Download Population Growth

Changes in Population Size
Population Dynamics
• Populations always changing in size
– Deaths, births
• Main determinants (measured per unit time):
– Natality = number of births
– Mortality = number of deaths
– Emigration = # of individuals that move away
– Immigration = # of individuals that move into an
existing population
Effect on Determinants
• The determinants vary from species to species
• Environmental Conditions
• Fecundity
– Potential for a species to produce offspring in one
lifetime
vs.
Limits on Fecundity
• Fertility often less than fecundity
– Food availability
– Mating success
– Disease
– Human factors
– Immigration/Emigration
Calculating Changes in Population Size
1. Population Change (∆N) = [(births + immigration) – (deaths + emigration)]
- just plug in the values as determined.
2. To calculate the rate of population growth: gr = ∆N/∆t
eg. Snail population in Banff Springs is 3800 in 1997, but falls to 1800 in
1999. Calcluate the growth rate.
gr = 1800-3800
2 years
= - 1000 snails/year
the population declined at a rate of 1000 snails per year.
Calculating Changes in Population Size
3. Calculating the per capita growth rate (cgr): ∆N/N (N= initial pop. size)
cgr = [(birth + immigration) – (deaths + emigration)] x 100 (%)
initial population size (n)
• Positive Growth: Birth + Immigration > Death + Emigration
• Negative Growth: Birth + Immigration <Death + Emigration
Calculate:
a) the change in a population in which there were 20 births, 25
immigrants, 10 deaths, and 5 emigrants.
b) What is the per capita growth if the original population was
75?.
+ 30
+ 40%
Open/Closed Population
• Growth can depend on type of population
• Open: influenced by natality, mortality and
migration
• Closed: determined by natality and mortality
alone
Population Growth in Unlimited Environments
• Under ideal conditions – no predators and unlimited
resources…
• A species can reach its biotic potential - the highest
possible per capita growth rate for a population.
• Factors that determine biotic potential are related to
fecundity:
•
•
•
•
•
# of offspring per reproductive cycle
# of offspring that survive to reproduce
The age of reproductive maturity
# of times that an individual reproduces in its life span
the life span of the individuals
Population Growth Models
1) Exponential Population Growth:
• Population grows at its max. biotic potential
• Starts with a lag phase and forms a J-shaped curve.
• Really only see in lab conditions.
Hypothetical model
Example
• A petri dish contains a population of bacteria
that is growing exponentially. If the intrinsic
growth rate (r) is equal to 0.02 per hour and
the initial population is 1000.
– A) what is the initial instantaneous growth rate of
the population
– B) what is the time it would take for the
population to double in size?
Pop. Growth in Limited Environments
• If one bacterium divided every 30 minutes for 4 days – the mass would be
greater than that of the earth.
• Doesn’t happen – resources run low and growth rate slows.
• Eventually, the habitat reaches its carrying capacity: the maximum
number of organisms that can be sustained by available resources.
• This is shown by a logistic growth curve:
Logistic Growth Curve
• S-shaped curve (sigmoidal)
• 3 phases:
• Lag (slow growth)
• Log (rapid growth)
• Stationary (no growth)
• At stationary phase, population is in dynamic equilibrium, it
will fluctuate around the carrying capacity of its habitat.
• carrying capacity changes in response to environmental
conditions – resource supply, predation, limited space, disease
etc.
Example
• A population is growing continuously. The
carrying capacity of the environment is 500
individuals and its maximum growth rate is
0.25. Determine the population growth based
on a population size of 10, 50, 100, 200, 350,
and 500
Geometric Growth Model
• Births are restricted to one part of the year –
“breeding season”
• Growth rate is constant and is calculated from
yearly change
Example
• A population of Lynx was studied in Northern
Ontario. There was an initial population of 120
lynx. During the next 12 months, 10 lynx were
born into this population and 40 adults died.
– What is the growth rate for this population?
– If this growth rate remains constant, what would
the population be in 5 years?
Population Growth Models and Life History:
•Organisms use strategies to maximize the # of offspring that survive
to reproductive age.
•Theoretically, the best idea is
• reach sexual maturity early
• have a long life span
• produce large #s of offspring
• provide them with high quality care until they can reproduce.
•Not realistic…
•There are different life strategies which relate to the environment in
which the organism lives.
•These are known as r-selected or K-selected strategies
r-selected strategy
•Species that have an r-selected strategy live close to their biotic
potential.
•In general, these organisms:
• Have a short life span
• Become sexually mature at a young age
• Produce large broods of offspring
• Provide little or no parental care to their offspring.
•Insects, annual plants and algae are examples – take advantage of
favorable conditions in the summer – reproduce exponentially, but die
at the end of the season.
K-selected strategy:
•Organisms with a K-selected strategy live close to the carrying
capacity of their habitats.
•In general, these organisms:
• Have a relatively long life span
• Become sexually mature later in life
• Produce few offspring per reproductive cycle
• Provide a high level of parental care
•Mammals and birds are examples of organisms that use this.
•Many populations are in-between these strategies and describing a
population usually involves a comparison – rabbits could be
described as K-selected…compared to mosquitoes. Compared to
bears, rabbits are r-selected.