Transcript Population Growth

Population Growth
December 7, 2010
Text p. 660-669
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
Survivorship
• 3 patterns in survivorship of
species
• Type I
– Low mortality rates until past
reproductive years
– Long life expectancy
– Slow to reach sexual maturity,
produce small numbers of
offspring
Type II
• Uniform risk of mortality throughout life
Type III
• High mortality rates when they are young
• Those that reach sexual maturity have
reduced mortality rates
Calculating Changes in Population
Size
Population Change = [(birth + immigration) – (deaths + emigration)] x 100
(%)
initial population size (n)
• Can be used to calculate growth rate of a population in a
give time period
•Positive Growth: Birth + Immigration > Death + Emigration
•Negative Growth: Birth + Immigration <Death + Emigration
Open/Closed Population
• Growth can depend on type of population
• Open: influenced by natality, mortality and
migration
• Closed: determined by natality and mortality
alone
Biotic Potential
• The maximum rate a population can increase
under ideal conditions
• Or intrinsic rate of natural increase
• Represented as r
Carrying Capacity
• Maximum number of organisms sustained by
available resources
• Represented as k
Population Growth Models
• Basic model
– No inherent limit to growth
Hypothetical model
Geometric Growth Model
• In humans, growth is continuous (deaths and
births all times of year)
• In other organisms deaths may be year round,
but births may be restricted
• Population typically grows rapidly during
breeding season only
• Growth rate is constant at fixed intervals of
time (breeding seasons)
Geometric Growth Model
λ = the geometric growth rate
N = population size
t = time
N (t + 1) = population size in year X
λ = N (t + 1)
N (t)
So...
or
N(t + 1) = N(t) λ
N(t) = N(0) λt
Initial population of 2000 harp seals, gives birth to 950 pups, and
during next 12 months 150 die
Assuming geometric growth, what is the population in 2 years?
Year 1, Population Change = 950 births – 150 deaths
= 800
Initial Population N(0) = 2000
Population at end of Year 1, N(1) = 2000 + 950 – 150
Geometric Growth Rate (λ) = 2800 = 1.4
2000
Year 2 (t = 2): N(t) = N(0) λt
N(2) = (2000) (1.4)2 = 3920
Exponential Growth Model
• Populations growing continuously at a fixed
rate in a fixed time interval
• The chosen time interval is not restricted to a
particular reproductive cycle
• Can determine the instantaneous growth rate,
which is the intrinsic (per capita) growth rate
Intrinsic growth rate (r)
N = population size
dN = instantaneous growth rate of population
dt
Population Growth Rate:
dN = rN
dt
Population’s Doubling time (td) = 0.69
r
2500 yeast cells growing exponentially. Intrinsic growth rate
(r) is 0.030 per hour
Initial instantaneous growth rate: dN = rN
dt
= 0.030 x 2500
= 75 per hour
Amount of time for population to double in size:
Td = 0.69 = 0.69 = 23 hrs
r
0.030
Population size after each of 4 doubling times:
Td = 23 hrs, initial population = 2500
Curve Shapes
Exponential = J-shaped curve
Smooth vs. geometric, which fluctuates
Logistic Growth Model
• Geometric and exponential assume
population will grow at same rate indefinitely
• This means intrinsic growth rate (r) is a
maximum (rmax)
• In reality, resources become limited over time
• Population nears the ecosystem’s carrying
capacity, and growth rate drops below rmax
Logistic Growth Model
• Growth levels off as size of population approaches its
carrying capacity
Instantaneous growth rate:
rmax: maximum intrinsic growth rate
N: population size at any given time
K: carrying capacity of the environment
Logistic Growth Curve
•
•
•
•
S-shaped curve (sigmoidal)
3 phases
Lag, Log, Stationary
At stationary phase, population is in dynamic equilibrium
• Useful model for predictions
• Fits few natural populations perfectly
r & K Selection
• Species can be characterized by their relative
importance of r and K in their life cycle
r-Selected Species
Population numbers (N)
Carrying capacity, K
r-selected species
Time
• Rarely reach K
• High biotic
potential
• Early growth
• Rapid
development
• Fast population
growth
K-Selected Species
Population numbers (N)
Carrying capacity, K
K-selected species
Time
• Exist near K most
of the time
• Competition for
resources
important
• Fewer offspring
• Longer lives
Work:
Text Page 669, # 1-5