Deterministic elasticity patterns of age-structured animals
Henry F. Mollet, Moss Landing Marine Labs, Moss Landing CA 95039 and Monterey Bay Aquarium, Monterey CA 93940
The elasticity pattern (E-pattern) of an age-structured animal comprising the elasticities E(fertility, m), E(juvenile survival, Sj) and E(adult survival, Sa) is determined by age at first reproduction (alpha) and mean age of the reproducing females at the stable age distribution (Abar ): E(m) = 1/Abar , E(Sj) = alpha/Abar , E(Sa) = (Abar-alpha)/Abar . The sum of the E-pattern is 1 + E(m), and has to be normalized when graphed in an elasticity triangle for easy interpretation. It is important to include the survival part in the discounted fertilities of the Leslie matrix when calculating the E-pattern, otherwise post- and pre-breeding census will yield different and biased E-patterns. This bias is largest for animals with alpha = 1 yr. Assuming age-independent m and Sa, a new 3-term algebraic equation for Abar is presented that facilitates the understanding and interpretation of E-patterns.