Flashcards — 235–244 (Life table metrics → logistic growth → density dependence & Allee effects → plant self-thinning)

net reproductive rate

expected total number of female offspring produced by an average female over her lifetime; R₀ = ∑ l_x b_x.

generation time

average period between the birth of an individual and the birth of its offspring; T = ∑ x l_x b_x/∑ l_x b_x.

doubling time

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

infection point

inflection point on the logistic growth curve where growth switches from accelerating to decelerating; occurs at N = K/2.

density-dependent

factors whose effects increase with crowding and can regulate population size (for example, food, space, predators, parasites, disease).

density-independent

factors that affect birth and death rates regardless of population density (for example, temperature, precipitation, catastrophic events).

negative density dependence

the typical pattern where increasing density reduces survival and birth rates, lowering population growth.

positive or inverse density dependence

growth rate increases with increasing density at low densities (often due to Allee effects).

recruitment

number of new offspring per breeder that later join the breeding population.

self-thinning curve

relationship in crowded plant populations where density declines as individuals grow larger, often forming a straight line on a log–log plot of average plant weight vs density.

-3/2 power law

the self-thinning relationship where the log–log slope of average plant weight vs density is approximately -3/2.

What does (l_x b_x) represent in life-table calculations?

Expected number of offspring produced at age (x) by a newborn individual (survive to x, then reproduce).

What does (x l_x b_x) represent?

Births weighted by age; used to compute generation time.

If (R₀ > 1), what does that imply under constant conditions?

Population should increase (above replacement).

How does generation time influence growth rate, holding (R₀) constant?

Shorter (T) leads to faster growth/decline because generations turn over more quickly.

What is carrying capacity (K)?

The maximum population size the environment can support; in logistic growth, growth slows as (N) approaches (K).

What is the logistic growth equation (differential form)?

dN/dt = r₀N ( 1 - N/K)

What does (r₀) mean in logistic growth?

The intrinsic exponential growth rate when (N) is near 0 (low density).

When does the logistic growth curve change from accelerating to decelerating?

At the inflection point, where (N = K/2).

What are density-dependent factors?

Factors whose effects increase with crowding and can regulate population size (food, space, disease, predators, parasites).

What are density-independent factors?

Factors affecting birth/death regardless of density (temperature, precipitation, catastrophic events).

What is negative density dependence?

The typical case: as density increases, survival and birth rates decrease, so the population growth rate decreases.

What is positive (inverse) density dependence?

At low density, growth rate increases with density (often due to Allee effects).

What is the Allee effect (one main mechanism)?

Low density reduces fitness because individuals struggle to find mates, gain protection, or maintain genetic diversity.

What is recruitment (in the fisheries example)?

Number of new offspring per breeder that later join the breeding population.

Why can very small plant populations suffer reduced reproduction (Primula veris example)?

Fewer individuals leads to less pollen transfer / fewer pollinators → fewer fruits and seeds (a plant Allee effect).

What is a reaction norm in the flax density experiment context?

A phenotype’s change across environments; here, plant size changes with density/resource availability.

What is self-thinning in crowded plant populations?

As plants grow, many die, so density decreases while survivors increase in size.

What is the self-thinning curve and the “-3/2 power law”?

On a log–log plot, average plant weight vs density often forms a line with slope ~(-3/2).