Flashcards — 227–237 (Age structure → stable age distribution → life tables + survivorship curves + R₀, T, intrinsic increase, doubling time intro)

age structure

proportions of individuals in each age class in a population.

stable age distribution

a condition where the percentage of individuals in each age class remains constant over time (when age-specific survival and fecundity rates are constant).

life tables

summaries of age-specific schedules of survival and fecundity used to model additions and removals of individuals in a population.

fecundity (b_x)

female offspring produced per reproductive season or age interval by females of age x.

survival (s_x)

probability an individual survives from age x to age x+1.

cohort (dynamic) life table

follows a group born at the same time from birth to death of the last individual.

life table (variables)

uses age x and age-specific values such as n_x (number alive), b_x (fecundity), s_x (survival), and l_x (survivorship).

static (time-specific) life table

measures survival and fecundity for individuals of known age during a single time interval (under the same environmental conditions).

intrinsic rate of increase (λ_m or r_m)

the geometric or exponential growth rate assumed by a population with a stable age distribution under constant life-table conditions.

net reproductive rate (R₀)

sum of l_x b_x; the expected total number of female offspring produced by an average female over her lifetime.

generation time (T)

average age at which an individual gives birth to offspring; T = (sum x l_x b_x) / (sum l_x b_x).

doubling time (t₂)

time required for a population to double; t₂ = ln(2)/ln(λ) (equivalently, t₂ = ln(2)/r).

carrying capacity (K)

the number of individuals the environment can support; in logistic growth, growth slows as N approaches K.

What is a stable age distribution?

When the percentage of individuals in each age class stays constant over time, assuming constant age-specific survival and fecundity.

Why might λ fluctuate before stabilizing in a population projection?

Because the starting population may not have the stable age distribution; it takes time for age structure to “settle.”

What is a life table?

A summary of age-specific survival and fecundity used to model additions/removals of individuals.

Why are life tables often based on females?

Because paternity is hard to determine; female reproduction is easier to track and usually sufficient for modeling.

What does (x) mean in life-table notation?

Age, with subscript (x) indicating age-specific values.

What is (n_x)?

Number of individuals alive at age (x).

What is fecundity (b_x)?

Female offspring produced per season/interval by females of age (x).

What is survival (s_x)?

Probability of surviving from age (x) to (x+1).

What is survivorship (l_x)?

Probability a newborn survives to be alive at age (x) (cumulative survival).

How can (s_x) be calculated from a “numbers alive” column?

(s_x = n_x+1/n_x).

What is a cohort (dynamic) life table?

Follows a group born at the same time from birth to death.

What is a static (time-specific) life table?

Uses individuals of known age measured during a single time interval (same conditions) to infer survival/fecundity.

Why can cohort life tables confound age effects with environmental effects?

Because time and age change together; “bad years” can look like aging.

What are Type I, II, and III survivorship curves?

Type I: low early mortality, high late mortality; Type II: constant mortality; Type III: high early mortality, lower later mortality.

What is the intrinsic rate of increase ((lambda λ_m) or (r_m))?

The growth rate a population would have under constant conditions with a stable age distribution.

Why might intrinsic rate not predict long-term growth well in nature?

Real environments vary; age structure and life-table values change over time.

What is the net reproductive rate (R₀)?

(R₀=∑ l_x b_x): expected lifetime number of female offspring produced by an average female.

What is generation time (T)?

(T = ∑ x l_x b_x/∑ l_x b_x): average age at reproduction (mean age of mothers when producing offspring).

How do you approximate intrinsic λ from (R₀) and (T)?

(R₀ = λ^T which implies λ_a =R₀^1/T).

How do you approximate intrinsic r from (R₀) and (T)?

(r_a = {n(R₀)/T).

What is doubling time (t₂)?

Time required to double: (t₂ = ln 2/ln λ) or (t₂ = ln 2/r).