Flashcards — 257–262 (Time delays & cycles → metapopulations → rescue effect → stochastic extinction)

habitat patches (or simply patches)

areas of habitat with the necessary resources and conditions for a population to persist.

metapopulation

a set of discrete subpopulations connected by occasional movement of individuals between habitat patches.

rescue effect

immigration from large, productive subpopulations prevents small declining subpopulations from reaching extinction.

deterministic

models whose outcomes we can predict with certainty because they use average birth and death rates without random variation.

catastrophe

an unpredictable event (such as a predator, disease, or intense fire) that causes reproductive failure or high mortality across a population.

stochastic process

random variation in outcomes (such as deaths or births) that can affect population size even in a constant environment.

random walk

a population trajectory that increases or decreases strictly by chance under stochastic birth and death processes.

Why can time delays in density dependence cause population oscillations?

Because negative effects of crowding are felt later, so populations “overshoot,” producing cycles.

What did Nicholson’s fly experiment demonstrate about reducing time delays?

Limiting adults’ egg production immediately (fecundity response) reduced delayed larval mortality and damped fluctuations.

What is a habitat patch?

An area with resources/conditions needed for a population to persist.

What is a subpopulation in the metapopulation context?

The individuals of a species living in one habitat patch.

What is a metapopulation?

A set of discrete subpopulations in patches connected by occasional movement among patches.

Why are metapopulation models important for conservation?

Fragmentation creates isolated patches; persistence depends on balancing local extinctions with recolonization and maintaining connectivity.

What two processes drive metapopulation dynamics?

(1) within-patch growth/regulation; (2) between-patch colonization and extinction.

How does migration rate change the “behavior” of a metapopulation?

High migration makes it behave like one large population; no migration leads to independent extinctions; intermediate migration produces a shifting mosaic.

In the basic patch-occupancy model, what is (p)?

The fraction of suitable habitat patches currently occupied.

What is the extinction term in the basic occupancy model?

(ep), where (e) is extinction probability/rate per occupied patch.

What is the colonization term in the basic occupancy model?

cp(1-p), because colonization depends on occupied sources (p) and empty patches (1-p).

What is the patch-occupancy differential equation?

dp/dt = cp(1 - p) - ep

What is equilibrium patch occupancy (p̂) in the basic model?

p̂ = 1 - e/c = (as long as (c > e))

What happens to a metapopulation when extinction exceeds colonization (e > c)?

Occupancy declines toward 0 and the metapopulation goes extinct.

What is the rescue effect?

Immigration from productive patches prevents small declining subpopulations from going extinct.

Why do small populations have higher extinction risk even without environmental change?

Stochasticity: random variation in births/deaths has larger proportional impact when N is small.

What is a deterministic model?

Uses average rates to give predictable outcomes (no randomness).

What is a stochastic process in population dynamics?

Random variation in outcomes (births/deaths) that can change population size even under constant conditions.

What is a random walk (population context)?

A trajectory where population size moves up or down by chance; without stabilizing mechanisms, eventual extinction is expected.

Name three types of randomness affecting populations (as noted).

Catastrophes, environmental variation, and stochastic demographic processes.

Why can density-independent stochastic extinction models still matter in conservation?

Fragmentation creates tiny isolated populations, environmental change can depress fecundity, competitors can prevent recovery, and Allee effects can accelerate decline.

What pattern did Channel Islands bird data illustrate?

Extinction rates were much higher on smaller islands—extinction risk is inversely related to island size.