Euler-Lotka equation

b (a)

, death rate

d (a)

and exponential population growth rate

r

, the Euler-Lotka equation is

1 = \int_{0}^{\infty} b (a) exp (- r a - \int_{0}^{a} d (s) d s) d a .

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- Discrete Euler-Lotka equation Euler-Lotka equation

Discrete Euler-Lotka equation

For annual survival probabilities

1 - μ_{i}

, age-specific offspring numbers

b_{a}

, and a population multiplier

γ

, the discrete Euler-Lotka equation is

1 = \sum_{a = 1}^{\infty} [\prod_{i = 0}^{a - 1} (1 - μ_{i})] γ^{- a} b_{a} .

Its value at

γ = 1

is the expected lifetime offspring count of a newborn under the fixed vital rates. A value above one implies a growing mode

γ > 1

, while a value below one implies decline.

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Euler–Lotka equation by

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The Euler–Lotka equation is a fundamental equation in population dynamics and ecology that describes the relationship between the age-specific birth and death rates of a population and its growth rate. It is particularly useful in modeling the growth of structured populations where individuals can have age-dependent survival and fertility rates.

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