Population Size equation
Nt+1 = Nt + B - D
t+1= pop size at the end of time
t = pop size at the beginning of time
With a constant 10% annual rate of increase:
A population of 100 will add 10 individuals per year.
• A
population of 1000 will add 100 individuals per year.
• A
population of 10 billion adds 1 billion individuals per year.
constant rate would rapidly climb toward infinity
Geometric growth happens during a single time period uses the equation
N(t+1)=N(t) λ
N(t + 1) = number of individuals at end of period
N(t) = number of individuals at start of period
lambda(λ) = geometric population growth
rate
(the multiple by which the population grows in each time period)
Geometric Growth happens during multiple periods, uses the equation
Fig 11.4 (has both expontential and logistic growth)
Nt = N0 λ t
Nt = # individuals after t units of time
N0 = initial population size at time(0)
lambda(λ) = geometric population growth rate (the
multiple by which the population grows in each time period)
t = number of time periods (hours, days, years, etc)
GO OVER EXAMPLES ON SLIDES 24
Expotentionel pop growth equation
Nt = N0 ert
Nt = number of individuals after t time units
N0 = initial population size at time(0)
r = exponential growth rate per unit time (or
intrinsic rate of increase)
e = base of the natural logarithms (about 2.72)
t = number of units of time
Rate of increase in pop size equation
dN/dt = rN
(r) expresses population increase on a “per capita”
or “per individual” basis.
• The instantaneous increase/decrease
in population size per unit time (dN/dt) varies in
direct proportion to N (the current
population size).
Geometric and exponetial growth patterns overlap equation
λ = er
Per capita exponential growth rate equation:
r=b-d
If birth rate is higher than death rate, then r is positive.
If
death rate is higher than birth rate, then r is negative.
Growth rates whether the pop size increases, decreases or stays the same
You have a continuously
decelerating curve of
decrease when r < 0
You have a continuously
accelerating curve of
increase when r > 0.
Density-independent factors affect population size and
per capita growth rate
Ex. abiotic factors such as weather,
climate, and natural disasters
Fig 11.8 (highest year 1939 for thrips)
Density Dependent factors affect pop size and
growth rate as a consequence of pop density
Ex. food availability, habitat availability, predation rates, and parasite infection loads
Basically, when pop is large and food is scare, death is on the rise and birth rates decrease (Fig 11.11)
Density dependent reproduction and death rates can regulate pop size but
at high densities, pop growth may decline
Fig 11.12 (Pop growth rates declining)
The types of limits to exponential and geometric pop growth are
Populations exhibit geometric and exponential growth when resources
are abundant. However, since resources eventually become limited, this
growth cannot continue indefinitely.
Concept 11.3, Objective 1,
Slide 43
Proposal of Pearl and Reed to changing exponential growth equation to logistic growth equation is
dN/dt = r0N(1 - N/K)
r0 = maximum exponential growth rate
N = actual population size
K = carrying capacity, or the maximum N supportable
by the
resources in the environment.
This means population size always converges on equilibrium
carrying
capacity (K):
read slides 48-55
populations below K grow
• populations above K
decrease
• a population at K remains constant
Birth rates tend to decline in countries where income
increases.
With rising income,
children are increasingly perceived as a
liability rather than
an asset.
Population projections vary greatly, the median scenario predicting a plateau at
10.4 billion in 2050
When each new cohort is larger than the last, the pop is
When each new cohort is
smaller than the last, the pop is
growing
declining
Fig 11.16
In Fig 11.17, which survorship curive best describes humans?
Type 1 where most individuals survive to old age
Type 2 Straight line down (die at any age)
Type 3 Individuals die young