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Population Growth December 7, 2010 Text p. 660-669.
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Transcript of Population Growth December 7, 2010 Text p. 660-669.
Population Growth
December 7, 2010Text 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 Modelλ = the geometric growth rateN = population sizet = timeN (t + 1) = population size in year X
λ = N (t + 1) or N(t + 1) = N(t) λ N (t)So...
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 – 150Geometric 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 sizedN = instantaneous growth rate of populationdt
Population Growth Rate:dN = rNdt
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 ShapesExponential = J-shaped curveSmooth 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 timeK: 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
• Rarely reach K• High biotic
potential• Early growth• Rapid
development• Fast population
growth
Carrying capacity, K
Popu
latio
n nu
mbe
rs (N
)
Time
r-selected species
K-Selected Species
• Exist near K most of the time
• Competition for resources important
• Fewer offspring• Longer livesPo
pula
tion
num
bers
(N)
Time
K-selected species
Carrying capacity, K
Work:
Text Page 669, # 1-5