 26.15 yr (an age)
(Abar/alpha = 1.39; T/alpha = 1.54)

Elasticities from life history table or 45x45 Leslie matrix (assuming gestation period (GP) of 1 yr):
E(fertility) = E(m) = E1 = 1/Abar = 0.05225;
E(juvenile survival) = E(JS) = E2 = 0.7838 (ratio ER2 = alpha - GP = 15);
E(adult survival) = E(AS) = E3 = 1 - E2 = 0.2162 (ratio ER3 = Abar - alpha + GP = 4.14);
E1 + E2 + E3 = 1.0523;
ER2 + ER3 = Abar = 19.1)

Elasticities from life history table or 45x45 Leslie matrix (assuming gestation period (GP) of 1 yr):
E(fertility) = E(m) = E1 = 1/Abar = 0.0468;
E(juvenile survival) = E(JS) = E2 =( alpha - GP) E1 = 0.6999 (ratio ER2 = alpha - GP = 15);
E(adult survival) = E(AS) = E3 = 1 - E2 = 0.3001 (ratio ER3 = Abar - alpha + GP = 6.43);
(E1 + E2 + E3 = 1.0468;
ER2 + ER3 = Abar = 20.9

Normalized elasticities (from LHT resutls above)
E(fertility) = 5.0%;
E(juvenile survival) = 74.5%
E(adult survival) = 20.5
Normalized elasticities (LHT results above)
E(fertility) = 4.5%;
E(juvenile survival) = 66.9%
E(adult survival) = 28.7%

Estimated elasticities from age-at-first reproduction alone!
(Abar/alpha was assumed to be 1.5 , thus Abar = 24 yr)same a T and T was approximated as 1.3 alpha = 20.8 yr (Gestation time was assumed to be 1.0.)
E(fertility) = 1/Abar = 0.0481;
E(juvenile survival) = 0.721 (from ratio ER2 = alpha - GP = 15.0);
E(adult survival) = 0.279 (from ratio ER3 = Abar - alpha + GP = 5.4);

Normalized elasticities from alpha and Abar estimate without the need for any calculations (see left columns for details):

E(fertility) = 4.6%;
E(juvenile survival) = 68.8%;
E(adult survival) = 26.6%.

Created April November 2002, revised November 2002. Back to previous page.

Please send comments or corrections to mollet@pacbell.net

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). I used the following values for a preliminary demographics analysis:
A) M ~-ln(0.01)/45 = 0.1023 yr^-1 (S = 90%) for pups, juveniles, and adults (fraction of females left at age 45 yr is 1%); Alpha ~16 yr; w ~ 45 years; m ~ 79/(2x2) ~ 20 .	B) M (pups) = 0.69 yr^-1 (S = 50%) ,M (juveniles) = 0.2231 (S = 80%) then M ~-ln(0.01)/45 = 0.1023 yr^{-1 (S = 90%) (fraction of females left at age 45 yr is 0.1%);} Alpha ~16 yr (same as in A); w ~ 45 years (same as in A); m ~ 79/(2x2) ~ 20 (same as in A).
Solution using life history table or 45x45 Leslie matrix: Lambda = 1.1898, (r = ln (lambda) = 0.1738 yr^-1); Net reproductvie rate Ro = 38.13; Generation "times": Abar = 19.14 yr (an age), T = ln(Ro)/r = 20.96 yr, mu1 = 23.82 yr (an age) (Abar/alpha = 1.20; T/alpha = 1.31)	Solution using life history table or 45x45 Leslie matrix: Lambda = 1.0082, (r = ln (lambda) = 0.0816 yr^-1); Net reproductvie rate Ro = 6.163; Generation "times": Abar = 20.91 yr (an age), T = ln(Ro)/r = 23.11 yr, mu1 = 26.15 yr (an age) (Abar/alpha = 1.39; T/alpha = 1.54)
Elasticities from life history table or 45x45 Leslie matrix (assuming gestation period (GP) of 1 yr): E(fertility) = E(m) = E1 = 1/Abar = 0.05225; E(juvenile survival) = E(JS) = E2 = 0.7838 (ratio ER2 = alpha - GP = 15); E(adult survival) = E(AS) = E3 = 1 - E2 = 0.2162 (ratio ER3 = Abar - alpha + GP = 4.14); E1 + E2 + E3 = 1.0523; ER2 + ER3 = Abar = 19.1)	Elasticities from life history table or 45x45 Leslie matrix (assuming gestation period (GP) of 1 yr): E(fertility) = E(m) = E1 = 1/Abar = 0.0468; E(juvenile survival) = E(JS) = E2 =( alpha - GP) E1 = 0.6999 (ratio ER2 = alpha - GP = 15); E(adult survival) = E(AS) = E3 = 1 - E2 = 0.3001 (ratio ER3 = Abar - alpha + GP = 6.43); (E1 + E2 + E3 = 1.0468; ER2 + ER3 = Abar = 20.9
Normalized elasticities (from LHT resutls above) E(fertility) = 5.0%; E(juvenile survival) = 74.5% E(adult survival) = 20.5	Normalized elasticities (LHT results above) E(fertility) = 4.5%; E(juvenile survival) = 66.9% E(adult survival) = 28.7%
Estimated elasticities from age-at-first reproduction alone! (Abar/alpha was assumed to be 1.5 , thus Abar = 24 yr)same a T and T was approximated as 1.3 alpha = 20.8 yr (Gestation time was assumed to be 1.0.) E(fertility) = 1/Abar = 0.0481; E(juvenile survival) = 0.721 (from ratio ER2 = alpha - GP = 15.0); E(adult survival) = 0.279 (from ratio ER3 = Abar - alpha + GP = 5.4);	Normalized elasticities from alpha and Abar estimate without the need for any calculations (see left columns for details): E(fertility) = 4.6%; E(juvenile survival) = 68.8%; E(adult survival) = 26.6%.