Part 1
Measuring and Modeling Population Change
Sunday, June 14, 15
An ecosystem is finite and therefore has a limited supply of biotic and abiotic resources
Carrying capacity - maximum number of organisms that can be sustained by available resources over a given time
Carrying capacity is dynamic (always changing) since environmental conditions are always changing
Sunday, June 14, 15
Population dynamics - changes in population's characteristics over a period of time
Main factors that influence populations are:
natality (number of births)mortality (number of deaths)immigration (number that enter population)emigration (number that leave population)
One characteristic of populations that is influenced by these factors is survivorship of species
Sunday, June 14, 15
Survivorship can be graphed to illustrate age at which individuals within species die
3 general patterns in survivorship of species:
Num
ber
of s
urvi
vors
Age Age
Num
ber
of s
urvi
vors
AgeN
umbe
r of
sur
vivo
rs
Type IPopulations show high survivorship
until late in life
Type IIPopulations show a fairly constant
rate of death
Type IIIPopulations show
lowest survivorship early in life
Sunday, June 14, 15
[(births + immigration)
Growth rate - percentage change in a population in a given time period
Population Change = (deaths + emigration)]− X 100
Initial population size (n)
Growth rate can be calculated as follows:
Sunday, June 14, 15
Population Growth ModelsIn situations where a population is well under its carrying capacity its size can continue to increase at a constant rate that can be calculated
If population only reproduces during a breeding season it will show geometric growth
If population breeds continuously it will show
exponential growth
Sunday, June 14, 15
Population Growth ModelsRate of geometric growth (λ) is given by equation:
N(t)
N(t + 1)=
Rate of exponential growth is given by equation:
dNdt = rN
N(t) = pop. size at time t
N (t + 1) = pop. size at time (t + 1)
r = per capita growth rate
N = population size
λ
Sunday, June 14, 15
For any population growing exponentially, time needed to double is constant
Following formula gives useful approximation of doubling time (td) when value “r” is known:
Population Growth Models
td =0.69r
Sunday, June 14, 15