Population ecology

Exponential growth occurs when resources are not limiting.

Logistic growth occurs when resources become more and more limiting as population size increases.

• Population growth

Population ecology

– Does population growth continue without limits?• Number of resources usually prevent populations from

growing exponentially • Carrying capacity (K) = maximum number of individual

that an environment can support– When population reaches carrying capacity

» birth rate = death rate

» population growth rate = 0

Population ecology

– Logistic growth model• Population growth rates decreases as population

approaches its carrying capacity

dN

dtrN

K NK

Population growth rate

Per capita growth rate

Population size

Adjustment for limited resources

Population ecology

• Logistic growth produces S-shaped curve; population growth rate decreases as N approaches K

Population size

(N)

Time (t)

K

Population ecology

– Examples of logistic growth

Population ecology

• When N is very small (imagine N is 1 and K is 1000)...K NK

is close to 1, so population grows exponentially

Population size

(N)

Time (t)

dN

dtrN

K NK

(1)

– How does logistic growth model work?

dN

dtrN

K NK

Population ecology

• When N approaches K (imagine N is 500, 600, ...900 and K is 1000)...K NK

Gets closer and closer to 0, so population growth

slowly approaches 0

Population size

(N)

Time (t)

dN

dtrN

K NK

Population ecology

• When N equals K (imagine N is 1000 and K is 1000)...K NK

is 0, so population growth is 0

Population size

(N)

Time (t)

dN

dtrN

K NK

• Population growth

Population ecology

– Density-dependent population regulation• As populations near carrying capacity…population

growth rate declines – Per capita birth rates decrease (fewer resources available for

production of offspring)

– Per capita death rates increase (fewer resources for survival, predators focus attention on common prey)

» fewer resources available for production of offspring

» fewer resources for survival

» predators focus attention on common prey

• Population growth

Population ecology

– Example of density-dependence

• As population size increases, fecundity decreases

• As population size increases, mortality increases

• Population growth

Population ecology

– Density-dependent factors include:• disease• predators• competition for resources

• Allee effect = population growth rate reduced at low population density

– Difficulty finding mates could reduce birth rates at low population size

– Not all density-dependent factors result in reduced population growth rates as population size increase

• Population growth

Population ecology

– Sometimes population regulated by density-independent factors

• Birth rates decrease and death rates increase regardless of population size

– Extremely cold winter

– drought

– fires

• Type of population regulation may influence life-history traits:

Population ecology

– Species regulated by density-dependent factors are selected to be good competitors (populations are often close to carrying capacity)

• Such species invest heavily in survival• But at a cost of reduced reproductive potential (i.e. a life

history trade-off)• Called K-selected species• Examples: elephants, oak trees

• Type of population regulation may influence life-history traits:

Population ecology

– Species regulated by density-independent factors are selected to be good reproducers (populations are often below carrying capacity)

• Such species invest heavily in reproductive output• But at a cost of reduced survival (i.e. a life history trade-off)• Called r-selected species• Examples: cockroaches, birch trees

• r- and K-selected life history traits (ends of continuum)

Population ecology

trait r-selected K-selected – age at 1st

reproduction early late – lifespan short long – Survivorship low (type III) high

(type I)– Fecundity high low– Parity semelparity

iteroparity– Offspring size small large– Parental care none lots