| Vital rates needed for demograhic analysis are
age-specific mortality rate M (can be estimated from longevity), age-at-first
reproduction (alpha = age-at-first reproduction), 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; 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%); alpha, w, and m (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 = 1.196. |
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. |
|
Elasticities from life history table or 45x45 Leslie matrix: E(fertility) = E(m) = E1 = 1/Abar = 0.05225; E(juvenile survival) = E(JS) = E2 = 0.8359 (ratio ER2 = alpha = 16); E(adult survival) = E(AS) = E3 = 1 - E2 = 0.1641 (ratio ER3 = Abar - alpha = 5.14); E1 + E2 + E3 = 1.0523; ER2 + ER3 = Abar = 19.14) |
Elasticities from life history table or 45x45 Leslie matrix
(assuming gestation period (GP) of 1 yr): E(fertility) = E(m) = E1 = 1/Abar = 0.0478; E(juvenile survival) = E(JS) = E2 =( alpha - GP) E1 = 0.7652 (ratio ER2 = alpha = 16); E(adult survival) = E(AS) = E3 = 1 - E2 = 0.2348 (ratio ER3 = Abar - alpha = 4.91); (E1 + E2 + E3 = 1.0468; ER2 + ER3 = Abar = 20.91 |
|
Normalized elasticities (from LHT resutls above) |
Normalized elasticities (LHT results above) E(fertility) = 4.56%; E(juvenile survival) = 73.0% E(adult survival) = 22.4% |