population growth december 7, 2010 text p. 660-669
TRANSCRIPT
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Population Growth
December 7, 2010Text p. 660-669
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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
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Effect on Determinants
• The determinants vary from species to species• Environmental Conditions• Fecundity– Potential for a species to produce offspring in one
lifetime
vs.
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Limits on Fecundity
• Fertility often less than fecundity– Food availability– Mating success– Disease– Human factors– Immigration/Emigration
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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
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Type II• Uniform risk of mortality throughout life
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Type III• High mortality rates when they are young• Those that reach sexual maturity have
reduced mortality rates
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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
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Open/Closed Population• Growth can depend on type of population• Open: influenced by natality, mortality and
migration• Closed: determined by natality and mortality
alone
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Biotic Potential• The maximum rate a population can increase
under ideal conditions• Or intrinsic rate of natural increase• Represented as r
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Carrying Capacity
• Maximum number of organisms sustained by available resources
• Represented as k
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Population Growth Models• Basic model– No inherent limit to growth
Hypothetical model
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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)
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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
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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
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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
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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
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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
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Population size after each of 4 doubling times:
Td = 23 hrs, initial population = 2500
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Curve ShapesExponential = J-shaped curveSmooth vs. geometric, which fluctuates
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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
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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
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Logistic Growth Curve• S-shaped curve (sigmoidal)• 3 phases• Lag, Log, Stationary• At stationary phase, population is in dynamic equilibrium
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• Useful model for predictions• Fits few natural populations perfectly
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r & K Selection
• Species can be characterized by their relative importance of r and K in their life cycle
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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
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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
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Work:
Text Page 669, # 1-5