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