Download 14.2 Measuring and Modeling Population Change

14.2 Measuring and Modeling
Population Change
Carrying capacity
• The maximum number of organisms that
can be sustained by available resources over
a given period of time
• Is dynamic because environmental
conditions are always changing
Population growth: factors
Population dynamics: changes in
population characteristics
The main determinants are:
– natality (birth rate)
– mortality (death rate)
– Immigration (individuals moving in)
– Emigration (individuals moving out)
Population change:
[(births + immigration) - (deaths + emigration)] x100
initial population size
[(B+I)-(D+E)/ n] x 100
CLOSED POPULATION
• A population whose growth is influenced only by
natality and mortality
OPEN POPULATION
• A population whose growth is influenced by natality,
mortality and migrations
Factors affecting Birth rate
Fecundity:
theoretical
maximum
number of
offspring that
could be
produced by a
species in one
lifetime
Fertility: the
number of
offspring actually
produced by an
individual during
its lifetime.
• affected by food
supply, disease,
mating success,
etc.
Type I survivorship
• Type I: species that have a
high survival rate of the
young, live out most of their
expected life span and die in
old age.
• Example: Elephants are slow
to reach sexual maturity and
have few offspring. They have
a long life expectancy
Type III survivorship
• Type III: species that
have many young, most
of which die very early
in their life.
• Example: Plants, oysters
and sea urchins.
Type II survivorship
• Type II :species that have a relatively
constant death rate throughout their life span.
Death could be due to hunting or diseases.
• Examples:coral, squirrels, honey bees and
many reptiles.
Biotic potential
• maximum reproductive rate under ideal
conditions (intrinsic rate of natural
increase)
• Example: Under ideal conditions, a population of
bacteria can grow to more than 10 in 24 h.
• Limiting Factor: the name applied to an essential
resource that is in short supply or unavailable, and
prevents an organism from achieving this potential
Geometric Growth
- births take place at one time of the year (i.e.,
breeding season), but deaths may occur all year
- population grows rapidly during breeding
season, declines throughout year until next breeding
season
- constant growth rate must be compared by
looking at same time each year
- annual growth rate can be determined
- line of best fit (on graph) produces J-curve
- examples: seals, deer, salmon
Geometric growth
• A population
that grows
rapidly during
breeding season,
then declines
through the year
until the next
breeding season
• Populations with geometric growth curves
experience a constant growth rate
• Determine growth rate with formula:
 = N(t+1)/N(t)
where  (lambda) represents the geometric
growth rate
N(t+1) represents the population size in a
given year
N(t) represents the population size at the same
time in the previous year. (See page 663)
• This equation can be generalized and
rearranged to find population size at any
given time:
• N(t) = N(0) t
• See page 633-634, Sample Problem
Exponential growth
• reproduction is continuous throughout year (i.e.,
no breeding season)
- constant growth rate
- instantaneous growth rate can be determined,
more complex than ageometric formula
- examples: yeast, bacteria, humans
• In natural populations, exponential growth does
not continue indefinitely because of limited
amounts of: energy, water, shelter, space
• Can use a modified form of exponential
growth formula to estimate doubling time.
• See Sample Problem p.665
• Both geometric
and exponential
growth models
produce similar
graphs, known a
J-curves.
Logistic Growth Curve
Stationary
phase stabilizing
Log phase –
very rapid
growth
Lag phase – small population size, therefore slow
population growth
r- and k- species
• Depending on their reproductive
strategies, species can be characterized
as r or k species.
• r is the instantaneous rate of population
increase while k is the carrying capacity.
• The r-species possess characteristics
of high biotic potential, rapid
development, early reproduction, single
period of reproduction per individual,
short life cycle, and small body size.
• Populations of r-species usually remain
below the carrying capacity and are
regulated by density-independent
factors
• k-species possess characteristics of
low biotic potential, slow development,
delayed reproduction, multiple periods
of reproduction per individual, long life
cycle and larger body size.
• populations of k-species are usually
maintained near the carrying capacity
and regulated by density dependent
factors
• In disrupted habitats r-species are more
common while k-species are common in
stable habitats. Many of our agricultural
pests are r-species. Most organisms
however actually have attributes that fit
both r and k species.