Biology 5C ~ Lecture 9 ~ Population Growth

Change in population size...

births + immigrants - deaths - emigrants leaving population

-if immigration and emigration are ignored, a population's growth rate (per capita increase) equals birth rate minus death rate

Exponential growth

-the parameter r is the instantaneous per capita rate of increase
-the balance of births and deaths determine r

-in an open population, you would include immigrants with births (=gains per capita) and emigrants with deaths (=losses per capita)

Exponential growth where...

b=the instantaneous number of births *per capita --- [the per capita birth rate]

m=the instantaneous number of deaths *per capita --- [the per capita death rate]

if r, the instantaneous per capita rate of increase, is constant...

the population grows exponentially

In unrestrained growth, with constant r,...

dN/dt increases as population size increases (i.e., growth accelerates)

Populations cannot continue to increase indefinitely b/c...

-exponential growth cannot be sustained for long in any population

A more realistic population model limits growth by...

incorporating carrying capacity (K), which is the maximum population size the environment can support

The logistic growth model

-Starts with the exponential model and adds an expression that reduces the instantaneous per capita rate of increase as N approaches K

the instantaneous per capita rate of increase under logistic growth is always less than or equal to r:

the logistic model of population growth produces a sigmoid (S-shaped) curve
-insert image slide 11

Examples of limited growth:

the growth of laboratory populations in a constant environment lacking predators but with limited food
-insert image slide 12

Under the logistic growth model,...

the per capita instantaneous population growth rate is negatively density-dependent

As N increases,...

the instantaneous growth rate decreases

Logistic growth of a hypothetical population (K = 1,500):

Population density vs. birth or death rate per capita graph: slide 17

-when the density is low, b > m
-when the density is high, m > b

Negative density dependence:

-when a population growth is reduced by crowding, predators and competition

SLIDES TO KNOW FOR THE EXAM

-exponential growth
-logistic growth
-negative density dependence
-watch the video for more understanding