Slide Set 5 Population Growth Part 2

What is carrying capacity (K)?

The maximum population size that an environment can support

Does carrying capacity vary?

Yes, it varies over space and time

How do crowding and resource limitation affect population growth?

They reduce the population growth rate (r)

What happens to population growth as density approaches K?

Population growth slows

What is logistic growth?

A model where population growth slows as it approaches carrying capacity

How is the exponential growth model modified in logistic growth?

By incorporating changes in r as population size approaches K

What does K represent in the logistic growth model?

Maximum sustainable population size

What does (K − N) represent?

The number of individuals the environment can still support

What does (K − N)/K represent?

The fraction of carrying capacity available for population growth

What is the logistic growth equation?

dN/dt = rN((K − N)/K)

What happens to population growth when N is much smaller than K?

Population growth increases

What happens to population growth when N is near K?

Population growth decreases

What happens to population growth at large values of N?

Growth becomes small because (K − N)/K becomes small

In the example r = 0.03, K = 1000, N = 500, what is population growth?

7.5 new recruits per time step

In the example r = 0.03, K = 1000, N = 900, what is population growth?

2.7 new recruits per time step

What was the starting population size of Anole lizards after the hurricane?

200 individuals

What was the per capita growth rate of the Anole lizards?

20% (0.20)

What was the carrying capacity of the island?

400 individuals

How many new recruits were added at the end of year 1?

20

What is the total population size at the start of year 2?

220

How well does the logistic model fit natural populations?

Small organisms fit well; many populations deviate from the model

When are logistic model predictions most accurate?

When environments are constant with no predators or competitors

Why does the logistic model often fail for natural populations?

Because its assumptions are rarely met

What is the first assumption of the logistic growth model?

Each individual added has the same negative effect on population growth

What is the second assumption of the logistic growth model?

The population approaches K smoothly

What causes populations to overshoot or undershoot K?

Time lags between population increase and negative effects

What happens when time lags exist?

Populations may oscillate around K

What is the third assumption of the logistic growth model?

Populations are large and density regulates growth

Which organisms often violate logistic model assumptions?

Insects and microorganisms

What are limiting factors?

Any essential resource in short supply that limits population growth

What is density-dependent control?

Factors affecting birth or death rates that depend on population density

What is the effect of density-dependent factors?

They stabilize population density

Give examples of density-dependent factors

Predation, parasitism, competition, herbivory, disease

What disease illustrates density-dependent control?

Bubonic plague

What causes bubonic plague?

Yersinia pestis bacterium

How is bubonic plague transmitted?

Flea bites from infected mammals

When did bubonic plague devastate Europe?

1346–1353

How many deaths occurred during the European plague?

25 million

What happened during the 1994 Indian plague outbreak?

Higher density increased infection and mortality

What is density-independent control?

Factors affecting birth or death rates regardless of population density

Do density-independent factors stabilize populations?

No

Give examples of density-independent factors

Weather, drought, freezes, floods, fire

What species illustrates density-independent control?

Monarch butterfly

Where do Monarch butterflies overwinter?

Mexico (Michoacan)

What caused mass Monarch butterfly mortality in 2002?

A freezing storm

How many Monarch butterflies died in 2002?

Over 200 million (>80%)

Did Monarch density affect mortality?

No

What ultimately stabilizes populations over long time scales?

Density-dependent control

What causes short-term population fluctuations?

Density-independent factors

What is population regulation?

The processes that maintain populations near equilibrium

What is stable equilibrium?

Birth rate equals death rate

What happens to a population at stable equilibrium if disturbed?

It returns to initial density

What forces act in stable equilibrium?

Stabilizing, density-dependent forces

What is unstable equilibrium?

A population that does not return to initial density after disturbance

What forces act in unstable equilibrium?

Destabilizing forces

What can cause unstable equilibrium?

Inverse density dependence or long time lags

What is a metapopulation?

Discrete sub-populations connected by immigration and emigration

Who proposed the metapopulation concept?

Levins (1969)

What occurs within patches in a metapopulation?

Growth and reproduction

What occurs between patches in a metapopulation?

Migration and colonization

What happens when migration is high in metapopulations?

Extinction probability decreases

What happens when migration is low in metapopulations?

Extinction probability increases

What happens at intermediate migration rates?

A shifting mosaic of occupied and unoccupied patches

What is the metapopulation dynamics equation?

df/dt = I − E

What does f represent?

Fraction of occupied sites

What does 1 − f represent?

Fraction of unoccupied sites

What does I represent?

Immigration rate

What does E represent?

Extinction rate

How is immigration calculated?

I = pi(1 − f)

How is extinction calculated?

E = pef

What does pi represent?

Probability of local colonization

What does pe represent?

Probability of local extinction

What happens if I > E?

The fraction of occupied sites increases

What happens if I < E?

The fraction of occupied sites decreases

What was the prairie dog town colonization probability?

60%

What was the prairie dog town extinction probability?

20%

What was the fraction of occupied prairie dog towns?

50%

What was the net change in occupied prairie dog towns?

20% increase

What butterfly illustrates metapopulation dynamics?

Bay checkerspot butterfly

What do Bay checkerspot larvae feed on?

Specialized plants on serpentine soils

What environmental factor caused subpopulation extinctions?

Drought

What subpopulation served as a source of colonists?

Morgan Hill

How many subpopulations went extinct between 1975–1977?

Three