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26 Cards in this Set
- Front
- Back
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____ ____ ____ (lambda) - change in population size over a specific time interval (eg. 1 year)
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finite growth rate
best for individuals that don't reproduce continuously (distinct "breeding" season) called "geometric growth" or "discrete growth" |
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_____ ____ ____ - theoretical rate of change as the "time step" becomes smaller and smaller, approaching zero
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instantaneous growth rate
appropriate for continuously reproducing populations (bacteria, some tropical insects, humans) called "exponential growth" or "continuous growth" |
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equation for geometric growth
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Nt = N0 * lambda(t)
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equation for exponential growth
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Nt = N0 * e^rt
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r
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per capita growth rate
r = b - d |
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computational form of r formula
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r = [ln(Nt) - ln(N0)] / t
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lambda = 1
r = 0 |
population size is constant
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lambda > 1
r > 0 |
population is growing
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lambda < 1
r < 0 |
population is declining
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conversion of lambda to r
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r = ln(lambda)
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equation for finding doubling time in an exponentially growing population
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rt = 0.693
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continuous reproduction
stable age distribution constant "b" and 'd' (constant 'r') implies constant environment and unlimited resources |
assumptions for exponential growth model
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when are exponential growth requirements met in nature?
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introduction of species into new habitat (zebra mussel)
population recovering from disturbance modern humans |
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Thomas Malthus came up with these ideas in an essay on the principle of population in 1798
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reproductive powers exhaust means of sustenance
increasing death rates and decreasing birth rates must limit population populations do not increase exponentially w/o bound population growth varies w/ population size |
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describes a population limited by resources
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logistic population growth
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equation for logistic population growth model
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dN/dt = r max(N) * [(K-N)/K]
rate of population increase = max possible rate * proportion of resources available |
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the realized growth rate of the population (dN/dt) depends on the ____ ____
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population size
example of density-dependent population regulation |
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density-dependent regulation requires...
-- birth rates (b) that ____ w/ increasing N and/or... -- death rates (d) that _____ w/ increasing N |
decrease
increase |
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what happens if b or d are non-linear functions of N?
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can have stable and unstable equilibrium points
unstable equilibrium point = "critical minimum N" |
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population growth rates decline if N drops below a minimum critical value
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Allee effect
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due to a decline in birth rates (b) at low and high values of N
b declines at high N due to density-dependent effects (competition) b declines at low N due to difficulty in: mate location social interactions (group defense, foraging, etc.) |
allee effect
important implications for conservation biology |
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humans
in 1975, the population was growing at an annual rate of nearly __% |
2%
at this rate, a population will double in size every 35 years, and we would reach 32 billion by 2080 |
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growth rate has slowed recently, to about ____% per year
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1.21%
if this rate is maintained, there would be roughly 16 billion ppl on earth in 2080 |
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current population size
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about 7 billion
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at current rate...
how many ppl are added/day how long to add 1 billion? what is doubling time? |
230,000 /day
1 billion every 13 years 58 yr doubling time |
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in net reproductive rate went to r0 = 1 right now, would the population stop growing tomorrow?
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NO
it would take several decades (probably a few generations) for the population age structure and growth rate to stabilize |
