Ecology CH 16 Population Growth

Exponential growth

Change in the size of a population by a constant proportion at each instant in time

Exponential population growth formula

N_{t}=\mathbb{N}_0e^{rt}

Geometric Growth Formula

N_{t}=\lambda^{t}N_0

if \lambda =1 or r=0

The population size does not change

When \lambda <1 or r<1

The population will decrease in size

When \lambda >1 or r>1

the population is increasing in size

The population will increase in size

Logistic growth

A pattern in which abundance increases rabidly at first, then stabilizes at the carrying capacity (K); S-curve

Logistic population growth formula

dN/dt=rN(1-(N/K))

Density dependent factors

Factors that limit population growth based on density (food or space)

Density independent factors

factors that influence population growth that are not density dependent but can still influence population growth (weather, temperature)

Population sizes change as a result of 4 processes:

Births

Deaths

Immigration

Emigration

Patterns of Population Growth/Change

Exponential Growth

Logistic Growth

Fluctuating Density

Population Cycles

Fluctuating Density

Most common

Sometimes has exponential growth and sometimes logistic growth

Many density-dependent and independent factors influence population growth

Population cycles

Regular and predictable fluctuations in population density

Small populations have greater risk of extinction. Why?

Chance events are greater in smaller populations; genetic drift/inbreeding, demographic effects, environmental stochasticity

Metapopulations

Set of distinct populations that are linked by dispersal

A population within a metapopulation can be a ____ or a _____ of individuals

source; sink

Rescue effect

each population within a metapopulation can go extinct and be recolonized